Why a preset can fall short of the mission in its own name. This is ideal delta-v, with one specific impulse per stage — and a first stage is given its sea-level figure, which it keeps all the way up. Most of that burn actually happens in near-vacuum, where the same engine is about 10% better: Falcon 9's first stage is 283 s at the pad and around 311 s in vacuum, worth roughly 360 m/s on its own. Add approximate public masses and a deliberately conservative budget, and the Falcon 9 preset reads about 650 m/s below the 9,400 shown for LEO. The vehicle is fine; the single-Isp model is what is missing the difference.
The sawtooth is the whole point of staging. Thrust is roughly constant while a stage burns but its mass is falling, so acceleration climbs steadily — then drops off a cliff the moment a fresh, heavier stage lights. Without throttling, the peak at the end of a burn is what sizes the structure.
This curve is the tyranny of the rocket equation, drawn. It is not a straight line: near the left it costs very little Δv to add a tonne, and by the right-hand end the same tonne costs several times as much.
| Stage | Propellant | Dry | Isp | Thrust | Burn | T/W ign→out | Mass ratio | ε | Δv |
|---|
| Mission | Typical Δv needed | This vehicle |
|---|
Two numbers decide everything: effective exhaust velocity ve = Isp·g₀ and the mass ratio m₀/mf.
It is a logarithm, so each extra unit of mass ratio buys less Δv: why real rockets are mostly propellant, and why staging pays.
How efficiently an engine turns propellant into thrust: hydrolox about 450 s (light hydrogen, fast exhaust), solids about 250 s, ions 1,500–4,000+ but with tiny thrust.
No gravity, no air. A real ascent spends thrust fighting both, typically an extra 1.5–2 km/s beyond orbital speed.
They describe the same thing two ways: a mass ratio of 10 means 90% of that stage’s mass is propellant. The logarithm is why chasing ever-higher mass ratios pays off less and less.
A first stage fights gravity and drag near the ground, where raw thrust-to-weight matters and a bit of Isp is worth sacrificing. An upper stage burns in vacuum with no rush, so a slower, far more propellant-efficient engine (often hydrolox) pays off over the longer burn. Ion engines have superb Isp but thrust in millinewtons, nowhere near a launch vehicle’s weight: set a stage to the ion preset and watch the thrust-to-weight readout.
Required propellant grows exponentially with desired delta-v, so going a little further gets disproportionately expensive: every extra kilogram of payload needs fuel to lift it, plus a heavier structure to hold that fuel, plus fuel to lift that structure.
Every kilogram of empty tank and engine a spent stage carries must be accelerated along with the fuel still burning. Dropping it the moment it is empty means the next stage only accelerates what is left, which the logarithm rewards heavily. The animation integrates v(t) = ve·ln(m₀/m(t)) as propellant burns, which is why velocity gain visibly accelerates late in each burn: the rocket is lightest right before it runs out.
A burn at high speed, low in a gravity well, adds more kinetic energy per unit of delta-v than the same burn far away: why the escape and transfer budgets route through a low parking orbit rather than trying to escape from a standing start.
Mass flow is T/(Isp·g₀), fixing each burn time, the mass at every instant, the acceleration and thrust-to-weight: exact, and assuming nothing about the trajectory. The losses need a trajectory, and this page flies a prescribed pitch programme (vertical, then over hard, flattening to the horizon), landing in the published range: about 1.5 km/s of gravity loss and 35 kPa max-q for the Falcon 9 preset. Treat them as good estimates, not a flight plan. It flies the whole stack as one continuous ascent, so a stage that departs after coasting in a parking orbit (Saturn V to trans-lunar injection) should be read for its delta-v budget, not its altitude curve. No separated steering loss, wind, Earth-rotation benefit, transonic drag rise, or separate sea-level and vacuum Isp.
Every kilogram of empty tank and engine a spent stage carries has to be accelerated right along with the fuel that's still burning — dropping that dead structure the moment it's empty means the next stage only has to accelerate what's actually left, which the logarithm in the rocket equation rewards heavily.
Essentially how efficiently an engine converts propellant mass into thrust — a higher Isp means more delta-v from the same propellant mass. Hydrolox engines run high (~450s) because hydrogen's low molecular mass gives very high exhaust velocity; solid rockets run low (~250s) but make up for it with simplicity and enormous thrust.
Ion engines have superb Isp (1,500–4,000+ seconds) but famously low thrust — often measured in millinewtons — nowhere near enough to overcome a launch vehicle's own weight at liftoff. They're extraordinary for gradually raising an already-orbiting spacecraft's delta-v over months, not for the seconds-to-minutes, high-thrust demands of getting off a planet. Set a stage to the ion preset and watch the thrust-to-weight readout: the delta-v is superb and the vehicle never leaves the pad.
The headline number is the ideal delta-v from mass ratios alone — no gravity, no air. A real rocket spends thrust fighting gravity for the whole ascent and pushing through the atmosphere, which typically costs an extra 1.5–2 km/s beyond orbital velocity, and the commonly cited ~9.4 km/s LEO figure already has that penalty baked in. The Where the Δv goes chart splits those losses out, so the two numbers can be compared directly rather than taken on trust.
From thrust. Mass flow is T / (Isp g0), which fixes each burn time, the mass at every instant, the acceleration and the thrust-to-weight ratio — all of that is exact and assumes nothing about the trajectory. The losses need a trajectory, and a real one is steered by a guidance computer. This page flies a prescribed pitch programme instead: vertical off the pad, then over hard and flattening toward the horizon. That is robust for any vehicle you can dial in, and it lands in the published range — about 1.5 km/s of gravity loss and 35 kPa of max-q for the Falcon 9 preset. Treat the loss figures as good estimates, not as a flight plan.
It flies the whole stack as one continuous ascent. A vehicle whose upper stage departs after coasting in a parking orbit — Saturn V to trans-lunar injection is exactly that — does not fly this way, so read its delta-v budget and ignore its altitude curve. There is no steering loss separated out, no wind, no benefit from Earth's rotation, one drag coefficient with no transonic rise, and one Isp per stage rather than separate sea-level and vacuum figures.
Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.