Rocket Equation Calculator

Tsiolkovsky Rocket Equation:

\[ \Delta v = I_{sp} \cdot g_0 \cdot \ln\left(\frac{m_0}{m_f}\right) \]

Delta-V (Δv):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Rocket Equation?

The Tsiolkovsky rocket equation, also known as the ideal rocket equation, describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself by expelling part of its mass with high velocity. It relates the delta-v (the maximum change in velocity) with the effective exhaust velocity and the initial and final mass of the rocket.

2. How Does the Calculator Work?

The calculator uses the Tsiolkovsky rocket equation:

\[ \Delta v = I_{sp} \cdot g_0 \cdot \ln\left(\frac{m_0}{m_f}\right) \]

Where:

\( \Delta v \) — Change in velocity (m/s)
\( I_{sp} \) — Specific impulse (seconds)
\( g_0 \) — Standard gravity (9.81 m/s²)
\( m_0 \) — Initial total mass including propellant (kg)
\( m_f \) — Final mass after propellant is expended (kg)
\( \ln \) — Natural logarithm function

Explanation: The equation shows that the delta-v depends on the specific impulse (engine efficiency) and the natural logarithm of the mass ratio (initial to final mass).

3. Importance of Delta-V Calculation

Details: Delta-v is crucial in mission planning as it determines what maneuvers a spacecraft can perform. It's used to calculate fuel requirements, payload capacity, and mission feasibility.

4. Using the Calculator

Tips: Enter specific impulse in seconds, initial and final mass in kilograms. All values must be positive, and initial mass must be greater than final mass.

5. Frequently Asked Questions (FAQ)

Q1: What is specific impulse?
A: Specific impulse (I_sp) measures how efficiently a rocket uses propellant. Higher values mean more efficient engines.

Q2: What are typical delta-v requirements?
A: For example: ~9,300 m/s to reach low Earth orbit, ~4,100 m/s for lunar landing, ~3,700 m/s for Mars landing.

Q3: Why is the natural logarithm used?
A: The logarithmic relationship comes from the exponential nature of mass reduction as fuel is burned.

Q4: What are limitations of this equation?
A: Assumes constant exhaust velocity, no external forces (gravity, drag), and instantaneous burns.

Q5: How does staging affect delta-v?
A: Staging (dropping empty tanks/engines) increases delta-v by reducing dry mass during flight.