What if a rocket carried less fuel?

A rocket is very tall. But most of it is just fuel!

The fuel burns and pushes the rocket up. What if the rocket carried only half as much?

A rocket on the launch pad looks huge, but most of it is tanks full of fuel. NASA explains that most of a launcher's weight is its propellant, the material its engines burn.

So why carry so much? What would happen if the rocket were only half fuel, with the other half its engines, tanks and cargo? Would it go half as fast, or would something surprising happen? In this lab you can change how much of a rocket is fuel and watch its speed.

NASA Glenn notes that for full-scale satellite launchers, the payload is only a small portion of the lift-off weight and most of the weight is propellant. The reason lies in the ideal rocket equation, Δv = v_e ln(m₀/m_f), where m₀ is the full mass and m_f the empty mass.

This lab takes a single-stage rocket with an effective exhaust speed of 3 km/s (the model's kerosene setting) and changes its propellant fraction from 85% to 50%. The question: how much of its speed gain survives, and why is the answer not simply proportional?

Our rocket is mostly fuel. It burns and burns.

As the fuel burns, the rocket gets lighter. So it speeds up more and more!

A rocket pushes hot gas out of its engines very fast. The gas shoots backward, and the rocket moves forward. As it burns fuel, the rocket gets lighter, so each push speeds it up a little more than the last.

In the model, a rocket that is 85 percent fuel, with exhaust shooting out at 3 kilometers per second, gains about 5.7 kilometers per second. That is fast, but still only about three quarters of the speed needed to stay in orbit around Earth.

With an 85% propellant fraction the mass ratio is 1/(1 − 0.85) = 6.67, and Δv = 3 × ln 6.67 = 5.69 km/s: 73% of the model's 7.8 km/s low-orbit speed, and below its 9.4 km/s round figure for reaching orbit including climbing losses.

The model burns in empty space with no gravity or air, where the rocket equation is exact. The animation is sped up; only the speeds are to scale.

Now Olly fills the rocket only halfway with fuel.

It burns for a short time. It goes much slower. It is not nearly fast enough to circle Earth.

Set the fuel to half the rocket. Now it gains only about 2.1 kilometers per second, less than half of the 5.7 it got before, and only about a quarter of orbit speed.

Here's the surprise: fuel doesn't add speed evenly. Going from half fuel to three quarters fuel adds about 2.1 kilometers per second. Going from 75 to about 87.5 percent adds another 2.1. Each step needs a smaller and smaller empty rocket. That's why, in the model, a rocket like this would need almost 96 percent fuel to reach orbit, more than the slider allows.

At 50% the mass ratio is 2 and Δv = 3 ln 2 = 2.08 km/s, 37% of the 85% case and 27% of orbital speed. The logarithm makes the gains depend on the ratio, not the difference: 50% → 75% (mass ratio 2 → 4) adds 2.08 km/s, and so does 75% → 87.5% (4 → 8) and 87.5% → 93.75% (8 → 16).

The model's fuel needed for its 9.4 km/s orbit figure is f = 1 − e^(−9.4/3) = 95.6%, above the slider's 95% maximum: at 95% the rocket reaches 8.99 km/s. With the faster hydrogen exhaust (4.4 km/s), 88.2% would do, and 89% clears it at 9.71 km/s.

The rocket has to carry its own fuel. Fuel is heavy!

The first bits of fuel have to push all the rest. So a rocket needs lots and lots of fuel.

Think of a long hike where you must carry all your water from the start. At first, every step means lugging the whole heavy load. Near the end, with most of the water gone, you move easily. A rocket's fuel is its load, and it has to carry all of it from the launch pad.

Each bit of burned fuel gives the same push, but a push moves a light rocket much more than a heavy one. Early fuel mostly pushes the rest of the fuel. That's why a rocket with less fuel loses so much speed: it misses out on those last, light, speedy pushes.

Momentum conservation gives m dv = −v_e dm, so each kilogram of propellant adds v_e·dm/m: the same exhaust impulse buys more velocity when the rocket is lighter. Integrating from m₀ to m_f gives the logarithm, and so Δv depends only on the ratio m₀/m_f.

Model limits: a single stage, a constant exhaust speed, a burn in empty space with no gravity or drag, and comparison speeds (7.8 km/s orbit, 9.4 km/s with losses, 11.2 km/s escape) that are round figures. Real launches also lose speed to gravity while the engines burn (NASA Glenn adds a −g₀·t_b term to the equation) and to air drag, which the ideal equation leaves out.

Real rockets are made of parts called stages.

When one part runs out of fuel, it drops away. Then the rocket is lighter and can go faster.

NASA uses the rocket equation to work out that an ideal rocket going to orbit is about 90 percent fuel by weight. The other 10 percent is everything else, and the cargo it carries is only about 1 percent of the rocket.

That's why most rockets are built in stages. When a stage runs out of fuel, it drops away, so the rest of the rocket doesn't have to carry empty tanks. NASA's Saturn V Moon rocket had three stages. The Space Shuttle dropped its side boosters, which were later pulled from the ocean and used again.

NASA Glenn's worked example uses a specific impulse of about 350 s for a hydrogen–oxygen engine and about 25,000 ft/s for a 200 mile orbit, giving a mass ratio of 10: about 90% of a rocket going to orbit is propellant, and the payload only about 1% of the launch weight.

NASA's staging page explains that as propellant burns, more of the remaining weight is near-empty tankage, so most launchers discard part of the vehicle to reach orbital velocity. Saturn V used serial staging with three stages; the Space Shuttle used parallel staging, and its solid boosters were retrieved from the ocean, refilled and reused. Staging restarts the mass ratio for each stage, which a single-stage model like this one cannot show.