AAWSAP DIRD, Aneutronic Fusion Propulsion I, November 2010

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d. Compute the mass of fuel that must be consumed by the rocket to complete the one-way trip.

$$
\Delta V := V_{\text{midway}} \qquad \frac{\Delta V}{c} = 0.066
$$

$$
\text{mass}_{\text{ratio}} := e^{\left( \frac{c}{I_{\text{sp}}} \cdot \text{atanh}\left( \frac{\Delta V}{c} \right) \right)} \qquad \text{mass}_{\text{ratio}} = 1.741
$$

$$
m_{\text{final}} := \frac{m_{\text{rocket}}}{\text{mass}_{\text{ratio}}} \qquad m_{\text{final}} = 2.198 \times 10^5 \text{ kg}
$$

$$
\Delta m := 2 \cdot (m_{\text{rocket}} - m_{\text{final}}) \qquad \text{Mass of fuel consumed.}
$$

$$
\Delta m = 3.257 \times 10^5 \text{ kg}
$$

$$
\frac{\Delta m}{m_{\text{rocket}}} = 85.111\%
$$

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