• SpaceX’s Starship Super Heavy booster uses 33 Raptor engines.
• These engines burn massive amounts of fuel per second.
• We’ll explore how the variation in fuel consumption across launches can be modeled with a normal distribution.
• The Starship is the focus here.

set.seed(42)
fuel_starship <- rnorm(100, mean = 3300, sd = 150)
head(fuel_starship)
summary(fuel_starship)

## [1] 3505.644 3215.295 3354.469 3394.929 3360.640 3284.081
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2851    3207    3313    3305    3399    3643

Here we’re randomly simulating 100 fuel flow rates for the Starship rocket, and here we show 6 of the results, along with a quick summary.

This histogram shows the simulated fuel flow rates for Starship across 100 launches. The data is centered around an average assumed fuel burn rate of 3300 kg/s. The shape is roughly bell-shaped, like a normal distribution.

Boxplot shows distribution of simulated Starship fuel flow rates. Median fuel use is about 3300 kg/s, with most values between ~3200 and ~3400 kg/s. Outliers appear below 3100 kg/s, possibly under-thrust.

Similar to the previous ggplot2 Histogram. Shape again looks normal, which reinforces our model.

• The mean \(\mu = 3300\) kg/s reflects average fuel burn rate.
• The standard deviation \(\sigma = 150\) captures variability.

\[ P(3150 < X < 3450) \approx 68\% \text{ of launches} \]

Suppose we want to know the probability that Starship fuel flow is between
3200 kg/s and 3400 kg/s on a launch.

Assuming a normal distribution: \[ X \sim N(3300, 150^2) \] We can standardize:

\[ \begin{align*} P(3200 < X < 3400) &= P\left( \frac{3200 - 3300}{150} < Z < \frac{3400 - 3300}{150} \right) \\ &= P(-0.67 < Z < 0.67) \end{align*} \]

• Starship’s fuel flow is variable but centered; it varies due to many small influences.
• A normal model allows engineers to predict it; because despite the variation, it follows a predictable normal distribution.
• This statistical model can help the rocket engineers estimate performance and design safer launches.