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Physics of Batman: The Dark Knight

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Batman Angular

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.

http://www.popsci.com/entertainment-%2526-gaming/article/2008-08/physics-batman

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?

To hold his arms out, Batman has to exert the same force back on the air. So while he moves in a circle, we can calculate the force that will be exerted on Batman’s arms.

circle radius = 20 meters

man + equipment mass = 80 kg

speed remains constant during this turn

Let’s estimate the force on Batman’s arms as he sweeps through the bottom of the arc.

F = weight + centripetal force

F = m g + m v2/r = m ( g + v2/r )

= 80 kg (9.8 m/s2 + [40 m/s]2 /20 m) = 7200 N

= about 1600 pounds

This means that Batman has to hold 800 pounds on each arm!  Imagine lying on your back, on a workout bench, holding your arms out and having 800 pounds of weights placed on each one!  This is probably impossible for someone to do without super-strength.

Perhaps there is a way out of this. Maybe there are some hinges that connect the wings to the Bat suit. If so, then these hinges could be doing some of the supporting, rather than Batman’s arms.

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