Model Rocket Coast Altitude and Time to Apogee Calculator

Ignore drag and the arithmetic is a line long: a rocket leaving the motor at 330 ft/s coasts to 1,692 ft, because that is what the kinetic energy is worth against gravity. Put a 2.6 in tube and a 14 oz airframe into the same sum and the answer drops to 673 ft. Drag takes 60 percent of the height, and it takes it in the first second, where the speed is highest and the force goes as the square. This works the coast with drag in it, both the height and the time, and then says where the rocket actually is at the moment a given delay runs out.

From your altimeter log for this airframe and motor, or worked forward from the thrust curve. It is the one input the answer is most sensitive to.
The rocket after the propellant has gone. Weigh it loaded, weigh the spent casing later, and the difference is real rather than assumed.
The outside diameter of the main tube. Frontal area goes as the square of this, so it matters twice over.
Referenced to the body frontal area. This is the softest number on the page: it moves with nose shape, fin count, surface finish, launch lugs and speed, and nobody has a measured value without a wind tunnel or a flight log to fit against.
Optional. Fin frontal area, rail buttons, a camera pod — anything sticking into the airstream. Multiplied by the same drag coefficient. Leave at 0 to ignore it.
Falls with altitude and with heat. A hot afternoon at 5,000 ft of field elevation runs nearer 1.0 than 1.2, which is worth 10 percent of the coast height.
How high the rocket already was when the motor stopped. Added to the coast to give the peak. Enter 0 to report the coast alone.
The delay figure from the certification sheet for that exact motor, measured from the end of the thrust. Enter 0 to skip the delay block.
Model Rocket Coast Altitude Calculator with Drag LossBuildFigure

Drag takes most of it

Run the defaults. A 14 oz rocket on a 2.6 in tube leaves the motor at 330 ft/s, 300 ft up. With no drag it would coast 1,692 ft in 10.26 seconds. With a drag coefficient of 0.75 on 5.31 square inches of frontal area it coasts 673 ft in 5.64 seconds, for a peak of 973 ft. Drag has taken 1,019 ft — 60 percent of the flight that never happened.

That ratio is not a constant. It is set by how far above the drag scale speed the rocket is at burnout. For this airframe that speed is 163 ft/s, which is where the drag force equals the weight; burnout at 330 ft/s is twice that, so drag starts out four times the weight and the deceleration starts at five g rather than one.

The asymmetry nobody expects

Ten percent more speed at burnout buys 9.6 percent more coast — near enough proportional, and much worse than the 21 percent a drag-free rocket would get, because energy goes as the square of speed and drag eats the difference. Ten percent less drag area buys 5.4 percent more height. And ten percent more mass, at the same burnout speed, buys 4.9 percent more height, which reads backwards until you notice what the sentence assumes: the same burnout speed. A heavier rocket has more momentum per unit of frontal area, so it pushes through the air better once the motor is done. Getting it to that same speed is the part that costs you, and it is not on this page.

The practical reading is that the drag coefficient and the tube diameter are where the leverage is, and the drag coefficient is the number you know least about.

Where the delay block comes from

The coast has a closed-form solution rather than a simulation behind it. With quadratic drag and constant mass, the height to apogee is the drag scale speed squared over twice gravity, times the natural log of one plus the square of the burnout speed over the drag scale speed. The time is the drag scale speed over gravity, times the arctangent of the same ratio. Both are exact, which means the page can also run the clock the other way and say where the rocket is at any instant rather than only at the top.

At the defaults, apogee arrives 5.64 seconds after burnout. A delay printed as 6 seconds puts the moment 0.36 seconds past the top, by which point the rocket has fallen 2 ft and is doing 11.6 ft/s. A delay of 4 seconds puts it 1.64 seconds short, still climbing at 54.6 ft/s and 44 ft below the top. Those are numbers to take to somebody, not verdicts. Nothing on this page knows what your recovery arrangement tolerates, and the nominal delay on a certification sheet has a spread around it that this arithmetic does not model.

The honest limits

One fixed drag coefficient across the whole coast is a fiction. It is a reasonable fiction below about 500 ft/s and an increasingly poor one above it, because the coefficient starts to climb as the flow approaches sonic and can more than double through the transonic range. A page that quietly applies a subsonic figure to a supersonic coast will overstate the altitude badly, and this one will do exactly that if you let it, which is why it says so rather than refusing.

Constant air density is the other fiction, and it runs the opposite way: the air thins as the rocket climbs, so the real drag falls off and the real coast is a little longer than this says. For a 673 ft coast the effect is negligible. For a 5,000 ft one it is not.

The way out of both is calibration rather than better theory. Fly the airframe, read the altimeter, and adjust the drag coefficient here until the page reproduces what the altimeter said. The coefficient you land on is no longer a physical drag coefficient — it has absorbed the density profile, the angle of attack, the launch lug and everything else — but it will predict that rocket on that field better than any tabulated value.

Questions people ask

What drag coefficient should I use for a model rocket?

The page will not tell you, because the honest answer is that it depends on the nose, the fin count and thickness, the finish, whether there is a launch lug in the airstream, and how fast the rocket is going — and the spread across those is wider than most people assume. The 0.75 in the field is a placeholder to replace. The reliable route is backwards: fly the rocket, read the altimeter, and adjust the coefficient here until the page reproduces the reading. Then it is yours rather than a guess.

Why does a heavier rocket coast higher?

Only at the same burnout speed, which is the catch. Drag depends on the frontal area and the speed, not on the mass, so a heavier rocket carries more momentum through the same drag force and decelerates less. At the defaults, adding 10 percent to the burnout mass while holding the burnout speed adds 4.9 percent to the coast. In a real flight the extra mass also costs you burnout speed, usually more than it gains you here, which is why nobody adds ballast to go higher.

How do I get the burnout velocity to put in?

An altimeter that logs velocity gives it directly. Otherwise it comes from integrating the motor thrust curve against a mass that falls as the propellant goes, minus drag on the way up, which is a longer piece of arithmetic than this page does. If you have flown the airframe, you can also work backwards: put in the altimeter peak as the target and solve for the burnout speed that produces it at your drag coefficient.

Does this work for a supersonic flight?

Not well. The whole page rests on one drag coefficient holding constant, and a coefficient does not hold constant through the transonic range — it rises sharply and then settles at a different value. A coast starting above roughly 700 ft/s is outside what this describes, and the page will still print a confident-looking number, which is exactly the failure mode to watch for. Use it below that, or use it as a comparison between two versions of the same rocket rather than as a prediction.

Should the mass be the loaded mass or the burnout mass?

Burnout, because the coast starts after the propellant has gone. On a small motor the difference is a few percent and hardly moves the answer. On a large one it is substantial, and using the loaded mass will overstate the coast by more than the drag coefficient uncertainty does. Weigh the rocket ready to fly, weigh the spent hardware afterwards, and the difference is measured rather than assumed.

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