From Experimental

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.

Rx Testing Weekend and Homemade Test Stand

This week, my dad and I built a test stand for testing Rx motors. It’s made of 3/4″ and 1/2″ EMT Conduit and a few assorted bolts and rods. It’s adjustable for motors 38mm to 75mm, at any length. It can withstand 5000N (~1100 Lbs) of downward thrusting force without bending.

IMG_0976

The test stand is based on Richard Nakka’s design. We currently don’t have any data acquisition equipment, but this test stand will be useful for static burning for the sake of reassurance.

IMG_0980

This upcoming weekend, we will be testing two motors: a 6 Grain 38mm and a 6 Grain 54mm.

The 38mm is around a 65% J670, and the 54mm is an ~8% L890. Both utilize a stepped core geometry with my favorite “Soylent Green” propellant.

 

The 54mm L

IMG_0512

 

The 38mm J1383094_10200856530711377_2056581232_n

38mm 6GXL Soylent Green

1383094_10200856530711377_2056581232_n

An extremely long case with an cool result! Burnsim classifies this as a 68% J-560

Pc_max is 820Psi, and Kn is 299-414. Peak mass flux is 1.8 with the stepped core configuration shown in the picture above, but with straight cores it peaks at 2.2! Another reason to step cores on long motors is to reduce erosive burning. Erosive burning is when  the core of the propellant grains gets eroded by the oncoming mass flux of the motor, exposing more surface area and skyrocketing the Kn and Pc. This motor uses a 28/64″ throat expanding to 0.73″.

There are 6 Grains, each 3.4″ long. The bottom two grains are stepped to 9/16 core, while the top four have a 1/2″ core.

The case is 23.25″ long, with 20.6″ total propellant length.

The propellant is “Soylent Green”, a moderate metals, 76% solids propellant. The propellant burns with a beautiful yellow-white flame. The green color comes from Chromium Oxide, a burn rate catalyst.

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UPDATE: This motor was static tested successfully on the 19th of April, 2014. http://sojourner.me/?p=242