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Detailed analysis of ANCP experimental motor

A 2" ANCP experimental PVC motor was fabricated according to the posts here: 

The following physical parameters describe the motor:
  • Casting Tube outer diameter:  1.55 inch
  • Bore diameter:  .75 inch
  • Grain length 3.875 inch
  • Number of Grains: 4
  • Nozzle Throat:  0.375 inch

The propellant has been previously characterized with the following parameters:
  • a = 0.0048 in / sec
  • n = 0.543 
  • C* = 4565 ft/s
  • Density = 0.0527 lb / in^3

Based on the composition of the propellant the following predictions were made:

  • Max Pressure:  352 PSI
  • Burn Time 3.75 s
  • Average Thrust 35.5 lb
  • Propellant Weight 1.18 lb


Predicted Pressure vs Time curve

Predicted Thrust vs Time curve


After burning the motor, the following data was obtained: 

Pressure(psi) vs. Time(s) curve obtained from the pressure transducer
Thrust(lbs) vs Time(s) obtained from S type Load Cell


 Unfortunately, there is no access to the theoretical raw curve data, so only the following comparisons can be made:

  • Max pressure Theoretical:  352 PSI
  • Max Pressure measured:  353 PSI  +- 3 PSI
  • Max Thrust Theoretical:  41.44 lb
  • Max Thrust Measured:  43.9 lb +- 3 lb

Measured values agree with predictions within uncertainty, which lead a good level of confidence in the characterization of the propellant. 

The empirical value for C* can be calculated from the pressure vs time graph as follows:

C* = (Area of pressure vs time) * Area of throat (in^2) * 32.2 (ft/s^2)  / Weight of propellant (lbs)

Integrating the experimental pressure time graph gives 1343 psi . s.  Given that the weight of the propellant was 1.18 lbs:

C* = 1343 * .11 in^2 * 32.2 / 1.18 = 4031 ft/s  

There is large uncertainty in this value since the grains were NOT weighed before final assembly.  

Given a mass uncertainty of 1.18lbs + .1 - .2 gives range of C* values from 3715 to 4853 ft/sec

While this value is consistent with the theoretical value for C*, it is not consistent with our value for the delivered C* based on the exit cone efficiency.  This is not surprising since the exit cone was initially drilled straight and machined itself into an ideal parabola during the burn as shown below.  However, this does point to a weakness in the model employed.









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