What if a spacecraft traveled faster?

A rocket burns fuel. Hot gas rushes out of the bottom, and the rocket goes up!

What if the gas rushed out even faster?

When a rocket's engines fire, a blast of hot gas roars out of the bottom and the rocket climbs into the sky. Getting into orbit takes enormous speed: about 7.8 kilometers every second.

There are two obvious ways to try: carry more fuel, or make the exhaust gas shoot out faster. What happens to a rocket's top speed if its exhaust is faster? In this lab you can change a rocket's exhaust speed in a model and find out.

A rocket in space has nothing to push against, so it accelerates by throwing mass backward. How much speed it can gain, its Δv, depends on two things: the effective exhaust speed and the ratio of its full mass to its empty mass.

This lab holds the propellant fraction fixed and asks how Δv responds when the exhaust speed rises from a kerosene-like 3.0 km/s to a hydrogen-like 4.4 km/s.

Gas rushes out of the back one way. The rocket moves the other way.

The more fuel it burns, the faster it goes.

A rocket works by pushing gas backward; in return, the gas pushes the rocket forward. As it burns fuel, the rocket also gets lighter, so it speeds up more and more easily.

In the model, a single-stage rocket that is 85 percent fuel, with exhaust leaving at 3 kilometers per second (the model's setting for a kerosene engine), gains about 5.7 kilometers per second. That is fast, but only about three quarters of the speed needed to stay in orbit around Earth.

Momentum conservation for a rocket ejecting mass at relative speed v_e gives m dv = −v_e dm, which integrates to Δv = v_e ln(m₀/m_f). With 85 percent propellant the mass ratio is 1/(1 − 0.85) ≈ 6.7, and with v_e = 3.0 km/s the model gives Δv = 5.69 km/s, about 73 percent of the 7.8 km/s low-orbit speed.

The model's 'enough for orbit' test uses a typical 9.4 km/s budget, which includes losses to gravity and air on the way up.

In our pretend lab, Olly gives the rocket a faster engine.

Now the gas shoots out faster, and the rocket goes much faster too!

Switch the engine to hydrogen, with exhaust leaving at 4.4 kilometers per second, and keep the rocket 85 percent fuel. Now it gains about 8.3 kilometers per second, nearly half as much speed again. It even beats the 7.8 kilometer-per-second orbit speed, though not the model's 9.4, a round figure that also allows for climbing through air and gravity.

The faster engine also means less fuel is needed for orbit: about 88 percent of the rocket instead of about 96.

At v_e = 4.4 km/s and the same 6.7 mass ratio, the model gives Δv = 8.35 km/s, 107 percent of orbital speed but below the 9.4 km/s budget. Because Δv is linear in v_e, a 47 percent faster exhaust gives exactly 47 percent more Δv.

The propellant fraction needed for 9.4 km/s, f = 1 − e^(−Δv/v_e), falls from 95.6 to 88.2 percent. This is a model of an ideal rocket burning in empty space; real engines and launches differ.

Throwing something hard pushes you back hard.

Faster gas gives the rocket a bigger push from the same fuel.

Imagine sitting on a skateboard and throwing heavy balls backward. Each throw pushes you forward a little. Throw the balls harder and each one gives you a bigger push, even though you are throwing the same number of balls.

Rocket exhaust works the same way. Every kilogram of fuel thrown out faster gives the rocket more push, so the same amount of fuel adds more speed. But more fuel is not as helpful: the rocket has to carry that extra fuel too.

Δv grows linearly with exhaust speed but only logarithmically with mass ratio, so improving v_e is far more effective than adding propellant. NASA expresses engine efficiency as specific impulse, I_sp = v_eq / g₀; a higher I_sp means a higher effective exhaust speed.

The model's limits: an ideal single stage burning in empty space with no gravity or air, a constant exhaust speed and an animation that is not to time scale. The 9.4 km/s orbit budget is a typical round figure, not a calculation for a real rocket.

Big rockets drop their empty parts as they climb. That makes them lighter.

Then they can go faster and reach space.

Different engines give different exhaust speeds. The hydrogen-burning RS-25, which flew on the Space Shuttle, reaches about 4.4 kilometers per second in space; in the model, 3 stands for a kerosene engine. Most real launchers also drop parts on the way up, called staging (the Saturn V Moon rocket had three stages): when one part runs out of fuel, it drops away, so the rest of the rocket does not have to carry an empty tank.

In the model, a single rocket with a hydrogen engine reaches orbit speed only if it is about 88 percent fuel or more. Try 90 percent: it makes it to orbit. Try 95 percent and it even beats escape speed.

Staging resets the mass ratio for each stage, which is why most launchers discard parts on the way to orbit (NASA notes the Saturn V had three stages). A single stage that is 96 percent propellant would leave only 4 percent of its launch mass for tanks, engines and payload, and NASA's own worked example for a hydrogen-oxygen rocket finds about 90 percent of a rocket going to orbit is propellant. The RS-25 hydrogen-oxygen engine has a vacuum specific impulse of 452 s, an effective exhaust speed of about 4.4 km/s; the model's 3.0 km/s stands in for a kerosene engine.

With v_e = 4.4 km/s the model reaches 10.1 km/s at 90 percent propellant, enough for orbit, and 13.2 km/s at 95 percent, above Earth's 11.2 km/s escape speed.