Using Mr Nakka's Solid Rocket Motor Design spreadsheet, I came up with the basic design of my new motor.
The dimensions of the motor casing are determined by the casing material. For this motor I have chosen to use the same material that I used in the original motor. The material is steel fence post material available at most home improvement stores. It has a 2.375" diameter x 0.049" wall thickness and I paid around $10 for 5 feet of it. (More on the use of steel in a later post) The next step is to determine the propellant grain geometry. The grain geometry offers a lot of room to play around with. For this motor I know that I will be using two inch mailing tubes to cast my propellant segments into, so that sets the outer diameter of my grain at two inches or 54mm. Then I played with the individual segment length and core diameter in an effort to produce a nice neutral burn profile as seen in Graph 1. The next decision I made was to increase the number of segments to six versus the four segments of the original motor. This essentially increases the total impulse by 50%. The resulting motor is on the long side with a L/D of around 10, but it shouldn't present any serious issues.
The next thing that I did was to lower the grain density ratio from the default of .95 to a more likely .093 given the fact that I don't want to spend a lot of extra time processing propellant for this motor and the performance lose is small and in this case perfectly acceptable.
The last thing that I did was to determine the Kn range that I wanted this motor to operate at. I chose 375 as the starting Kn which results in a max chamber pressure of around 1100psi.
The spreadsheet uses the grain geometry and Kn information to determine the nozzles throat diameter. It then takes all of that info, plus assumed combustion efficiency, nozzle efficiency, and other data and gives us our first glimpse of the designs performance.
It also gives you a nice summary of the key parameters of the designs performance.
Next step will be to take a closer look at the casing and come up a bolt ring design to retain the nozzle and bulkhead.