Purpose
After a motor test fire, the data acquisition system collects roughly
a million data points describing motor pressure, temperature, and force throughout the burn.
The goal of the data processing program is to organize and perform calculations with this data
to determine motor efficiency parameters. The parameters determined and their calculation method
are listed below:
| Parameter | Description | Equation |
|---|---|---|
| Burning Time | Interval between the first sign of pressure build up to the last data point above zero. | `t_"burn" = t_"final"-t_"initial"` |
| Grain Density | Density of the propellant. Inputs are number of grains, outer and inner diameter, length, and mass. This equation is for the bates grain configuration. | `rho = (4*m_"propellant")/(N*L*pi*(D_"outer"^2-D_"inner"^2))` |
| Average Mass Flow Rate | Average mass of propellant flowing through the nozzle per second. Derived by dividing total propellant mass by burn time. | `dotm_"avg"=m_"propellant"/t_"burn"` |
| Total Impulse | Defined as the area under the force-time curve. | `I_"t" = int_"0"^"t"Fdt"` |
| Specific Impulse | The efficiency of a rocket motor. How much thrust you get out for a propellant input. Specific also means “divided by weight”, so in this case specific impulse is total impulse divided by the weight of the propellant. | `I_"sp" = I_t/(g_0*m)` |
| Characteristic Velocity | Used to compare the efficiency of propellent combustion processes. Also known as C* (see-star), it is independent of nozzle characteristics. Inputs are chamber pressure, throat area, and mass flow rate. | `c^"*"=(A_t* int_0^tp_1dt)/m_"propellant"` |
| Thrust Coefficient | The amount of amplification the nozzle provides to thrust output of the motor. | `C_F=F/(p_1*A_t)` |
Operation
To ensure rapid turnaround during heavy testing days, an efficient data processing program was needed. The current program was written in MATLAB and was made to be used with a post-test procedure like the one below:
Data Process Procedure:
-Data is recorded to a USB using the data acquisition box during testing
-USB is inserted into a computer
-Post Processing MATLAB Program is opened and prompts for the data files
-Time range of burn is selected and relevant info related to the test is entered (date, ambient temperature, grain size, grain mass)
-Program outputs performance parameters and graphs into a single folder
----------Rocket Motor Test Fire #2, 2020-05-18---------- Ambient Temperature = 68 F ~Propellant Properties~ Fuel Mixture: potassium nitrate - sorbitol Burn Time = 1.55 s Grain Mass = 303 g Segment Lengths = 4, 3.86 in Grain Density = 1.7519 g/cm^3 ~Performance~ Average mass flow = 0.19548 kg/s Impulse = 332.5367 N-s Isp = 111.9125 s c* = 979.2567 m/s Avg. CF = 1.1207 ~Peak Values~ Max Thrust= 382.2352 N at t= 0.82273 s Max Pressure= 724.905 psi at t= 0.82773 s Max Temeprature= 91.4739 F at t= 1.3737 s ~Misc.~ Burn start time after DAQ start: 69.65 s Burn end time after DAQ start: 71.2 s Note: red grain, no rtv, cast 5/17 9pm ----------------------------------------------------------
A sample data output file from the 5/18 test fire
