# Mass ratio of black powder motors?

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#### RGClark

##### Mathematician
Can't find much on the specs of black powder rockets made by amateurs. After a web search, I gather black powder motors have a combustion chamber pressure in the range of just 100 PSI. Correct? This would explain why they commonly use just paper or cardboard casings. But in strength to weight terms this is much weaker than using an aluminum or carbon fiber casing.

If you look at the specs of higher performance APCP motors, such as by Cesaroni, their combustion chamber pressures are in the range of 500 PSI, and their mass ratios using aluminum casings are about 2.5 to 1. Since mass ratio is (dry mass + propellant mass)/(dry mass) = 1 + (propellant mass)/(dry mass), this means their propellant to dry mass ratio is 1.5 to 1. But the required thickness of the casing walls is proportional to the chamber pressure. But if the chamber pressure with black powder propellant is 1/5th as large, that means the wall thickness can be 1/5th as much and the casing weight will be 1/5th as much. Since black powder propellant and APCP have similar densities at around 1.7 g/cc, this means the propellant to dry mass ratio for the black powder using aluminum casing will be 5*1.5 = 7.5 to 1, and the mass ratio will be 8.5 to 1.

Even more, since carbon fiber is about twice as strong per weight as aluminum, meaning the casing could weigh half as much, a carbon fiber black powder casing would get a propellant to dry mass ratio of 15 to 1, for a mass ratio of 16 to 1. These are very high mass ratios for solid rocket motors. For instance with a 90 s Isp, or about 900 m/s exhaust velocity, common for black powder motors, a bare stage with aluminum casing could get a delta-v of 900*ln(8.5) = 1,920 m/s. And with a carbon fiber casing it could get 900*ln(16) = 2,500 m/s.

But this gets really interesting when you look at the Isp possible for black powder motors with vacuum-optimized nozzles, say for upper stage use. According to rocket engine performance software such as Propep or RPA, black powder motors can get a vacuum-optimized Isp of 158 s, about 1,580 m/s exhaust velocity. Then the aluminum casing would give a delta-v of 1,580*ln(8.5) = 3,380 m/s. And the carbon-fiber casing would give a delta-v of 1,580*ln(16) = 4,380 m/s.

Now these are quite high delta-v's of the size commonly attained by orbital stages. So the conclusion is IF the combustion pressure of black powder rockets really is only 100 psi, then giving them lightweight aluminum or carbon fiber casings and vacuum-optimized nozzles means black powder motors could be used for orbital stages.

Bob Clark

I'd imagine any BP motors of sufficient mass to reach orbit would be Extremely prone to crack formation and come down with a case of the Booms.
At what stage of burn and grain geometry are you getting these "standard" chamber pressures?

*sighhhhhhhhhhhhhhh* Oh boy. This guy.

Bob's magnum opus is this blog post: https://forum.kerbalspaceprogram.co...-now-easy-page-2-solid-rockets-for-cube-sats/

Wherein he uses an online delta-V calculator to make the case that it should be easy to strap a few Cesaroni rockets together and launch something into space. He's been posting it around Reddit for months and getting torn down.

His designs consist of, at most:
1) Propellant
2) Motor casing

as can be seen in his original post above, which calculates delta-V using mass ratio assuming only a casing and propellant.

When this is brought to his attention, he seems to ignore it, and when reminded that no other company or agency has done what he suggests, his counterargument boils down to "they just don't want to/are lazy."

So maybe he'll listen to you guys.

I'd imagine any BP motors of sufficient mass to reach orbit would be Extremely prone to crack formation and come down with a case of the Booms.
At what stage of burn and grain geometry are you getting these "standard" chamber pressures?

Perhaps binders like the dextrin mentioned here can ameliorate the cracking:

Black powder rocket motor.
https://en.wikipedia.org/wiki/Black_powder_rocket_motor#Formulations

Another possible solution is to take an idea used in construction to reduce cracking in brittle materials such as concrete, the addition of strong but ductile materials such as steel bars to the concrete. For lightness you might might want to use carbon fiber instead of steel for this purpose.

But another possibility for the cause of the CATOS besides cracking for large black powder motors especially in those built by amateurs might be unexpected peaks in the chamber pressure during the burn. For instance look at this thrust curve for the Estes D11:

https://nar.org/SandT/pdf/Estes/D11.pdf

That high thrust peak near the beginning, 3 times higher than the steady state thrust, is quite likely accompanied by a high pressure peak. Then perhaps shaping the grain geometry can give a more even burn.

Bob Clark

*sighhhhhhhhhhhhhhh* Oh boy. This guy.

Bob's magnum opus is this blog post: https://forum.kerbalspaceprogram.co...-now-easy-page-2-solid-rockets-for-cube-sats/

Wherein he uses an online delta-V calculator to make the case that it should be easy to strap a few Cesaroni rockets together and launch something into space. He's been posting it around Reddit for months and getting torn down.

His designs consist of, at most:
1) Propellant
2) Motor casing

as can be seen in his original post above, which calculates delta-V using mass ratio assuming only a casing and propellant.

When this is brought to his attention, he seems to ignore it, and when reminded that no other company or agency has done what he suggests, his counterargument boils down to "they just don't want to/are lazy."

So maybe he'll listen to you guys.

The mass of the additional systems such as avionics, nose cone, etc. commonly make a small fraction of the dry mass of the rocket, and therefore subtract a small portion from the payload mass to orbit. You therefore commonly calculate what is the payload to orbit using the bare rocket, then calculate what fraction of this has to be subtracted off due to the extra systems required.

Bob Clark

Perhaps binders like the dextrin mentioned here can ameliorate the cracking:

Black powder rocket motor.
https://en.wikipedia.org/wiki/Black_powder_rocket_motor#Formulations

Another possible solution is to take an idea used in construction to reduce cracking in brittle materials such as concrete, the addition of strong but ductile materials such as steel bars to the concrete. For lightness you might might want to use carbon fiber instead of steel for this purpose.

But another possibility for the cause of the CATOS besides cracking for large black powder motors especially in those built by amateurs might be unexpected peaks in the chamber pressure during the burn. For instance look at this thrust curve for the Estes D11:

https://nar.org/SandT/pdf/Estes/D11.pdf

That high thrust peak near the beginning, 3 times higher than the steady state thrust, is quite likely accompanied by a high pressure peak. Then perhaps shaping the grain geometry can give a more even burn.

Bob Clark

The dextrin is already in tiny motors, which occasionally crack anyway.

The thrust spike is there on purpose.

CF to hold 100 PSI is so thin as to provide almost no support to fuel grains.

Milled CF as a structural additive is well characterized.

Common grain geometries are well characterized.

At risk of falling into the rabbit hole, do you have any documented empirical data from personal.experiments here? Or is this purely a thought experiment.....

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