Trajectory of a Deluscious Foam Basketball*

Height of ball (m) vs Distance from shooter (m)

Set the initial conditions for the ball below. The program calculates and plots the trajectory. Change the values and run it again to compare trajectories for different initial conditions. See below for further explanation and suage suggestions.

Initial Speed: m/s
Drag coefficient:
Shooter Angle: degrees
Shooter Height: inches
Hoop Height: 28 inches
61 inches
98 inches

The Details

This program uses a trajectory calculation for an 8" diameter Deluscious foam basketball with weight of about 11.2 ounces. Since air resistance has a sizable impact on the trajectory, we attempt to include its effects (called drag). Unfortunately we don't yet have the means to measure the drag coefficient, but a standard baskbetball is 0.5, so we assume this ball to be about the same.

There is an excellent discussion of how to do this calculation for yourself at this web site:

It describes the modified equations of motion taking into account drag as well as the effects of gravity. It also prescribes a computational approach to plotting the trajectory.

Note that currently we ahve not included the effects of spin. Top spins and back spins can be used to modify a ball's trajectory, like a curve ball in baseball. Incorporating those effects however, makes the equation of motion even more complicated and involves even more guess-work.

Suggestions on How to Use

The hoop height is a constraint. The trajectory calculation runs until either the ball hits reaches the hoop height while travelling downwards, or, if it didn't have enough initial energy to achieve that condition, the ball hits the floor.

To compare the trajectory to a "perfect world" calculation where there is no drag, set the drag coefficient to 0 and note that the ball goes further.

Note the angle that the trajectory has when it hits the hoope height. Some trajectories at lower angles would have the ball enter the hoop at a small incidence angle that may be nearly impossible to achieve in reality.

The shooter height is the height at which the ball loses contact with the shooter mechanism during a shot. Set a value appropriate for your situation.

The Clear button clears out the accumulated plots.

* Currently only compatible with recent Firefox browsers.