Solid Propellant Burn Rate Sensitivity

[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

 

[cesiumfrog]

What does your intuition tell you?

 

[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.

 

[Astronuc]

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.

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.

 

[good_ken]

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.

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.

 

[Astronuc]

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.

 

[cesiumfrog]

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 [..]

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..)

 

[FredGarvin]

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..)

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

 

[Astronuc]

In addition to what FredGarvin wrote, think about -

What causes 'chamber pressure' and what controls the reaction rate.