If i have 4 ion thrusters(IFM Nano Thrusters), how would the rocket equation have to be done to calculate the total delta-v?
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asked Feb 20, 2020 at 0:40
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The number of thrusters doesn't matter (that will change how quickly you can execute your $\Delta v$, not the ultimate amount of change you can perform). Just take the efficiency figure from the engine (the linked page says $I_{sp}$ up to 5000s), and plug it in. You can then either take an existing mass fraction and solve for $\Delta v$, or plug in some required $\Delta v$ to find the minimum mass fraction.
Let's say that when you start using those thrusters, your ship is 65% thruster fuel by mass. That means the non-fuel fraction is 0.35, and the reciprocal is 2.857.
$$\Delta v = I_{sp}\, g_0\, \ln{\frac{m_0}{m_f}}$$ $$\Delta v = 5000\text{s} \, 9.8\text{m/s}^2\, \ln{2.857}$$ $$\Delta v = 51.4 \text{km/s}$$
Higher fuel fraction, more change for the rest of the craft.
