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The Wright brothers and the 1 pound crow that flies at 37 km/h expending just 7.68 W

In an 1905 letter to Octave Chanute, Wilbur Wright evaluated the power, used by a 1 lb bird to fly at 34 ft/s, utilizing a relation that can be rewritten as:

eff x Power = Thrust X Speed = Drag x Speed,

where: eff (the efficiency of the crow) = 75%, Drag/Lift = Drag/(mg) = 1/8 and mg = 1 lbf.

In consequence, Power = (1 lbf x (1/8) x 34 ft/s ) / 75% = 7.68 W.

"The power consumed by any bird or flying machine may be figured from the formula wv/ac, in which w = weight, v = velocity, 1/a = ratio of drift to lift, and 1/c = efficiency of the screws or wings as propellers. In the case of the crow flying at 34 ft. per second, or 2,100 ft. per minute, I would fix the value of l/a at 1/8, and 1/c at 1/.75; when we have (1 x 2100)/(8 x .75) = 350 ft. lbs. per pound of weight.1 The minimum value of l/a may be rendered independent of velocity by regulating the size of the wings. The value of 1/c is about the practical limit of the efficiency of screws under usual conditions, and I see no reason for believing that wings are more efficient than screws, as propellers. It is quite incredible that, when flapping, the wing can be kept at the optimum angle at every point, as in soaring; and there are losses due to the fact that the pressure is not vertical throughout the stroke. Although I think 25 percent a fair estimate of the probable loss from both sources. Birds unquestionably develop power many times greater than is consumed by our Flyer, per pound weight. if you will fix in your mind the distance within which a small bird acquires full speed, say 30 miles an hour, and then figure the power necessary to accelerate its weight to this velocity, I think you will be astonished. I know I was almost dumbfounded, especially in view of the fact that the power available for acceleration is over and above that used in flying. I shall be curious to know what distance you fix upon as that within which a sparrow acquires full speed.",
Letter of Wilbur Wright to Octave Chanute, Dayton, March 11, 1905

7.68 W/lb seems a quite low figure as long as, it's generally accepted that any model plane with less than 50W/lb is going to struggle (see The Watts Per Pound rule)

Does a crow only expend 7.68 W/lb or at least it is possible to build a model plane able to fly at 37.3 km/h (34 ft/s) developing just 7.68 W/lb shaft power?

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  • $\begingroup$ A crow doesn't have a shaft to power. A prop is not very efficient either. $\endgroup$
    – ratchet freak
    Oct 12, 2015 at 13:17
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    $\begingroup$ ratchet freak, read carefully the text I quoted because W. Wright gives there some explanations that will clarify your remarks. $\endgroup$
    – Robert Werner
    Oct 12, 2015 at 13:31
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    $\begingroup$ Simple answer: we suck compared to nature. Although in our defence, nature has had more practice. $\endgroup$
    – Jon Story
    Oct 13, 2015 at 23:59
  • $\begingroup$ Nature never invented a wheel though. $\endgroup$
    – Koyovis
    Sep 12, 2017 at 3:31
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    $\begingroup$ I came here expecting an eventual comparison of the crow to a European swallow carrying a coconut. Learned some historic trivia instead. $\endgroup$
    – AEhere supports Monica
    Sep 12, 2017 at 9:48

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The number cited by Orville looks quite reasonable. The crow is just cruising along, not banking, accelerating or climbing.

Now add a climb speed of just 1 meter (3.3 feet) per second, and the additional power is 5,93 W. Let it circle with 60° bank angle, which would double the required lift, and the power for staying aloft increases to 15.36 W.

Next comes the flight speed, which goes up with the root of the wing loading. The American crow has a wing chord between 25 and 33 cm and a wing span between 85 and 100 cm. Taking the average puts their wing area at maybe 0.25 m² (it is almost rectangular, after all), and their wing loading at 1.8 kg/m². I would expect that a battery-powered model would have a higher wing loading, maybe 5 kg/m². The required power goes up with the third power of speed, and the speed itself increases with the square root of the wing loading. This makes the model of the crow fly at 62 km/h and consume a power of 35.5 W - just for straight and level flight. Add some margin for acceleration, banking flight and climbing, and the 50W/lb rule looks quite reasonable.

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  • $\begingroup$ I need an example of ~ 1 lb model plane that can fly at about 10 m/s (36 km/h) using maximum 10 W. It is quite clear that 7.68 W/lb x 745 lb x 75%/66% = 8.77 hp which is quite close to the 8.73 hp the two brothers estimated they needed to fly their 745 lb, 66% efficient, 1903 plane. In other words the Wright brothers simply assumed the efficiency of the bird is 75% and scaled down to 1 lb the power needed for their 745 lb plane to fly. This is pure math. $\endgroup$
    – Robert Werner
    Oct 12, 2015 at 18:17
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    $\begingroup$ An airplane which needs 10 W for straight and level flight will have maybe three times as much power installed to be useable. Don't expect to find one which has a 10 W engine installed, even though it will need only 10 W for flying at its best efficiency. On the other hand, the Flyer I could only fly straight - it needed already all the installed power for flying at its best efficiency $\endgroup$
    – Peter Kämpf
    Oct 12, 2015 at 19:20
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    $\begingroup$ Any model plane that stays in the air can be useful for something. If W. Wright was right, there should be 1 lb planes that fly using just 7.68 W. $\endgroup$
    – Robert Werner
    Oct 12, 2015 at 19:58
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    $\begingroup$ I made a solar model airplane (the LUSA, facebook.com/LUSAonline) that at ~2 pounds required 18 watts to fly. And it wasnt even uber-optimized from an aerodynamic point of view.... $\endgroup$
    – Caterpillaraoz
    Sep 12, 2017 at 6:58
  • $\begingroup$ @Caterpillaraoz: What wing loading does it have? I bet it is quite a bit below the 5 kg/m² that I used for the example. $\endgroup$
    – Peter Kämpf
    Sep 12, 2017 at 8:07

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