How much water gives the highest flight?

In one line: for a bare 1 L bottle at 40 psi the model's best fill is only about a quarter (230 mL, about 22 m), but anything from about 100 to 400 mL gets within 10% of that. A full bottle does nothing, and no water at all still flies, lower. A different rocket, a 2 L bottle with a nose cone and fins, goes about 37 m in the same thrust model (section 7).

What I assumed (nothing here is measured yet)

The home launch was 10 Oct 2026, with a 1 L soda bottle. Every height here is still the model, not a measured flight. The copy this replaces, including the sim on main, treated a full bottle as 2000 mL. This one is 1 L. The page says a floor pump with a gauge, and to stop at about 40–60 psi. The pressure slider and the chart run from 10 psi to 60 psi, every 10 psi, never above. The numbers in parts 1 to 7 are for 40 psi; part 8 gives the other pressures. The chart is a bare bottle: no nose cone, no fins. Launched straight up, from a cork with no launch tube, on a still 20 °C day at sea level.

1. Pumping stores the push in the air

Water hardly squeezes at all; air does. Pumping to 40 psi on the gauge means the air inside is at 40 psi above the outside air, about 3.7 times normal air pressure in total. That squeezed air is the only thing doing the work. With no air in the bottle (full to the top) there is nothing to push, so nothing happens.

2. The water burst: how fast the water leaves

When the cork lets go, the only way out is the neck. A soda-bottle neck has an opening 21.74 mm across (the standard "PCO 1881" neck), about 3.7 cm². The squeezed air pushes the water out through it. Bernoulli's rule for a liquid says the pressure difference turns into speed: ½ × density × speed² = pressure difference. So the water leaves at about 23.6 m/s at the start (compared with the bottle).

The push on the bottle is the water thrown out each second times its speed. That works out to twice the pressure difference times the opening: about 206 newtons at the start, the weight of about 21 kg. With the best fill the whole rocket weighs 0.27 kg, so the push is about 78 times its weight. That's why it leaps.

3. Why the push fades

Every drop that leaves gives the air more room, and air with more room pushes less. It happens too fast for the air to take heat from anything (a few hundredths of a second), so it cools as it spreads, and its pressure drops faster than it would at a steady temperature. Physicists call that adiabatic: pressure × volume^1.4 stays the same. With a third of the bottle (333 mL of water), by the time the water is out the gauge would read only about 16 psi, and the air has cooled to about −24 °C. (That cooling is why you often see a puff of fog.)

4. The air puff, then the coast

If there's still squeezed air when the water is gone, it rushes out through the neck: one last, short puff. At first it leaves at the speed of sound, about 300 m/s (the neck can't pass it any faster), then slower, until the inside is back to outside pressure. With the best fill the water is out after about 0.03 s and the puff lasts about another 0.01 s. By then the bottle is only about 1.1 m up but going about 47 m/s. Everything after that is coasting: no push, just weight and air drag slowing it down. It reaches the top about 1.7 s after launch, and then falls back down.

When does it speed up hardest? Not at the start. At the start the push is biggest (about 206 N), but the bottle is heavy with water (0.27 kg), so it speeds up by about 75 g (g = the pull of gravity; 75 g means gaining speed 75 times as fast as a dropped stone). As the water leaves, the push fades (the air spreads out), but the bottle gets lighter much faster. So it speeds up harder and harder, and hardest in the last instant before the water runs out: about 300 g, from about 120 N on only about 39 g of bottle and air. Then the air puff pushes less (about 85 N at first), so the speeding-up drops to about 220 g and fades to nothing as the puff ends. From then on it only slows down, at first by about 15 g, mostly from drag. That peak at the moment the water runs out is real physics, and the picture shows it because it runs at one steady slow-motion rate. (The model's peak is sharp because it treats the last water as leaving cleanly; in a real launch the last water sprays out mixed with air, so the real peak is lower and more rounded.)

Drag matters a lot here. Drag = ½ × air density × drag coefficient × the bottle's cross-section × speed². For a bare bottle I used a drag coefficient of 0.75: a physics paper on water rockets (Gommes, 2010) gives "about 0.75" for a rocket with a round cross-section and no fins. The bottle is 84 mm wide. The empty bottle weighs so little (36 g with the air left inside) that drag equals its weight at only about 12 m/s. At the 47 m/s it starts coasting with, drag is about 16 times its weight. So it slows down fast.

5. So why is there a best amount of water?

• Too little water: the air ends up throwing mostly air. Air is so light that, for the same energy, it gives much less push. With no water at all the bottle gets a total push of about 0.8 newton-seconds; with a third of the bottle it's about 7.
• Too much water: there's little air to do the pushing, and the bottle has to lift all that water first. Above about 610 mL the air is back to outside pressure before the water is all out, and the bottle carries the rest up with it. With 900 mL it hops about 21 cm. Full to the top: nothing.
• In between, the model's best is 230 mL, about 22 m, just under a quarter of the bottle. A fifth (200 mL, the button) sits on that peak. A third of the bottle (333 mL) reaches about 21 m, 97% of the best. The nearest 100 mL step to that third is 300 mL, about 21 m. About a fifth flies well. On this light bottle a third is close, not better.

6. No water isn't nothing

You might expect air alone to do almost nothing, or to do as well as water. In the model it does neither: the empty bottle throws out only about 3 g of air in about 0.02 s, and it coasts to about 11 m, 50% of the best. That's several times less push than with water, but a very light bottle doesn't need much. The classic "air alone does almost nothing" is true for heavier rockets: the 133 g rocket with a nose cone and fins in the next section gets only about 6 m on air alone. A real empty bottle with no fins is also the one most likely to tumble, which makes drag far bigger.

7. With a nose cone and fins

A streamlined rocket slips through the air much more easily. A 2 L bottle rocket with a nose cone and fins, weighing 133 g and 106 mm wide, was measured in timed drops at a drag coefficient of 0.345 (Barrio-Perotti and colleagues, 2009), less than half the bare bottle's 0.75. That is a different bottle from the 1 L one on the chart. In the same thrust model, with that rocket's own 2 L, 106 mm and 133 g, its best fill is about a quarter (560 mL), about 37 m, and a third of its bottle gives about 37 m. It wants more water because it's heavier. That finned rocket is not a line on the chart. Cardboard fins alone, without a nose cone, would land somewhere in between; I have no measured number for that.

8. Other pressures

Same model, same bare 1 L bottle, the pressures on the chart. More pressure goes higher. The best fill shifts: about 170 mL at 10 psi, then about 230 mL from 30 psi up. A fifth (200 mL) stays on that peak the whole way.

The table and the slider stop at 60 psi, the top of the page's band.

9. Why real flights come in lower

The model is a best case: the bottle flies straight up, pointing the right way, with no leaks. Real launches lose height to all of these:

• No fins: the bottle wobbles and can turn sideways, and a sideways bottle has far more drag than even the 0.75 used here. I have no measured number for a tumbling bottle, so the model doesn't guess one.
• Leaks and early release: a cork seal leaks while you pump and usually pops before the gauge reaches 40–60 psi. Less pressure, less height (see the table).
• Not straight up, and wind: some of the push goes sideways.

The model also leaves out three things that push both ways: water vapour condensing in the cooling air (the fog), which gives back a little push; the rocket's own acceleration pressing the water toward the neck; and flow that isn't perfectly steady. A careful study (Gommes, American Journal of Physics, 2010) worked these out and found they "mostly cancel each other". He also compares with high-speed-camera measurements of a 2 L soda-bottle rocket (Kagan and colleagues, 1995): the real bottle speeds up substantially faster at the very start than this kind of model says, while its speed at the end of the push comes out about right. That comparison is what the next sentence rests on: the push itself isn't why real flights come in lower; drag on a finless bottle, wobble, tumbling, tilt and leaks are.

Where the numbers come from

• Neck opening 21.74 mm: the PCO 1881 soda-bottle neck standard (ISBT), bore "21.74 mm or nominally, 22 mm".
• Bottle 34.5 g empty and 84 mm wide: a catalog 1.0 L PET bottle with a 28 mm PCO 1881 neck (Precision Concepts, 33.8 oz billboard bottle: weight 34.5 g, diameter 3.31 in). Not a measurement of the home bottle. A heavier 50 g bottle goes a bit higher in the model, about 24 m. The 2 L sim this replaces used 42 g and 106 mm (PET Resin Association; Barrio-Perotti and colleagues, 2009).
• Drag coefficient 0.75 for the bare bottle: Gommes (American Journal of Physics, 2010), "about 0.75" for "a rocket with a circular cross section and no side wings", taken from Landau and Lifshitz's Fluid Mechanics. It's a rough textbook value, not a measurement on a soda bottle. The coefficient is the same as on the old 2 L sim. The drag force is smaller because it uses this bottle's 84 mm cross-section, not the 2 L bottle's 106 mm.
• Drag coefficient 0.345 with a nose cone and fins: Barrio-Perotti and colleagues (2009), from timed drops. They dropped it from 14 m, so the fastest they actually tested was about 15 m/s at the bottom of the drop. They give the number for speeds up to about 29 m/s, because on a general chart of drag against speed the number for a shape like this stays nearly flat over that range. That rocket is going about 34 m/s when its push ends: more than twice the speed of their drops, and a bit past even the range they give. So for the fastest part of its climb, 0.345 is a reasonable guess, not a measurement.
• Air: 1.4 for how it cools as it spreads, 287 J/(kg·K) for its gas constant (U.S. Standard Atmosphere). Water: 998 kg/m³ at 20 °C (CRC Handbook). Gravity 9.81 m/s² (standard gravity).

Model: straight-up flight; adiabatic air; Bernoulli exit speed through the neck; mass lost as water and then air leave; gravity, the air's buoyancy and drag (bare bottle, drag coefficient 0.75).