齐奥尔科夫斯基方程计算器
使用此齐奥尔科夫斯基方程计算器快速获得准确的计算结果。
Required Mass Ratio (m0/mf)
22.9504
Required Mass Ratio (m0/mf) vs Required Delta-V
公式
## Tsiolkovsky Equation: Mass Ratio Form Given a target delta-v and an engine's exhaust velocity, this tells you how massive the rocket must be at launch relative to its dry mass. ### Formula **m0/mf = exp(dv / ve)** The fuel fraction is 1 - 1/(m0/mf). For orbital velocity (9.4 km/s) with a 3 km/s exhaust, over 95% of the rocket must be propellant.
计算示例
Reach LEO (dv = 9400 m/s) with ve = 3000 m/s.
- 01m0/mf = exp(dv / ve)
- 02m0/mf = exp(9400 / 3000)
- 03m0/mf = exp(3.133) = 22.94
- 04Fuel fraction = 1 - 1/22.94 = 0.9564 = 95.64%
常见问题
What limits the mass ratio in practice?
Structural mass. Tanks, engines, and the payload set a floor for the dry mass. Typical first stages achieve mass ratios of about 8 to 12.
How does exhaust velocity affect the mass ratio?
Higher exhaust velocity dramatically reduces the required mass ratio. Doubling ve halves the exponent, which can reduce the mass ratio by orders of magnitude.
What is a typical exhaust velocity?
Chemical rockets: 2500 to 4500 m/s. Ion engines: 30 000 to 70 000 m/s, but with very low thrust.