In this post I consider the possibility, by modifying the physical properties of the propellant, of reducing the odds of having a KNSB solid rocket engine crack its propellant grain during operation. Cracks in solid propellant result in an increase in burning area, which creates an increase in chamber pressure, which can (and recently did) result in the bursting of the rocket motor’s casing.
Here is the burst that was the impetus for these FEA experiments:
What is KNSB propellant? In short, it is a mix of potassium nitrate, which is an oxidizer, and sorbitol, a sugar-like fuel. Read more about it on Richard Nakka’s website.
What are the physical properties that I look at modifying? The first is Young’s modulus, which is a measure of the stiffness of a material. Materials with high Young’s modulus do not flex easily. Normal KNSB has a Young’s modulus higher than that of MDF, the fake wood used to make furniture: difficult to bend, like a desk top.
The other property I consider modifying is the tensile strength of the KNSB. As described on Richard Nakka’s website, KNSB appears to have a tensile strength of around 1050psi, roughly a quarter or half that of epoxy.
In the following plots the factor of safety, or FOS, is plotted on a star-core rocket grain inside an aluminum casing. 1000 psi of gas pressure has been applied to the inside of the star, to simulate the pressure of the motor starting to burn. The plot shown is a slice through the middle of the grain, where stresses are at their lowest; this is the best case in the entire grain. If the FOS here is below 1, the grain will crack. The FOS is plotted from 0 (red) to 3 (blue); 1.5 is a minimum value that we’d like to see, 3 is much better.
This first plot is basically the same situation in the earlier case cast post; it is a reference image at the given KNSB material properties of 850ksi Young’s and 1050psi tensile. Too much yellow, red, and orange, where it would (and probably did) crack.
What happens if we drop the Young’s modulus to 70ksi, i.e. less than a tenth, making it as flexible as a plastic bottle? A significant improvement, but the outer points of the star are still weak.
What if we had a KNSB that had that modulus of 70ksi and we managed to double the strength of the material to 2000psi? A dramatic improvement! No orange left in the plot, and almost the entire grain has a FOS of greater than 3.
What’s it look like with just the increased tensile strength, and no modification to Young’s modulus? Here it is with 2000psi tensile KNSB. Not as good, but still a dramatic improvement over 1050psi KNSB.
Finally, how about that original 850ksi Young’s but a tripling of tensile strength to 3000psi? Improvement on roughly the same level as the previous best. Most of the grain has good margin.
Reducing the Young’s modulus to a tenth of its original value may require a lot of plasticizer. But tripling the tensile strength might be achievable by incorporating a relatively small proportion of fibers into the propellant.
Both plasticizers and reinforcing fibers are likely to be fuels, so the proportion of oxidizer would have to be adjusted to keep maximum performance. Depending on what was used as plasticizer, it could leave the propellant reasonably castable, whereas the fibers would likely make the molten propellant pastier and harder to cast.
On a more dogmatic level, one of the major objectives of Sugarshot to Space is to reach space with an inexpensive and low tech propellant, for which a two part plasticizer (as used in APCP motors) probably doesn’t qualify.
Either course would be an interesting science experiment, but to characterize the change well would require both physical material testing and instrumented test firing to see how the performance of the blend changes.
In the end, it may be more effective to first attempt changes to the grain geometry to reduce stresses on it during operation. Though such changes reduce the ultimate mass efficiency of the engine, they are more of an engineering problem than the “rocket science” of modifying the formulation.