# How to calculate rocket Burn Rate?

I’m trying to calculate the burn rate of a theoretical sugar rocket (for a computer game). The equation I have is $r = aP^n$ . Where $r$ is the burn rate, $a$ is the burn rate coefficient, $n$ is the burn rate pressure exponent and $P$ is the pressure.

I am struggling to use use equation in general as I’m not sure how to get some of the values. The theoricial propellant is a mixture of sugar and $KNO_3$.

Unfortunately the Piobert-Vieille's law

$$r_b = aP^n$$

is strongly empirical. In order to get the right values for the tuning coefficients what you need to do is experiments. For example sample burning experiments in which you craft a small sample of propellant, you ignite it and then you record (for example with a high-freq camera, but there are other methods...) the flame propagation speed. Knowing the material properties and repeating the experiment at different conditions, you can plot burning rate charts that then you can fit to obtain the values for the coefficient.

For what concerns practical suggestions, for $KNO_3 + \textrm{sugar}$ propellants you can check out the Nakka's Website. In particular in the software section of his page you can find an Excel spreadsheet where you can somehow design your SRM (Solid Rocket Motor) on the base of his own experimental burning rate data.

In my experience when working in my university rocket team, sugar-based formulations are very, very, dependent on the environment in which you prepare the grains. In particular the degree of humidity was highly influencing our combustion chamber pressure and, hence, burning rate and thrust.

• Thanks for the info. The simulation is an entry for a competition and I’ve got a time limit for when I have to complete it by. It doesn’t have to be the most accurate thing in the world but it should at least be in the ballpark of reality. In the game the rocket size is fixed and the user and only dedicate on how much KNO3, and suger to add. I need a burn rate to calculate how much thrust the rocket could produce and for how long the rocket would run for. I could get an average burn rate coefficient from experimentation etc. and use that but how can I get the other values for P and n? – J A Mar 20 '18 at 12:50
• @JA Did you actually check the Excel I linked to you? Generally the pressure in combustion chamber is fixed by structural constraints. It depends on which are your needs... – DiTTiD Mar 20 '18 at 20:42
• I did take a look at the spreadsheet and it does calculate avg thrust based on the amount of propellant and rocket dimensions but does require you to input the thrust time which is a value I need to calculate based on burn rate not the user inputting it. It’s also a protected spreadsheet so I’m having trouble viewing the formulas – J A Mar 21 '18 at 8:29
• @JA the burn rate is a performance index of the propellant. The thrust burning time is retrieved based on the geometry (and amount) of the propellant in the grain. You can have furthermore regressive, neutral or progressive burning. And, moreover, the thrust over time (that is the Total Impulse) is generally a requirement (e.g. associated to the $\Delta V$ or altitude you want to achieve), hence it's reasonable to have it as an user input. – DiTTiD Mar 29 '18 at 22:51