Burn rate.

I just hope my propellant will be close enough to the one Nakka's using. I'll probably have to do the burn rate tests myself later on, but right now I just need a figure to work with.

The burn rate for KNDX follows mainly the Saint Robert's law but deviates from it slightly. The law goes as follows:
where r0 is usually set to zero or neglected.

Nakka provides us with a table of pressure ranges in which certain pressure exponents and factors are valid:
Since we are using SI units, the table to the right is of interest. The maximum allowed chamber pressure is P0 = Pmax = 5.0600 MPa. Therefore the third row gives us the correct parameters:
So the burn rate for this propellant is:
Note that the pressure value is scaled to MPa in the expression and that it is dimensionless. This is really weird, but it works this way. It's like having a factor in front of the pressure variable r = a(cP)^n that scales it down with a value of c = 10^-6 Pa^-1. Models can be really strange sometimes.

Now when we know the burn rate, we can actually estimate the burn time and the average thrust!

We know that the thickness of the grain is 4mm, therefore the burn depth d = 2 mm before all of the propellant is consumed. The burn time is then:
This is clearly too fast! It is possible that we could even increase the pressure in order to gain more thrust since the plastic is not that exposed to the heat as it would if it would burn for as long as 1 second. Burn rate exponent is smaller than 1, the burn rate doesn't stagnate asymptotically, but it increases more slowly with higher pressure, so if the exponent isn't to high or to low, we might do that. A higher chamber pressure results in higher mass flow and a higher exhaust velocity ve.

However, in this phase of the design I'm not willing to compromise safety. The chamber might explode and it's better to address that issue later when I got a working design. Instead, I believe it is better to at least try to change the grain geometry. A burn inhibiting doping might work, but I rather have a higher burn rate if possible in order to ensure a quick pressure buildup in the beginning.

Next, I will analyse the possibility to use an inhibited cylindrical grain with an inverted conical shape at the bottom. It has a nonuniform profile axially, but the idea I have is that the burn surface should be as even as an end burner, but the inverted conical shape would increase the burn surface area. It might be prone to erosive burning due to turbulence, but I have no idea yet. That's a thing to find out during test firing.

This was a setback, but a well expected one. I should've found out earlier, but this is a learning process. At least I seem to have a working design methodology going and that's a good thing. See ya'll.

(Please read the safety guidelines before attempting anything like this on your own.)