The Model Rocket Altitude calculator computes the estimated maximum altitude of a rocket based the distance from the launch point and the angle to top point of flight (zenith).
INSTRUCTION: Choose units and enter the following:
Max Altitude (Alt): The calculator returns the observed altitude in feet. However this can be automatically converted to other distance units (e.g. meters) via the pull-down menu.
Note this calculation makes a gross assumption that the rocket flight's apex is directly over the launch point, which in most model rocket flights is a reasonable approximation. The Model Rocket Altitude equation estimates the maximum altitude a rocket will achieve using the distance a spotter is from the launch pad and the angle from the ground the spotter notes at the rocket's apex. This altitude estimate is most accurate if the rocket flies straight up, perfectly vertical from the launch pad.
The Model Rocket Altitude equation can estimate the altitude of a rocket at any point in the rocket's flight path where the angle is measured. It does this by multiplying the distance from the launch pad by the tangent of the angle of the rocket's apex (See Figure 1). This equation is based on the Pythagorean Theorem1. The Pythagorean Theorem defines the relationship between the three sides of a right triangle; to calculate the altitude of a rocket using the Pythagorean Theorem the following must conditions need to be met:
If both of these conditions are met, the vertical flight path forms a right angle with the ground level and the calculation of apex altitude can be done.
Using the trigonometric functions of a right triangle2 the Altitude can be found by multiplying the angle, `alpha`, by the Distance of the spotter from the launch vertical.
`tan(alpha)="Altitude"/"Distance" => "Distance" * tan(alpha) = "Altitude"`
The following steps can be used to construct a homemade altitude finder to measure the apex angle.
The following supplies will be needed: