Rocket Equation Calculator
Calculate delta-v using the Tsiolkovsky rocket equation for spacecraft and rocket design
Tsiolkovsky Rocket Equation
Total mass including rocket and propellant
Dry mass after propellant is consumed
Speed of exhaust gases relative to rocket
Rocket Performance Results
Formula: Δv = ve × ln(m₀/mf)
Effective Exhaust Velocity: 3.00 km/s
Performance Analysis
Historical Rocket Examples
Saturn V First Stage
Mass Ratio: 3.5
Saturn V Second Stage
Mass Ratio: 5
Saturn V Third Stage
Mass Ratio: 4.8
Space Shuttle Main Tank
Mass Ratio: 8
Falcon 9 First Stage
Mass Ratio: 3.3
Equation Components
Delta-V (Δv)
Change in velocity achieved by the rocket
Exhaust Velocity (ve)
Speed of propellant ejection relative to rocket
Mass Ratio (m₀/mf)
Ratio of initial mass to final mass
Specific Impulse (Isp)
Engine efficiency: ve = Isp × g₀
Typical Rocket Values
Chemical Rockets
Isp: 200-450s, ve: 2-4.5 km/s
Ion Drives
Isp: 3000-10000s, ve: 30-100 km/s
Solid Fuel
Isp: 180-250s, ve: 1.8-2.5 km/s
Liquid Fuel
Isp: 300-450s, ve: 3-4.5 km/s
Key Formulas
Rocket Equation
Exhaust Velocity
Mass Ratio
Propellant Fraction
Understanding the Tsiolkovsky Rocket Equation
What is the Rocket Equation?
The Tsiolkovsky rocket equation, also known as the ideal rocket equation, describes the fundamental relationship between a rocket's mass, exhaust velocity, and the velocity change it can achieve. It's the cornerstone of astronautics and rocket design.
Key Principles
- •Conservation of momentum drives rocket motion
- •Higher exhaust velocity = better performance
- •Exponential relationship between mass ratio and delta-v
- •No external forces assumed (ideal vacuum)
Applications & Limitations
Applications
- • Spacecraft mission planning
- • Rocket stage optimization
- • Propulsion system comparison
- • Orbital maneuver calculations
Limitations
- • Ignores gravity losses
- • Ignores atmospheric drag
- • Assumes constant exhaust velocity
- • Ideal vacuum conditions only
Note: Real rockets need 30-50% more delta-v than theoretical due to gravity losses, drag, and steering losses.