# What would the rocket equation look like for 4 ion thrusters?

If i have 4 ion thrusters(IFM Nano Thrusters), how would the rocket equation have to be done to calculate the total delta-v?

## 1 Answer

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.