I'm trying to calculate a rocket nozzle throat area, $A_t$. My propellant is KNDX. I am trying to do this according to the following equations, taken from this reference:
So, according to Richard Nakka's web page the mass flow rate is:
where $A_b$ is the burning area, $P_p$ is the propellant mass density and $r$ is the propellant burn rate $r = a \times Pc^n$. According Richard Nakka's table
I choose $a = 3.841, n = 0.688$. The heat ratio $k = 1.1308$ for KNDX and I choose chamber maximum pressure as $P_c = 850$ psi (or 5.86 MPa).
As you know $R$ constant is 8314 and $M$ is 42.39 (for KNDX). As Richard Nakka is saying chamber temperature for KNDX is 1700 i.e Tc = 1700
and the grain density Pp = 1.785 g/cm3
.
So my grain's total burning area $A_b = 55411 \textrm{ mm}^2$, because Grain's outer diameter is 76mm and core diameter 10mm.
Putting all this together I'm getting $A_t = 37209240 \textrm{ mm}^2$ which is wrong , because as Richard Nakka's calculations shows it's $1179 \textrm{ mm}^2$.
Here is Richard Nakka's official web page's file(you should download SRM_2014.1.ZIP), where he's calculating it. Nozzle calculation file
What I'm doing wrong?