Let’s assume that the memory fiber used in “The Dark Knight” is real, and that it can be used to change the shape of a cape into gliding wings with the application of an electrical current. (No such material yet exists, but materials scientists may be getting close.)
Why don’t people use some form of bat wings? Let’s analyze the forces your arms would have to exert in order to successfully use bat wings.
Adapted from “The Physics of Batman: The Dark Knight – High Dive”, Adam Weiner, 08.15.2008
Batman spreads his wings & moves into a circular path.
His motion goes from vertical to horizontal.
The force of air resistance increases dramatically when he opens his wings.
This force turns his linear path into a circular path.
This inward pointing force is a centripetal force.
Law of physics: No object travels in a circular path (Newton’s 1st law), unless some force continually pulls it radially inward.
The balance of inertia and a radially inward force can create circular motion.
Centripetal force depends on the radius of the curve (r) and the radial velocity (v)
F = mv2/r
When a glider – or a Batwing – is bent into the wind, one can use the force to deflect the glider, plane or Batman.
Red arrow to upper right = “lift” (due to the wind hitting the wings)
Red arrow down = weight
Horizontal green arrow is the horizontal component of lift (aka centripetal force)
Vertical green arrow is the vertical component of lift. (If itis big enough, then one can glide for long periods of time)
What about Newton’s 3rd law of motion?