Since the dawn of man, we have always looked up at the sky to see birds flying above us and wondered how we can join them high above the earth. And that goal was achieved in 1903 when the Wright Brothers built a machine capable of powered manned flight. But that was a total cop out!
We at The Practice Set didn’t want to go through the air in a metal contraption. We want to feel the wind on our faces: we want to soar like freakin Super Man!
So that got us thinking. Could a human being actually fly through the air like Super Man? And we’re not going to cheat like the Wright Brothers by building some world altering feat of mechanical engineering design. We’re going to get you up in the sky like a bird; and you won’t even need to flap your arms! And we’re going to do it using the most powerful tool known to man: regular old math and physics.
The first thing that we need to do to is find out if a human being is aerodynamically capable of flying without some sort of engineered wings. And the answer to that question is, surprisingly: yes! As long as an object can create enough lift to counter its weight, it can fly. And it just so happens that human beings qualify as one of those objects: but sadly we won’t be looking like Superman while we do it. In order for us to achieve flight, we’ll have to hold our hands out like a plane: and more specifically like a Gullwing Plane.
A study on the lift of a human arm has shown us that if we hold our arms straight out and then angle our hands down at a 30° angle, we optimize the human being’s lift potential.
Now that we’ve determined that it’s even possible for a person to fly – which we think deserves a pat on the back: good job us for finding that out – then we need to come up with all of the different forces that’ll be acting on that person. That’ll allow us to see how fast that person needs to be moving to lift themselves up off of the ground using nothing but the magic of engineering mechanics!
If we draw up a Free Body Diagram, we see that only forces involved in lifting us up are Gravity and Lift. Air Resistance also acts in the horizontal direction, but we only care about the vertical direction because we’re trying to get up in the air yo.
Now that we have the forces necessary for flight, we plug them into a Net Force Equation. And it becomes a relatively simple 1 Dimensional Kinematics Problem because we only care about things moving up or down. And we at The Practice Set make our living on explaining these types of physics problems to students: so this’ll be easy!
FNET = Lift – Weight
Because we’re trying to find the slowest we need to travel in order to fly, we need to assume that the lift is exactly equal to our weight: so there is no Net Force. Our lift is exactly the same as our weight, that way if we travel any faster we will lift off of the ground.
0 = Lift – Weight
Weight = Lift
Then, we plug in the equations for lift and weight. ρ stands for the density of air (1.225 kg/m3). CL is the coefficient of Lift of the material which we found to be 0.9 based off of the same study that told us about the 30° angle. A is the surface area of the wing (our arms). V is the speed the object (us) is travelling. M is the mass of the object we’re trying to lift, and we got this value based off of the average weight of an American male. G is the acceleration due gravity, which is fixed at 9.81 m/s2.
mg = (0.5)(ρ)(CL)(A)(v2)
If we plug in all of our given and researched values we get:
(88.677)(9.81) = (0.5)(1.225)(0.9)(A)(v2)
869.9214 = 0.5513Av2
To get the surface area of a person’s arms, we use the DuBois and DuBois equation for measuring burns on the surface of the human body. This gives us the surface area of the arms of an average height and weight America man is 0.3694 m2.
869.9214 = 0.5513(0.3694)v2
Then, it just becomes a basic algebra problem where we simplify out the velocity variable. So when we do all of that and convert it to miles per hour, we find that the minimum speed that a human being needs to go to take flight with their arms out is…
And normally that wouldn’t be a problem, except that human terminal velocity is 120 miles/hr. And that means that air resistance against a person’s body would be so large they couldn’t go any faster: but that terminal velocity changes if you change the angle at which the body is moving through the air!
So if you wanted to take off and fly, all you’d have to go into the wind head first to allow you to reach the necessary speed to achieve lift off! Imagine that you look like a wingsuiter, but you know, without the wingsuit. Picture Superman but with his arms spread a little farther out. And just in case you can’t, here’s a picture!
The human body is both an ancient and modern marvel. With only a little bit of speed (well, actually a crap ton of speed) we can take to the skies and touch the clouds, and we can do it with the tenants of math and engineering statics: we don’t need those stinking Wright Brothers.