Human Powered Flight

Lumo has up a clever video of human powered flapping flight. It turns out to be a clever CGI fake, but I thought it might be fun to analyze the aerodynamics. Heavier than air fliers overcome gravity by accelerating air downward. That takes work against drag. It turns out that there are two components to that drag - so called induced drag that is a direct side effect of lift and frictional drag, often called form drag. Form drag is proportional to the square of velocity while induced drag is inversely proportional to the square of velocity - circumstances that combine to produce a velocity sweet spot of minimum drag that depends mostly on the wing loading, the ratio of mass to wing area.

That velocity sweet spot is given approximately by V = Sqrt[W/0.38A], where W is weight, A is area and the numerical factor (appropriate for MKS units) combines plausible values of air density and angle of attack. If we assume conservatively that the flier of the video plus equipment weighs at least 700 N (70 kg)and wing area is about 5 m^2 we get V = 19 m/s - an implausibly high velocity compared to what we see.

We can also compute the power needed to be expended against just induced drag at that speed. It's given approximately by P = W^2/(rho*V*b^2), where P is power, W is weight, rho is air density (1.2 kg/m^3), V is airspeed, and b is wingspan. If we figure b = 5 m for our aircraft, that works out to 860 Watts, more than 1 horsepower and a lot more than any athlete can sustain. There will also be a comparable contribution from form drag.

Real human powered aircraft feature 30 m wings with 30 m^2 of area, extensive streamlining, ultralight materials, and elite bicyclists retrained as pilot/power plants. They generate roughly 200 Watts and manage a speed of around 7 m/s. So the video is a fake, as CGI experts have independently established.

The equations and their derivations can be found in Henk Tennekes wonderful book: The Simple Science of Flight

Comments

Post a Comment

Popular posts from this blog

Anti-Libertarian: re-post

The most pointed critique of social security and liberalism in general is the libertarian critique. The problem with libertarians, for a liberal, is that we have too much in common. We both believe in individual rights, tolerance of individual differences, and dislike government prescription of religion. The basic difference, it seems to me, is the different answers we give to Cain's (with thanks to the Captain - my original version had the corpse asking the question!) famous question: "Am I my brother's keeper?" That's not really my basic bitch against the libertarians though. My real complaint is the same as my complaint against most religion - its premise is a fraud. For those who can't stand to wait for the punchline, I believe that trying to implement libertarian principles leads to tyranny or social disintegration. Demonstrating that takes some historical (and pre-historical) context. For all but the last 15,000 or so of the 100,000 years the human spec
Read more

Uneasy Lies The Head

Uneasy lies the head that wears a crown ........... Shakespeare Henry IV, Part II. So it is with us and our slightly distant primate cousins , so it seems. A 9-year study of wild baboons in Kenya by Princeton University and the Institute of Primate Research may turn conventional assumptions of alphas males upside down. The study found that alpha males have high testosterone levels, which allows them to dominate other baboons, get access to more food, and attract better mates. This is expected. Surprisingly, though, the alpha males also have high levels of stress hormone glucocorticoid, which scientists measured from their feces samples. In fact, the stress of alpha baboons was on par with low-ranking baboons. The convention wisdom is that access to food and females provides life security and thus less stress for dominant males. Conversely, weak males who are constantly threatened by starvation and physical violence from stronger males are thought to be more stressed. The st
Read more

We Call it Soccer

The US played its best, and maybe only good game of World Cup, but lost thanks to brilliant goalkeeping by the Swedish keeper and the bizarre method soccer uses to settle ties when three US stars could not put the ball on frame from the 12 yard spot.  At the end it came down to a blocked shot that spun in by maybe a couple of centimeters. Well, that's football - too much like life.   Which brings me to a modest proposal.  Replace the thirty minute overtimes with as many 7-player 15 minute periods as needed to settle it.  Scoring should be much easier with fewer players.
Read more