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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 $g_0$)?

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  • $\begingroup$ With 3 items in the equation, you must know 2 to get the 3rd... Usually there will be sufficient info in the original question... $\endgroup$ – Solar Mike Apr 15 at 14:39
  • $\begingroup$ Oh, so there I need to set an impulse or exhaust velocity? $\endgroup$ – 18ballz Apr 15 at 14:48
  • $\begingroup$ Do you know the mass flow rate when the rocket is producing 500 kN of thrust? $\endgroup$ – fibonatic Apr 15 at 15:17
  • $\begingroup$ Yes, it's 0.145, but I don't know the unit. I'm pretty sure its tons. $\endgroup$ – 18ballz Apr 15 at 15:20
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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.

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