The movie October Sky doesn't tell the audience everything the "Rocket Boys" used to construct their rockets but they did reveal a couple of ingredients.
They switched their fuel from black powder to potassium chlorate. They also experimented with potassium nitrate & sugar; a zinc – sulfur powder mix, and various binders.
Each switch the boys made was in response to a test failure that demanded a modification in their engineering design. The use of scientific method is fabulous. They identified a problem, came up with a probable solution, tested it, then either revised their approach or tossed it for a new one.
After finding that their nozzles could not take the heat inside the rockets, they had to special order a steel called S.A.E. 1018 bar stock. They learned to make new nozzles that could withstand the heat and eventually were completely successful in launching their rocket.
The answer is simple. Get a copy of Rocket Boys by Homer Hickam. October Sky is based on this book and Homer tells everything about his rockets in it.