Multistage Rocket Efficiency Chart
About This Chart
This interactive visualization demonstrates why rockets use multiple stages to reach orbit. Using the Tsiolkovsky rocket equation, it calculates the delta-v (change in velocity) achievable with different staging configurations.
The Tsiolkovsky Rocket Equation
\[\Delta v = v_e \times \ln\left(\frac{m_{initial}}{m_{final}}\right)\]
Where: - \(\Delta v\) = change in velocity (m/s) - \(v_e\) = exhaust velocity (m/s) - \(m_{initial}\) = initial mass (with fuel) - \(m_{final}\) = final mass (without fuel)
Why Staging Matters
The Problem with Single-Stage Rockets
A single-stage rocket must carry: - All the fuel for the entire journey - Empty fuel tanks (dead weight after fuel is used) - Engines sized for liftoff (oversized for upper atmosphere)
The Staging Solution
By dropping empty stages: 1. Less dead weight = better mass ratio 2. Each stage optimized for its flight phase 3. Logarithmic advantage compounds with each stage
Visual Elements
- Bar Chart: Delta-v comparison for 1-5 stages
- Rocket Diagram: Visual representation of current staging
- Reference Lines: LEO (7.8 km/s) and GTO (10.5 km/s) requirements
- Improvement Percentage: Gain over single-stage configuration
Controls
- Stage Slider: Select 1-5 stages to compare performance
Key Observations
- Dramatic improvement from 1 to 2 stages
- Diminishing returns after 3-4 stages
- Complexity cost limits practical staging
- Real rockets typically use 2-3 stages
Reference Velocities
| Destination | Required Δv |
|---|---|
| Low Earth Orbit (LEO) | ~7.8 km/s |
| Geostationary Transfer (GTO) | ~10.5 km/s |
| Moon | ~12 km/s |
| Mars | ~15+ km/s |
Real-World Examples
- Saturn V: 3 stages (Moon missions)
- Falcon 9: 2 stages (LEO/GTO)
- Electron: 2 stages (small satellites)
- SLS: 2 stages + boosters (deep space)