Playing around with the hyperspace fuel equation


#1

The hyperspace fuel equation is:

fuel = k \times ( \frac{dm}{o} )^p

Where:

  • fuel is the amount of fuel consumed in tons
  • k is based on the rating of the FSD:
    • A: 0.012
    • B: 0.010
    • C: 0.008
    • D: 0.010
    • E: 0.011
  • d is the distance in light years
  • m is the mass of the ship in tons
  • o is the optimized mass rating of the FSD
  • p is based on the class of the FSD:
    • 2: 2.00
    • 3: 2.15
    • 4: 2.30
    • 5: 2.45
    • 6: 2.60
    • 7: 2.75
    • 8: 2.90

Solving for d:

\begin{align} k \times ( \frac{dm}{o} )^p & = fuel \\ (\frac{dm}{o})^p & = \frac{fuel}{k} \\ \frac{dm}{o} & = \sqrt[p]{\frac{fuel}{k}} \\ dm & = \sqrt[p]{\frac{fuel}{k}} \times o \\ d & = \frac{\sqrt[p]{\frac{fuel}{k}} \times o}{m} \end{align}

If we set fuel to be equal to the maximum fuel per jump of the FSD, then we can determine the “distance factor” for the FSD since k, p, and o are all known based on the FSD. For example, given a 5A FSD with a maximum fuel per jump of 5 tons and an optimized mass of 1,175.4 tons, the distance factor would be:

\begin{align} \sqrt[2.45]{\frac{5}{0.012}} \times 1175.4 & = \\ \sqrt[2.45]{416.\overline{6}} \times 1175.4 & = \\ 11.730 \times 1175.4 & \approx \\ & \approx 13787.442 \end{align}

Divide that value by the current mass in tons of the ship and you’ll get the max distance that the ship can jump in light years.


Ship components and what they do