Interactive Rocket Launch Simulation

About this experiment

To stay in orbit a spacecraft must fly sideways at almost 8 km/s, fast enough that it falls around the Earth instead of back onto it. Getting there is the hard part. The rocket has to lift its own fuel, push through the thick lower atmosphere, and turn from going straight up to going sideways at the right moment. Change the thrust, fuel, exhaust speed and turning height, launch, and see whether your rocket reaches orbit, falls back, or escapes.

Learning goals

Explain why a rocket needs a thrust bigger than its weight to lift off
Use the rocket equation to find the ideal change of speed from the exhaust speed and mass ratio
Explain gravity losses and drag losses and why the real speed gained is less than the ideal Δv
Explain why orbit needs a high horizontal speed rather than a great height
Describe why rockets turn gradually from vertical to horizontal flight

How to use it

1Launch with the default settings. Read the orbit and the fuel left. How fast is the rocket going when the engine stops?
2Lower the thrust until the rocket cannot leave the pad. Compare the thrust with the weight at launch.
3Reset, then reduce the exhaust speed to 3.5 km/s. Why does the rocket no longer reach orbit, even though nothing else has changed?
4Reset, then increase the empty mass to 15 t. How does the ideal Δv change?
5Try flying level at 60 km and at 300 km. Which losses grow in each case?
6Switch off the automatic shutdown and launch with the default settings. What happens to the orbit?

The model

Δ v = v_{e} ln \frac{m _{0}}{m _{f}}

Tsiolkovsky rocket equation: exhaust speed times the log of full mass over empty mass

\frac{T}{m g} > 1

Thrust must exceed weight for lift-off

v_{circ} = \frac{GM}{R + h}

Speed for a circular orbit at height h, about 7.8 km/s at 200 km

F_{drag} = \frac{1}{2} ρ v^{2} C_{d} A, ρ = ρ_{0} e^{- h / H}

Air drag in an atmosphere whose density halves about every 6 km (H = 8.5 km)

q = \frac{1}{2} ρ v^{2}

Dynamic pressure: the stress the air puts on the rocket, largest at max Q

Assumptions

One stage only, so the rocket must carry its whole structure to orbit. Real rockets drop empty stages to reach the same speed with less fuel.
The Earth is a sphere that does not rotate, so there is no free 0.46 km/s boost from launching eastwards near the equator.
The rocket points straight up at first, then tilts east following θ = 90° √(h / turn height), and flies level above the turn height. The engine always runs at full thrust.
Drag uses a fixed drag coefficient times area of 5 m². The orbit is judged at engine shutdown; it counts as an orbit when its lowest point is at least 100 km up.

Try this in class

Q1Why is it much harder to reach orbit than to reach a height of 200 km and fall back?
Q2Doubling the fuel does not double the Δv. Use the rocket equation to explain why.
Q3Why do rockets launch vertically at first instead of flying sideways straight away?
Q4A rocket with very high thrust accelerates quickly. Why can that increase drag losses even though it reduces gravity losses?
Q5Why do real launch sites tend to be close to the equator and launch towards the east?

Frequently asked questions

Why is there no gravity in orbit?

There is. At 200 km, gravity is still about 94 % as strong as on the ground. Astronauts feel weightless because they and their spacecraft are falling together all the time; they just move sideways so fast that the ground curves away beneath them.

What are gravity losses?

While the rocket climbs, part of its thrust is used just to hold it up against gravity instead of making it go faster. The longer the climb takes, the more Δv is lost this way.

Why does the rocket need more than 7.8 km/s of Δv?

Because some of the Δv goes into fighting gravity and air drag on the way up. Real launches need about 9 to 10 km/s of Δv in total to reach a low orbit.