免费火箭速度增量计算器
使用齐奥尔科夫斯基方程计算火箭的速度增量(Δv)。
Delta-V
6,907.76 m/s
Delta-V vs Exhaust Velocity (ve)
公式
## Rocket Delta-V (Tsiolkovsky Equation) Delta-v is the total change in velocity a rocket can achieve by expelling all its propellant. ### Formula **dv = ve * ln(m0 / mf)** - *ve* = effective exhaust velocity - *m0* = initial (wet) mass - *mf* = final (dry) mass - *ln* = natural logarithm The logarithmic dependence means that most of a rocket's mass must be propellant to achieve high delta-v.
计算示例
ve = 3000 m/s, m0 = 100 000 kg, mf = 10 000 kg.
- 01dv = ve * ln(m0 / mf)
- 02mass ratio = 100000 / 10000 = 10
- 03dv = 3000 * ln(10)
- 04dv = 3000 * 2.3026 = 6907.8 m/s
常见问题
Why is the rocket equation logarithmic?
Because the rocket must accelerate its remaining fuel. The heavier you are, the less efficient each kilogram of fuel becomes, leading to diminishing returns.
What delta-v is needed to reach orbit?
Low Earth orbit requires about 9.4 km/s including gravity and drag losses. The theoretical minimum is about 7.8 km/s.
How does staging help?
Staging discards empty tanks, reducing dry mass. Each stage starts fresh with a better mass ratio, achieving more total delta-v.