# Solid Propellant Burn Rate Sensitivity

1. May 13, 2007

### good_ken

I have been flying some model rockets powered by commercially available solid propellant engines. I have been flying at an elevation of 2550 above sea level. I am headed to a competition next week and will be flying near sea level.

The air density will change approximately 5% due to the elevation change. Will this air density change affect the burn rate of the propellant the same way it would an air breathing engine (ie more thrust at sea level)?

thanks

2. May 13, 2007

### cesiumfrog

What does your intuition tell you?

3. May 13, 2007

### good_ken

My instinct tells me that the difference in atmospheric pressure won't be significant compared to the chamber pressure, which is what burn rate (thrust) depends on.

4. May 13, 2007

### Staff: Mentor

Well the chamber pressure depends on the burn rate. One is correct that atmospheric pressure is much less than atmospheric pressure.

In solid rockets the fuel and oxidizer are mixed, so oxygen in air has no effect on the combustion process. Once the chemical reaction initiates - it goes.

Rocket performance improves as atmospheric pressure decreases, which is why one will see performance numbers for sea level and low pressure or vacuum of space. Rocket motors perform better in space.

Also, drag increases as atmospheric density increases. At higher altitudes, the same rocket can fly higher (with respect to its starting point) than it would taking off at sea level.

So, at higher altitudes with lower air density, rockets have better motor performance and less drag.

5. May 13, 2007

### good_ken

That makes sense. We have calculated a 5% increase in drag by going to sea level, so that is accounted for. It was engine that we didn't have a feel for.

6. May 13, 2007

### Staff: Mentor

Do you know what the chamber pressure is for the solid rocket motor? Anyway, the differential pressure should be insignificant between 2550 ft and sea level, so drag is the biggest factor.

7. May 13, 2007

### cesiumfrog

Really? You mean, even regardless of drag due to increased air density (say, consider some bench-mounted thrust test) higher atmospheric pressure will slightly decrease performance? (If anything, I would have thought chamber pressure and reaction rate would go up..)

8. May 14, 2007

### FredGarvin

If you look at the thrust for most applications, it is degraded at lower altitudes. Mostly because at lower altitudes the backpressure on the nozzle is greater. The ideal thrust equation is

$$F = A_t P_1 \sqrt{\frac{2 \gamma^2}{\gamma-1}\left (\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{\gamma-1}}\left[1-\left(\frac{P_2}{P_1}\right)\right]^{(\frac{\gamma-1}{\gamma})} }+(P_2-P_3)A_2$$

Where
$$F$$ = Thrust
$$P_1$$ = Chamber Pressure
$$\gamma$$ = Specific Heat Ratio
$$A_t$$ = Throat Area
$$P_2$$ = Pressure at the exit plane of the nozzle
$$P_3$$ = Ambient Pressure
$$A_2$$ = Exit Area

Last edited: May 14, 2007
9. May 14, 2007