Bates Grain Burn Rate Simulator

I saw a need for a fast, easy method to simulate a Bates grain motor burn, thus the Bates Grain Burn Rate Simulator.

Input Data Box:

You can choose a propellant type by checking the radio box next to APCP, KNSU, KNER or KNSB, by checking a radio box the basic values for of a, n and C* are entered for you. Of course, you should enter those values manually for your propellant if you have them. In that case, you don't need to check any of the radio boxes.

Grain diameter and grain length are in inches.

Number of grains is self explanatory. If you have dissimilar grain lengths, you can simply add up the total length of the propellant and divide by the number of grains providing each grain is at least twice the web thickness in length.

Density is the propellant weight in pounds per cubic inch.

Core diameter is in inches.

Exponent is a value that must be determined experimentally through either ballistic motor tests or strand burn rate tests.

C* can be determined experimentally or through software such as Propep.

Exit Pressure is in PSI. If you launch at sea level this value is 14.7 psi. If you launch from higher altitudes or air start a motor, you will have to convert the altitude pressure to psi.

Coefficient, like the Exponent is a value that must be determined experimentally through either ballistic motor tests or strand burn rate tests.

Throat Diameter is in inches.

Output Box:

After all the input data boxes have been completed, click the Calculate button.

Propellant Weight is the total weight of the propellant in pounds.

Burn Time is the total motor burn time in seconds neglecting start up and tail off times.

Web is the thickness of the grain web in inches.

Burn Rate is the max burn rate of the propellant in inches per second.

Kn Max is the Propellant surface burn area divided by the throat area at its maximum.

Motor Class is the commercial motor class letter designation and the average thrust in Newton-seconds.

Initial Max Flux is the propellant weight flowrate in pounds per square inch of core area.

Initial Thrust in pounds force.

Max Thrust in pounds force.

Max Pressure is pounds per square inch.

Total Impulse in pounds force.

(To convert to pounds force to Newton's multiply pounds by 4.448)

Isp is the expected propellant performance in seconds.

Exit Diameter in inches of an optimized nozzle exit cone.

Notes: No software can calculate a motor burn perfectly, and this software is no exception to that. Keep that in mind when running simulations. Also remember the simulation is only as good as the data you enter into the simulation. If you don't have good a, n and C* numbers, the output will be rough at best. The only way to get a and n values for "your" propellant is through testing, and even then, scaling a given design rarely results in linear performance output.

This software uses some generalizations.

• Gamma for example is fixed to the nozzle coefficient at 1.22, since Gamma is a fairly weak function of performance, and Gamma tends to vary little in amateur propellants, the resulting loss of accuracy is minimal.
• The nozzle exit diameter output is calculated from a lookup table calibrated in .5 units of expansion ratio. Since it's better to slightly under expand than over expand a nozzle, the table uses the minimum value when computing the exit diameter.
• Burn rate is determined from a perspective of maximum burn at rate once a steady state of combustion is reached. The resulting burn time therefore, neglects the start up and tail off pressure times and the resulting burn time is slightly shorter than an actual motor burn time.
• Performance output is theoretical maximum. Since there are some losses, such as heat loss to the casing and nozzle expansion loss, you should probably adjust performance output to somewhere between .93 and .95 of reported. Most burn sim software has a nozzle loss input function, I debated adding one here as well. But if the user understands actual performance will be somewhat less, that function didn't seem necessary. While it may have led to more confusion had it been put in place.
• KNSB is not a propellant I've used. The a and n numbers I used with the radio check box were numbers I calculated from other peoples test burns in the 400 to 600 psi chamber pressure range. KNSB is reported to not follow the standard burn rate equation throughout the full pressure range. So be careful calculating burns outside the pressure range indicated. It's always best to gather your own a and n values, and use the numbers in simulations of similar pressure ranges.
• KNER is a little tricky too. KNER won't sustain good combustion at Kn's under 400, and I haven't tested it at Kn ranges much above 500. Try to keep KNER in the mid 400's Kn range. KNER also doesn't scale down well in small motors, a long "I" class is about the smallest practical KNER motor I've tested. KNER really shines in "M" class and larger motors.

Now that you understand all that, what I can say is I've tested the output of the software against my actual motor test numbers, and found it to be as accurate as any software I've used. I hope you find it easy to use and helpful.