Delta V Calculator
Calculate spacecraft velocity change using the Tsiolkovsky rocket equation
Calculate Delta-V
Engine efficiency rating (typical: 200-450s)
Calculated from Isp × g₀
Total spacecraft mass with fuel
Dry mass after fuel consumption
Delta-V Results
Propellant Mass
Delta-V (Alternative Units)
Rocket Equation: Δv = Isp × g₀ × ln(m₀/mt)
Calculation: 2942 × ln(100000/20000) = 4735 m/s
Mission Category: Interplanetary missions
Reverse Calculation
For 4735 m/s delta-v with 20,000 kg dry mass:
Common Delta-V Requirements
Example: Apollo Lunar Transfer
Mission Parameters
Engine: J-2 (Saturn V third stage)
Specific Impulse: 421 seconds
Initial Mass: 31,000 kg
Dry Mass: 11,900 kg
Calculation
ve = 421 × 9.81 = 4,127 m/s
Mass ratio = 31,000/11,900 = 2.61
Δv = 4,127 × ln(2.61)
Δv = 3,960 m/s
Propulsion Systems
Chemical Rockets
Isp: 200-450s (most common)
Nuclear Thermal
Isp: 800-1000s (high efficiency)
Ion Drives
Isp: 3000-10000s (very high)
Solid Rocket
Isp: 180-300s (simple, reliable)
Delta-V Facts
Delta-v is additive for sequential burns
Higher Isp engines need less fuel
Mass ratio grows exponentially with Δv
Staging improves overall efficiency
Oberth effect enhances delta-v efficiency
Understanding Delta-V and the Rocket Equation
What is Delta-V?
Delta-v (Δv) represents the change in velocity that a spacecraft can achieve. In space, where there's no air resistance, the concept of distance becomes less important than the velocity changes needed to reach your destination. Delta-v is the "fuel budget" for space missions.
The Tsiolkovsky Rocket Equation
Developed by Konstantin Tsiolkovsky in 1903, this fundamental equation describes how rockets work. It shows the relationship between the rocket's mass, exhaust velocity, and the velocity change it can achieve.
Mass Ratio Importance
The mass ratio (initial mass ÷ final mass) is crucial. Because it appears in a logarithm, achieving high delta-v requires exponentially more fuel. This is why multistage rockets are essential for reaching orbit.
Rocket Equation Formula
Δv = ve × ln(m₀/mt)
Δv = Isp × g₀ × ln(m₀/mt)
- Δv: Change in velocity (m/s)
- ve: Effective exhaust velocity (m/s)
- Isp: Specific impulse (seconds)
- g₀: Standard gravity (9.80665 m/s²)
- m₀: Initial mass (kg)
- mt: Final mass (kg)
- ln: Natural logarithm
Specific Impulse vs Exhaust Velocity
Specific impulse (Isp) measures engine efficiency in seconds - how long 1 kg of propellant can provide 1 kg of thrust. Exhaust velocity (ve) is the actual speed of exhaust gases. They're related by: ve = Isp × g₀
Low Earth Orbit
- • Surface to LEO: ~9,400 m/s
- • Atmospheric losses: ~1,500 m/s
- • Gravity losses: ~1,500 m/s
- • Theoretical minimum: ~7,800 m/s
- • Requires massive first stage
- • Most expensive part of journey
Interplanetary Travel
- • LEO to Moon: ~4,000 m/s
- • LEO to Mars: ~6,000 m/s
- • LEO to Jupiter: ~8,000 m/s
- • LEO to Saturn: ~9,000 m/s
- • Uses efficient transfers
- • Hohmann transfers common
Station Keeping
- • ISS: ~50 m/s per year
- • GEO satellites: ~50 m/s per year
- • James Webb: ~2-4 m/s per year
- • Lagrange points: ~30 m/s per year
- • Atmospheric drag compensation
- • Orbital decay prevention