Ejection Charge Calculations
By Darrell Mobley
This is an article posted on the WEB by Darrell Mobley.
The theory behind the numbers.
If you've never had a rocket crash because the parachute didn't come out right, go on to read something else. But if you know what the term "core sampling" is from experience, here is some good information. Parachute failure often comes from an incorrect or insufficient amount of ejection charge. This is caused by either having too large a parachute compartment inside the rocket, or not using the right amount of black powder in a reloadable motor.
Ejection charge weight can be calculated based on the desired ejection pressure and the internal "free-volume" of the rocket airframe. Normally the volume of the parachute and rigging inside is neglected. This approach is used in industry for closed bomb calculations and pulsar (pressure cartridge) applications.
First you need to determine the required pressure to separate and deploy the recovery system. This depends on the area of the bulkhead, hence body diameter, and the mass of the nose section. The force from the pressure must be enough to overcome the inertia and drive the mass of the nose section the length of the coupler inside the tube to the point of separation, plus a little more for momentum to fully deploy everything. If you consider the nose having to deploy into a wind, or not near apogee, you need a little more push again.
Assume that the gas expands and the pressure occurs instantly and uniformly throughout the volume. The pressure exerts an instant force on the forward bulkhead intended for extension. Neglect any change in pressure and temperature from the change in volume as the nose moves forward, (unless you just like calculus.) This is the simplest case for a single set of variables and adequate for most ejection systems.
The ejection charge equation is: