Burnsim numbers fiasco – What are C*, Isp*, Isp, and Ve?

So I’ve solved the ‘crazy numbers in BurnSim’ problem that I was having. This particular problem resulted in a crazy claim of a 38mm K motor – from a 76% solids formulation. This has since been corrected.

The origin of this issue comes from the thrust equation (1):

where the left hand term in the equation represents the integral of the pressure forces (the resultant force) acting on the chamber and nozzle.

th_pbal1

According to this equation, total impulse of the motor is proportional to a term in the right hand side of the equation, Vₑ, the effective gas exit velocity of the motor. This term is directly proportional to the C* of the motor, a term for the characteristic gas velocity of the propellant when combusted at a specific pressure value with no nozzle expansion (typically 1000 psi chamber/14.7 psi ambient). The Isp* value that BurnSim uses is this C* value divided by the gravitational constant (in this case, 32.2 f/s), so gas velocity (dist/time) becomes just time, and C* becomes Isp*. Confusing, right? What makes it even more confusing is that Burnsim refers to this Isp* value as “Char. Isp” even though it is not the characterized Isp at all.

In reality, the characterized/delivered Isp should almost always be higher than the Isp*, since rocket motor nozzles should have an expansion section, increasing velocity of the gas flow, in turn increasing efficiency. This expanded gas flow velocity is Vₑ, and if divided by the gravitational constant, we get the motor’s effective delivered Isp. So C* is related to Vₑ by how much the expansion of the nozzle increases efficiency. This value is known as the thrust coefficient (Cf). In short, Vₑ > C* and Isp > Isp*.

The issue that I was having came from using a delivered Isp value for the Isp* input in BurnSim. Because the characterized/delivered Isp was around 210 seconds, the program output a new delivered Isp of 278 seconds. In reality, Isp* values should be around 150-165 seconds (or C* = 4800-5280 feet/second).

So the moral of the story is to correctly calculate your C* before trying to run BurnSim calculations on a motor. Having the wrong Isp* or C* value can lead to wildly inaccurate outputs of thrust, total impulse, and mass flux. Garbage in, garbage out.

 

 

source: http://nakka-rocketry.net/th_thrst.html

Note: this was originally published in September 2013, however I decided to edit it and republish it because I felt that it did not adequately explain the problem I was having and how I came to understand it and solve it.

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