Humans With Bird Wings

There's a project to build human wings, but the creator may not have taken a good look at a chart of wingspan-to-mass ratios. Dot Physics blogger Rhett Allain shows why the numbers are so important.

I know I said humans couldn't fly. Did I actually say that? I guess I did.

Well, here is a human flying. Yes, he cheats a little bit. Oh, you can find more details on their site at Human Bird Wings.

Ok, so it seems it isn't just human powered. Also, he just kind of flew. Anyway, I thought I should compare these human wings to my other wing data. Let me just make some guesses. Here is a nice shot of the wings so that I can estimate the size:

Drawings.key

So, 7 meters. That sounds about right. And what about the mass? Let me just ballpark it at 10 kg for the wings and stuff. That would make the mass of the person plus wings at around 80-85 kg.

In my previous post about flying, I plotted wingspan squared vs. the mass of the bird. Where would this flying human machine fit in this plot?

Drawings.key 1

Two things jump in my mind. First: wow. That would be a big bird (not Big Bird). Second, it looks like it would fit the trend of the other birds. Actually, it makes the data look a little better. The really small birds seemed to fit a different function than the bigger birds. One commenter suggested that this was because they use different methods for flying. Big birds tend to glide more.

How about one more plot? I can't remember who suggested this, but this is a plot of the natural log of the wingspan vs. the natural log of the mass. This way you don't have to guess at the power relation between the wingspan and mass. Suppose I started with some function like this:

La te xi t 1 4

Where w is the wingspan and m is the mass. I don't know the powers (a and b) - oh and K is another constant. Now taking the natural log of both sides, I get:

La te xi t 1 5

If I plot ln(w) vs. ln(m), it should be a linear fit (if there is a power-function relationship between these two variables). I might be able to get the powers from the slope. Here is that plot.

Drawings.key 2

The plot looks better than I expected. The fitting linear function has a slope of 0.408 and an intercept of 0.049. I can't exactly solve for a, b, and K since I have three variables and 2 things (slope and intercept). However, it looks like a = 2 and b = 1 would about work.

Ok. I always like to end by saying something. Let me just say that I, for one, welcome our human bird winged overlords.