Serious rocket science calls for "static testing" rocket engines (firing them anchored to a test bench and fitted with instrumentation. A static test can accurately determine the motor's thrust, burn time, chamber pressure, and other data that assist in propellant evaluation as well as engine design and engineering. In any case, is better to have a new motor malfunction in a safe test bay than flying high overhead out of control.
Propellant chemists and engineers static test thousands of different formulations to "characterize" propellant performance and improve motor designs. By static testing your own rocket engines before flying them, you'll learn much and better understand how to improve them.
So how do you go about static testing a small rocket motor? First, you need to find or build a safe "test bay" or remote site where the noise, smoke, and possible flying debris of a malfunction won't disturb anyone. The early rocket pioneers at Cal Tech built sandbag bunkers in a remote canyon near Pasadena, and rigged instrument gauges onto simple wooden support frames. They used remote controlled movie cameras to record both the engine operation and the related gauges nearby.
If you're testing smaller rocket motors, you will probably want to measure and record the thrust performance. Jigs and fixtures to measure thrust have been made from simple postal scales (the newer digital models are quite versatile for this application). Sometimes small mirrors are installed, so the video camera can capture events yet be "out of the line of fire" in case a motor fails.
Advanced rocket experimenters use small thrust measuring devices called "load cells," which are connected to simple circuitry and feed into a computer. Load cells come in all sizes, capacities, and levels of precision. You can find load cells to measure a few ounces of thrust, and others capable of measuring thousands of pounds.
Thrust (the amount of "push" the rocket motor is producing, and usually measured in ounces or pounds, or grams or Newtons) is somehow recorded, and from the data you can draw a "thrust curve" of engine performance. The thrust curve shows how the engine thrust rises and falls over the period the propellant is burning. This curve is often the most important single chart used to evaluate engine and propellant performance. (Back in the 1950s and 60s, when the Apollo engines were being developed, static test thrust curves were plotted directly onto paper charts with an electric oscillograph. Before that, Goddard and many other pioneers recorded engine thrust on a piece of smoked glass, with a simply scratch-stylus connected to some kind of transducer.)
Along with burn time (duration of thrust), the next most important thing to measure is combustion chamber pressure. How much pressure is being generated in the motor case? Chamber pressure (usually designated as Pc, or "P-sub-c") for most rockets is a few to several hundred pounds per square inch. Many rocket engines operate at between 300 and 600 psi chamber pressure. And of course, chamber pressure directly relates to engine thrust. All other things being the same, the higher the chamber pressure, the higher the thrust. So it's very useful to plot chamber pressure along with engine thrust.
Thus many amateur rocket experimenters design at least a simple static test bench, in a remote (safe and legal) location, and fit it with a thrust measuring device and a pressure gauge, along with a video camera to capture data during the firing. After the test, they plot thrust and chamber pressure curves (from ignition to burn-out) of each firing. By studying the spent motor (possibly by dissecting it, or cutting it into sections) along with the static test curves, you can analyze what you've built. This is rocket science, at it's most simple levels.
To get many other ideas on designing and using static test for your own motors, review the devices used by notable rocket pioneers. You'll find a wealth of good information in Robert Goddard's books, as well in How to Design, Build and Test Your Own Small Liquid Rocket Engines, Amateur Guide to Building Rockets, and (the Ft. Sill) Guide to Amateur Rocketry.
The best handbook for static testing small solid propellant rockets (Estes-size and larger) is certainly David Sleeter's excellent text Amateur Rocket Motor Construction. David's new book covers every aspect of static test, including how to build your own simple static test jigs and fixtures.
For a study of large-scale static testing of rocket engines, read the NASA Captive-Fired Testing of Solid Rocket Motors, and the classic Rocketdyne Unit of Instructions for Test Facility Systems. All of these important texts about rocket testing are usually in-stock in our eBay Store.