Wednesday, February 1st, 2012 11:18 am GMT -6 Wednesday, February 1st, 2012 11:18 am GMT -6Wednesday, February 1st, 2012 11:18 am GMT -6
 

Let’s take measurements of birds and use that to guide the design of our model airplanes. Would our model airplanes end up looking any different than they do now?

 

 

 

Bird Measurements

Researchers have painstakingly measured the wings, weights and flight performances of many bird species. By studying the data, they have been able to discover consistent patterns. By starting from the weight of a bird, they can predict with high accuracy what its wing looks like and how much energy it needs to fly.

Humble Hummingbird

Hummingbird in flightThe one notable exception to these patterns is the humble Hummingbird. Given the unique way that it can hover, it just doesn’t fit the pattern of other birds. In the following analysis, the data for Hummingbirds has been excluded. Sorry, little fellow.

Curve Fitted Results

The numbers were plotted in terms of the bird mass (weight) and curve fitting was then used to derive a formula for each quantity. The numbers in the following table are based on these formulas.

weight wing span wing area wing loading AR max endurance
g oz cm in cm^2 in^2 N/m^2 oz/ft^2
m/s mph W W/lb
25 0.9 41.1 16.2 112.4 17.4 22.1 7.4 6.9 3.2 12.5 5.4 98.1
50 1.8 53.8 21.2 185.1 28.7 26.9 9.0 7.2 3.5 14.0 6.2 56.0
100 3.5 70.5 27.8 304.9 47.3 32.6 10.9 7.5 3.9 15.6 7.0 31.9
200 7.1 92.4 36.4 502.2 77.8 39.6 13.2 7.8 4.4 17.4 8.0 18.2
300 10.6 108.2 42.6 672.4 104.2 44.4 14.8 8.0 4.7 18.6 8.7 13.1
400 14.1 121.1 47.7 827.2 128.2 48.1 16.1 8.1 4.9 19.5 9.2 10.4
600 21.2 141.8 55.8 1107.6 171.7 53.9 18.0 8.3 5.3 20.8 9.9 7.5
800 28.2 158.6 62.5 1362.5 211.2 58.4 19.5 8.4 5.5 21.8 10.4 5.9
900 31.7 166.1 65.4 1483.1 229.9 60.4 20.2 8.5 5.6 22.2 10.7 5.4
2000 70.5 226.8 89.3 2635.5 408.5 75.5 25.2 8.9 6.4 25.2 12.4 2.8
4000 141.1 297.2 117.0 4341.1 672.9 91.7 30.6 9.3 7.1 28.1 14.2 1.6

 

Table Notes

Note that a pound is a unit of mass, not force. Ever hear of the “force of gravity”? Yup. You have to multiply a pound (or ounce) by the gravitational constant to get a force. So when I say “ounces per square foot”, I really mean “ounces of force per square foot”. One newton is the force of gravity on a mass of about 100 grams.

AR stands for aspect ratio. This is a dimensionless quantity, so no units are listed. For the other columns I tried to give reasonable metric and U.S. customary (shaded columns) quantities.

The max endurance columns correspond to the flying speed where the least amount of power is required to maintain altitude. In a propeller-driven airplane, the efficiency of the propeller at various airspeeds is taken into account. Maximum endurance airspeed is about 76% of the best L/D or best glide speed.

Caveats on the Source Data

Keep in mind that birds, just like model airplanes, are designed for different types of flying missions. Some birds are for soaring, others value speed or controllability much more. These numbers are based on averages across many different birds. If you have to put a label on them, I would say they are for a “sport model” bird.

Also, the means of propulsion for birds is quite different than a model airplane. At least, most model airplanes. Flapping wing RC models are pretty rare. The fact that birds flap their wings to fly probably skews the data in ways that we are still trying to figure out.

Most birds are small. I’m much more comfortable comparing these numbers to an indoor model airplane or at most a park flyer RC model. Going much beyond these sizes we would be running the risk of extrapolating instead of interpolating the data, which would be a far more speculative use of the results. In other words, I’m not going there.

Interpreting the Table

So what can we conclude from the table? Using my ModiFly design as a point of comparison, the main difference that I see is a higher aspect ratio. That’s it! Are you surprised? I am.

Going up in size, the average aspect ratio for birds goes up to about 10. Large birds tend to be soaring birds, so that is not a surprise. But the number for watts per pounds goes way down, to an almost unbelievable level. The only obvious conclusion that I can reach is that large soaring birds are extremely efficient.

What else do you see in these numbers?

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