# Q & A: Model Rocket Engines

Q:
I wanted to know what kinds of solid fuel cells are used in model rockets. And I also wish to know how to calculate how much thrust is produced so i may find out how to calculate its velocity.
- Nicholas Rice (age 16)
Barstow,CA, USA
A:
The solid fuel engines in model rockets are made out of a mixture of materials very similar to gunpowder -- they contain some kind of nitrate compound like potassium nitrate or sodium nitrate, carbon, and sulfur (which gives them that distinctive smell). High-tech solid rocket boosters used on the shuttle use aluminum powder instead of the carbon and sulfur (yup, aluminum burns!) See for a comparison of the composition of model rocket fuel and gunpowder. The nitrate compound is there to supply oxygen -- the formula for potassium nitrate is KN03, which helps to burn the carbon and sulfur very rapidly without the need for an air intake. Model rocket engines may be purchased at hobby stores. People have been injured and killed mixing explosives -- don't do it yourself. There are laws governing the use of model rockets and explosives that vary state-to-state -- be aware of these before doing anything.

The thrust is the product of the rate at which mass is lost by the engine as the combustion gases exit times the speed of the hot gases as they escape the engine. You can estimate the first bit by weighing an engine before and after it has burned and measuring with a stopwatch how long it burns in flight. This won't be exactly right because the engine will contain other components, like a delay charge and an ejection charge for multistage rockets, but it will be close. The speed at which the gases escape is much harder to measure -- if you know the density of the gases (and this depends on how hot they are) you can use the mass you obtained before and the area of the exhaust exit in the engine to estimate the speed:

(change in engine mass/gas density)/((burn time)*exhaust exit area) should give you the speed of the gases coming out (that's just the total volume of the gases divided by the area and the burn time). Make sure you do everything in consistent units! I recommend kilograms, meters, and seconds for everything, and you should get the thrust in Newtons. The hard parts are estimating the density of the escaping gases and also the exit hole size because it usually will be a small hole with a slowly increasing flare -- the gases will slow down as they exit the engine exhaust structure.

Note: what is important is not only the thrust, but the burn time -- if the engine supplies its thrust for only a short amount of time it won't make your rocket go as fast as one that supplies the same amount of thrust over a longer time. Thrust*time = impulse, and this is what engines are usually rated in. Divide impulse by the mass of the rocket (with the engine) to get the speed of the rocket, but be sure to subtract off the acceleration due to gravity times the burn time (gravity will slow it up!) to get the maximum speed -- there is also the effect of air resitstance to make your life difficult calculating the final speed of your rocket.

For a good site on model rockets, see together with some . Due to the way the propellant is arranged in a typical engine, the thrust it provides changes with time. The calculation above I suggest only as an estimate if you would like to verify the measurements independently.

Here's also a with specifications of various commercially available model rocket engines.

Tom

(published on 10/22/2007)