Input Data:
- Burn rate exponent (n)
- Burn rate Coefficient (a)
- Throat diameter (inch)
- Propellant grain OD (inch)
- Bore diameter (inch)
- Combustion efficiency (%)
- C* characteristic velocity
- Thrust Coefficient Cf
n, a, efficiency C* and Cf are determined empirically by burning propellant in motors with a constant nozzle area.
- For the design of any motor the propellant needs to be reasonably well characterized to determine both the burn rate exponent (n) and the burn rate coefficient (a).
- The theoretical Characteristic velocity (C* of the propellant can be calculated from chemistry (not my area!). There is software to do this.
- When the propellant is characterized, the ratio of the theoretical C* to the measured C* gives the Combustion efficiency.
- The Thrust coefficient is determined empirically from the Force and pressure graphs assuming that the nozzle area is constant.
A future post will discuss empirical techniques for measuring these two parameters from pressure vs time and thrust vs time data.
Once the propellant is characterized the motor is designed to a pressure based on the materials of the motor. Look up the continuous rated pressure of material. For the 2" PVC used in this example the maximum continuous pressure is 400 PSI, however, this is derated with temperature. Since we will be using an inner thick PVC liner, and our burn time is short, we will just worry about ambient temperature derating, for typical Southern California desert temperatures we derate the max pressure by 88% which gives a maximum pressure of 350 PSI.
Finally the mechanical properties of the motor are designed to give desired burn profile.
- Throat diameter (inch)
- Propellant grain OD (inch)
- Bore diameter (inch)
- Bore diameter is double throat diameter
- Propellant grain OD is sized to available materials. 1.55: for 2" motor
- Ball park throat size can be calculated from Area of throat = Force desired / Motor Pressure * Cf. Choose a size that fits an available drill bit.
Next the final mechanical properties of the motor are determined.
- grain length
- number of grains
- propellant weight
All parameters are entered into the FPRED software and a neutral burn is selected. This will calculate the grain length for a neutral burn. Adjust the length of the grain up for a more progressive burn and down for a regressive burn. After pressing calculate, check the pressure graph to determine that it has the desired shape.
Now increase or decrease the number of grains until you are close to your desired maximum pressure. Once the pressure is close, increase or decrease the grain length to the nearest 1/8" to dial in the pressure further.
Record the following parameters:
- Length of grains (inch)
- number of cartridges (grains)
- Propellant weight (lb)
The propellant weight will help determine how much propellant to manufacture per motor and the other two parameters will allow you to prepare your casting tubes.
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