# Calculating real or more accurate specific impulse

This may fall a little under chemistry processes but I felt it has enough pertaining to aerospace to put it here. Basically, I'm in the process of attempting to develop a way to derive $I_{sp}$ as pertaining to rocket engines rather than rely on charted information.

Since specific impulse is essentially the exhaust gas velocity working against gravitational force,

$$I_{sp} = \frac{v_e}{g_0}$$

...it stands to reason that the ideal exhaust gas velocity equation can be substituted in here, giving something like

$$I_{sp} = \frac{\sqrt{\frac{TR}{M}\cdot\frac{2\gamma}{\gamma-1}\cdot(1-\frac{\rho_e}{\rho}^{\frac{\gamma - 1}{\gamma}})}}{g_0}$$

The obvious problem here is that this is the ideal exhaust gas velocity, so this is a sort of "perfect-universe" $I_{sp}$. Because most rocket engines use either hydrocarbon or hydrogen/oxygen propellants, water vapor is a major fraction of this exhaust. And as is usually taught early on in chemistry courses, water vapor is a textbook failure of ideal gas behaviors because of its intermolecular forces.

So my question is - is there a "real" specific impulse formula; something like the van der Waals equation for this application?

• Considering the number of variables unaccounted for in measurement of exhaust speed - imperfect flow, condensation, many more - the most accurate practical formula would be $I_{sp} = {\Delta v \over g_0}{ m_1 \over m_0}$ derived from Tsiolkovsky Equation. These values can be accurately measured and there are no hidden variables, simplifications or other dependencies in this equation.
– SF.
Sep 25, 2015 at 22:21