# Is there an easier way to calculate rocket engine Isp?

I am trying to calculate the $$I_{sp}$$ of a rocket with a thrust of 500 kN. I know that you can calculate $$I_{sp}$$ with $$I_{sp} = \dfrac{v_e}{g_0}$$. However, to calculate $$v_e$$, you need the $$I_{sp}$$: $$v_e = g_0 \cdot I_{sp}$$. How do I calculate both without having to set one value (Other than $$g_0$$)?

• With 3 items in the equation, you must know 2 to get the 3rd... Usually there will be sufficient info in the original question... Apr 15 '19 at 14:39
• Oh, so there I need to set an impulse or exhaust velocity? Apr 15 '19 at 14:48
• Do you know the mass flow rate when the rocket is producing 500 kN of thrust? Apr 15 '19 at 15:17
• Yes, it's 0.145, but I don't know the unit. I'm pretty sure its tons. Apr 15 '19 at 15:20

## 1 Answer

Easiest: from thrust.

$$T = v_e {dm\over dt}$$

Both fuel mass flow and thrust are simply, directly measurable quantities - measure the force exerted by the engine on a test stand and fuel flow rate.

That way you're getting the exhaust speed, and as result, the specific impulse.

An alternative is using the rocket equation - $$\Delta v = {I_{sp} \over g_0} \ln {m_0 \over m_f}$$ - measure rocket mass change (fuel expenditure) over time, and change in velocity, find the specific impulse.

But since $$I_{sp}$$ is directly proportional to $$v_e$$, and nothing else ($$g_0$$ is a constant), you can't change one without changing the other.