In honor of the end of my volleyball career…

A volleyball player’s approach and arm swing when they hit is very intentional and can be quite intricate. The angle of approach, depth of wind up, shoulder rotation, and hand contact and length of contact with the ball are just a few technicalities that ultimately affect the ball’s direction and velocity. But let’s try to simplify it in order to calculate the force I can exert on the ball.

If I hit a 0.28kg volleyball at 80mph or about 36m/s (close to the top male Olympic speeds, but let's just pretend!), that means the ball had a momentum of 10.1 kgm/s because p=mv.

We will assume the ball started at rest. This is decently accurate because when the ball leaves the setter’s hands it is traveling parallel to the net. We will assume I am hitting ‘down the line’, which means I am manipulating the ball with my arm swing and wrist to cross the net perpendicularly. So the ball was only moving in the x-direction before I hit it, and afterwards it moves in the y-direction.

We know that F= Δp/Δt. Contact time between my hand and the ball depends on what I want the ball to do. If I want the ball to have top-spin and drop quickly to the floor my fingers wrap around the ball and I remain in contact with it longer. If I want the ball to ‘float’ I make very brief contact with the ball with mostly my palm.

Let’s say I want the ball to float and that t=0.008 seconds. That leads us to: F= 10.1kg/s * 0.008s. F= 1262.5 N. So a volleyball player’s arm is really quite the weapon! 

P.S. Notice how the figure's knees are buckling inward before he jumps? That reduces the amount of force they can put into their jump. BAD FORM