To operate the calculator, you first select the planet using the choice button at the top left. For ballistic flight, select the “Ignore Drag” option with the middle choice button. On another page we develop the equations for flight with drag. You can perform the calculations in English (Imperial) or metric units. Enter the initial velocity, then press the red “Compute” button to compute the maximum height and the time to maximum height. Notice that entering a different value for the weight or the area does not change the computed maximum height.
Now consider the impact with the ground at the end of the flight. At impact the altitude is zero. Using the altitude equation:
y = 0
Vo t = .5 g t^2
t = 2 Vo / g
The total flight time varies linearly with the launch velocity. The total flight time is twice the time to reach maximum altitude. So a ballistic shell takes as long coming down as it does going up. If we substitute this time into the velocity equation:
V = Vo – g (2 Vo / g)
V = – Vo
The velocity at impact has the same magnitude but opposite direction as the velocity at launch.
You can study ballistic flight characteristics by using the HitModeler simulation program for the flight of a baseball. Or you can use the RocketModeler program to simulates the flight of a model rocket. Or you can use the SoccerNASA simulation program for the flight of a soccer ball.
Calculation with Drag
If we are performing the calculation with drag, we must specify the object’s weight, cross sectional area, and a drag coefficient. The air density is determined by the altitude, or it can be input directly. Press the red “Compute” button to compute the maximum height and the time to maximum height. The program also outputs the terminal velocity as described above.
Notice If you toggle the middle choice button between “Ignore Drag” and “Include Drag”, you will notice that the computed height is always less when including the drag. The amount of the difference indicates the importance of drag for certain flight conditions. Also consult the terminal velocity web page for some warnings concerning cases with high terminal velocity. If you hold the initial velocity constant, and increase only the weight, you will notice that the maximum height gradually approaches the ballistic flight value.