AI Impacts Wiki power_of_evolution:evolution_engineering_comparison

Energy efficiency of Airbus A320

2022-09-21T07:37:41+00:00

@@ -1 +1,99 @@
+ ====== Energy efficiency of Airbus A320 ======
+ 
+ // Published 05 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>The Airbus A320:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">covers around 0.0078 m/kJ</div></li>
+ <li><div class="li">and moves mass at around 0.33 – 0.61 kg.m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>The <em>Airbus A320</em> is a 1987 passenger plane.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2743"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2743" title='&amp;#8220;The&amp;nbsp;&lt;strong&gt;Airbus A320 family&lt;/strong&gt;&amp;nbsp;are&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Narrow-body_aircraft"&gt;narrow-body airliners&lt;/a&gt;&amp;nbsp;designed and produced by&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Airbus"&gt;Airbus&lt;/a&gt;. The A320 was launched in March 1984,&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Maiden_flight"&gt;first flew&lt;/a&gt;&amp;nbsp;on 22 February 1987, and was introduced in April 1988 by&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Air_France"&gt;Air France&lt;/a&gt;.”&lt;/p&gt; &lt;p&gt;“Airbus A320 Family.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 30, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Airbus_A320_family&amp;amp;oldid=986182483"&gt;https://en.wikipedia.org/w/index.php?title=Airbus_A320_family&amp;amp;oldid=986182483&lt;/a&gt;.'><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>The plane uses 2.91 kg of fuel per km on a medium haul flight.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2743"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2743" title='“Fuel Economy in Aircraft.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 22, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Fuel_economy_in_aircraft&amp;amp;oldid=984919809"&gt;https://en.wikipedia.org/w/index.php?title=Fuel_economy_in_aircraft&amp;amp;oldid=984919809&lt;/a&gt;.'><sup>2</sup></a></span> We do not know what type of fuel it uses, but typical values for aviation fuel are around 44MJ/kg.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2743"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2743" title='&amp;#8220;The&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Net_energy_content"&gt;net energy content&lt;/a&gt;&amp;nbsp;for aviation fuels depends on their composition. Some typical values are:&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/Aviation_fuel#cite_note-15"&gt;[15]&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt; &lt;ul&gt;&lt;li&gt;BP Avgas 80,&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)#1E6"&gt;44.65&lt;/a&gt;&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Joule"&gt;MJ&lt;/a&gt;/kg, density at 15&amp;nbsp;°C is 690&amp;nbsp;kg/&lt;a href="https://en.wikipedia.org/wiki/Cubic_metre"&gt;m&lt;sup&gt;3&lt;/sup&gt;&lt;/a&gt;&amp;nbsp;(30.81&amp;nbsp;MJ/litre).&lt;/li&gt;&lt;li&gt;Kerosene type BP Jet A-1, 43.15&amp;nbsp;MJ/kg, density at 15&amp;nbsp;°C is 804&amp;nbsp;kg/m&lt;sup&gt;3&lt;/sup&gt;&amp;nbsp;(34.69&amp;nbsp;MJ/litre).&lt;/li&gt;&lt;li&gt;Kerosene type BP Jet TS-1 (for lower temperatures), 43.2&amp;nbsp;MJ/kg, density at 15&amp;nbsp;°C is 787&amp;nbsp;kg/m&lt;sup&gt;3&lt;/sup&gt;&amp;nbsp;(34.00&amp;nbsp;MJ/litre).&amp;#8221;&lt;/li&gt;&lt;/ul&gt; &lt;p&gt;“Aviation Fuel.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 13, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Aviation_fuel&amp;amp;oldid=978262126"&gt;https://en.wikipedia.org/w/index.php?title=Aviation_fuel&amp;amp;oldid=978262126&lt;/a&gt;.'><sup>3</sup></a></span> Thus to fly a kilometer, the plane needs 2.91kg of fuel, which is 2.91 x 44 MJ = 128MJ of fuel. This gives us 0.0078 m/kJ</p>
+ </HTML>
+ 
+ 
+ ==== Mass.distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>According to modernairliners.com, the A320’s ‘operating empty weight’ is 42,600 kg and its ‘maximum take-off weight’ is 78,000 kg.<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2743"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2743" title='“Airbus A320 Specs &amp;#8211; Modern Airliners.” Accessed November 5, 2020. &lt;a href="https://modernairliners.com/airbus-a320-introduction/airbus-a320-specs/"&gt;https://modernairliners.com/airbus-a320-introduction/airbus-a320-specs/&lt;/a&gt;.'><sup>4</sup></a></span> We use the range 42,600—78,000 kg, since we do not know at what weight in that range the relevant speeds were measured.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Distance per kilojoule: 0.0078 m/kJ</div></li>
+ <li><div class="li">Mass: 42,600—78,000 kg</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This gives us a range of 0.33 – 0.61 kg.m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><br/>
+ <br/>
+ <em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2743"></span>“The <strong>Airbus A320 family</strong> are <a href="https://en.wikipedia.org/wiki/Narrow-body_aircraft">narrow-body airliners</a> designed and produced by <a href="https://en.wikipedia.org/wiki/Airbus">Airbus</a>. The A320 was launched in March 1984, <a href="https://en.wikipedia.org/wiki/Maiden_flight">first flew</a> on 22 February 1987, and was introduced in April 1988 by <a href="https://en.wikipedia.org/wiki/Air_France">Air France</a>.”
+                   <p>“Airbus A320 Family.” In <em>Wikipedia</em>, October 30, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Airbus_A320_family&amp;oldid=986182483">https://en.wikipedia.org/w/index.php?title=Airbus_A320_family&amp;oldid=986182483</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2743"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2743"></span>“Fuel Economy in Aircraft.” In <em>Wikipedia</em>, October 22, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Fuel_economy_in_aircraft&amp;oldid=984919809">https://en.wikipedia.org/w/index.php?title=Fuel_economy_in_aircraft&amp;oldid=984919809</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2743"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2743"></span>“The <a href="https://en.wikipedia.org/wiki/Net_energy_content">net energy content</a> for aviation fuels depends on their composition. Some typical values are:<sup><a href="https://en.wikipedia.org/wiki/Aviation_fuel#cite_note-15">[15]</a></sup>
+ <ul>
+ <li><div class="li">BP Avgas 80, <a href="https://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)#1E6">44.65</a> <a href="https://en.wikipedia.org/wiki/Joule">MJ</a>/kg, density at 15 °C is 690 kg/<a href="https://en.wikipedia.org/wiki/Cubic_metre">m<sup>3</sup></a> (30.81 MJ/litre).
+                     </div></li>
+ <li><div class="li">Kerosene type BP Jet A-1, 43.15 MJ/kg, density at 15 °C is 804 kg/m<sup>3</sup> (34.69 MJ/litre).</div></li>
+ <li><div class="li">Kerosene type BP Jet TS-1 (for lower temperatures), 43.2 MJ/kg, density at 15 °C is 787 kg/m<sup>3</sup> (34.00 MJ/litre).”</div></li>
+ </ul>
+ <p>“Aviation Fuel.” In <em>Wikipedia</em>, September 13, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Aviation_fuel&amp;oldid=978262126">https://en.wikipedia.org/w/index.php?title=Aviation_fuel&amp;oldid=978262126</a>.<a class="easy-footnote-to-top" href="#easy-footnote-3-2743"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2743"></span>“Airbus A320 Specs – Modern Airliners.” Accessed November 5, 2020. <a href="https://modernairliners.com/airbus-a320-introduction/airbus-a320-specs/">https://modernairliners.com/airbus-a320-introduction/airbus-a320-specs/</a>.<a class="easy-footnote-to-top" href="#easy-footnote-4-2743"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Energy efficiency of Airbus Zephyr S

2022-10-21T21:16:08+00:00

@@ -22,9 +22,9 @@
  Wikimedia Foundation. (2022, September 27). Airbus Zephyr. Wikipedia. Retrieved October 21, 2022, from https://en.wikipedia.org/wiki/Airbus_Zephyr )) In August 2022, Zephyr S flew 56,000 km over the course of 26 days.(("During this flight, Zephyr 8 more than doubled the previous UAS endurance record, just under 26 days, and flew in excess of 30,000 nautical miles – more than one lap around the Earth. The 1,500 flight hours beat all known unmanned aircraft endurance records, marking significant capability and informing future mission requirements."
  
  APNT/Space CFT concludes high altitude experimentation. www.army.mil. (n.d.). Retrieved October 21, 2022, from https://www.army.mil/article/259542/apntspace_cft_concludes_high_altitude_experimentation )) This gives us 1490 m/kJ.
  
- ==== Mass.distance per Joule ====
+ ==== Mass*distance per Joule ====
  
  Zephyr S has a mass of 75 kg.(("The Airbus Zephyr is the world’s leading solar-electric stratospheric Unmanned Aerial System (UAS), with a wingspan of 25 meters and it weighs less than 75kg."
  
  Wang, B. (2021, October 24). Airbus solar powered aircraft can fly for 18 days and replace 250 cell towers. NextBigFuture.com. Retrieved October 21, 2022, from https://www.nextbigfuture.com/2021/10/173564.html ))

Energy efficiency of Boeing 747-400

2022-09-21T07:37:41+00:00

@@ -1 +1,99 @@
+ ====== Energy efficiency of Boeing 747-400 ======
+ 
+ // Published 05 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>The Boeing 747-400:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">covers around 0.0021m/kJ.</div></li>
+ <li><div class="li">and moves mass at around 0.39 – 0.83 kg.m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>The <em>Boeing 747-400</em> is a 1987 passenger plane.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2745"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2745" title='&amp;#8220;The&amp;nbsp;&lt;strong&gt;Boeing 747-400&lt;/strong&gt;&amp;nbsp;is a&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Wide-body_aircraft"&gt;wide-body airliner&lt;/a&gt;&amp;nbsp;produced by&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Boeing_Commercial_Airplanes"&gt;Boeing Commercial Airplanes&lt;/a&gt;, an advanced variant of the initial&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Boeing_747"&gt;Boeing 747&lt;/a&gt;. The &amp;#8220;Advanced Series 300&amp;#8221; was announced at the September 1984&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Farnborough_Airshow"&gt;Farnborough Airshow&lt;/a&gt;, targeting a 10% cost reduction with more efficient engines and 1,000&amp;nbsp;nmi (1,850&amp;nbsp;km) more range.&amp;nbsp;”&lt;/p&gt; &lt;p&gt;“Boeing 747-400.” In &lt;em&gt;Wikipedia&lt;/em&gt;, November 2, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Boeing_747-400&amp;amp;oldid=986725646"&gt;https://en.wikipedia.org/w/index.php?title=Boeing_747-400&amp;amp;oldid=986725646&lt;/a&gt;.'><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>The plane uses 10.77 kg/km of fuel on a medium haul flight.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2745"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2745" title='“Fuel Economy in Aircraft.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 22, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Fuel_economy_in_aircraft&amp;amp;oldid=984919809"&gt;https://en.wikipedia.org/w/index.php?title=Fuel_economy_in_aircraft&amp;amp;oldid=984919809&lt;/a&gt;.'><sup>2</sup></a></span> We do not know what type of fuel it uses, but typical values for aviation fuel are around 44MJ/kg.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2745"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2745" title='&amp;#8220;The&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Net_energy_content"&gt;net energy content&lt;/a&gt;&amp;nbsp;for aviation fuels depends on their composition. Some typical values are:&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/Aviation_fuel#cite_note-15"&gt;[15]&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt; &lt;ul&gt;&lt;li&gt;BP Avgas 80,&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)#1E6"&gt;44.65&lt;/a&gt;&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Joule"&gt;MJ&lt;/a&gt;/kg, density at 15&amp;nbsp;°C is 690&amp;nbsp;kg/&lt;a href="https://en.wikipedia.org/wiki/Cubic_metre"&gt;m&lt;sup&gt;3&lt;/sup&gt;&lt;/a&gt;&amp;nbsp;(30.81&amp;nbsp;MJ/litre).&lt;/li&gt;&lt;li&gt;Kerosene type BP Jet A-1, 43.15&amp;nbsp;MJ/kg, density at 15&amp;nbsp;°C is 804&amp;nbsp;kg/m&lt;sup&gt;3&lt;/sup&gt;&amp;nbsp;(34.69&amp;nbsp;MJ/litre).&lt;/li&gt;&lt;li&gt;Kerosene type BP Jet TS-1 (for lower temperatures), 43.2&amp;nbsp;MJ/kg, density at 15&amp;nbsp;°C is 787&amp;nbsp;kg/m&lt;sup&gt;3&lt;/sup&gt;&amp;nbsp;(34.00&amp;nbsp;MJ/litre).&amp;#8221;&lt;/li&gt;&lt;/ul&gt; &lt;p&gt;“Aviation Fuel.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 13, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Aviation_fuel&amp;amp;oldid=978262126"&gt;https://en.wikipedia.org/w/index.php?title=Aviation_fuel&amp;amp;oldid=978262126&lt;/a&gt;.'><sup>3</sup></a></span> Thus to fly a kilometer, the plane needs 10.77 kg of fuel, which is 10.77 x 44 MJ = 474 MJ of fuel. This gives us 0.0021m/kJ.</p>
+ </HTML>
+ 
+ 
+ ==== Mass.distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>According to Wikipedia, the 747’s ‘operating empty weight’ is 183,523 kg and its ‘maximum take-off weight’ is 396,893 kg.<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2745"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2745" title='“Boeing 747-400.” In &lt;em&gt;Wikipedia&lt;/em&gt;, November 2, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Boeing_747-400&amp;amp;oldid=986725646"&gt;https://en.wikipedia.org/w/index.php?title=Boeing_747-400&amp;amp;oldid=986725646&lt;/a&gt;.'><sup>4</sup></a></span> We use the range 183,523 kg—396,893 kg since we do not know at what weight in that range the relevant speeds were measured.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Distance per kilojoule: 0.0021m/kJ</div></li>
+ <li><div class="li">Mass: 183,523 kg—396,893 kg</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This gives us a range of 0.39 – 0.83 kg.m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><br/>
+ <br/>
+ <em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2745"></span>“The <strong>Boeing 747-400</strong> is a <a href="https://en.wikipedia.org/wiki/Wide-body_aircraft">wide-body airliner</a> produced by <a href="https://en.wikipedia.org/wiki/Boeing_Commercial_Airplanes">Boeing Commercial Airplanes</a>, an advanced variant of the initial <a href="https://en.wikipedia.org/wiki/Boeing_747">Boeing 747</a>. The “Advanced Series 300” was announced at the September 1984 <a href="https://en.wikipedia.org/wiki/Farnborough_Airshow">Farnborough Airshow</a>, targeting a 10% cost reduction with more efficient engines and 1,000 nmi (1,850 km) more range. ”
+                   <p>“Boeing 747-400.” In <em>Wikipedia</em>, November 2, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Boeing_747-400&amp;oldid=986725646">https://en.wikipedia.org/w/index.php?title=Boeing_747-400&amp;oldid=986725646</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2745"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2745"></span>“Fuel Economy in Aircraft.” In <em>Wikipedia</em>, October 22, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Fuel_economy_in_aircraft&amp;oldid=984919809">https://en.wikipedia.org/w/index.php?title=Fuel_economy_in_aircraft&amp;oldid=984919809</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2745"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2745"></span>“The <a href="https://en.wikipedia.org/wiki/Net_energy_content">net energy content</a> for aviation fuels depends on their composition. Some typical values are:<sup><a href="https://en.wikipedia.org/wiki/Aviation_fuel#cite_note-15">[15]</a></sup>
+ <ul>
+ <li><div class="li">BP Avgas 80, <a href="https://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)#1E6">44.65</a> <a href="https://en.wikipedia.org/wiki/Joule">MJ</a>/kg, density at 15 °C is 690 kg/<a href="https://en.wikipedia.org/wiki/Cubic_metre">m<sup>3</sup></a> (30.81 MJ/litre).
+                     </div></li>
+ <li><div class="li">Kerosene type BP Jet A-1, 43.15 MJ/kg, density at 15 °C is 804 kg/m<sup>3</sup> (34.69 MJ/litre).</div></li>
+ <li><div class="li">Kerosene type BP Jet TS-1 (for lower temperatures), 43.2 MJ/kg, density at 15 °C is 787 kg/m<sup>3</sup> (34.00 MJ/litre).”</div></li>
+ </ul>
+ <p>“Aviation Fuel.” In <em>Wikipedia</em>, September 13, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Aviation_fuel&amp;oldid=978262126">https://en.wikipedia.org/w/index.php?title=Aviation_fuel&amp;oldid=978262126</a>.<a class="easy-footnote-to-top" href="#easy-footnote-3-2745"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2745"></span>“Boeing 747-400.” In <em>Wikipedia</em>, November 2, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Boeing_747-400&amp;oldid=986725646">https://en.wikipedia.org/w/index.php?title=Boeing_747-400&amp;oldid=986725646</a>.<a class="easy-footnote-to-top" href="#easy-footnote-4-2745"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Energy efficiency of MacCready Gossamer Albatross

2022-09-21T07:37:41+00:00

@@ -1 +1,148 @@
+ ====== Energy efficiency of MacCready Gossamer Albatross ======
+ 
+ // Published 09 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>The MacCready <em>Gossamer Albatross</em>:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">covered around 2.0—4.6 m/kJ</div></li>
+ <li><div class="li">and moved mass at around 0.1882 —0.4577 kg⋅m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>The <strong>MacCready <em>Gossamer Albatross</em></strong> was a human-powered flying machine that crossed the English Channel in 1979.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2756"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2756" title='&amp;#8220;The&amp;nbsp;&lt;em&gt;&lt;strong&gt;Gossamer Albatross&lt;/strong&gt;&lt;/em&gt;&amp;nbsp;is a&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Human-powered_aircraft"&gt;human-powered aircraft&lt;/a&gt;&amp;nbsp;built by&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/United_States"&gt;American&lt;/a&gt;&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Aeronautical_engineer"&gt;aeronautical engineer&lt;/a&gt;&amp;nbsp;Dr.&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Paul_B._MacCready"&gt;Paul B. MacCready&lt;/a&gt;&amp;#8216;s company&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/AeroVironment"&gt;AeroVironment&lt;/a&gt;. On June 12, 1979, it completed a successful crossing of the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/English_Channel"&gt;English Channel&lt;/a&gt;&amp;nbsp;to win the second £100,000 (£509644&amp;nbsp;today)&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Kremer_prize"&gt;Kremer prize&lt;/a&gt;.&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/MacCready_Gossamer_Albatross#cite_note-Gossamer_Albatross_ECN-12665-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&amp;#8220;&lt;/p&gt; &lt;p&gt;“MacCready &lt;em&gt;Gossamer Albatross&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 7, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;amp;oldid=982283381"&gt;https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;amp;oldid=982283381&lt;/a&gt;.'><sup>1</sup></a></span> The pilot pedaled the craft, seemingly as if on a bicycle. It had a gross mass of 100kg, flying across the channel,<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2756"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2756" title='&amp;#8220;The empty mass of the structure was only 71&amp;nbsp;lb (32&amp;nbsp;kg), although the gross mass for the Channel flight was almost 220&amp;nbsp;lb (100&amp;nbsp;kg).&amp;nbsp;&amp;#8220;&lt;/p&gt; &lt;p&gt;“MacCready &lt;em&gt;Gossamer Albatross&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 7, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;amp;oldid=982283381"&gt;https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;amp;oldid=982283381&lt;/a&gt;.'><sup>2</sup></a></span> and flew 35.7 km in 2 hours and 49 minutes.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2756"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2756" title='&amp;#8220;Allen completed the 22.2&amp;nbsp;mi (35.7&amp;nbsp;km) crossing in 2&amp;nbsp;hours and 49&amp;nbsp;minutes, achieving a top speed of 18&amp;nbsp;mph (29&amp;nbsp;km/h) and an average altitude of 5&amp;nbsp;ft (1.5&amp;nbsp;m).&amp;#8221;&lt;/p&gt; &lt;p&gt;“MacCready &lt;em&gt;Gossamer Albatross&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 7, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;amp;oldid=982283381"&gt;https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;amp;oldid=982283381&lt;/a&gt;.'><sup>3</sup></a></span> The crossing was difficult however, so it seems plausible that the <em>Gossamer Albatross</em> could fly more efficiently in better conditions.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We do not know the pilot’s average power output, however:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Wikipedia claims at least 300W was required to fly the craft<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2756"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2756" title='&amp;#8220;To maintain the craft in the air, it was designed with very long, tapering wings (high&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Aspect_ratio_(wing)"&gt;aspect ratio&lt;/a&gt;), like those of a glider, allowing the flight to be undertaken with a minimum of power. In still air, the required power was on the order of 300&amp;nbsp;W (0.40&amp;nbsp;hp), though even mild turbulence made this figure rise rapidly.&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/MacCready_Gossamer_Albatross#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&amp;#8220;&lt;br&gt;&lt;br&gt;“MacCready &lt;em&gt;Gossamer Albatross&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 7, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;amp;oldid=982283381"&gt;https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;amp;oldid=982283381&lt;/a&gt;.'><sup>4</sup></a></span></div></li>
+ <li><div class="li">Chung 2006, an engineering textbook, claims that the driver, a cyclist, could produce around 200W of power.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-2756"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-2756" title="Chung, Yip-Wah. &lt;em&gt;Introduction to Materials Science and Engineering&lt;/em&gt;. CRC Press, 2006. p89"><sup>5</sup></a></span></div></li>
+ <li><div class="li">Our impression is that 200W is a common power output over houres for amateur cycling. For instance, one of our researchers is able to achieve this for three hours.<span class="easy-footnote-margin-adjust" id="easy-footnote-6-2756"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-2756" title="https://www.strava.com/activities/272615649/overview"><sup>6</sup></a></span></div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The best documented human cycling wattage that we could easily find is from professional rider Giulio Ciccone who won a stage of the Tour de France, then uploaded power data to the fitness tracking site Strava.<span class="easy-footnote-margin-adjust" id="easy-footnote-7-2756"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-2756" title='Strava. “Yellow Jersey &amp;#8211; Giulio Ciccone’s 158.8 Km Bike Ride.” Accessed November 9, 2020. &lt;a href="https://www.strava.com/activities/2525139293"&gt;https://www.strava.com/activities/2525139293&lt;/a&gt;.'><sup>7</sup></a></span> His performance suggests around 318W is a reasonable upper bound, supposing that the pilot of the <em>Gossamer Albatross</em> would have had lower performance.<span class="easy-footnote-margin-adjust" id="easy-footnote-8-2756"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-8-2756" title="For an upper value, we used a combination of two metrics given on the website. The first metric is his “weighted average power” for the Tour de France stage, which was 318W. Weighted average power is a way of averaging power over a ride with highly variable power which gives higher weight to higher power portions of the ride, and is used by athletes and coaches to estimate the maximum power that a rider could sustain for a long time, if they had a steady power output. The second metric is Ciccone’s maximum power from his Tour race applied over the duration of the MacCready flight (2 hours and 40 min) which is 5W/kg body weight. For the pilot, Allen, riding with the same power per body weight (65 kg), this would be equivalent to 322W, a similar value to his weighted average power. We use the lower of the two values, 318W."><sup>8</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>To find the energy used by the cyclist, we divided power output by typical efficiency for a human on a bicycle, which according to Wikipedia ranges from .18 to .26.<span class="easy-footnote-margin-adjust" id="easy-footnote-9-2756"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-9-2756" title='&amp;#8220;The required food can also be calculated by dividing the output power by the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Muscle#Efficiency"&gt;muscle efficiency&lt;/a&gt;. This is 18–26%.&amp;nbsp;&amp;#8220;&lt;/p&gt; &lt;p&gt;“Bicycle Performance.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 9, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Bicycle_performance&amp;amp;oldid=982652996"&gt;https://en.wikipedia.org/w/index.php?title=Bicycle_performance&amp;amp;oldid=982652996&lt;/a&gt;.'><sup>9</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>For distance per energy this gives us a highest measure of:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>35.7 km / ((200W * (2 hours + 49 minutes))/0.26) = 4,577 m/MJ</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>And a lowest measure of:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>35.7 km / ((318W * (2 hours + 49 minutes))/0.18) = 1,993 m/MJ</p>
+ </HTML>
+ 
+ 
+ ==== Mass per Joule ====
+ 
+ 
+ <HTML>
+ <p>For weight times distance per energy this gives us a highest measure of:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>(100kg * 35.7 km) / ((200W * (2 hours + 49 minutes))/0.26) = 0.4577 kg⋅m/j</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>And a lowest measure of:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>(100kg * 35.7 km) / ((318W * (2 hours + 49 minutes))/0.17) =  0.1882 kg⋅m/j</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><br/>
+ <br/>
+ <em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2756"></span>“The <em><strong>Gossamer Albatross</strong></em> is a <a href="https://en.wikipedia.org/wiki/Human-powered_aircraft">human-powered aircraft</a> built by <a href="https://en.wikipedia.org/wiki/United_States">American</a> <a href="https://en.wikipedia.org/wiki/Aeronautical_engineer">aeronautical engineer</a> Dr. <a href="https://en.wikipedia.org/wiki/Paul_B._MacCready">Paul B. MacCready</a>‘s company <a href="https://en.wikipedia.org/wiki/AeroVironment">AeroVironment</a>. On June 12, 1979, it completed a successful crossing of the <a href="https://en.wikipedia.org/wiki/English_Channel">English Channel</a> to win the second £100,000 (£509644 today) <a href="https://en.wikipedia.org/wiki/Kremer_prize">Kremer prize</a>.<sup><a href="https://en.wikipedia.org/wiki/MacCready_Gossamer_Albatross#cite_note-Gossamer_Albatross_ECN-12665-1">[1]</a></sup>“
+                   <p>“MacCready <em>Gossamer Albatross</em>.” In <em>Wikipedia</em>, October 7, 2020. <a href="https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;oldid=982283381">https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;oldid=982283381</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2756"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2756"></span>“The empty mass of the structure was only 71 lb (32 kg), although the gross mass for the Channel flight was almost 220 lb (100 kg). “
+                   <p>“MacCready <em>Gossamer Albatross</em>.” In <em>Wikipedia</em>, October 7, 2020. <a href="https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;oldid=982283381">https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;oldid=982283381</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2756"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2756"></span>“Allen completed the 22.2 mi (35.7 km) crossing in 2 hours and 49 minutes, achieving a top speed of 18 mph (29 km/h) and an average altitude of 5 ft (1.5 m).”
+                   <p>“MacCready <em>Gossamer Albatross</em>.” In <em>Wikipedia</em>, October 7, 2020. <a href="https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;oldid=982283381">https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;oldid=982283381</a>.<a class="easy-footnote-to-top" href="#easy-footnote-3-2756"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2756"></span>“To maintain the craft in the air, it was designed with very long, tapering wings (high <a href="https://en.wikipedia.org/wiki/Aspect_ratio_(wing)">aspect ratio</a>), like those of a glider, allowing the flight to be undertaken with a minimum of power. In still air, the required power was on the order of 300 W (0.40 hp), though even mild turbulence made this figure rise rapidly.<sup><a href="https://en.wikipedia.org/wiki/MacCready_Gossamer_Albatross#cite_note-2">[2]</a></sup>“<br/>
+ <br/>
+                   “MacCready <em>Gossamer Albatross</em>.” In <em>Wikipedia</em>, October 7, 2020. <a href="https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;oldid=982283381">https://en.wikipedia.org/w/index.php?title=MacCready_Gossamer_Albatross&amp;oldid=982283381</a>.<a class="easy-footnote-to-top" href="#easy-footnote-4-2756"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-2756"></span>Chung, Yip-Wah. <em>Introduction to Materials Science and Engineering</em>. CRC Press, 2006. p89<a class="easy-footnote-to-top" href="#easy-footnote-5-2756"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-2756"></span>https://www.strava.com/activities/272615649/overview<a class="easy-footnote-to-top" href="#easy-footnote-6-2756"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-2756"></span>Strava. “Yellow Jersey – Giulio Ciccone’s 158.8 Km Bike Ride.” Accessed November 9, 2020. <a href="https://www.strava.com/activities/2525139293">https://www.strava.com/activities/2525139293</a>.<a class="easy-footnote-to-top" href="#easy-footnote-7-2756"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-8-2756"></span>For an upper value, we used a combination of two metrics given on the website. The first metric is his “weighted average power” for the Tour de France stage, which was 318W. Weighted average power is a way of averaging power over a ride with highly variable power which gives higher weight to higher power portions of the ride, and is used by athletes and coaches to estimate the maximum power that a rider could sustain for a long time, if they had a steady power output. The second metric is Ciccone’s maximum power from his Tour race applied over the duration of the MacCready flight (2 hours and 40 min) which is 5W/kg body weight. For the pilot, Allen, riding with the same power per body weight (65 kg), this would be equivalent to 322W, a similar value to his weighted average power. We use the lower of the two values, 318W.<a class="easy-footnote-to-top" href="#easy-footnote-8-2756"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-9-2756"></span>“The required food can also be calculated by dividing the output power by the <a href="https://en.wikipedia.org/wiki/Muscle#Efficiency">muscle efficiency</a>. This is 18–26%. “
+                   <p>“Bicycle Performance.” In <em>Wikipedia</em>, October 9, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Bicycle_performance&amp;oldid=982652996">https://en.wikipedia.org/w/index.php?title=Bicycle_performance&amp;oldid=982652996</a>.<a class="easy-footnote-to-top" href="#easy-footnote-9-2756"></a></p>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Energy efficiency of monarch butterfly flight

2022-09-21T07:37:41+00:00

@@ -1 +1,395 @@
+ ====== Energy efficiency of monarch butterfly flight ======
+ 
+ // Published 25 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>According to very rough estimates, the monarch butterfly:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">can fly around 100,000-600,000 m/kJ</div></li>
+ <li><div class="li">and move mass at around 0.065-0.36 kg⋅m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>The <strong>Monarch Butterfly</strong> is a butterfly known for its migration across North America.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2776" title='&amp;#8220;The monarch butterfly, Danaus plexippus, is famous for its spectacular annual migration across&lt;br&gt;North America&amp;#8221;&lt;/p&gt; &lt;p&gt;Zhan, Shuai, Wei Zhang, Kristjan Niitepõld, Jeremy Hsu, Juan Fernández Haeger, Myron P. Zalucki, Sonia Altizer, Jacobus C. de Roode, Steven M. Reppert, and Marcus R. Kronforst. “The Genetics of Monarch Butterfly Migration and Warning Colouration.” &lt;em&gt;Nature&lt;/em&gt; 514, no. 7522 (October 2014): 317–21. &lt;a href="https://doi.org/10.1038/nature13812"&gt;https://doi.org/10.1038/nature13812&lt;/a&gt;.'><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Mass ====
+ 
+ 
+ <HTML>
+ <p>The average mass of a monarch butterfly prior to its annual migration has been estimated to be 600mg<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2776" title='&amp;#8220;Each year in late summer and fall in southern Ontario, monarch butterflies, &lt;em&gt;Danaus plexippus plexippus L.&lt;/em&gt;, engage in migratory flight to the southern U.S.A. and Mexico&amp;#8230;&lt;/p&gt; &lt;p&gt;&amp;#8230;Late summer monarchs average approximately 600mg.&amp;#8221;&lt;br&gt;&lt;br&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;.'><sup>2</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>The following table gives some very rough estimates of energy expenditures, speeds and distances for several modes of flight, based on confusing information from a small number of papers (see footnotes for details).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-table is-style-regular">
+ <table>
+ <tbody>
+ <tr>
+ <td>Activity</td>
+ <td>Description</td>
+ <td>Energy expenditure per mass ( J/g⋅hr)</td>
+ <td>Energy expenditure for 600mg butterfly (J/s)</td>
+ <td>Speed (m/s)</td>
+ <td>distance/energy (m/J)</td>
+ </tr>
+ <tr>
+ <td>Soaring/gliding</td>
+ <td>Unpowered flight, including gradual decline and ascent via air currents</td>
+ <td>8-33<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2776" title='Gibo and Pallet (1979) appear to think energy expenditure of soaring is well approximated by energy expenditure for resting:&lt;br&gt;&lt;br&gt;&amp;#8220;The most efficient flying technique, in terms of&lt;br&gt;cost per unit of distance travelled, is soaring (Pennycuick 1969, 1975). During soaring flight, altitude&lt;br&gt;is gained or maintained by gliding in rising air currents. Since a soaring animal is actually gliding,&lt;br&gt;the wings are held more or less motionless and&lt;br&gt;the high-energy expenditure of powered flight is&lt;br&gt;avoided&amp;#8230;&lt;br&gt;&lt;br&gt;&amp;#8230;if soaring requires approximately&lt;br&gt;the basal level of metabolic expenditure, an average D. piesippus with an initial fat supply of 140 mg,&lt;br&gt;which could fly under power for only I1 h, may be&lt;br&gt;able to soar for 1060 h.&amp;#8221;&lt;br&gt;&lt;br&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;.&lt;br&gt;&lt;br&gt;They say, &amp;#8220;Flying Lepidoptera have a metabolic rate that is as&lt;br&gt;much as 100 times above the basal rate (Zebe 1954).&amp;#8221; &lt;br&gt;&lt;br&gt;Zhan et al 2014 measure metabolic rates for monarch butterflies specifically, but only report that the resting rate is 25x lower than a flying rate they prompted:&lt;br&gt;&lt;br&gt;&amp;#8220;&amp;#8230;we tested it by measuring flight metabolic&lt;br&gt;rates. We found active flight to be exceptionally demanding energetically, utilizing 25 times&lt;br&gt;more energy than resting&amp;#8230;&amp;#8221;&lt;br&gt;&lt;br&gt;Zhan, Shuai, Wei Zhang, Kristjan Niitepõld, Jeremy Hsu, Juan Fernández Haeger, Myron P. Zalucki, Sonia Altizer, Jacobus C. de Roode, Steven M. Reppert, and Marcus R. Kronforst. “The Genetics of Monarch Butterfly Migration and Warning Colouration.” &lt;em&gt;Nature&lt;/em&gt; 514, no. 7522 (October 2014): 317–21. &lt;a href="https://doi.org/10.1038/nature13812"&gt;https://doi.org/10.1038/nature13812&lt;/a&gt;.&lt;br&gt;&lt;br&gt;Also, their data makes very little sense to us. For instance, the figure suggests that flying is less energy intensive than resting. However it seems likely that this is a misunderstanding on our part, since for instance their y-axis in not labeled. Given this and the earlier claim that the difference between resting and flying can be 100x for butterflies, we use the relative number 25-100x, in combination with the flight and cruising energy estimates given below.&lt;br&gt;&lt;br&gt;high estimate: &lt;br&gt;837/25 J/g⋅hr = 33 J/g⋅hr (see below for flying rate)&lt;br&gt;&lt;br&gt;The lowest estimate would be the cruising speed energy expenditure divided by 100, but it seems like the 100 figure was meant as an upper bound on the difference, so probably referring to rest vs. maximal flight energy.&lt;br&gt;&lt;br&gt;Thus we take the lowest of the other combinations, as low end estimate: &lt;br&gt;min(209/25, 837/100) = min(8.4, 8.4) = 8.4 J/g⋅hr'><sup>3</sup></a></span></td>
+ <td>~0.0014 – 0.0056<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2776" title="8-33 J/g⋅hr * 0.6g= ~5-20 J/hr = 0.0014 &amp;#8211; 0.0056 J/s"><sup>4</sup></a></span></td>
+ <td>Very roughly 2.5-3.6 on average<span class="easy-footnote-margin-adjust" id="easy-footnote-5-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-2776" title='Gibo &amp;amp; Pallett (1979) assume this in estimating flight range possible via soaring:&lt;br&gt;&lt;br&gt;&amp;#8220;Consequently, if soaring requires approximately&lt;br&gt;the basal level of metabolic expenditure, an average D. piesippus with an initial fat supply of 140 mg,&lt;br&gt;which could fly under power for only I1 h, may be&lt;br&gt;able to soar for 1060 h. For gliding speeds ranging&lt;br&gt;from approximately 9 to 13 km/hr, the theoretical&lt;br&gt;maximum range, without pauses for feeding, would&lt;br&gt;fall between 9500 and 13 800 km.&amp;#8221;&lt;br&gt;&lt;br&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;.&lt;br&gt;&lt;br&gt;9-13km/hr = 2.5-3.6 m/s'><sup>5</sup></a></span></td>
+ <td>446- 2571<span class="easy-footnote-margin-adjust" id="easy-footnote-6-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-2776" title='2.5/.0056 = 446&lt;br&gt;&lt;br&gt;3.6/.0014 = 2571&lt;br&gt;&lt;br&gt;These numbers sound surprisingly high, but they are at least in line with Gibo &amp;amp; Pallett&amp;#8217;s estimate for maximal distance possibly flown with the 140mg of fat in a butterfly, if it could soar for the entire time:&lt;br&gt;&lt;br&gt;&amp;#8220;Consequently, if soaring requires approximately&lt;br&gt;the basal level of metabolic expenditure, an average D. piesippus with an initial fat supply of 140 mg,&lt;br&gt;which could fly under power for only 11 h, may be&lt;br&gt;able to soar for 1060 h. For gliding speeds ranging&lt;br&gt;from approximately 9 to 13 km/hr, the theoretical&lt;br&gt;maximum range, without pauses for feeding, would&lt;br&gt;fall between 9500 and 13 800 km.&amp;#8221;&lt;br&gt;&lt;br&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;. &lt;br&gt;&lt;br&gt;Our understanding is that this much soaring without the need for powered flight is implausible, but this efficiency figure should still be approximately correct for shorter distances where soaring is feasible.'><sup>6</sup></a></span></td>
+ </tr>
+ <tr>
+ <td>Cruising</td>
+ <td>Low speed powered flight</td>
+ <td>Very roughly 209<span class="easy-footnote-margin-adjust" id="easy-footnote-7-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-2776" title='Gibo and Pallett estimate cruising flight to be about one fourth as costly as sustained flapping flight:&lt;br&gt;&lt;br&gt;“Since profile drag is proportional to the square of the speed, doubling the speed increases the profile drag by four (Irving 1977). Consequently, it seems reasonable to assume that the slower, less energetic cruising flight of D. plexippus requires approximately 25% of the energy expenditure of vigorous flight.”&lt;br&gt;&lt;br&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;.&lt;br&gt;&lt;br&gt;Given an estimate of 837 J/g⋅hr for sustained flapping flight (see below), this gives us 209 J/g⋅hr for cruising.'><sup>7</sup></a></span></td>
+ <td>0.035<span class="easy-footnote-margin-adjust" id="easy-footnote-8-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-8-2776" title="209 J/g⋅hr * 0.6g = 125J/hr = 0.035 J/s"><sup>8</sup></a></span></td>
+ <td>Maximum: &gt;5<span class="easy-footnote-margin-adjust" id="easy-footnote-9-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-9-2776" title='&amp;#8220;However, during migration D.&lt;br&gt;plexippus adults usually adopt a slower cruising&lt;br&gt;flight at an airspeed of 18 km/hr (Urquhart 1960), a&lt;br&gt;flying strategy that should result in less fuel being&lt;br&gt;consumed as a result of reduced drag at lower&lt;br&gt;airspeeds.&amp;#8221;&lt;br&gt;&lt;br&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;.'><sup>9</sup></a></span></td>
+ <td>Maximum: &gt;143<span class="easy-footnote-margin-adjust" id="easy-footnote-10-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-10-2776" title="&amp;gt;5/0.035 = 143"><sup>10</sup></a></span></td>
+ </tr>
+ <tr>
+ <td>Sustained flapping</td>
+ <td>High speed powered flight</td>
+ <td>Very roughly 837<span class="easy-footnote-margin-adjust" id="easy-footnote-11-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-11-2776" title='We were not able to find the flight metabolic rate of monarch butterflies. Instead we use the flight metabolic rate of 200 calories per gram per hour (837 J/g⋅hr) that was measured as a minimum for another butterfly species during energetic flight, as Gibo and Pallet (1979) seem to think is somewhat reasonable, in their paper on soaring flight of monarch butterflies:&lt;br&gt;&lt;br&gt;“If we assume that the metabolic rate of D. plexippus during sustained flapping flight is only 200 cal/g h^-1, the minimal value determined by Zebe (1954) for another butterfly (Vanessa sp.)&amp;#8230;”&lt;br&gt;&lt;br&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;.'><sup>11</sup></a></span></td>
+ <td>~0.14<span class="easy-footnote-margin-adjust" id="easy-footnote-12-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-12-2776" title="837 J/g⋅hr * 0.6g = 502 J/hr = 0.14 J/s"><sup>12</sup></a></span></td>
+ <td>Maximum: &gt;13.9<span class="easy-footnote-margin-adjust" id="easy-footnote-13-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-13-2776" title='Maximal observed in one study: &lt;br&gt;&lt;br&gt;&amp;#8220;On some days, the butterflies were achieving estimated ground speeds of more than 50 km/hr.&amp;#8221;&lt;br&gt;&lt;br&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;.&lt;br&gt;&lt;br&gt;Also, airspeed during sustained flapping is around 40km/hr, and it seems unlikely that the motion of air can&amp;#8217;t add a further 10km/hr to ground speed: &lt;br&gt;&lt;br&gt;&amp;#8220;In D. plexippus vigorous flight of this type produces an airspeed&lt;br&gt;of approximately 40 kmlh (Urquhart 1960).&amp;#8221;&lt;br&gt;&lt;br&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;.&lt;br&gt;'><sup>13</sup></a></span></td>
+ <td>Maximum: &gt;99<span class="easy-footnote-margin-adjust" id="easy-footnote-14-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-14-2776" title="&amp;gt;13.9/0.14 = 99"><sup>14</sup></a></span></td>
+ </tr>
+ </tbody>
+ </table>
+ <figcaption>
+ <strong>Table 1: Statistics for several modes of flight. All figures are very rough estimates, based on incomplete and confusing information from a small number of papers (see footnotes for details).</strong>
+ </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><br/>
+               Soaring is estimated to be potentially very energy efficient (see Table 1), since it mostly makes use of air currents for energy. It seems likely that at least a small amount of powered flight is needed for getting into the air, however monarch butterflies can apparently fly for hundreds of kilometers in a day<span class="easy-footnote-margin-adjust" id="easy-footnote-15-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-15-2776" title='&amp;#8220;The farthest ranging monarch butterfly recorded traveled 265 miles in one day.&amp;#8221; [265 miles = 426km]&lt;br&gt;&lt;br&gt;“Monarch Butterfly Migration and Overwintering.” Accessed November 25, 2020. &lt;a href="https://www.fs.fed.us/wildflowers/pollinators/Monarch_Butterfly/migration/index.shtml"&gt;https://www.fs.fed.us/wildflowers/pollinators/Monarch_Butterfly/migration/index.shtml&lt;/a&gt;.'><sup>15</sup></a></span>, so supposing that they don’t stop many times in a day, taking off seems likely a negligible part of the flight.<span class="easy-footnote-margin-adjust" id="easy-footnote-16-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-16-2776" title="For instance, if it pessimistically takes 100 meters of powered flight to take off, then it would be .02% of the distance, so if it was 25x as much energy as usual for that distance, it would add .5% to the total energy use, which is far within the margin of error for this very rough calculation."><sup>16</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This would require ideal wind conditions, and our impression is that in practice, butterflies do not often fly very long distances without using at least a small amount of powered flight.<span class="easy-footnote-margin-adjust" id="easy-footnote-17-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-17-2776" title='For instance, in this video of soaring butterflies, most of them appear to flap their wings occasionally: &lt;a href="https://www.youtube.com/watch?v=a-8SPgG--6I"&gt;https://www.youtube.com/watch?v=a-8SPgG&amp;#8211;6I&lt;/a&gt;&lt;/p&gt; &lt;p&gt;Usa Monarch. &lt;em&gt;Soaring MONARCH BUTTERFLIES at Their Mexico Migration Site&lt;/em&gt;, 2019. &lt;a href="https://www.youtube.com/watch?v=a-8SPgG--6I"&gt;https://www.youtube.com/watch?v=a-8SPgG&amp;#8211;6I&lt;/a&gt;.'><sup>17</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>There is stronger evidence that monarch butterflies can realistically soar around 85% of the time, from Gibo &amp; Pallett, who report their observations of butterflies under relatively good conditions.<span class="easy-footnote-margin-adjust" id="easy-footnote-18-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-18-2776" title='“A description of the thermal soaring activity observed on September 7, a particularly favourable day, provides a clear picture of the relative importance of this type of flight. On this day we recorded the greatest proportion of soaring flights for any single day of observation.&lt;/p&gt; &lt;p&gt;Soaring accounted for 1964 s or 83.5% of this time, and powered flight for 359 s or 15.3%.”&lt;/p&gt; &lt;p&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;.'><sup>18</sup></a></span> So as a high estimate, we use this fraction of the time for soaring, and suppose that the remaining time is the relatively energy-efficient cruising, and take the optimistic end of all ranges. This gives us:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>One second of flight = 0.15 seconds cruising + 0.85 seconds soaring</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span class="has-inline-color has-white-color">________________</span>= 0.15s * 5 m/s cruising + 0.85s * 3.6m/s soaring</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span class="has-inline-color has-white-color">________________</span>= 0.75m cruising + 3.06m soaring</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span class="has-inline-color has-white-color">________________</span>= 3.81m total</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This also gives us:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 0.75m / 143 m/J cruising + 3.06m / 2571 m/J soaring</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 0.0064 J total</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus we have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>distance/energy = 3.81m/0.0064 J = 595 m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>For a low estimate of efficiency, we will assume that all of the powered flight is the most energetic flight, that powered flight is required half the time on average, and that the energy cost of gliding is twice that of resting. This gives us:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Energy efficiency = (50% * soaring distance + 50% * powered distance) / (50% * soaring energy + 50% * powered energy)</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= (50% * soaring distance/time + 50% * powered distance/time) / (50% * soaring energy/time + 50% * powered energy/time)</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= (0.5 * 2.5m/s + 0.5 * 13.9m/s) / (0.5 * (0.0056 * 2) J/s + 0.5 * 0.14 J/s)</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 108 m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus we have, very roughly:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>distance/energy = 100,000-600,000 m/kJ</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>For concreteness, a kJ is the energy in around a quarter of a raspberry. <span class="easy-footnote-margin-adjust" id="easy-footnote-19-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-19-2776" title='“FoodData Central.” Accessed December 10, 2020. &lt;a href="https://fdc.nal.usda.gov/fdc-app.html#/food-details/167755/nutrients"&gt;https://fdc.nal.usda.gov/fdc-app.html#/food-details/167755/nutrients&lt;/a&gt;.'><sup>19</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Mass⋅distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>As noted earlier, the average mass of a monarch butterfly prior to its annual migration has been estimated to be 600mg<span class="easy-footnote-margin-adjust" id="easy-footnote-20-2776"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-20-2776" title='&amp;#8220;Each year in late summer and fall in southern Ontario, monarch butterflies, &lt;em&gt;Danaus plexippus plexippus L.&lt;/em&gt;, engage in migratory flight to the southern U.S.A. and Mexico&amp;#8230;&lt;/p&gt; &lt;p&gt;&amp;#8230;Late summer monarchs average approximately 600mg.&amp;#8221;&lt;br&gt;&lt;br&gt;Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” &lt;em&gt;Canadian Journal of Zoology&lt;/em&gt;, July 1979. &lt;a href="https://doi.org/10.1139/z79-180"&gt;https://doi.org/10.1139/z79-180&lt;/a&gt;.'><sup>20</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus we have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>mass*distance/energy = 0.0006 kg * 108 — 0.0006 kg * 595 m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 0.065 — 0.36 kg⋅m/J<br/>
+ <br/>
+ <br/></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2776"></span>“The monarch butterfly, Danaus plexippus, is famous for its spectacular annual migration across<br/>
+                   North America”
+                   <p>Zhan, Shuai, Wei Zhang, Kristjan Niitepõld, Jeremy Hsu, Juan Fernández Haeger, Myron P. Zalucki, Sonia Altizer, Jacobus C. de Roode, Steven M. Reppert, and Marcus R. Kronforst. “The Genetics of Monarch Butterfly Migration and Warning Colouration.” <em>Nature</em> 514, no. 7522 (October 2014): 317–21. <a href="https://doi.org/10.1038/nature13812">https://doi.org/10.1038/nature13812</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2776"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2776"></span>“Each year in late summer and fall in southern Ontario, monarch butterflies, <em>Danaus plexippus plexippus L.</em>, engage in migratory flight to the southern U.S.A. and Mexico…
+                   <p>…Late summer monarchs average approximately 600mg.”<br/>
+ <br/>
+                   Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2776"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2776"></span>Gibo and Pallet (1979) appear to think energy expenditure of soaring is well approximated by energy expenditure for resting:<br/>
+ <br/>
+                   “The most efficient flying technique, in terms of<br/>
+                   cost per unit of distance travelled, is soaring (Pennycuick 1969, 1975). During soaring flight, altitude<br/>
+                   is gained or maintained by gliding in rising air currents. Since a soaring animal is actually gliding,<br/>
+                   the wings are held more or less motionless and<br/>
+                   the high-energy expenditure of powered flight is<br/>
+                   avoided…<br/>
+ <br/>
+                   …if soaring requires approximately<br/>
+                   the basal level of metabolic expenditure, an average D. piesippus with an initial fat supply of 140 mg,<br/>
+                   which could fly under power for only I1 h, may be<br/>
+                   able to soar for 1060 h.”<br/>
+ <br/>
+                   Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<br/>
+ <br/>
+                   They say, “Flying Lepidoptera have a metabolic rate that is as<br/>
+                   much as 100 times above the basal rate (Zebe 1954).”<br/>
+ <br/>
+                   Zhan et al 2014 measure metabolic rates for monarch butterflies specifically, but only report that the resting rate is 25x lower than a flying rate they prompted:<br/>
+ <br/>
+                   “…we tested it by measuring flight metabolic<br/>
+                   rates. We found active flight to be exceptionally demanding energetically, utilizing 25 times<br/>
+                   more energy than resting…”<br/>
+ <br/>
+                   Zhan, Shuai, Wei Zhang, Kristjan Niitepõld, Jeremy Hsu, Juan Fernández Haeger, Myron P. Zalucki, Sonia Altizer, Jacobus C. de Roode, Steven M. Reppert, and Marcus R. Kronforst. “The Genetics of Monarch Butterfly Migration and Warning Colouration.” <em>Nature</em> 514, no. 7522 (October 2014): 317–21. <a href="https://doi.org/10.1038/nature13812">https://doi.org/10.1038/nature13812</a>.<br/>
+ <br/>
+                   Also, their data makes very little sense to us. For instance, the figure suggests that flying is less energy intensive than resting. However it seems likely that this is a misunderstanding on our part, since for instance their y-axis in not labeled. Given this and the earlier claim that the difference between resting and flying can be 100x for butterflies, we use the relative number 25-100x, in combination with the flight and cruising energy estimates given below.<br/>
+ <br/>
+                   high estimate:<br/>
+                   837/25 J/g⋅hr = 33 J/g⋅hr (see below for flying rate)<br/>
+ <br/>
+                   The lowest estimate would be the cruising speed energy expenditure divided by 100, but it seems like the 100 figure was meant as an upper bound on the difference, so probably referring to rest vs. maximal flight energy.<br/>
+ <br/>
+                   Thus we take the lowest of the other combinations, as low end estimate:<br/>
+                   min(209/25, 837/100) = min(8.4, 8.4) = 8.4 J/g⋅hr<a class="easy-footnote-to-top" href="#easy-footnote-3-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2776"></span>8-33 J/g⋅hr * 0.6g= ~5-20 J/hr = 0.0014 – 0.0056 J/s<a class="easy-footnote-to-top" href="#easy-footnote-4-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-2776"></span>Gibo &amp; Pallett (1979) assume this in estimating flight range possible via soaring:<br/>
+ <br/>
+                   “Consequently, if soaring requires approximately<br/>
+                   the basal level of metabolic expenditure, an average D. piesippus with an initial fat supply of 140 mg,<br/>
+                   which could fly under power for only I1 h, may be<br/>
+                   able to soar for 1060 h. For gliding speeds ranging<br/>
+                   from approximately 9 to 13 km/hr, the theoretical<br/>
+                   maximum range, without pauses for feeding, would<br/>
+                   fall between 9500 and 13 800 km.”<br/>
+ <br/>
+                   Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<br/>
+ <br/>
+                   9-13km/hr = 2.5-3.6 m/s<a class="easy-footnote-to-top" href="#easy-footnote-5-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-2776"></span>2.5/.0056 = 446<br/>
+ <br/>
+                   3.6/.0014 = 2571<br/>
+ <br/>
+                   These numbers sound surprisingly high, but they are at least in line with Gibo &amp; Pallett’s estimate for maximal distance possibly flown with the 140mg of fat in a butterfly, if it could soar for the entire time:<br/>
+ <br/>
+                   “Consequently, if soaring requires approximately<br/>
+                   the basal level of metabolic expenditure, an average D. piesippus with an initial fat supply of 140 mg,<br/>
+                   which could fly under power for only 11 h, may be<br/>
+                   able to soar for 1060 h. For gliding speeds ranging<br/>
+                   from approximately 9 to 13 km/hr, the theoretical<br/>
+                   maximum range, without pauses for feeding, would<br/>
+                   fall between 9500 and 13 800 km.”<br/>
+ <br/>
+                   Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<br/>
+ <br/>
+                   Our understanding is that this much soaring without the need for powered flight is implausible, but this efficiency figure should still be approximately correct for shorter distances where soaring is feasible.<a class="easy-footnote-to-top" href="#easy-footnote-6-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-2776"></span>Gibo and Pallett estimate cruising flight to be about one fourth as costly as sustained flapping flight:<br/>
+ <br/>
+                   “Since profile drag is proportional to the square of the speed, doubling the speed increases the profile drag by four (Irving 1977). Consequently, it seems reasonable to assume that the slower, less energetic cruising flight of D. plexippus requires approximately 25% of the energy expenditure of vigorous flight.”<br/>
+ <br/>
+                   Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<br/>
+ <br/>
+                   Given an estimate of 837 J/g⋅hr for sustained flapping flight (see below), this gives us 209 J/g⋅hr for cruising.<a class="easy-footnote-to-top" href="#easy-footnote-7-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-8-2776"></span>209 J/g⋅hr * 0.6g = 125J/hr = 0.035 J/s<a class="easy-footnote-to-top" href="#easy-footnote-8-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-9-2776"></span>“However, during migration D.<br/>
+                   plexippus adults usually adopt a slower cruising<br/>
+                   flight at an airspeed of 18 km/hr (Urquhart 1960), a<br/>
+                   flying strategy that should result in less fuel being<br/>
+                   consumed as a result of reduced drag at lower<br/>
+                   airspeeds.”<br/>
+ <br/>
+                   Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<a class="easy-footnote-to-top" href="#easy-footnote-9-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-10-2776"></span>&gt;5/0.035 = 143<a class="easy-footnote-to-top" href="#easy-footnote-10-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-11-2776"></span>We were not able to find the flight metabolic rate of monarch butterflies. Instead we use the flight metabolic rate of 200 calories per gram per hour (837 J/g⋅hr) that was measured as a minimum for another butterfly species during energetic flight, as Gibo and Pallet (1979) seem to think is somewhat reasonable, in their paper on soaring flight of monarch butterflies:<br/>
+ <br/>
+                   “If we assume that the metabolic rate of D. plexippus during sustained flapping flight is only 200 cal/g h^-1, the minimal value determined by Zebe (1954) for another butterfly (Vanessa sp.)…”<br/>
+ <br/>
+                   Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<a class="easy-footnote-to-top" href="#easy-footnote-11-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-12-2776"></span>837 J/g⋅hr * 0.6g = 502 J/hr = 0.14 J/s<a class="easy-footnote-to-top" href="#easy-footnote-12-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-13-2776"></span>Maximal observed in one study:<br/>
+ <br/>
+                   “On some days, the butterflies were achieving estimated ground speeds of more than 50 km/hr.”<br/>
+ <br/>
+                   Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<br/>
+ <br/>
+                   Also, airspeed during sustained flapping is around 40km/hr, and it seems unlikely that the motion of air can’t add a further 10km/hr to ground speed:<br/>
+ <br/>
+                   “In D. plexippus vigorous flight of this type produces an airspeed<br/>
+                   of approximately 40 kmlh (Urquhart 1960).”<br/>
+ <br/>
+                   Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<br/>
+ <a class="easy-footnote-to-top" href="#easy-footnote-13-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-14-2776"></span>&gt;13.9/0.14 = 99<a class="easy-footnote-to-top" href="#easy-footnote-14-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-15-2776"></span>“The farthest ranging monarch butterfly recorded traveled 265 miles in one day.” [265 miles = 426km]<br/>
+ <br/>
+                   “Monarch Butterfly Migration and Overwintering.” Accessed November 25, 2020. <a href="https://www.fs.fed.us/wildflowers/pollinators/Monarch_Butterfly/migration/index.shtml">https://www.fs.fed.us/wildflowers/pollinators/Monarch_Butterfly/migration/index.shtml</a>.<a class="easy-footnote-to-top" href="#easy-footnote-15-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-16-2776"></span>For instance, if it pessimistically takes 100 meters of powered flight to take off, then it would be .02% of the distance, so if it was 25x as much energy as usual for that distance, it would add .5% to the total energy use, which is far within the margin of error for this very rough calculation.<a class="easy-footnote-to-top" href="#easy-footnote-16-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-17-2776"></span>For instance, in this video of soaring butterflies, most of them appear to flap their wings occasionally: <a href="https://www.youtube.com/watch?v=a-8SPgG--6I">https://www.youtube.com/watch?v=a-8SPgG–6I</a>
+ <p>Usa Monarch. <em>Soaring MONARCH BUTTERFLIES at Their Mexico Migration Site</em>, 2019. <a href="https://www.youtube.com/watch?v=a-8SPgG--6I">https://www.youtube.com/watch?v=a-8SPgG–6I</a>.<a class="easy-footnote-to-top" href="#easy-footnote-17-2776"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-18-2776"></span>“A description of the thermal soaring activity observed on September 7, a particularly favourable day, provides a clear picture of the relative importance of this type of flight. On this day we recorded the greatest proportion of soaring flights for any single day of observation.
+                   <p>Soaring accounted for 1964 s or 83.5% of this time, and powered flight for 359 s or 15.3%.”</p>
+ <p>Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<a class="easy-footnote-to-top" href="#easy-footnote-18-2776"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-19-2776"></span>“FoodData Central.” Accessed December 10, 2020. <a href="https://fdc.nal.usda.gov/fdc-app.html#/food-details/167755/nutrients">https://fdc.nal.usda.gov/fdc-app.html#/food-details/167755/nutrients</a>.<a class="easy-footnote-to-top" href="#easy-footnote-19-2776"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-20-2776"></span>“Each year in late summer and fall in southern Ontario, monarch butterflies, <em>Danaus plexippus plexippus L.</em>, engage in migratory flight to the southern U.S.A. and Mexico…
+                   <p>…Late summer monarchs average approximately 600mg.”<br/>
+ <br/>
+                   Gibo, David L., and Pallett, Megan J., “Soaring Flight of Monarch Butterflies, Danaus Plexippus (Lepidoptera: Danaidae), during the Late Summer Migration in Southern Ontario.” <em>Canadian Journal of Zoology</em>, July 1979. <a href="https://doi.org/10.1139/z79-180">https://doi.org/10.1139/z79-180</a>.<a class="easy-footnote-to-top" href="#easy-footnote-20-2776"></a></p>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Energy efficiency of North American P-51 Mustang

2022-09-21T07:37:41+00:00

@@ -1 +1,128 @@
+ ====== Energy efficiency of North American P-51 Mustang ======
+ 
+ // Published 05 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>The North American P-51 Mustang:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">flew around 0.073—0.092 m/kJ</div></li>
+ <li><div class="li">and moved mass at around 0.25 – 0.50 kg.m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>The <em>North American P-51 Mustang</em> was a 1940 US WWII fighter and fighter-bomber.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2737"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2737" title='The&amp;nbsp;&lt;strong&gt;North American Aviation P-51 Mustang&lt;/strong&gt;&amp;nbsp;is an American long-range, single-seat&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Fighter_aircraft"&gt;fighter&lt;/a&gt;&amp;nbsp;and&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Fighter-bomber"&gt;fighter-bomber&lt;/a&gt;&amp;nbsp;used during&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/World_War_II"&gt;World War II&lt;/a&gt;&amp;nbsp;and the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Korean_War"&gt;Korean War&lt;/a&gt;, among other conflicts. The Mustang was designed in April 1940 by a design team headed by James Kindelberger&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/North_American_P-51_Mustang#cite_note-6"&gt;[6]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;of&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/North_American_Aviation"&gt;North American Aviation&lt;/a&gt;&amp;nbsp;(NAA) in response to a requirement of the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/British_Purchasing_Commission"&gt;British Purchasing Commission&lt;/a&gt;.”&lt;/p&gt; &lt;p&gt;“North American P-51 Mustang.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 19, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;amp;oldid=984347874"&gt;https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;amp;oldid=984347874&lt;/a&gt;.'><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Mass ====
+ 
+ 
+ <HTML>
+ <p>According to Wikipedia<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2737"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2737" title='“North American P-51 Mustang.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 19, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;amp;oldid=984347874"&gt;https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;amp;oldid=984347874&lt;/a&gt;.'><sup>2</sup></a></span>:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Empty weight:</strong> 7,635 lb (3,465 kg)</div></li>
+ <li><div class="li"><strong>Gross weight:</strong> 9,200 lb (4,175 kg)</div></li>
+ <li><div class="li"><strong>Max takeoff weight:</strong> 12,100 lb (5,488 kg)</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We use the range 3,465—5,488 kg, since we do not know at what weight in that range the relevant speeds were measured.</p>
+ </HTML>
+ 
+ 
+ ==== Distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>Wikipedia tells us that cruising speed was 362 mph (162 m/s)<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2737"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2737" title='“North American P-51 Mustang.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 19, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;amp;oldid=984347874"&gt;https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;amp;oldid=984347874&lt;/a&gt;.'><sup>3</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>A table from <em>WWII Aircraft Performance</em> gives combinations of flight parameters apparently for a version of the P-51, however it has no title or description, so we cannot be confident. <span class="easy-footnote-margin-adjust" id="easy-footnote-4-2737"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2737" title='“P-51D_15342_AppendixB.Pdf.” Accessed November 5, 2020. &lt;a href="http://www.wwiiaircraftperformance.org/mustang/P-51D_15342_AppendixB.pdf"&gt;http://www.wwiiaircraftperformance.org/mustang/P-51D_15342_AppendixB.pdf&lt;/a&gt;.'><sup>4</sup></a></span> We extracted some data from it <a href="https://docs.google.com/spreadsheets/d/1RsewNj8d8JDlL9628xioi2vcVeG0oPMKlC8u59FVvA4/edit?usp=sharing">here</a>. This data suggests the best combination of parameters gives a fuel economy of 6.7 miles/gallon (10.8km)</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We don’t know what fuel was used, but fuel energy density seems likely to be between 31—39 MJ/L = 117—148 MJ/gallon.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-2737"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-2737" title='Wikipedia lists energy densities for a variety of fuels, and those for petroleum, 100LL avgas, diesel, and jet fuel are within this range and seem likely to be similar to that used.&lt;/p&gt; &lt;p&gt;“Energy Density.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 21, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Energy_density&amp;amp;oldid=979608484"&gt;https://en.wikipedia.org/w/index.php?title=Energy_density&amp;amp;oldid=979608484&lt;/a&gt;.'><sup>5</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus the plane flew about 10.8km on 117—148 MJ of fuel, for 0.073—0.092 m/kJ</p>
+ </HTML>
+ 
+ 
+ ==== Mass.distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>We have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Distance per kilojoule: 0.073—0.092 m/kJ</div></li>
+ <li><div class="li">Mass: 3,465—5,488 kg</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This gives us a range of 0.25 – 0.50 kg.m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><br/>
+ <br/>
+ <em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2737"></span>The <strong>North American Aviation P-51 Mustang</strong> is an American long-range, single-seat <a href="https://en.wikipedia.org/wiki/Fighter_aircraft">fighter</a> and <a href="https://en.wikipedia.org/wiki/Fighter-bomber">fighter-bomber</a> used during <a href="https://en.wikipedia.org/wiki/World_War_II">World War II</a> and the <a href="https://en.wikipedia.org/wiki/Korean_War">Korean War</a>, among other conflicts. The Mustang was designed in April 1940 by a design team headed by James Kindelberger<sup><a href="https://en.wikipedia.org/wiki/North_American_P-51_Mustang#cite_note-6">[6]</a></sup> of <a href="https://en.wikipedia.org/wiki/North_American_Aviation">North American Aviation</a> (NAA) in response to a requirement of the <a href="https://en.wikipedia.org/wiki/British_Purchasing_Commission">British Purchasing Commission</a>.”
+                   <p>“North American P-51 Mustang.” In <em>Wikipedia</em>, October 19, 2020. <a href="https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;oldid=984347874">https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;oldid=984347874</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2737"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2737"></span>“North American P-51 Mustang.” In <em>Wikipedia</em>, October 19, 2020. <a href="https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;oldid=984347874">https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;oldid=984347874</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2737"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2737"></span>“North American P-51 Mustang.” In <em>Wikipedia</em>, October 19, 2020. <a href="https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;oldid=984347874">https://en.wikipedia.org/w/index.php?title=North_American_P-51_Mustang&amp;oldid=984347874</a>.<a class="easy-footnote-to-top" href="#easy-footnote-3-2737"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2737"></span>“P-51D_15342_AppendixB.Pdf.” Accessed November 5, 2020. <a href="http://www.wwiiaircraftperformance.org/mustang/P-51D_15342_AppendixB.pdf">http://www.wwiiaircraftperformance.org/mustang/P-51D_15342_AppendixB.pdf</a>.<a class="easy-footnote-to-top" href="#easy-footnote-4-2737"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-2737"></span>Wikipedia lists energy densities for a variety of fuels, and those for petroleum, 100LL avgas, diesel, and jet fuel are within this range and seem likely to be similar to that used.
+                   <p>“Energy Density.” In <em>Wikipedia</em>, September 21, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Energy_density&amp;oldid=979608484">https://en.wikipedia.org/w/index.php?title=Energy_density&amp;oldid=979608484</a>.<a class="easy-footnote-to-top" href="#easy-footnote-5-2737"></a></p>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Energy efficiency of paramotors

2022-09-21T07:37:41+00:00

@@ -1 +1,179 @@
+ ====== Energy efficiency of paramotors ======
+ 
+ // Published 24 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>We estimate that a record-breaking two-person paramotor:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">covered around = 0.36 m/kJ</div></li>
+ <li><div class="li">and moved mass at around 0.058 – 0.10 kg⋅m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>Paramotors are powered parachutes that allow the operator to steer.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2765"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2765" title='&amp;#8220;&lt;strong&gt;Powered&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Paragliding"&gt;paragliding&lt;/a&gt;&lt;/strong&gt;, also known as&amp;nbsp;&lt;strong&gt;paramotoring&lt;/strong&gt;&amp;nbsp;or&amp;nbsp;&lt;strong&gt;PPG&lt;/strong&gt;, is a form of&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Ultralight_aviation"&gt;ultralight aviation&lt;/a&gt;&amp;nbsp;where the pilot wears a back-mounted motor (a&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Paramotor"&gt;paramotor&lt;/a&gt;) which provides enough thrust to take off using a paraglider. It can be launched in still air, and on level ground, by the pilot alone — no assistance is required&amp;#8230;.Powered paragliders are smaller, use more efficient (but more difficult to manage) paraglider wings, and steer with brake toggles like sport parachutists.&amp;#8221;&lt;/p&gt; &lt;p&gt;“Powered Paragliding.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 31, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Powered_paragliding&amp;amp;oldid=986450866"&gt;https://en.wikipedia.org/w/index.php?title=Powered_paragliding&amp;amp;oldid=986450866&lt;/a&gt;.'><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>The Fédération Aéronautique Internationale (FAI) maintains records for a number of classes of paramotor contest. We look at subclass RPF2T—(Paramotors : Paraglider Control / Foot-launched / Flown with two persons / Thermal Engine)—which is appears to be the most recent paramotor record for ‘Distance in a straight line with limited fuel’.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2765"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2765" title='Recent paramotor records for distance in a straight line with limited fuel:&lt;/p&gt; &lt;p&gt;“Records | World Air Sports Federation.” Accessed November 18, 2020. &lt;a href="https://www.fai.org/records?f%5B0%5D=field_record_sport%3A2025&amp;amp;f%5B1%5D=field_type_of_record%3A488&amp;amp;record=&amp;amp;order=field_date_single_custom&amp;amp;sort=desc"&gt;https://www.fai.org/records?f%5B0%5D=field_record_sport%3A2025&amp;amp;f%5B1%5D=field_type_of_record%3A488&amp;amp;record=&amp;amp;order=field_date_single_custom&amp;amp;sort=desc&lt;/a&gt;.&lt;/p&gt; &lt;p&gt;Details of Mark Morgan&amp;#8217;s 2013 record:&lt;/p&gt; &lt;p&gt;“Mark Morgan (GBR) (16956),” October 10, 2017. &lt;a href="https://www.fai.org/record/16956"&gt;https://www.fai.org/record/16956&lt;/a&gt;.'><sup>2</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The record distance was 123.18 km.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2765"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2765" title='“Mark Morgan (GBR) (16956),” October 10, 2017. &lt;a href="https://www.fai.org/record/16956"&gt;https://www.fai.org/record/16956&lt;/a&gt;.'><sup>3</sup></a></span> The FAI rules state that no more than 7.5 kg of fuel may be used.<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2765"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2765" title="&amp;#8220;Special rules for distance in a straight line with limited fuel&amp;#8230;&lt;/p&gt; &lt;p&gt;The aircraft must carry no more than 7.5 kg of fuel which may be used as required.&amp;#8221;&lt;/p&gt; &lt;p&gt;FAI. “FAI Sporting Code: Section 10 – Microlights and Paramotors,” 2017."><sup>4</sup></a></span> We will assume that in the process of breaking this record, all of the available fuel was used. We will also assume that regular gasoline was used. Gasoline has an energy density of 45 MJ/kg.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-2765"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-2765" title='“Energy Density of Gasoline &amp;#8211; The Physics Factbook.” Accessed November 18, 2020. &lt;a href="https://hypertextbook.com/facts/2003/ArthurGolnik.shtml"&gt;https://hypertextbook.com/facts/2003/ArthurGolnik.shtml&lt;/a&gt;.'><sup>5</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Distance per energy = 123.18 km / (7.5 kg * 45 MJ/kg)</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 0.36 m/kJ</p>
+ </HTML>
+ 
+ 
+ ==== Mass.distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>The weight of an entire paramotoring apparatus appears to be the weights of the passengers plus motor plus wing plus clothing and incidentals, based on forum posts.<span class="easy-footnote-margin-adjust" id="easy-footnote-6-2765"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-2765" title='&amp;#8220;You are 102kg, the motor is probably 25kg, wing weight say 5kg, clothing and incidentals about 8kg. So you total is 140kg.&amp;#8221;&lt;/p&gt; &lt;p&gt;www.Paramotorclub.org. “Is This Wing for Me.” Accessed November 24, 2020. &lt;a href="https://www.paramotorclub.org/topic/13451-is-this-wing-for-me/"&gt;https://www.paramotorclub.org/topic/13451-is-this-wing-for-me/&lt;/a&gt;.&lt;/p&gt; &lt;p&gt;&amp;#8220;Wife at 59kg, plus a 20kg motor (light) plus clothing and instruments say 7kg plus weight of wing (should be included) 5.6kg, that equals 91.6kg.&amp;#8221;&lt;/p&gt; &lt;p&gt;www.Paramotorclub.org. “Roadster 3 Weight/Sizing Question.” Accessed November 24, 2020. &lt;a href="https://www.paramotorclub.org/topic/12973-roadster-3-weightsizing-question/"&gt;https://www.paramotorclub.org/topic/12973-roadster-3-weightsizing-question/&lt;/a&gt;.'><sup>6</sup></a></span> These posts put clothing and incidentals at around 8kg, but are estimates for single person flying, whereas this record was a two person flight. We guess that two people need around 1.5x as much additional weight, for 12kg.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Wikipedia says that the weight of a paramotor varies from 18kg to 34 kg.<span class="easy-footnote-margin-adjust" id="easy-footnote-7-2765"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-2765" title='&amp;#8220;A typical paramotor will weigh on average around 50 lbs. (23 kg) with some models as light at 40 lbs. (18 kg) and some models as high as 75 lbs. (34 kg.)&amp;#8221;&lt;/p&gt; &lt;p&gt;“Paramotor.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 1, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Paramotor&amp;amp;oldid=981354167"&gt;https://en.wikipedia.org/w/index.php?title=Paramotor&amp;amp;oldid=981354167&lt;/a&gt;.'><sup>7</sup></a></span> However it is unclear whether this means the motor itself, or all of the equipment involved.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The glider used appears to be MagMax brand, a typical example of which weighs around 8kg, though this may have been different in 2013, or they may have used a different specific glider.<span class="easy-footnote-margin-adjust" id="easy-footnote-8-2765"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-8-2765" title='&amp;#8220;Aircraft&amp;nbsp; Mag Max&amp;#8221;&lt;/p&gt; &lt;p&gt;“Mark Morgan (GBR) (16956),” October 10, 2017. &lt;a href="https://www.fai.org/record/16956"&gt;https://www.fai.org/record/16956&lt;/a&gt;.&lt;/p&gt; &lt;p&gt;&amp;#8220;Glider Weight (kg) 8 8.4&amp;#8221;&lt;/p&gt; &lt;p&gt;Ozone Paramotor. “MagMax.” Accessed November 18, 2020. &lt;a href="https://www.flyozone.com/paramotor/products/gliders/magmax"&gt;https://www.flyozone.com/paramotor/products/gliders/magmax&lt;/a&gt;.'><sup>8</sup></a></span> To account for this uncertainty, we shall add the glider weight to the high estimate, and so estimate the weight of the glider and motor together at 18-42kg.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We will assume that the apparently male pilots weighed between 65 and 115 kgs each, based on normal male weights<span class="easy-footnote-margin-adjust" id="easy-footnote-9-2765"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-9-2765" title='Pilots appear to be male in this picture: &lt;a href="https://www.fai.org/sites/default/files/record/recs-documents/16956-2_0.jpg"&gt;https://www.fai.org/sites/default/files/record/recs-documents/16956-2_0.jpg&lt;/a&gt;&lt;/p&gt; &lt;p&gt;10th to 90th percentile male weights, from: &lt;/p&gt; &lt;p&gt;DQYDJ – Don’t Quit Your Day Job&amp;#8230; “Weight Percentile Calculator for Men and Women in the United States,” February 13, 2019. &lt;a href="https://dqydj.com/weight-percentile-calculator-men-women/"&gt;https://dqydj.com/weight-percentile-calculator-men-women/&lt;/a&gt;.'><sup>9</sup></a></span>. </p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus we have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>weight = motor + wing + people + clothing and incidentals</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>weight (low estimate) = 18 + 65*2 + 12 = 160kg</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>weight (high estimate) = 42 + 115*2 + 12 = 284kg</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>High efficiency estimate:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>284kg * 0.36 m/kJ  = 0.10 kg⋅m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Low efficiency estimate:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>160kg * 0.36 m/kJ  = .058 kg⋅m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This gives us a range of 0.058 – 0.10 kg⋅m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><br/>
+ <br/>
+ <br/>
+ <em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2765"></span>“<strong>Powered <a href="https://en.wikipedia.org/wiki/Paragliding">paragliding</a></strong>, also known as <strong>paramotoring</strong> or <strong>PPG</strong>, is a form of <a href="https://en.wikipedia.org/wiki/Ultralight_aviation">ultralight aviation</a> where the pilot wears a back-mounted motor (a <a href="https://en.wikipedia.org/wiki/Paramotor">paramotor</a>) which provides enough thrust to take off using a paraglider. It can be launched in still air, and on level ground, by the pilot alone — no assistance is required….Powered paragliders are smaller, use more efficient (but more difficult to manage) paraglider wings, and steer with brake toggles like sport parachutists.”
+                   <p>“Powered Paragliding.” In <em>Wikipedia</em>, October 31, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Powered_paragliding&amp;oldid=986450866">https://en.wikipedia.org/w/index.php?title=Powered_paragliding&amp;oldid=986450866</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2765"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2765"></span>Recent paramotor records for distance in a straight line with limited fuel:
+                   <p>“Records | World Air Sports Federation.” Accessed November 18, 2020. <a href="https://www.fai.org/records?f%5B0%5D=field_record_sport%3A2025&amp;f%5B1%5D=field_type_of_record%3A488&amp;record=&amp;order=field_date_single_custom&amp;sort=desc">https://www.fai.org/records?f%5B0%5D=field_record_sport%3A2025&amp;f%5B1%5D=field_type_of_record%3A488&amp;record=&amp;order=field_date_single_custom&amp;sort=desc</a>.</p>
+ <p>Details of Mark Morgan’s 2013 record:</p>
+ <p>“Mark Morgan (GBR) (16956),” October 10, 2017. <a href="https://www.fai.org/record/16956">https://www.fai.org/record/16956</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2765"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2765"></span>“Mark Morgan (GBR) (16956),” October 10, 2017. <a href="https://www.fai.org/record/16956">https://www.fai.org/record/16956</a>.<a class="easy-footnote-to-top" href="#easy-footnote-3-2765"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2765"></span>“Special rules for distance in a straight line with limited fuel…
+                   <p>The aircraft must carry no more than 7.5 kg of fuel which may be used as required.”</p>
+ <p>FAI. “FAI Sporting Code: Section 10 – Microlights and Paramotors,” 2017.<a class="easy-footnote-to-top" href="#easy-footnote-4-2765"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-2765"></span>“Energy Density of Gasoline – The Physics Factbook.” Accessed November 18, 2020. <a href="https://hypertextbook.com/facts/2003/ArthurGolnik.shtml">https://hypertextbook.com/facts/2003/ArthurGolnik.shtml</a>.<a class="easy-footnote-to-top" href="#easy-footnote-5-2765"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-2765"></span>“You are 102kg, the motor is probably 25kg, wing weight say 5kg, clothing and incidentals about 8kg. So you total is 140kg.”
+                   <p>www.Paramotorclub.org. “Is This Wing for Me.” Accessed November 24, 2020. <a href="https://www.paramotorclub.org/topic/13451-is-this-wing-for-me/">https://www.paramotorclub.org/topic/13451-is-this-wing-for-me/</a>.</p>
+ <p>“Wife at 59kg, plus a 20kg motor (light) plus clothing and instruments say 7kg plus weight of wing (should be included) 5.6kg, that equals 91.6kg.”</p>
+ <p>www.Paramotorclub.org. “Roadster 3 Weight/Sizing Question.” Accessed November 24, 2020. <a href="https://www.paramotorclub.org/topic/12973-roadster-3-weightsizing-question/">https://www.paramotorclub.org/topic/12973-roadster-3-weightsizing-question/</a>.<a class="easy-footnote-to-top" href="#easy-footnote-6-2765"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-2765"></span>“A typical paramotor will weigh on average around 50 lbs. (23 kg) with some models as light at 40 lbs. (18 kg) and some models as high as 75 lbs. (34 kg.)”
+                   <p>“Paramotor.” In <em>Wikipedia</em>, October 1, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Paramotor&amp;oldid=981354167">https://en.wikipedia.org/w/index.php?title=Paramotor&amp;oldid=981354167</a>.<a class="easy-footnote-to-top" href="#easy-footnote-7-2765"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-8-2765"></span>“Aircraft  Mag Max”
+                   <p>“Mark Morgan (GBR) (16956),” October 10, 2017. <a href="https://www.fai.org/record/16956">https://www.fai.org/record/16956</a>.</p>
+ <p>“Glider Weight (kg) 8 8.4”</p>
+ <p>Ozone Paramotor. “MagMax.” Accessed November 18, 2020. <a href="https://www.flyozone.com/paramotor/products/gliders/magmax">https://www.flyozone.com/paramotor/products/gliders/magmax</a>.<a class="easy-footnote-to-top" href="#easy-footnote-8-2765"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-9-2765"></span>Pilots appear to be male in this picture: <a href="https://www.fai.org/sites/default/files/record/recs-documents/16956-2_0.jpg">https://www.fai.org/sites/default/files/record/recs-documents/16956-2_0.jpg</a>
+ <p>10th to 90th percentile male weights, from:</p>
+ <p>DQYDJ – Don’t Quit Your Day Job… “Weight Percentile Calculator for Men and Women in the United States,” February 13, 2019. <a href="https://dqydj.com/weight-percentile-calculator-men-women/">https://dqydj.com/weight-percentile-calculator-men-women/</a>.<a class="easy-footnote-to-top" href="#easy-footnote-9-2765"></a></p>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Energy efficiency of The Spirit of Butt’s Farm

2022-09-21T07:37:41+00:00

@@ -1 +1,183 @@
+ ====== Energy efficiency of The Spirit of Butt’s Farm ======
+ 
+ // Published 18 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>The Spirit of Butt’s Farm:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">covered around 31.67 m/kJ</div></li>
+ <li><div class="li">and moved mass at around 0.16 – 0.086 kg⋅m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>The Spirit of Butt’s Farm was a record setting model airplane that crossed the Atlantic on one gallon of fuel.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2759"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2759" title='&amp;#8220;&lt;em&gt;&lt;strong&gt;The Spirit of Butts&amp;#8217; Farm&lt;/strong&gt;&lt;/em&gt;&amp;nbsp;(also known as&amp;nbsp;&lt;strong&gt;TAM 5&lt;/strong&gt;) was the first&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Model_aircraft"&gt;model aircraft&lt;/a&gt;&amp;nbsp;to cross the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Atlantic_Ocean"&gt;Atlantic Ocean&lt;/a&gt;&amp;nbsp;on August 11, 2003&amp;#8230;Fuel tank: Approx. 118 US fluid ounces (3.5 l)&amp;#8221; [118 US fluid ounces = 0.92 US liquid gallons according to Google] &lt;p&gt;“&lt;em&gt;The Spirit of Butts’ Farm&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 29, 2019. &lt;a href="https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;amp;oldid=918639855"&gt;https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;amp;oldid=918639855&lt;/a&gt;.'><sup>1</sup></a></span> Fully fueled it weighed 4.987 kg, dry it weighed 2.705 kg.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2759"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2759" title='From Wikipedia:&lt;/p&gt; &lt;figure class="wp-block-table is-style-regular"&gt;&lt;table&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;Weight:&lt;/td&gt;&lt;td&gt;Dry: 5.96&amp;nbsp;lb (2.705&amp;nbsp;kg); Fully fueled: 10.99&amp;nbsp;lb (4.987&amp;nbsp;kg)&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/The_Spirit_of_Butts%27_Farm#cite_note-FAIappl-11"&gt;[11]&lt;/a&gt;&lt;/sup&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/figure&gt; &lt;p&gt;“&lt;em&gt;The Spirit of Butts’ Farm&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 29, 2019. &lt;a href="https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;amp;oldid=918639855"&gt;https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;amp;oldid=918639855&lt;/a&gt;.'><sup>2</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The record setting flight used 117.1 fluid ounces of fuel.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2759"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2759" title='&amp;#8220;The flight used 99.2% of its fuel&amp;#8230;Fuel tank: Approx. 118 US fluid ounces (3.5 l)&amp;#8221;&lt;br&gt;&lt;br&gt;“&lt;em&gt;The Spirit of Butts’ Farm&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 29, 2019. &lt;a href="https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;amp;oldid=918639855"&gt;https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;amp;oldid=918639855&lt;/a&gt;.&lt;br&gt;&lt;br&gt;Multiplying these values we find that the vehicle crossed the Atlantic using 99.2%*118 = 117.1 fluid ounces'><sup>3</sup></a></span> The straight line distance of the flight was 3,028.1 km.<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2759"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2759" title='&amp;#8220;It was recognized by the FAI as a double world record[2] flight for its duration of 38h 52 min 19 sec[3] and straight-line distance of 1,881.6 mi (3,028.1 km) using an autopilot,[4]&amp;#8230;&amp;#8221;&lt;/p&gt; &lt;p&gt;“&lt;em&gt;The Spirit of Butts’ Farm&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 29, 2019. &lt;a href="https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;amp;oldid=918639855"&gt;https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;amp;oldid=918639855&lt;/a&gt;.'><sup>4</sup></a></span> It was powered by 88% Coleman lantern fuel, mixed with lubricant.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-2759"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-2759" title='From Wikipedia:&lt;/p&gt; &lt;figure class="wp-block-table is-style-regular"&gt;&lt;table&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;Fuel:&lt;/td&gt;&lt;td&gt;&lt;a href="https://en.wikipedia.org/wiki/Coleman_fuel"&gt;Coleman lantern fuel&lt;/a&gt;&amp;nbsp;with 16&amp;nbsp;US&amp;nbsp;fl&amp;nbsp;oz (470&amp;nbsp;ml) of Indopol L-50 lubricant additive per 1&amp;nbsp;US&amp;nbsp;gal (3,785&amp;nbsp;ml). Single fuel tank in the fuselage at the CG point&amp;nbsp;&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/The_Spirit_of_Butts%27_Farm#cite_note-barnardmicro-12"&gt;[12]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;(normal:&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Alcohol"&gt;alcohol&lt;/a&gt;)&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/figure&gt; &lt;p&gt;“&lt;em&gt;The Spirit of Butts’ Farm&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 29, 2019. &lt;a href="https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;amp;oldid=918639855"&gt;https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;amp;oldid=918639855&lt;/a&gt;.'><sup>5</sup></a></span> Coleman fuel is based on naphtha <span class="easy-footnote-margin-adjust" id="easy-footnote-6-2759"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-2759" title='&amp;#8220;&amp;#8230;Coleman Camp Fuel, which is a common naphtha-based fuel used in many lanterns and stoves&amp;#8221;&lt;/p&gt; &lt;p&gt;“Coleman Fuel.” In &lt;em&gt;Wikipedia&lt;/em&gt;, August 22, 2019. &lt;a href="https://en.wikipedia.org/w/index.php?title=Coleman_fuel&amp;amp;oldid=911926038"&gt;https://en.wikipedia.org/w/index.php?title=Coleman_fuel&amp;amp;oldid=911926038&lt;/a&gt;.'><sup>6</sup></a></span>, so we can use the energy density of naphtha—31.4 MJ/L<span class="easy-footnote-margin-adjust" id="easy-footnote-7-2759"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-2759" title='&amp;#8220;&lt;/p&gt; &lt;figure class="wp-block-table is-style-regular"&gt;&lt;table&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;&lt;strong&gt;Liquid Fuel&lt;/strong&gt;&lt;/td&gt;&lt;td&gt;&lt;/td&gt;&lt;td&gt;&lt;/td&gt;&lt;td&gt;&lt;strong&gt;MJ / liter&lt;/strong&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/figure&gt; &lt;p&gt;&amp;#8230;&lt;/p&gt; &lt;figure class="wp-block-table is-style-regular"&gt;&lt;table&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;Naphtha&lt;/td&gt;&lt;td&gt;&lt;/td&gt;&lt;td&gt;31.4&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/figure&gt; &lt;p&gt;“List of Common Conversion Factors (Engineering Conversion Factors) &amp;#8211; IOR Energy Pty Ltd.” Accessed November 17, 2020. &lt;a href="http://w.astro.berkeley.edu/~wright/fuel_energy.html"&gt;http://w.astro.berkeley.edu/~wright/fuel_energy.html&lt;/a&gt;.'><sup>7</sup></a></span>—as a rough guide to its energy content, though naphtha appears to vary in its content, and it is unclear whether Coleman fuel consists entirely of naphtha.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>From all this, we have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Distance per energy = 3,028.1 km / (117.1 fl oz * 0.88 * 31.4 MJ/L)</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 31.67 m/kJ</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>For weight times distance per energy we will calculate a best and a worst score. To calculate the best score we will use the fully fueled weight, and to calculate the worst score we will use the dry weight. All other values are the same in both calculations. </p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Best score:<br/>
+ <br/>
+               Distance*mass/energy = 4.987 kg * 31.67 m/kJ</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 0.16 kg⋅m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>(4.987 kg * 3,028.1km) / (117.1 US fluid ounces * 31.4MJ/litre) = 0.1389 kg*m/j</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Worst score:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Distance*mass/energy = 2.705 kg * 31.67 m/kJ</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= .086 kg⋅m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><br/>
+ <br/>
+ <em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <p><a href="https://commons.wikimedia.org/wiki/File:Tam5.jpg">Photo</a> by Ronan Coyne, licensed under the <a href="https://en.wikipedia.org/wiki/en:Creative_Commons">Creative Commons</a> <a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en">Attribution-Share Alike 3.0 Unported</a> license, unaltered.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2759"></span>“<em><strong>The Spirit of Butts’ Farm</strong></em> (also known as <strong>TAM 5</strong>) was the first <a href="https://en.wikipedia.org/wiki/Model_aircraft">model aircraft</a> to cross the <a href="https://en.wikipedia.org/wiki/Atlantic_Ocean">Atlantic Ocean</a> on August 11, 2003…Fuel tank: Approx. 118 US fluid ounces (3.5 l)” [118 US fluid ounces = 0.92 US liquid gallons according to Google]
+                   <p>“<em>The Spirit of Butts’ Farm</em>.” In <em>Wikipedia</em>, September 29, 2019. <a href="https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;oldid=918639855">https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;oldid=918639855</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2759"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2759"></span>From Wikipedia:
+                   <figure class="wp-block-table is-style-regular">
+ <table>
+ <tbody>
+ <tr>
+ <td>Weight:</td>
+ <td>Dry: 5.96 lb (2.705 kg); Fully fueled: 10.99 lb (4.987 kg)<sup><a href="https://en.wikipedia.org/wiki/The_Spirit_of_Butts%27_Farm#cite_note-FAIappl-11">[11]</a></sup></td>
+ </tr>
+ </tbody>
+ </table>
+ </figure>
+ <p>“<em>The Spirit of Butts’ Farm</em>.” In <em>Wikipedia</em>, September 29, 2019. <a href="https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;oldid=918639855">https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;oldid=918639855</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2759"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2759"></span>“The flight used 99.2% of its fuel…Fuel tank: Approx. 118 US fluid ounces (3.5 l)”<br/>
+ <br/>
+                   “<em>The Spirit of Butts’ Farm</em>.” In <em>Wikipedia</em>, September 29, 2019. <a href="https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;oldid=918639855">https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;oldid=918639855</a>.<br/>
+ <br/>
+                   Multiplying these values we find that the vehicle crossed the Atlantic using 99.2%*118 = 117.1 fluid ounces<a class="easy-footnote-to-top" href="#easy-footnote-3-2759"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2759"></span>“It was recognized by the FAI as a double world record[2] flight for its duration of 38h 52 min 19 sec[3] and straight-line distance of 1,881.6 mi (3,028.1 km) using an autopilot,[4]…”
+                   <p>“<em>The Spirit of Butts’ Farm</em>.” In <em>Wikipedia</em>, September 29, 2019. <a href="https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;oldid=918639855">https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;oldid=918639855</a>.<a class="easy-footnote-to-top" href="#easy-footnote-4-2759"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-2759"></span>From Wikipedia:
+                   <figure class="wp-block-table is-style-regular">
+ <table>
+ <tbody>
+ <tr>
+ <td>Fuel:</td>
+ <td>
+ <a href="https://en.wikipedia.org/wiki/Coleman_fuel">Coleman lantern fuel</a> with 16 US fl oz (470 ml) of Indopol L-50 lubricant additive per 1 US gal (3,785 ml). Single fuel tank in the fuselage at the CG point <sup><a href="https://en.wikipedia.org/wiki/The_Spirit_of_Butts%27_Farm#cite_note-barnardmicro-12">[12]</a></sup> (normal: <a href="https://en.wikipedia.org/wiki/Alcohol">alcohol</a>)
+                           </td>
+ </tr>
+ </tbody>
+ </table>
+ </figure>
+ <p>“<em>The Spirit of Butts’ Farm</em>.” In <em>Wikipedia</em>, September 29, 2019. <a href="https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;oldid=918639855">https://en.wikipedia.org/w/index.php?title=The_Spirit_of_Butts%27_Farm&amp;oldid=918639855</a>.<a class="easy-footnote-to-top" href="#easy-footnote-5-2759"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-2759"></span>“…Coleman Camp Fuel, which is a common naphtha-based fuel used in many lanterns and stoves”
+                   <p>“Coleman Fuel.” In <em>Wikipedia</em>, August 22, 2019. <a href="https://en.wikipedia.org/w/index.php?title=Coleman_fuel&amp;oldid=911926038">https://en.wikipedia.org/w/index.php?title=Coleman_fuel&amp;oldid=911926038</a>.<a class="easy-footnote-to-top" href="#easy-footnote-6-2759"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-2759"></span>“
+                   <figure class="wp-block-table is-style-regular">
+ <table>
+ <tbody>
+ <tr>
+ <td><strong>Liquid Fuel</strong></td>
+ <td></td>
+ <td></td>
+ <td><strong>MJ / liter</strong></td>
+ </tr>
+ </tbody>
+ </table>
+ </figure>
+ <p>…</p>
+ <figure class="wp-block-table is-style-regular">
+ <table>
+ <tbody>
+ <tr>
+ <td>Naphtha</td>
+ <td></td>
+ <td>31.4</td>
+ </tr>
+ </tbody>
+ </table>
+ </figure>
+ <p>“List of Common Conversion Factors (Engineering Conversion Factors) – IOR Energy Pty Ltd.” Accessed November 17, 2020. <a href="http://w.astro.berkeley.edu/~wright/fuel_energy.html">http://w.astro.berkeley.edu/~wright/fuel_energy.html</a>.<a class="easy-footnote-to-top" href="#easy-footnote-7-2759"></a></p>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Energy efficiency of Vickers Vimy plane

2022-09-21T07:37:41+00:00

@@ -1 +1,174 @@
+ ====== Energy efficiency of Vickers Vimy plane ======
+ 
+ // Published 05 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>The Vickers Vimy:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">flew around 0.025—0.050 m/kJ</div></li>
+ <li><div class="li">and moved mass at around 0.081 – 0.25 kg.m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>The <em>Vickers Vimy</em> was a 1917 British WWI bomber.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2734"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2734" title='&amp;#8220;The&amp;nbsp;&lt;strong&gt;Vickers Vimy&lt;/strong&gt;&amp;nbsp;was a British&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Heavy_bomber"&gt;heavy bomber&lt;/a&gt;&amp;nbsp;aircraft developed and manufactured by&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Vickers_Limited"&gt;Vickers Limited&lt;/a&gt;. Developed during the latter stages of the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/World_War_I"&gt;First World War&lt;/a&gt;&amp;nbsp;to equip the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Royal_Flying_Corps"&gt;Royal Flying Corps&lt;/a&gt;&amp;nbsp;(RFC), the Vimy was designed by&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Rex_Pierson"&gt;Reginald Kirshaw &amp;#8220;Rex&amp;#8221; Pierson&lt;/a&gt;, Vickers&amp;#8217; chief designer&amp;#8230;On 16 August 1917 Vickers was issued with a contract for three prototype aircraft…&amp;nbsp; the manufacture of the three prototypes was completed within four months.”&lt;/p&gt; &lt;p&gt;“Vickers Vimy.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 27, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;amp;oldid=985669067"&gt;https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;amp;oldid=985669067&lt;/a&gt;.'><sup>1</sup></a></span> It was used in the <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_transatlantic_passenger_travel">first non-stop transatlantic flight</a>.</p>
+ </HTML>
+ 
+ 
+ ==== Mass ====
+ 
+ 
+ <HTML>
+ <p>According to Wikipedia<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2734"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2734" title='“Vickers Vimy.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 27, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;amp;oldid=985669067"&gt;https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;amp;oldid=985669067&lt;/a&gt;.'><sup>2</sup></a></span>:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Empty weight:</strong> 7,104 lb (3,222 kg)</div></li>
+ <li><div class="li"><strong>Max takeoff weight:</strong> 10,884 lb (4,937 kg)</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We use the range 3,222—4,937 kg, since we do not know at what weight in that range the relevant speeds were measured.</p>
+ </HTML>
+ 
+ 
+ ==== Energy use per second ====
+ 
+ 
+ <HTML>
+ <p>We also have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Power:</strong> 360 horsepower = 270 kW<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2734"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2734" title='&amp;#8220;&lt;strong&gt;Powerplant:&lt;/strong&gt;&amp;nbsp;2 ×&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Rolls-Royce_Eagle"&gt;Rolls-Royce Eagle VIII&lt;/a&gt;&amp;nbsp;water-cooled&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/V12_engine"&gt;V12 engines&lt;/a&gt;, 360&amp;nbsp;hp (270&amp;nbsp;kW) each&amp;#8221;&lt;br&gt;&lt;br&gt;“Vickers Vimy.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 27, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;amp;oldid=985669067"&gt;https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;amp;oldid=985669067&lt;/a&gt;.'><sup>3</sup></a></span></div></li>
+ <li><div class="li">
+ <strong>Efficiency of use of energy from fuel:</strong> we did not find data on this, so use an estimate of 15%-30%, based on what we know about the <a href="/doku.php?id=power_of_evolution:evolution_engineering_comparison:energy_efficiency_of_wright_flyer#Efficiency_of_energy_conversion_from_fuel_to_motor_power">energy efficiency of the Wright Flyer</a>.
+                 </div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>From these we can calculate:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Energy use per second<br/>
+               = power of engine x 1/efficiency in converting energy to engine power<br/>
+               = 270kJ/s / .15—270kJ/s / .30<br/>
+               = 900—1800 kJ/s</p>
+ </HTML>
+ 
+ 
+ ==== Distance per second ====
+ 
+ 
+ <HTML>
+ <p>Wikipedia gives us:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong><strong>Maximum speed:</strong> </strong>100 mph (160 km/h, 87 kn)<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2734"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2734" title='“Wright Model B.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 16, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;amp;oldid=978792334"&gt;https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;amp;oldid=978792334&lt;/a&gt;.'><sup>4</sup></a></span></div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Note that the figures for power do not obviously correspond to the highest measured speed. This is a rough estimate.</p>
+ </HTML>
+ 
+ 
+ ==== Distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>We now have (from above):</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">speed = 100 miles/h = 44.7m/s</div></li>
+ <li><div class="li">energy use = 900—1800 kJ/s</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus, on average each second the plane flies 44.7 m and uses 900—1800 kJ, for 0.025—0.050 m/kJ.</p>
+ </HTML>
+ 
+ 
+ ==== Mass.distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>We have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Distance per kilojoule: 0.025—0.050 m/kJ</div></li>
+ <li><div class="li">Mass: 3,222—4,937 kg</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This gives us a range of 0.081 – 0.25 kg.m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><br/>
+ <br/>
+ <em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2734"></span>“The <strong>Vickers Vimy</strong> was a British <a href="https://en.wikipedia.org/wiki/Heavy_bomber">heavy bomber</a> aircraft developed and manufactured by <a href="https://en.wikipedia.org/wiki/Vickers_Limited">Vickers Limited</a>. Developed during the latter stages of the <a href="https://en.wikipedia.org/wiki/World_War_I">First World War</a> to equip the <a href="https://en.wikipedia.org/wiki/Royal_Flying_Corps">Royal Flying Corps</a> (RFC), the Vimy was designed by <a href="https://en.wikipedia.org/wiki/Rex_Pierson">Reginald Kirshaw “Rex” Pierson</a>, Vickers’ chief designer…On 16 August 1917 Vickers was issued with a contract for three prototype aircraft…  the manufacture of the three prototypes was completed within four months.”
+                   <p>“Vickers Vimy.” In <em>Wikipedia</em>, October 27, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;oldid=985669067">https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;oldid=985669067</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2734"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2734"></span>“Vickers Vimy.” In <em>Wikipedia</em>, October 27, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;oldid=985669067">https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;oldid=985669067</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2734"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2734"></span>“<strong>Powerplant:</strong> 2 × <a href="https://en.wikipedia.org/wiki/Rolls-Royce_Eagle">Rolls-Royce Eagle VIII</a> water-cooled <a href="https://en.wikipedia.org/wiki/V12_engine">V12 engines</a>, 360 hp (270 kW) each”<br/>
+ <br/>
+                   “Vickers Vimy.” In <em>Wikipedia</em>, October 27, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;oldid=985669067">https://en.wikipedia.org/w/index.php?title=Vickers_Vimy&amp;oldid=985669067</a>.<a class="easy-footnote-to-top" href="#easy-footnote-3-2734"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2734"></span>“Wright Model B.” In <em>Wikipedia</em>, September 16, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;oldid=978792334">https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;oldid=978792334</a>.<a class="easy-footnote-to-top" href="#easy-footnote-4-2734"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Energy efficiency of wandering albatross flight

2022-09-21T07:37:41+00:00

@@ -1 +1,151 @@
+ ====== Energy efficiency of wandering albatross flight ======
+ 
+ // Published 24 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>The wandering albatross:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">can fly around 240m/kJ</div></li>
+ <li><div class="li">and move mass at around 1.4—3.0kg.m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>The wandering albatross is a very large seabird that flies long distances on wings with the largest span of any bird.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2772"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2772" title='&amp;#8220;The&amp;nbsp;&lt;strong&gt;wandering albatross&lt;/strong&gt;,&amp;nbsp;&lt;strong&gt;snowy albatross&lt;/strong&gt;,&amp;nbsp;&lt;strong&gt;white-winged albatross&lt;/strong&gt;&amp;nbsp;or&amp;nbsp;&lt;strong&gt;goonie&lt;/strong&gt;&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/Wandering_albatross#cite_note-Robertsonft-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;(&lt;em&gt;Diomedea exulans&lt;/em&gt;) is a large&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Seabird"&gt;seabird&lt;/a&gt;&amp;nbsp;from the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Family_(biology)"&gt;family&lt;/a&gt;&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Diomedeidae"&gt;Diomedeidae&lt;/a&gt;, which has a circumpolar range in the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Southern_Ocean"&gt;Southern Ocean&lt;/a&gt;&amp;#8230;It is one of the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/List_of_largest_birds"&gt;largest&lt;/a&gt;, best known, and most studied species of bird in the world, with it possessing the greatest known wingspan of any living bird.&amp;nbsp;&amp;#8230;Some individual wandering albatrosses are known to&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Circumnavigation"&gt;circumnavigate&lt;/a&gt;&amp;nbsp;the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Southern_Ocean"&gt;Southern Ocean&lt;/a&gt;&amp;nbsp;three times, covering more than 120,000&amp;nbsp;km (75,000&amp;nbsp;mi), in one year&amp;#8221;&lt;/p&gt; &lt;p&gt;“Wandering Albatross.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 27, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wandering_albatross&amp;amp;oldid=985673754"&gt;https://en.wikipedia.org/w/index.php?title=Wandering_albatross&amp;amp;oldid=985673754&lt;/a&gt;.'><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Distance per Joule ====
+ 
+ 
+ === Speed ===
+ 
+ 
+ <HTML>
+ <p>In a study of wandering albatrosses flying in various wind speeds and directions, average ground speed was 12 m/s, though the fastest ground speed measured appears to be around 24m/s, <span class="easy-footnote-margin-adjust" id="easy-footnote-2-2772"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2772" title='&amp;#8220;The average ground speed is 12.0 (± 0.1) m/s.&amp;#8221;&lt;/p&gt; &lt;p&gt;See Figure 3 for all ground speed measurements. Though also, &lt;br&gt;&lt;br&gt;&amp;#8220;Notably, due to the combination of fast airspeeds and leeway the fastest ground speeds (~ 22&amp;nbsp;m/s) tend to be located in the diagonal downwind direction.&lt;/p&gt; &lt;p&gt;Richardson, Philip L., Ewan D. Wakefield, and Richard A. Phillips. “Flight Speed and Performance of the Wandering Albatross with Respect to Wind.” &lt;em&gt;Movement Ecology&lt;/em&gt; 6, no. 1 (March 7, 2018): 3. &lt;a href="https://doi.org/10.1186/s40462-018-0121-9"&gt;https://doi.org/10.1186/s40462-018-0121-9&lt;/a&gt;.'><sup>2</sup></a></span> We use average ground speed for this estimate because we only have data on average energy expenditure, though it is likely that higher ground speeds involve more energy efficient flight, since albatross flight speed is dependent on wind and it appears that higher speeds are substantially due to favorable winds.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2772"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2772" title='&amp;#8220;Notably, due to the combination of fast airspeeds and leeway the fastest ground speeds (~ 22&amp;nbsp;m/s) tend to be located in the diagonal downwind direction.&amp;#8221;&lt;/p&gt; &lt;p&gt;Richardson, Philip L., Ewan D. Wakefield, and Richard A. Phillips. “Flight Speed and Performance of the Wandering Albatross with Respect to Wind.” &lt;em&gt;Movement Ecology&lt;/em&gt; 6, no. 1 (March 7, 2018): 3. &lt;a href="https://doi.org/10.1186/s40462-018-0121-9"&gt;https://doi.org/10.1186/s40462-018-0121-9&lt;/a&gt;.'><sup>3</sup></a></span></p>
+ </HTML>
+ 
+ 
+ === Energy expenditure ===
+ 
+ 
+ <HTML>
+ <p>One study produced an estimate that when flying, albatrosses use 2.35 times their basal metabolic rate<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2772"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2772" title='&amp;#8220;Energy cost of flight was estimated to be 2.35 times measured BMR.&amp;#8221;&lt;/p&gt; &lt;p&gt;Adams, N. J., C. R. Brown, and K. A. Nagy. “Energy Expenditure of Free-Ranging Wandering Albatrosses Diomedea&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Exulans.” &lt;em&gt;Physiological Zoology&lt;/em&gt; 59, no. 6 (November 1, 1986): 583–91. &lt;a href="https://doi.org/10.1086/physzool.59.6.30158606"&gt;https://doi.org/10.1086/physzool.59.6.30158606&lt;/a&gt;.'><sup>4</sup></a></span> which same paper implies is around 1,833 kJ/bird.day.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-2772"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-2772" title='&amp;#8220;This is equivalent to an overall energy expenditure of 3,354 kJ bird⁻¹ day⁻¹ or 1.83 times measured basal metabolic rate (BMR).&amp;#8221;&lt;/p&gt; &lt;p&gt;Adams, N. J., C. R. Brown, and K. A. Nagy. “Energy Expenditure of Free-Ranging Wandering Albatrosses Diomedea&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Exulans.” &lt;em&gt;Physiological Zoology&lt;/em&gt; 59, no. 6 (November 1, 1986): 583–91. &lt;a href="https://doi.org/10.1086/physzool.59.6.30158606"&gt;https://doi.org/10.1086/physzool.59.6.30158606&lt;/a&gt;. &lt;/p&gt; &lt;p&gt;From this we infer that the basal metabolic rate is 1,833 kJ/ bird.day.'><sup>5</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>That gives us a flight cost for flying of 0.050 kJ/second.<span class="easy-footnote-margin-adjust" id="easy-footnote-6-2772"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-2772" title="2.35 * 3,354 kJ/1.83 * 1/86400 seconds/day"><sup>6</sup></a></span> </p>
+ </HTML>
+ 
+ 
+ === Distance per Joule calculation ===
+ 
+ 
+ <HTML>
+ <p>This gives us a distance per energy score of:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>distance/energy</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 12 m/s / 0.050 kJ/s</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 240m/kJ</p>
+ </HTML>
+ 
+ 
+ ==== Mass.distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>Albatrosses weigh 5.9 to 12.7 kg.<span class="easy-footnote-margin-adjust" id="easy-footnote-7-2772"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-2772" title='&amp;#8220;Adults can weigh from 5.9 to 12.7 kg (13 to 28 lb)&amp;#8221;&lt;/p&gt; &lt;p&gt;“Wandering Albatross.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 27, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wandering_albatross&amp;amp;oldid=985673754"&gt;https://en.wikipedia.org/w/index.php?title=Wandering_albatross&amp;amp;oldid=985673754&lt;/a&gt;.'><sup>7</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus we can estimate:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>mass.distance/Joule</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 5.9kg * 240 m/kJ to 12.7kg*240 m/kJ</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 1.4—3.0kg.m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p id="block-501d3537-b05b-415d-8040-d337eae506e4"><br/>
+ <br/>
+ <em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2772"></span>“The <strong>wandering albatross</strong>, <strong>snowy albatross</strong>, <strong>white-winged albatross</strong> or <strong>goonie</strong><sup><a href="https://en.wikipedia.org/wiki/Wandering_albatross#cite_note-Robertsonft-3">[3]</a></sup> (<em>Diomedea exulans</em>) is a large <a href="https://en.wikipedia.org/wiki/Seabird">seabird</a> from the <a href="https://en.wikipedia.org/wiki/Family_(biology)">family</a> <a href="https://en.wikipedia.org/wiki/Diomedeidae">Diomedeidae</a>, which has a circumpolar range in the <a href="https://en.wikipedia.org/wiki/Southern_Ocean">Southern Ocean</a>…It is one of the <a href="https://en.wikipedia.org/wiki/List_of_largest_birds">largest</a>, best known, and most studied species of bird in the world, with it possessing the greatest known wingspan of any living bird. …Some individual wandering albatrosses are known to <a href="https://en.wikipedia.org/wiki/Circumnavigation">circumnavigate</a> the <a href="https://en.wikipedia.org/wiki/Southern_Ocean">Southern Ocean</a> three times, covering more than 120,000 km (75,000 mi), in one year”
+                   <p>“Wandering Albatross.” In <em>Wikipedia</em>, October 27, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wandering_albatross&amp;oldid=985673754">https://en.wikipedia.org/w/index.php?title=Wandering_albatross&amp;oldid=985673754</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2772"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2772"></span>“The average ground speed is 12.0 (± 0.1) m/s.”
+                   <p>See Figure 3 for all ground speed measurements. Though also,<br/>
+ <br/>
+                   “Notably, due to the combination of fast airspeeds and leeway the fastest ground speeds (~ 22 m/s) tend to be located in the diagonal downwind direction.</p>
+ <p>Richardson, Philip L., Ewan D. Wakefield, and Richard A. Phillips. “Flight Speed and Performance of the Wandering Albatross with Respect to Wind.” <em>Movement Ecology</em> 6, no. 1 (March 7, 2018): 3. <a href="https://doi.org/10.1186/s40462-018-0121-9">https://doi.org/10.1186/s40462-018-0121-9</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2772"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2772"></span>“Notably, due to the combination of fast airspeeds and leeway the fastest ground speeds (~ 22 m/s) tend to be located in the diagonal downwind direction.”
+                   <p>Richardson, Philip L., Ewan D. Wakefield, and Richard A. Phillips. “Flight Speed and Performance of the Wandering Albatross with Respect to Wind.” <em>Movement Ecology</em> 6, no. 1 (March 7, 2018): 3. <a href="https://doi.org/10.1186/s40462-018-0121-9">https://doi.org/10.1186/s40462-018-0121-9</a>.<a class="easy-footnote-to-top" href="#easy-footnote-3-2772"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2772"></span>“Energy cost of flight was estimated to be 2.35 times measured BMR.”
+                   <p>Adams, N. J., C. R. Brown, and K. A. Nagy. “Energy Expenditure of Free-Ranging Wandering Albatrosses Diomedea                Exulans.” <em>Physiological Zoology</em> 59, no. 6 (November 1, 1986): 583–91. <a href="https://doi.org/10.1086/physzool.59.6.30158606">https://doi.org/10.1086/physzool.59.6.30158606</a>.<a class="easy-footnote-to-top" href="#easy-footnote-4-2772"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-2772"></span>“This is equivalent to an overall energy expenditure of 3,354 kJ bird⁻¹ day⁻¹ or 1.83 times measured basal metabolic rate (BMR).”
+                   <p>Adams, N. J., C. R. Brown, and K. A. Nagy. “Energy Expenditure of Free-Ranging Wandering Albatrosses Diomedea                Exulans.” <em>Physiological Zoology</em> 59, no. 6 (November 1, 1986): 583–91. <a href="https://doi.org/10.1086/physzool.59.6.30158606">https://doi.org/10.1086/physzool.59.6.30158606</a>.</p>
+ <p>From this we infer that the basal metabolic rate is 1,833 kJ/ bird.day.<a class="easy-footnote-to-top" href="#easy-footnote-5-2772"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-2772"></span>2.35 * 3,354 kJ/1.83 * 1/86400 seconds/day<a class="easy-footnote-to-top" href="#easy-footnote-6-2772"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-2772"></span>“Adults can weigh from 5.9 to 12.7 kg (13 to 28 lb)”
+                   <p>“Wandering Albatross.” In <em>Wikipedia</em>, October 27, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wandering_albatross&amp;oldid=985673754">https://en.wikipedia.org/w/index.php?title=Wandering_albatross&amp;oldid=985673754</a>.<a class="easy-footnote-to-top" href="#easy-footnote-7-2772"></a></p>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Energy efficiency of Wright Flyer

2022-09-21T07:37:41+00:00

@@ -1 +1,284 @@
+ ====== Energy efficiency of Wright Flyer ======
+ 
+ // Published 04 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>The Wright Flyer:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">flew around 0.080-0.18m/kJ</div></li>
+ <li><div class="li">and moved mass at around .022 – .061 kg.m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>The <em>Wright Flyer</em> (<em>Flyer I</em>) was the first successful plane, built in 1903.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2729" title='&amp;#8220;The&amp;nbsp;&lt;em&gt;&lt;strong&gt;Wright Flyer&lt;/strong&gt;&lt;/em&gt;&amp;nbsp;(often retrospectively referred to as&amp;nbsp;&lt;strong&gt;&lt;em&gt;Flyer&lt;/em&gt;&amp;nbsp;I&lt;/strong&gt;&amp;nbsp;or&amp;nbsp;&lt;strong&gt;1903&amp;nbsp;&lt;em&gt;Flyer&lt;/em&gt;&lt;/strong&gt;) was the first successful heavier-than-air powered aircraft&amp;#8230;.The Wrights built the aircraft in 1903 using&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Sitka_Spruce"&gt;giant spruce&lt;/a&gt;&amp;nbsp;wood as their construction material.&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/Wright_Flyer#cite_note-NASM-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&amp;#8220;&lt;/p&gt; &lt;p&gt;“&lt;em&gt;Wright Flyer&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 30, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;amp;oldid=986246127"&gt;https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;amp;oldid=986246127&lt;/a&gt;.'><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Mass ====
+ 
+ 
+ <HTML>
+ <p>According to Wikipedia<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2729" title='“&lt;em&gt;Wright Flyer&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 30, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;amp;oldid=986246127"&gt;https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;amp;oldid=986246127&lt;/a&gt;.'><sup>2</sup></a></span>:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Empty weight:</strong> 605 lb (274 kg)</div></li>
+ <li><div class="li"><strong>Max takeoff weight:</strong> 745 lb (338 kg)</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ ==== Energy use per second ====
+ 
+ 
+ === Fuel use per hour ===
+ 
+ 
+ <HTML>
+ <p>A 1904 article in the Minneapolis Journal says the plane consumed ‘a little less than than ten pounds of gasoline per hour’.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2729" title="&amp;#8220;At the speed of 1200 revolutions per minute the engine develops sixteen-brake horsepower, with a consumption of a little less than ten pounds of gasoline per hour.&amp;#8221; "><sup>3</sup></a></span> A pound of gasoline contains around 20MJ<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2729" title='&amp;#8220;Gasoline has an energy density of about 45 megajoules per kilogram (MJ/kg)&amp;#8221;&lt;br&gt;&lt;br&gt;“Energy Density of Gasoline &amp;#8211; The Physics Factbook.” Accessed November 3, 2020. &lt;a href="https://hypertextbook.com/facts/2003/ArthurGolnik.shtml"&gt;https://hypertextbook.com/facts/2003/ArthurGolnik.shtml&lt;/a&gt;.&lt;br&gt;&lt;br&gt;45MJ/kg = 20.4MJ/lb'><sup>4</sup></a></span> So we have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Hourly fuel consumption: 10lb/h x 20MJ/lb = 200MJ/h = 55kJ/s</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We don’t know how reliable this source is. For instance, a 1971 book, <em>The Write Brothers’ Engines and their Design</em> does not give data on fuel consumption in their table of engine characteristics for lack of available comprehensive data<span class="easy-footnote-margin-adjust" id="easy-footnote-5-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-2729" title='&amp;#8220;No fuel consumption figures are given, primarily because no comprehensive data have been found. This is most probably because in the early flight years, when the Wrights were so meticulously measuring and recording technical information on the important factors affecting their work, the flights were of such short duration that fuel economy was of very minor importance.&amp;#8221;&lt;/p&gt; &lt;p&gt;Hobbs, Leonard S. &lt;em&gt;The Wright Brothers’ Engines and Their Design&lt;/em&gt;. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. &lt;a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm"&gt;https://www.gutenberg.org/files/38739/38739-h/38739-h.htm&lt;/a&gt;.'><sup>5</sup></a></span>, suggesting that its authors did not consider the article strong evidence, though it is also possible that they didn’t have access to the 1904 article.</p>
+ </HTML>
+ 
+ 
+ === Utilized motor power / efficiency ===
+ 
+ 
+ <HTML>
+ <p>To confirm, we can estimate the plane’s energy use per second by a second means: combining the claimed power (energy/second) made use of by the engine, and a guess about how much fuel is needed to deliver that amount of energy.</p>
+ </HTML>
+ 
+ 
+ == Utilized motor power ==
+ 
+ 
+ <HTML>
+ <p>According to Wikipedia, the plane had a 12 horsepower (9 kJ/s), gasoline engine.<span class="easy-footnote-margin-adjust" id="easy-footnote-6-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-2729" title='&amp;#8220;Since they could not find a suitable automobile engine for the task, they commissioned their employee&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Charlie_Taylor_(mechanic)"&gt;Charlie Taylor&lt;/a&gt;&amp;nbsp;to build a new design from scratch, effectively a crude 12-horsepower (9-kilowatt)&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Gasoline_engine"&gt;gasoline engine&lt;/a&gt;.&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/Wright_Flyer#cite_note-4"&gt;[4]&lt;/a&gt;&lt;/sup&gt;&lt;br&gt;&lt;br&gt;“&lt;em&gt;Wright Flyer&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 30, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;amp;oldid=986246127"&gt;https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;amp;oldid=986246127&lt;/a&gt;.'><sup>6</sup></a></span> The 1904 Minneapolis Journal article put it at 16 horsepower (12 kJ/s), and Orville Wright, quoted by Hobbs (1971), puts it at ‘almost 16 horsepower’ at one point.<span class="easy-footnote-margin-adjust" id="easy-footnote-7-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-2729" title='&amp;#8220;Speaking of the first engine, Orville Wright wrote, &amp;#8220;Since putting in heavier springs to actuate the valves on our engine we have increased its power to nearly 16 hp and at the same time reduced the amount of gasoline consumed per hour to about one-half of what it was.&amp;#8221;&amp;#8221;&lt;/p&gt; &lt;p&gt;Hobbs, Leonard S. &lt;em&gt;The Wright Brothers’ Engines and Their Design&lt;/em&gt;. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. &lt;a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm"&gt;https://www.gutenberg.org/files/38739/38739-h/38739-h.htm&lt;/a&gt;.'><sup>7</sup></a></span> Hobbs says that at one point this engine achieved 25 horsepower, though this probably isn’t representative of what was ‘actually utilized’.<span class="easy-footnote-margin-adjust" id="easy-footnote-8-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-8-2729" title='&amp;#8220;In the table, performance is given in ranges which are thought to be the most representative of those actually utilized. Occasionally performances were attained even beyond the ranges given. For example, the 4×4-in. flat development engine eventually demonstrated 25 hp at an MEP of approximately 65 psi.&amp;#8221;&lt;/p&gt; &lt;p&gt;Hobbs, Leonard S. &lt;em&gt;The Wright Brothers’ Engines and Their Design&lt;/em&gt;. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. &lt;a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm"&gt;https://www.gutenberg.org/files/38739/38739-h/38739-h.htm&lt;/a&gt;.'><sup>8</sup></a></span> For that he gives a range of 8.25-16 horsepower.<span class="easy-footnote-margin-adjust" id="easy-footnote-9-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-9-2729" title='See first table in Appendix. It appears that the lower number is for the first flight, though this is confusing:&lt;/p&gt; &lt;p&gt;&amp;#8220;One important figure—the horsepower actually utilized during the first flight—is quite accurately known. In 1904 the 1904-1905 flight engine, after having been calibrated by their prony-brake test-fan method, was used to turn the 1903 flight propellers, and Orville Wright calculated this power to be 12.05 bhp by comparing the calibrated engine results with those obtained with the flight engine at Kitty Hawk when tested under similar conditions. However, since the tests were conducted in still air with the engine stationary, this did not exactly represent the flight condition. No doubt the rotational speed of the engine and propellers increased somewhat with the forward velocity of the airplane so that unless the power-rpm curve of the engine was flat, the actual horsepower utilized was probably a small amount greater than Orville&amp;#8217;s figures. The lowest power figure shown for this engine is that of its first operation.&amp;#8221;&lt;/p&gt; &lt;p&gt;Hobbs, Leonard S. &lt;em&gt;The Wright Brothers’ Engines and Their Design&lt;/em&gt;. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. &lt;a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm"&gt;https://www.gutenberg.org/files/38739/38739-h/38739-h.htm&lt;/a&gt;.'><sup>9</sup></a></span> In light of these estimates, we will use 8.25-16 horsepower, which is 6.15-12 kJ/s.</p>
+ </HTML>
+ 
+ 
+ == Efficiency of energy conversion from fuel to motor power ==
+ 
+ 
+ <HTML>
+ <p>A quote from Orville Wright suggests fuel consumption as 0.580lb of fuel per horsepower hour.<span class="easy-footnote-margin-adjust" id="easy-footnote-10-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-10-2729" title='&amp;#8220;Orville Wright quotes an early figure of brake thermal efficiency for the 1903 engine that gives a specific fuel consumption of .580 lb of fuel per bhp/hr based on an estimate of the heating value of the fuel they had. This seems low, considering the compression ratio and probable leakage past their rather weak piston rings, but it is possible.&amp;#8221;&lt;/p&gt; &lt;p&gt;Hobbs, Leonard S. &lt;em&gt;The Wright Brothers’ Engines and Their Design&lt;/em&gt;. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. &lt;a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm"&gt;https://www.gutenberg.org/files/38739/38739-h/38739-h.htm&lt;/a&gt;.&lt;/p&gt; &lt;p&gt;Note that the quote says bhp/h, but we think it must mean bhp.h.&lt;/p&gt; &lt;p&gt;Also, bhp is &amp;#8216;brake horsepower&amp;#8217;, meaning horsepower measured empirically through a particular mechanism:&lt;/p&gt; &lt;p&gt;&amp;#8216;Brake horsepower (bhp) is the power measured using a brake type (load) dynamometer at a specified location, such as the crankshaft, output shaft of the transmission, rear axle or rear wheels.&amp;#8217;&lt;br&gt;&lt;br&gt;“Horsepower.” In &lt;em&gt;Wikipedia&lt;/em&gt;, November 3, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Horsepower&amp;amp;oldid=986863945"&gt;https://en.wikipedia.org/w/index.php?title=Horsepower&amp;amp;oldid=986863945&lt;/a&gt;. '><sup>10</sup></a></span> This would imply 23% of energy was utilized from the fuel.<span class="easy-footnote-margin-adjust" id="easy-footnote-11-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-11-2729" title='fuel/power = 0.580lb fuel / hp.h &lt;br&gt;= 0.580 * &lt;a href="https://aiimpacts.org/?p=2729&amp;amp;preview=true#easy-footnote-bottom-4-2729"&gt;20MJ&lt;/a&gt; / hp.h &lt;br&gt;= 11.6MJ/ 745J.h/s &lt;br&gt;= 11600kJ / (0.745 * 3600 kJ) &lt;br&gt;= 4.3. &lt;br&gt;&lt;br&gt;Thus power/fuel = 0.23.'><sup>11</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Hobbs notes that this seems low, but assumes a similar efficiency: 24.50%. Thus he presumably doesn’t find it implausible.<span class="easy-footnote-margin-adjust" id="easy-footnote-12-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-12-2729" title='&amp;#8220;Assuming a rich mixture, consumption of all the air, and an airbrake thermal efficiency of 24.50% for the original engine&amp;#8230;&amp;#8221;&lt;br&gt;&lt;br&gt;Hobbs, Leonard S. &lt;em&gt;The Wright Brothers’ Engines and Their Design&lt;/em&gt;. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. &lt;a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm"&gt;https://www.gutenberg.org/files/38739/38739-h/38739-h.htm&lt;/a&gt;.'><sup>12</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>According to Wikipedia, the thermal efficiency of a typical gasoline engine is 20%<span class="easy-footnote-margin-adjust" id="easy-footnote-13-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-13-2729" title='&amp;#8220;Typically, most petrol engines have approximately 20%(avg.) thermal efficiency, which is nearly half of diesel engines. However some newer engines are reported to be much more efficient (thermal efficiency up to 38%) than previous spark-ignition engines.&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/Petrol_engine#cite_note-5"&gt;[5]&lt;/a&gt;&lt;/sup&gt;&amp;#8220;&lt;br&gt;&lt;br&gt;“Petrol Engine.” In &lt;em&gt;Wikipedia&lt;/em&gt;, August 20, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Petrol_engine&amp;amp;oldid=973981680"&gt;https://en.wikipedia.org/w/index.php?title=Petrol_engine&amp;amp;oldid=973981680&lt;/a&gt;.'><sup>13</sup></a></span>. It seems that this has increased<span class="easy-footnote-margin-adjust" id="easy-footnote-14-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-14-2729" title="See above note."><sup>14</sup></a></span>, which would suggest that the typical figure was lower in 1903. We don’t think this undermines the more specific figures given above.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>It seems likely that Hobbs number is best here, since he knows about Wright’s number, and may have more information than us about for instance the exact fuel being used. So we use 24.5%.</p>
+ </HTML>
+ 
+ 
+ == Calculation of energy use from motor power/efficiency ==
+ 
+ 
+ <HTML>
+ <p>Combining these numbers, we have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>power spent = 6.15-12 kJ/s used by engine x 1 / 24.5% fuel energy needed to get one unit of energy used by engine, given inefficiency</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>= 25-49 kJ/s</p>
+ </HTML>
+ 
+ 
+ === Calculation of energy use ===
+ 
+ 
+ <HTML>
+ <p>We now have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">energy expenditure calculated via motor power and efficiency: 25-49 kJ/s</div></li>
+ <li><div class="li">energy expenditure calculated via hourly fuel use: 55kJ/s</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Neither figure seems clearly more reliable, so we will use the range 25-55kJ/s</p>
+ </HTML>
+ 
+ 
+ ==== Distance per second ====
+ 
+ 
+ <HTML>
+ <p>Two of the Wright Flyer’s first flights were 120 feet in 12 seconds and 852 feet in 59 seconds.<span class="easy-footnote-margin-adjust" id="easy-footnote-15-2729"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-15-2729" title='&amp;#8220;His first flight lasted 12 seconds for a total distance of 120 feet (37&amp;nbsp;m) – shorter than the wingspan of a&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Boeing_747"&gt;Boeing 747&lt;/a&gt;, as noted by observers in the 2003 commemoration of the first flight.&lt;sup&gt;&lt;a href="https://en.wikipedia.org/wiki/Wright_Flyer#cite_note-WDL-1"&gt;[1]&lt;/a&gt;&lt;a href="https://en.wikipedia.org/wiki/Wright_Flyer#cite_note-5"&gt;[5]&lt;/a&gt;&lt;/sup&gt;&amp;#8230;The last flight, by Wilbur, was 852 feet (260&amp;nbsp;m) in 59 seconds, much longer than each of the three previous flights of 120, 175 and 200 feet (37, 53 and 61&amp;nbsp;m).&amp;#8221;&lt;/p&gt; &lt;p&gt;“&lt;em&gt;Wright Flyer&lt;/em&gt;.” In &lt;em&gt;Wikipedia&lt;/em&gt;, October 30, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;amp;oldid=986246127"&gt;https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;amp;oldid=986246127&lt;/a&gt;.'><sup>15</sup></a></span> This gives speeds of 3m/s and 4.4m/s. We will use the second, since it better represents successful flight, still within the first days.</p>
+ </HTML>
+ 
+ 
+ ==== Distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>We now have (from above):</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">speed = 4.4 m/s</div></li>
+ <li><div class="li">energy use = 25-55 kJ/s</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus, on average each second the plane flies 4.4m and uses 25-55kJ, for 0.080-0.18m/kJ.</p>
+ </HTML>
+ 
+ 
+ ==== Mass.distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>We have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Distance per kilojoule: 0.080-0.18m/kJ</div></li>
+ <li><div class="li">Mass: 274-338kg</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This gives us a range of .022 – .061 kg.m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p id="block-501d3537-b05b-415d-8040-d337eae506e4"><br/>
+ <br/>
+ <em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2729"></span>“The <em><strong>Wright Flyer</strong></em> (often retrospectively referred to as <strong><em>Flyer</em> I</strong> or <strong>1903 <em>Flyer</em></strong>) was the first successful heavier-than-air powered aircraft….The Wrights built the aircraft in 1903 using <a href="https://en.wikipedia.org/wiki/Sitka_Spruce">giant spruce</a> wood as their construction material.<sup><a href="https://en.wikipedia.org/wiki/Wright_Flyer#cite_note-NASM-2">[2]</a></sup>“
+                   <p>“<em>Wright Flyer</em>.” In <em>Wikipedia</em>, October 30, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;oldid=986246127">https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;oldid=986246127</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2729"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2729"></span>“<em>Wright Flyer</em>.” In <em>Wikipedia</em>, October 30, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;oldid=986246127">https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;oldid=986246127</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2729"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2729"></span>“At the speed of 1200 revolutions per minute the engine develops sixteen-brake horsepower, with a consumption of a little less than ten pounds of gasoline per hour.” <a class="easy-footnote-to-top" href="#easy-footnote-3-2729"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2729"></span>“Gasoline has an energy density of about 45 megajoules per kilogram (MJ/kg)”<br/>
+ <br/>
+                   “Energy Density of Gasoline – The Physics Factbook.” Accessed November 3, 2020. <a href="https://hypertextbook.com/facts/2003/ArthurGolnik.shtml">https://hypertextbook.com/facts/2003/ArthurGolnik.shtml</a>.<br/>
+ <br/>
+                   45MJ/kg = 20.4MJ/lb<a class="easy-footnote-to-top" href="#easy-footnote-4-2729"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-2729"></span>“No fuel consumption figures are given, primarily because no comprehensive data have been found. This is most probably because in the early flight years, when the Wrights were so meticulously measuring and recording technical information on the important factors affecting their work, the flights were of such short duration that fuel economy was of very minor importance.”
+                   <p>Hobbs, Leonard S. <em>The Wright Brothers’ Engines and Their Design</em>. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. <a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm">https://www.gutenberg.org/files/38739/38739-h/38739-h.htm</a>.<a class="easy-footnote-to-top" href="#easy-footnote-5-2729"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-2729"></span>“Since they could not find a suitable automobile engine for the task, they commissioned their employee <a href="https://en.wikipedia.org/wiki/Charlie_Taylor_(mechanic)">Charlie Taylor</a> to build a new design from scratch, effectively a crude 12-horsepower (9-kilowatt) <a href="https://en.wikipedia.org/wiki/Gasoline_engine">gasoline engine</a>.<sup><a href="https://en.wikipedia.org/wiki/Wright_Flyer#cite_note-4">[4]</a></sup><br/>
+ <br/>
+                   “<em>Wright Flyer</em>.” In <em>Wikipedia</em>, October 30, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;oldid=986246127">https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;oldid=986246127</a>.<a class="easy-footnote-to-top" href="#easy-footnote-6-2729"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-2729"></span>“Speaking of the first engine, Orville Wright wrote, “Since putting in heavier springs to actuate the valves on our engine we have increased its power to nearly 16 hp and at the same time reduced the amount of gasoline consumed per hour to about one-half of what it was.””
+                   <p>Hobbs, Leonard S. <em>The Wright Brothers’ Engines and Their Design</em>. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. <a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm">https://www.gutenberg.org/files/38739/38739-h/38739-h.htm</a>.<a class="easy-footnote-to-top" href="#easy-footnote-7-2729"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-8-2729"></span>“In the table, performance is given in ranges which are thought to be the most representative of those actually utilized. Occasionally performances were attained even beyond the ranges given. For example, the 4×4-in. flat development engine eventually demonstrated 25 hp at an MEP of approximately 65 psi.”
+                   <p>Hobbs, Leonard S. <em>The Wright Brothers’ Engines and Their Design</em>. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. <a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm">https://www.gutenberg.org/files/38739/38739-h/38739-h.htm</a>.<a class="easy-footnote-to-top" href="#easy-footnote-8-2729"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-9-2729"></span>See first table in Appendix. It appears that the lower number is for the first flight, though this is confusing:
+                   <p>“One important figure—the horsepower actually utilized during the first flight—is quite accurately known. In 1904 the 1904-1905 flight engine, after having been calibrated by their prony-brake test-fan method, was used to turn the 1903 flight propellers, and Orville Wright calculated this power to be 12.05 bhp by comparing the calibrated engine results with those obtained with the flight engine at Kitty Hawk when tested under similar conditions. However, since the tests were conducted in still air with the engine stationary, this did not exactly represent the flight condition. No doubt the rotational speed of the engine and propellers increased somewhat with the forward velocity of the airplane so that unless the power-rpm curve of the engine was flat, the actual horsepower utilized was probably a small amount greater than Orville’s figures. The lowest power figure shown for this engine is that of its first operation.”</p>
+ <p>Hobbs, Leonard S. <em>The Wright Brothers’ Engines and Their Design</em>. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. <a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm">https://www.gutenberg.org/files/38739/38739-h/38739-h.htm</a>.<a class="easy-footnote-to-top" href="#easy-footnote-9-2729"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-10-2729"></span>“Orville Wright quotes an early figure of brake thermal efficiency for the 1903 engine that gives a specific fuel consumption of .580 lb of fuel per bhp/hr based on an estimate of the heating value of the fuel they had. This seems low, considering the compression ratio and probable leakage past their rather weak piston rings, but it is possible.”
+                   <p>Hobbs, Leonard S. <em>The Wright Brothers’ Engines and Their Design</em>. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. <a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm">https://www.gutenberg.org/files/38739/38739-h/38739-h.htm</a>.</p>
+ <p>Note that the quote says bhp/h, but we think it must mean bhp.h.</p>
+ <p>Also, bhp is ‘brake horsepower’, meaning horsepower measured empirically through a particular mechanism:</p>
+ <p>‘Brake horsepower (bhp) is the power measured using a brake type (load) dynamometer at a specified location, such as the crankshaft, output shaft of the transmission, rear axle or rear wheels.’<br/>
+ <br/>
+                   “Horsepower.” In <em>Wikipedia</em>, November 3, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Horsepower&amp;oldid=986863945">https://en.wikipedia.org/w/index.php?title=Horsepower&amp;oldid=986863945</a>. <a class="easy-footnote-to-top" href="#easy-footnote-10-2729"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-11-2729"></span>fuel/power = 0.580lb fuel / hp.h<br/>
+                   = 0.580 * <a href="https://aiimpacts.org/?p=2729&amp;preview=true#easy-footnote-bottom-4-2729">20MJ</a> / hp.h<br/>
+                   = 11.6MJ/ 745J.h/s<br/>
+                   = 11600kJ / (0.745 * 3600 kJ)<br/>
+                   = 4.3.<br/>
+ <br/>
+                   Thus power/fuel = 0.23.<a class="easy-footnote-to-top" href="#easy-footnote-11-2729"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-12-2729"></span>“Assuming a rich mixture, consumption of all the air, and an airbrake thermal efficiency of 24.50% for the original engine…”<br/>
+ <br/>
+                   Hobbs, Leonard S. <em>The Wright Brothers’ Engines and Their Design</em>. [For sale by Supt. of Docs., U.S. Govt. Print. Off.]; First Edition. Smithsonian Institution Press, 1971. <a href="https://www.gutenberg.org/files/38739/38739-h/38739-h.htm">https://www.gutenberg.org/files/38739/38739-h/38739-h.htm</a>.<a class="easy-footnote-to-top" href="#easy-footnote-12-2729"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-13-2729"></span>“Typically, most petrol engines have approximately 20%(avg.) thermal efficiency, which is nearly half of diesel engines. However some newer engines are reported to be much more efficient (thermal efficiency up to 38%) than previous spark-ignition engines.<sup><a href="https://en.wikipedia.org/wiki/Petrol_engine#cite_note-5">[5]</a></sup>“<br/>
+ <br/>
+                   “Petrol Engine.” In <em>Wikipedia</em>, August 20, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Petrol_engine&amp;oldid=973981680">https://en.wikipedia.org/w/index.php?title=Petrol_engine&amp;oldid=973981680</a>.<a class="easy-footnote-to-top" href="#easy-footnote-13-2729"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-14-2729"></span>See above note.<a class="easy-footnote-to-top" href="#easy-footnote-14-2729"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-15-2729"></span>“His first flight lasted 12 seconds for a total distance of 120 feet (37 m) – shorter than the wingspan of a <a href="https://en.wikipedia.org/wiki/Boeing_747">Boeing 747</a>, as noted by observers in the 2003 commemoration of the first flight.<sup><a href="https://en.wikipedia.org/wiki/Wright_Flyer#cite_note-WDL-1">[1]</a><a href="https://en.wikipedia.org/wiki/Wright_Flyer#cite_note-5">[5]</a></sup>…The last flight, by Wilbur, was 852 feet (260 m) in 59 seconds, much longer than each of the three previous flights of 120, 175 and 200 feet (37, 53 and 61 m).”
+                   <p>“<em>Wright Flyer</em>.” In <em>Wikipedia</em>, October 30, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;oldid=986246127">https://en.wikipedia.org/w/index.php?title=Wright_Flyer&amp;oldid=986246127</a>.<a class="easy-footnote-to-top" href="#easy-footnote-15-2729"></a></p>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Energy efficiency of Wright model B

2022-09-21T07:37:41+00:00

@@ -1 +1,173 @@
+ ====== Energy efficiency of Wright model B ======
+ 
+ // Published 05 November, 2020; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>The Wright model B:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">flew around 0.10—0.21m/kJ</div></li>
+ <li><div class="li">and moved mass at around 0.036 – 0.12 kg.m/J</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>The <em>Wright Model B</em> was a 1910 plane developed by the Wright Brothers.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2731"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2731" title='&amp;#8220;The&amp;nbsp;&lt;strong&gt;Wright Model B&lt;/strong&gt;&amp;nbsp;was an early&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Pusher_configuration"&gt;pusher&lt;/a&gt;&amp;nbsp;biplane designed by the&amp;nbsp;&lt;a href="https://en.wikipedia.org/wiki/Wright_brothers"&gt;Wright brothers&lt;/a&gt;&amp;nbsp;in the United States in 1910. It was the first of their designs to be built in quantity.&amp;nbsp;&amp;#8220;&lt;/p&gt; &lt;p&gt;“Wright Model B.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 16, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;amp;oldid=978792334"&gt;https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;amp;oldid=978792334&lt;/a&gt;.'><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Mass ====
+ 
+ 
+ <HTML>
+ <p>According to Wikipedia<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2731"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2731" title='“Wright Model B.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 16, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;amp;oldid=978792334"&gt;https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;amp;oldid=978792334&lt;/a&gt;.'><sup>2</sup></a></span>:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Empty weight:</strong> 800 lb (363 kg)</div></li>
+ <li><div class="li"><strong>Gross weight:</strong> 1,250 lb (567 kg)</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We use the range 363—567 kg, since we do not know at what weight in that range the relevant speeds were measured.</p>
+ </HTML>
+ 
+ 
+ ==== Energy use per second ====
+ 
+ 
+ <HTML>
+ <p>From Wikipedia, we have<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2731"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2731" title='“Wright Model B.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 16, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;amp;oldid=978792334"&gt;https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;amp;oldid=978792334&lt;/a&gt;.'><sup>3</sup></a></span>:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Power:</strong> 35 horsepower = 26kW</div></li>
+ <li><div class="li">
+ <strong>Efficiency of use of energy from fuel:</strong> we could not find data on this, so use an estimate of 15%-30%, based on what we know about the <a href="/doku.php?id=power_of_evolution:evolution_engineering_comparison:energy_efficiency_of_wright_flyer#Efficiency_of_energy_conversion_from_fuel_to_motor_power">energy efficiency of the Wright Flyer</a>.
+                 </div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>From these we can calculate:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Energy use per second<br/>
+               = power of engine x 1/efficiency in converting energy to engine power<br/>
+               = 26kJ/s / .15—26kJ/s / .30<br/>
+               = 86.6—173 kJ/s</p>
+ </HTML>
+ 
+ 
+ ==== Distance per second ====
+ 
+ 
+ <HTML>
+ <p>Wikipedia gives us<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2731"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2731" title='“Wright Model B.” In &lt;em&gt;Wikipedia&lt;/em&gt;, September 16, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;amp;oldid=978792334"&gt;https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;amp;oldid=978792334&lt;/a&gt;.'><sup>4</sup></a></span>:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Maximum speed:</strong> 45 mph (72 km/h, 39 kn)</div></li>
+ <li><div class="li"><strong>Cruise speed:</strong> 40 mph (64 km/h, 35 kn)</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We use the cruise speed, as it seems more likely to represent speed achieved with the energy usages reported.</p>
+ </HTML>
+ 
+ 
+ ==== Distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>We now have (from above):</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">speed = 40miles/h = 17.9m/s</div></li>
+ <li><div class="li">energy use = 86.6—173 kJ/s</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus, on average each second the plane flies 17.9m and uses 86.6—173 kJ, for 0.10—0.21m/kJ.</p>
+ </HTML>
+ 
+ 
+ ==== Mass.distance per Joule ====
+ 
+ 
+ <HTML>
+ <p>We have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Distance per kilojoule: 0.10—0.21m/kJ</div></li>
+ <li><div class="li">Mass: 363—567kg</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This gives us a range of 0.036 – 0.12 kg.m/J</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><br/>
+ <br/>
+ <em>Primary author: Ronny Fernandez</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2731"></span>“The <strong>Wright Model B</strong> was an early <a href="https://en.wikipedia.org/wiki/Pusher_configuration">pusher</a> biplane designed by the <a href="https://en.wikipedia.org/wiki/Wright_brothers">Wright brothers</a> in the United States in 1910. It was the first of their designs to be built in quantity. “
+                   <p>“Wright Model B.” In <em>Wikipedia</em>, September 16, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;oldid=978792334">https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;oldid=978792334</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2731"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2731"></span>“Wright Model B.” In <em>Wikipedia</em>, September 16, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;oldid=978792334">https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;oldid=978792334</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2731"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2731"></span>“Wright Model B.” In <em>Wikipedia</em>, September 16, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;oldid=978792334">https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;oldid=978792334</a>.<a class="easy-footnote-to-top" href="#easy-footnote-3-2731"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2731"></span>“Wright Model B.” In <em>Wikipedia</em>, September 16, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;oldid=978792334">https://en.wikipedia.org/w/index.php?title=Wright_Model_B&amp;oldid=978792334</a>.<a class="easy-footnote-to-top" href="#easy-footnote-4-2731"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

How energy efficient are human-engineered flight designs relative to natural ones?

2022-11-02T17:58:01+00:00

@@ -326,19 +326,16 @@
  <HTML>
  <p><strong>Table 1: Energy efficiency of flight for a variety of natural and man-made flying entities.</strong></p>
  </HTML>
  
- {{:power_of_evolution:evolution_engineering_comparison:distance_flown_per_kilojoule_proportional_to_weight_2.png|}}
+ [{{:power_of_evolution:evolution_engineering_comparison:distance_flown_per_kilojoule_proportional_to_weight_2.png|Figure 1: If you give each animal or machine energy proportional to its weight, how far can it fly? Note that the vertical axis is log scaled, so apparently small differences are in fact much larger.}}]
  
- Figure 1: If you give each animal or machine energy proportional to its weight, how far can it fly? Note that the vertical axis is log scaled, so apparently small differences are in fact much larger.
  
  <HTML>
  <p>On mass⋅distance/energy, engineers beat evolution. The efficiency of Airbus Zephyr S was two orders of magnitude above the Wandering Albatross, the most efficient animal. <span class="easy-footnote-margin-adjust" id="easy-footnote-2-2715"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2715" title="For the best case for engineers we compare the Boeing 747-400’s best score to the Albatross’s worst, and for the best case for evolution we do the opposite. This gives an advantage for evolution by a factor of somewhere between 1.7 and 7.7."><sup>2</sup></a></span> We found several flying machines more efficient on this metric than the monarch butterfly.</p>
  </HTML>
  
- {{:power_of_evolution:evolution_engineering_comparison:distance_flown_per_kilojoule.png|}}
- 
- Figure 2: How far animals and machines can fly on the same amount of energy. Note that the vertical axis is log scaled, so apparently small differences are in fact much larger.
+ [{{:power_of_evolution:evolution_engineering_comparison:distance_flown_per_kilojoule.png|Figure 2: How far animals and machines can fly on the same amount of energy. Note that the vertical axis is log scaled, so apparently small differences are in fact much larger.}}]
  
  <HTML>
  <p>On distance/energy, the natural solutions have a larger advantage. The best natural and engineered solutions respectively are the monarch butterfly (100,000-600,000 m/kJ) and the Airbus Zephyr S (1490 m/kJ), for roughly a 200x advantage to natural evolution.</p>
  </HTML>