Starship Fuel Efficiency Calculator

Estimate SpaceX Starship’s fuel efficiency based on payload mass, destination distance, and propulsion type.

Formulas Used

The fuel efficiency index is a simplified metric based on payload mass, distance, and propulsion type, expressed as a percentage score.

  1. Payload Score:

    \[ \text{PayloadScore} = \min\left(1, e^{-\frac{|\text{payload} – 100|}{50}}\right) \]

    Measures how close the payload mass is to Starship’s optimal 100 tons. Payloads between 50–150 tons score higher.

  2. Distance Score:

    \[ \text{DistanceScore} = \frac{384400}{\text{distance} + 384400} \]

    Normalizes distance relative to Earth-Moon distance (384,400 km). Shorter distances yield higher scores.

  3. Propulsion Factor:
    • Raptor Methalox: 1.0
    • Raptor Vacuum: 1.1 (higher efficiency in vacuum)
    • Hypothetical Nuclear: 1.5 (speculative high efficiency)

    Adjusts efficiency based on propulsion technology.

  4. Fuel Efficiency Index:

    \[ \text{FuelEfficiencyIndex} = (\text{PayloadScore} \times \text{DistanceScore} \times \text{PropulsionFactor} \times 100)\% \]

    Combines scores, scaled to a percentage. Higher scores indicate better fuel efficiency.

Example Calculations

Example 1: Earth to LEO (Methalox)

Inputs: Payload = 100 tons, Distance = 200 km, Propulsion = Raptor Methalox

Calculations:

  • Payload Score: \[ \min\left(1, e^{-\frac{|100 – 100|}{50}}\right) = 1 \]
  • Distance Score: \[ \frac{384400}{200 + 384400} \approx 0.999 \]
  • Propulsion Factor: 1.0
  • Fuel Efficiency Index: \[ (1 \times 0.999 \times 1.0 \times 100) \approx 99.90\% \]

Result: Fuel Efficiency Index: 99.90% (highly efficient for LEO)

Example 2: Mars Mission (Vacuum)

Inputs: Payload = 150 tons, Distance = 225000000 km, Propulsion = Raptor Vacuum

Calculations:

  • Payload Score: \[ \min\left(1, e^{-\frac{|150 – 100|}{50}}\right) \approx 0.368 \]
  • Distance Score: \[ \frac{384400}{225000000 + 384400} \approx 0.002 \]
  • Propulsion Factor: 1.1
  • Fuel Efficiency Index: \[ (0.368 \times 0.002 \times 1.1 \times 100) \approx 0.08\% \]

Result: Fuel Efficiency Index: 0.08% (low efficiency for long distances)

Example 3: Lunar Mission (Nuclear)

Inputs: Payload = 80 tons, Distance = 384400 km, Propulsion = Hypothetical Nuclear

Calculations:

  • Payload Score: \[ \min\left(1, e^{-\frac{|80 – 100|}{50}}\right) \approx 0.670 \]
  • Distance Score: \[ \frac{384400}{384400 + 384400} = 0.5 \]
  • Propulsion Factor: 1.5
  • Fuel Efficiency Index: \[ (0.670 \times 0.5 \times 1.5 \times 100) \approx 50.25\% \]

Result: Fuel Efficiency Index: 50.25% (moderate efficiency)

How to Use the Calculator

Follow these steps to estimate Starship’s fuel efficiency:

  1. Enter Payload Mass: Input the payload in metric tons (e.g., 100 for Starship’s optimal capacity).
  2. Enter Distance: Input the destination distance in kilometers (e.g., 200 for LEO, 384400 for Moon).
  3. Select Propulsion Type:
    • Raptor Methalox: Standard engines for atmospheric and orbital use.
    • Raptor Vacuum: Optimized for vacuum, slightly higher efficiency.
    • Hypothetical Nuclear: Speculative high-efficiency propulsion.
  4. Calculate: Click “Calculate Fuel Efficiency” to see the result.
  5. Interpret Result: The Fuel Efficiency Index (0–100%) indicates efficiency. Higher scores mean better fuel efficiency. If you see “Please fill in all fields,” ensure all inputs are provided.
  6. Share or Embed: Use the share buttons to post results on social media, copy the result, or get an embed code for the calculator.

Note: This is a simplified model. Actual fuel efficiency depends on factors like trajectory, gravity assists, and refueling.