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Let us use the Falcon 9 engines configuration as an example. It has nine engines: eight in the outer circle and one in the centre.

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How would I calculate the net force that all of these produce on the rocket and their horizontal and vertical components, if the thrust each of the generated was not identical. Essentially I want to be able to calculate the angle and value of the net thrust when some engines are producing a larger force than the rest

It is assumed that the centre of mass is 10m directly above the centre of the 9 engines.

My best guess is to calculate the forces of each engine assuming they act through the centre of mass of the object and sum the vertical and horizontal components to find the net vertical and horizontal components, from which I can calculate the angle from using simple trig.

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    $\begingroup$ Note that if the resultant thrust is not applied through the centre of mass, the rocket will rotate at an increasing rate. If the off-centre thrust continues the rocket gradually reaches a constant velocity while continuing to accelerate rotationally. $\endgroup$ Dec 25 '16 at 23:02
  • $\begingroup$ @sammygerbil Is there a way to calculate the rotation in a given time knowing the torque? $\endgroup$
    – Ronikos
    Dec 25 '16 at 23:07
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    $\begingroup$ Yes. Torque $\tau$ = moment of inertia $I$ x angular acceleration $\alpha$. Then angle through which rocket turns is $\theta=\frac12 \alpha t^2$. (This assumes that the thrust and moment of inertia both remain constant.) $\endgroup$ Dec 25 '16 at 23:28
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To get the net thrust you add the horizontal and vertical thrusts of each engine.

But what I really think you are asking about with unequal thrust is torque, turning force on the rocket. (which is the distance from the center of mass times the perpendicular component of thrust, which you then sum up - lots more on this basic physics is easy to find)

If the thrusts are vectored (which I don't know on falcon 9, they can compensate for torque. Or it might have lateral thrusters for this purpose at another location. Or both. Another way to do it is with a gyroscope, a reaction wheel)

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