# Calculating the projectile of rocket using RCS to tilt the flight path

If I have main solid rocket with 800 N Thrust, 9 kg in total and has RCS thrusters 0.5 m from the center mass. Mid flight the RCS with 1 N force is activated for 2 sec. How does it affect the flight path? How much tilt is generated in the rocket projectile instead of going vertically up? The RCS is fired during the main rockets burn time of 3.5 secs.

Do I just take the resultant of 800N and 1 N force over 2 sec burn period of RCS? Any formulas I can use for this case. I would like to get some plots for the flight path status.

Thank you.

• Hello @J... , As a newcomer to this, I am not fully aware of the different tags. We are using a small rocket for the student rocket competition. Our main rocket engine here, has a total burn time of about 3.5 sec. By mid flight, I meant, we are thinking of using RCS to tilt the rocket before the main engine burns out and see the tilt effect on the projectile,if there is any. Looks like with just 1 N RCS thruster, the effect will have no effect as the fins will restabilize the motion. Oct 26, 2021 at 3:34

You're lacking some essential data.

If the rocket flies in the atmosphere, pretty much all bets are off, because it will have some sort of stabilization whose influence on the trajectory and disturbance to it would be very complex to calculate (and if it doesn't, all bets are off, it's unstable and will fly completely randomly, with or without the RCS.)

So (also basing on the tag "orbital maneuver") let's assume this happens in vacuum and microgravity. Also, let's assume a magical motor that provides thrust over indefinitely long time, without affecting the mass of the rocket, because of the mess that would introduce - and while in realistic scenario "mid-flight" with "solid rocket" would be long, long after flame-out of the motor, we have way too little data about things like the burn duration to make any assumptions about the flight parameters up to that point.

The off-center RCS will add a minuscule perpendicular velocity component which I'm going to ignore (completely drowned out by what follows) and a lateral spin component (a set pitch rate) to the body of the rocket. The amount is at this point indeterminate as we don't have the mass distribution to find the moment of inertia, but if you obtain this information, you can calculate the trajectory - first find the angular velocity of the (inert, main engine off) rocket after such a pulse, then pick a convenient frame of reference - non-spinning, but with rocket's linear velocity zero at the moment of the RCS burn. Calculate the trajectory of the accelerating rocket as it spins at constant angular speed in that frame of reference - the trajectory will be some sort of spiral, as the linear velocity grows while angular velocity remains constant. Finally add the motion of the frame of reference (rocket's speed vector just before the RCS burn) which will stretch the spiral in the direction of motion.

The trajectory will look roughly like this:

• about "let's assume this happens in vacuum"... The OP mentions a 9kg, 800N thrust rocket. Unless its being launched in a vacuum chamber, air will most certainly be a factor Oct 25, 2021 at 14:43
• @PcMan or it's a final stage instead. Regardless, if we take aerodynamics into account, this can result in pretty much anything, from a momentary disturbance with no lasting effect, through a successful gravity turn all the way to hard lithobraking.
– SF.
Oct 25, 2021 at 15:09

You could just calculate the moment of inertia of the rocket, apply the thrust, and calculate the rate to rotation that results.

Easier still:
Load your rocket with fuel amount and distribution as it will be at the time of firing the RCS, so that you have the mass and mass distribution correct.
Now hang the (inert!) rocket on a string located at its center of mass.
Fire the RCS. Visually observe the rotation given to your rocket by the RCS. This will give you an incredibly accurate image of the turning impulse delivered.

Unfortunately, for a real rocket, this is only the first step.
Your flying rocket's forward thrust is irrelevant, assuming it is acting correctly, through the Center of Mass.
But, your rocket is moving. At a high rate of speed, one hopes. The air resistance is not likely to be symmetrical, especially if you have fins on the rear of your rocket!

So you take the observed turning impulse, and you calculate the aerodynamic righting force, and you play the two off against each other. This will give you the (very much reduced) amount of turn that your RCS imparts on the moving rocket.

Unfortunately, the math required to accurately model your aerodynamics is.. scary. Supercomputer-hours type of scary.

The easiest way would be to just guesstimate it, test, and adjust as needed.

• To make matters even more interesting, many modern rockets have thrusters that can be gimbaled and hence do not necessarily act through the center of mass. Oct 25, 2021 at 11:52