# Rockets and human power: Science and limits

Why the rocket equation leaves only crumbs for payload

Source page: https://www.materialinsights.org/energy/e_rockets/science/

What this tab covers What physically happens in the conversion, step by step, the science behind it, and the hard limits that physics sets on how well it can ever work.

A rocket burns fuel with oxidiser it carries and expands the hot gas through a nozzle into a very fast jet. A hydrogen engine turns about three-quarters of the chemical energy into jet kinetic energy (calculated), but only about 3% of a Falcon 9's lift-off mass reaches orbit. A cyclist turns about a fifth of food energy into pedal work.

#### The conversion, step by step
**Combustion in the chamber**
Chemical (propellant: fuel plus oxidiser) → Heat in high-pressure gas · near complete; the RS-25 burns hydrogen and oxygen at 2,994 psi (about 206 bar)^[2](https://l3harris.com/sites/default/files/2024-07/l3harris-ar-rs-25-spec-sheet.pdf)**Expansion through the nozzle**
Heat → Kinetic energy of the exhaust · about 76% for the RS-25 in vacuum (calculated: 452.3 s gives 4,436 m/s, or 9.8 MJ/kg of exhaust, against about 13.0 MJ/kg of chemical energy at the 6.03:1 oxygen-to-hydrogen mixture, taking 120 MJ/kg for the hydrogen that burns)^[2](https://l3harris.com/sites/default/files/2024-07/l3harris-ar-rs-25-spec-sheet.pdf)**Whole vehicle (rocket equation)**
Chemical (all propellant) → Kinetic and potential energy of payload in orbit · roughly 10% for a reusable Falcon 9 (calculated: 17.5 t at 7.6 km/s is about 0.5 TJ, against 488 t of kerosene-oxygen at an assumed 9-10 MJ/kg, about 4.4-4.9 TJ)^[1](https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/ideal-rocket-equation)^[3](https://en.wikipedia.org/wiki/Falcon_9)**Bicycle: muscles**
Chemical (food) → Work at the pedals · about 18-22% gross efficiency in trained cyclists; rarely above 23-24%^[6](https://johk.pl/wp-content/uploads/2023/03/10078-67-2019-v67-2019-10.pdf)**Bicycle: chain drive**
Pedal work → Rear wheel work · 81% to 98.6% in lab tests; larger sprockets and higher chain tension help, lubricant hardly matters when clean^[5](https://www.sciencedaily.com/releases/1999/08/990819180058.htm)

#### The science

A rocket obeys conservation of momentum: exhaust thrown backwards pushes it forwards. The figure of merit is specific impulse (Isp), seconds of thrust per unit weight of propellant; times g0 = 9.81 m/s2 it gives exhaust speed. Hot, light exhaust gives high Isp, so hydrogen-oxygen beats kerosene-oxygen. In vacuum the nozzle gas expands further, so Isp is higher (Merlin 1D: 283 s at sea level, 312 s in vacuum). The rocket equation, delta-v = Isp x g0 x ln(full mass / empty mass), makes each extra km/s multiply the mass needed, so about 90% of a Falcon 9 is propellant.

#### Limits set by science

| Limit | Value | Why it exists | Best today |
|---|---|---|---|
| **Rocket equation (mass ratio)** | mass ratio = exp(delta-v / (Isp x g0))^[1](https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/ideal-rocket-equation)^[3](https://en.wikipedia.org/wiki/Falcon_9) | Worked numbers (calculated): for 7,620 m/s (25,000 ft/s) with NASA's example Isp of 350 s, exp(7,620 / 3,434) = 9.2, close to NASA's round 10 (90% propellant, 1% payload). At 452 s it is 5.6; at 312 s, 12. Gravity and drag losses add more, hence staging. | Falcon 9 reusable: payload about 3.2% of lift-off mass (calculated, 17.5 t of 549 t) |
| **Chemical energy ceiling on specific impulse** | about 519 s for hydrogen-oxygen at the RS-25 mixture (calculated)^[2](https://l3harris.com/sites/default/files/2024-07/l3harris-ar-rs-25-spec-sheet.pdf) | If all 13.0 MJ/kg became exhaust kinetic energy, exhaust speed would be sqrt(2 x 13.0 MJ/kg) = 5,090 m/s, or 519 s. Heat left in the exhaust, dissociation and incomplete expansion keep real engines below this. | RS-25 452.3 s in vacuum, about 87% of the ceiling (calculated) |
| **Human power** | gross efficiency rarely above about 23-24%^[6](https://johk.pl/wp-content/uploads/2023/03/10078-67-2019-v67-2019-10.pdf) | Muscles lose most food energy as heat, even in cyclists with very high aerobic capacity. | about 21-22% in trained cyclists |

#### Sources

1. [Ideal rocket equation (Beginner's Guide to Aeronautics)](https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/ideal-rocket-equation) NASA Glenn Research Center
2. [RS-25 engine specification sheet](https://l3harris.com/sites/default/files/2024-07/l3harris-ar-rs-25-spec-sheet.pdf) L3Harris (Aerojet Rocketdyne), 2024
3. [Falcon 9](https://en.wikipedia.org/wiki/Falcon_9) Wikipedia (compiling SpaceX data; figures as reported), 2026
4. [Bicycle efficiency study (Spicer et al., Johns Hopkins University news release)](https://www.sciencedaily.com/releases/1999/08/990819180058.htm) ScienceDaily, 1999
5. [Gross efficiency and the relationship with maximum oxygen uptake in young elite cyclists during the competitive season (Artetxe-Gezuraga et al.), Journal of Human Kinetics 67, 123-131](https://johk.pl/wp-content/uploads/2023/03/10078-67-2019-v67-2019-10.pdf) Journal of Human Kinetics, 2019

## Other sections

- [Summary](https://www.materialinsights.org/energy/e_rockets/index.md)
- [Overview](https://www.materialinsights.org/energy/e_rockets/overview/index.md)
- [Correlation](https://www.materialinsights.org/energy/e_rockets/correlation/index.md)
- [Value chain](https://www.materialinsights.org/energy/e_rockets/valuechain/index.md)
- [Unit economics](https://www.materialinsights.org/energy/e_rockets/economics/index.md)
- [Engineering methods](https://www.materialinsights.org/energy/e_rockets/methods/index.md)
- [Equipment and suppliers](https://www.materialinsights.org/energy/e_rockets/equipment/index.md)
- [Relationships](https://www.materialinsights.org/energy/e_rockets/links/index.md)