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# Model Rocket Altitude

vCalc.Model Rocket Altitude

The **Model Rocket Altitude** calculator computes *Figure 1*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 your preferred units and enter the following:

- (
**α**) This is the angle from the horizon to the apex or zenith of the flight. - (
**D**) This is the distance from the launch spot to the spotter.

**Max Altitude:** 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.

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 Math / Science

This 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).

#### Derivation

This equation is based on the Pythagorean Theorem^{1}. 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:

- the distance from the spotter to a point directly beneath the rocket at its apex must be known and level
- the rocket must launch vertically from the launch pad

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 triangle^{2} 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"`

### Practical Application

The following steps can be used to construct a homemade altitude finder to measure the apex angle.

*Figure 2*

The following supplies will be needed:

- a standard transparent protractor
- a straight rod (e.g. the straight segment of coat hanger or thin dowel)
- a string with a weight attached at one end (e.g. a heavy washer)

Steps

- Attach the string near the top of the 90 degree line and allow the weight to hang down
- Attach the rod to the pivot point of the protractor so that the rod can rotate (on the opposite side from the string hanging down).
- While holding the protractor so that the string aligns with the 90 degree line, sight along the rod to the rocket at its apex. When the string aligns with 90 degrees, the base of the protractor is parallel to the Earth's surface and forms the 90 degree angle with the vertical at the launch pad.
- Read the angle of the rod against the protractor; this is angle `alpha`