Model Rocket Rail Exit Velocity Calculator

The rail is the only part of the flight where the rocket is being pointed by something other than its own fins, and it ends after a quarter of a second. What matters is not how long the rail is but how fast the rocket is going when the last guide leaves it, because from that instant onward the fins are the only thing holding heading — and fins do nothing at all until there is air moving past them. A rocket that steps off the rail at 25 ft/s in a 9 mph crosswind has the wind coming at it 27 degrees off the nose. This works the departure speed from three numbers and then says what that crosswind does to it.

The whole rocket on the scale with the motor in it, the recovery gear packed and anything else it carries. Weigh it, do not estimate it.
The average thrust figure from the certification sheet for that exact motor. If you are flying a cluster, add the averages of the motors you expect to light.
Also off the certification sheet. Only used to say what share of the burn the rail used up.
The full length of the rail or rod as it stands, not the part the rocket uses.
Stand the rocket on the pad and measure how much rail sits above the aft rail button or lug. That much travel does nothing for you, because the rocket is off the rail once the aft guide passes the top.
Zero is straight up. Tilting the rail takes some of the weight off the thrust axis, so the rocket accelerates very slightly harder, and it aims the flight somewhere else — which is the real reason anyone tilts it.
What the wind is doing at head height where the pad is, not the forecast for the county. Enter 0 to skip the crosswind block.
A rough allowance for buttons binding in the rail. Most people leave this at zero. It is here because a rocket that scrapes is a rocket that leaves slower, and the effect is not zero on a rod with a tight lug.
Rocket Rail Exit Velocity Calculator for Model RocketsBuildFigure

The rail is over before you have blinked

Put the defaults through it: 17.6 oz on the scale, a motor whose certification sheet says 20 N average, and a 48 in rail with 9 in of it sitting above the aft rail button. That leaves 39 in of travel. The weight is 4.89 N, so 15.11 N is left over to accelerate 0.499 kg, which is 30.3 m/s squared — a shade over three g. The rocket leaves the rail at 25.4 ft/s and it took 0.256 seconds to get there.

A quarter of a second is the whole of the guided part of the flight, and it used 16 percent of a 1.6 second burn. Everything after it is the fins.

Why the crosswind number is the useful output

At 25.4 ft/s with 9 mph of crosswind, the air arrives 27.5 degrees off the nose. That is not a small angle. It is the angle the fins have to work against from the moment they become fins, and it is the reason a rocket flown in wind leans into it rather than away from it.

The instinct is to reach for a longer rail, and the page prints exactly what that buys. To get the same rocket down to 10 degrees you need 74.9 ft/s at the top, which needs 338 in of travel — a 29 ft rail, for a rocket that fits in the back of a car. The reason is the square root: speed goes as the square root of the distance, so quadrupling the rail only doubles the speed. A 96 in rail instead of a 48 gets you to 38.0 ft/s and 19.2 degrees, which is a real improvement and nothing like a fix.

The other lever is thrust, and it is the strong one. Everything about the departure speed traces back to the net force divided by the mass, so a motor with twice the average thrust on the same airframe gets you 38.7 ft/s off the same 39 in, because the net force goes from 15.11 N to 35.11 N and the speed goes as the square root of that.

Where this arithmetic is wrong, and which way

It holds the thrust at the average and the mass at the liftoff figure. Neither holds. Most hobby motors put out considerably more than their average in the first tenth of a second and less at the end, so over the quarter second the rocket is actually on the rail, the real thrust is usually above the average. The mass is falling the whole time as well. Both errors point the same way, so the number here is the low one: an honest floor rather than a best guess.

The one term pushing the other way is friction, which is why the field exists and why it defaults to zero. A rail button running in a clean rail is close enough to frictionless that nobody bothers. A lug threaded onto a rod that is slightly bent is a different matter, and if you have ever heard a rocket scrape on the way up you have heard the thing this field is for. Nobody has a measured value for it. Put 5 percent in and see whether the departure speed moves enough to care about.

Tilt does almost nothing to the speed

Tilting the rail 10 degrees off vertical takes the weight component along the rail from 4.89 N down to 4.82 N, which lifts the acceleration by half a percent and the departure speed from 25.41 to 25.47 ft/s. That is noise. Tilt is not a lever on rail exit speed and this page will not pretend it is.

What tilt does is aim the flight, and where you may aim it is a matter for the range that owns the field. This page reports what the tilt does to the arithmetic and nothing else.

Questions people ask

What rail exit velocity should I be aiming for?

That is not a question this page will answer, because it is not a physics question — it is a rule question, and the rule belongs to the range you are flying at and to whoever certified you. What the page will give you is the actual number for your rocket, your motor and your rail, and the crosswind angle that goes with it, so that you can take a figure rather than an impression to the person who decides. If your club publishes a minimum, put your own numbers in and compare.

Why does my rail length not include the whole rail?

Because the rocket is only guided while both guides are on the rail, and it stops being guided the instant the aft one leaves the top. Whatever length of rail sits above the aft rail button when the rocket is standing on the pad is length the rocket never travels through. If that distance is 12 in out of a 48 in rail rather than 9, the usable travel drops from 39 in to 36, which is 8 percent less travel and 4 percent off the departure speed — 24.4 ft/s instead of 25.4.

Should I use average thrust or peak thrust?

The average, which is what the field asks for and what the certification sheet publishes alongside the total impulse. Using the peak would give a departure speed the rocket never reaches. Using the average gives a slightly low one, because most motors are above average early, which is exactly when the rocket is on the rail. The honest answer is that the exact figure needs the thrust curve integrated over the first quarter second, and the average gives you a floor without that work.

How do I work out the crosswind angle of attack myself?

It is the arctangent of the crosswind speed divided by the rocket speed, both in the same units. At 25.4 ft/s with 9 mph of wind, convert the wind to 13.2 ft/s, divide to get 0.520, and the arctangent is 27.5 degrees. The relationship is not linear: halving the wind roughly halves the angle at small angles, but doubling the rocket speed only takes 27.5 degrees down to 14.6, not to 13.7.

Does a cluster change how I use this?

Add the average thrust figures of the motors you expect to light and put the total in. The awkward part is the phrase you expect to light, because a cluster where one motor does not come up produces less thrust than the arithmetic says and produces it off the centreline. Run it twice, once with all of them and once with one missing, and look at what happens to both the departure speed and the crosswind angle. The cluster impulse arithmetic itself is on the motor cost per flight calculator.

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