Rocket Equation Simulator
Classroom worksheet · Interactive simulation: https://lkforge.com/tools/physics/rocket/
Name: Date:
Learning objectives
- Apply the Tsiolkovsky rocket equation.
- Relate delta-v to mass ratio and exhaust velocity.
- Explain why staging helps.
Variables to change
- Exhaust velocity / specific impulse
- Propellant mass
- Payload mass
Procedure
- Set a mass ratio and exhaust velocity and read the achievable delta-v.
- Increase the propellant fraction and observe delta-v rise.
- Increase exhaust velocity and observe the effect.
Observations
Record delta-v as you vary the mass ratio and exhaust velocity.
Questions
- Write the Tsiolkovsky rocket equation.
- Why is the relationship logarithmic in mass ratio?
- What is specific impulse?
- Why do rockets use multiple stages?
- How do you increase delta-v?
Answer key (instructors)
- 1. Δv = v_e · ln(m₀/m_f) = I_sp·g·ln(m₀/m_f).
- 2. As propellant burns, the remaining rocket also has to be accelerated, giving diminishing returns.
- 3. A measure of exhaust efficiency — effectively exhaust velocity divided by g; higher I_sp gives more delta-v per propellant.
- 4. Dropping empty tanks reduces the mass that must be accelerated, boosting the overall delta-v.
- 5. Increase exhaust velocity (I_sp) or the propellant-to-total mass ratio.
The Tsiolkovsky equation Δv = v_e·ln(m₀/m_f) ties a rocket’s velocity change to its exhaust velocity and mass ratio. The logarithm means propellant gives diminishing returns, so high specific impulse and staging (shedding dead mass) are key to reaching orbit.