Undergrad Centrifugal Effects During Rail Launch

[GrndCtrl2MjrTom]

TL;DR

Question about centrifugal effects on rocket during translation along a rail.

I’m writing a 3DOF sim for a rocket. I’m having a hard time visualizing centrifugal effects from the Earth's rotation on the rocket while it is moving along the rail (acceleration > 0).

I know that once it has left the rail I no longer need to account for it since it’s in the ECI frame and unconstrained with the earth. I’m just wondering how to deal with centrifugal effects during the rail launch since two of the body axes are still constrained.

I suppose I could rotate the centripetal ECEF components to the body coordinate frame and subtract out the roll component then I could rotate back to ECEF? Does this approach sound valid or am I missing something?

 

[Andrew Mason]

If the rail is aligned in the west-east direction (I assume you would be sending the rocket on a west to east path to take advantage of the Earth's rotational speed), it is easy to work out the centripetal force required to keep it on the rail: $F_c = \frac{mv^2}{R}$ where v is the total speed of the rocket relative to the inertial frame of the centre of the Earth (ie. it includes the speed due to Earth rotation).

If there is a component of the rail that is in the north-south direction other than at the equator, you would have to take into account the Coriolis effect. The Coriolis effect (or force, if you are analysing it from the non-inertial rocket reference frame) arises if the rocket is moving in a direction other than parallel to the Earth's axis of rotation. This change results from the change in the rotational speed of the Earth surface/rail. The distance to the axis of rotation changes with change in latitude.

AM

 

[GrndCtrl2MjrTom]

You are absolutely correct, thank you. I am trying to write this for any arbitrary launch azimuth and launch site, its just hard to remember everything that is acting on the rocket while on the ground haha.

 

[A.T.]

Im trying to write this for any arbitrary launch azimuth and launch site, its just hard to remember everything that is acting on the rocket while on the ground haha.

The formulas for the forces in the rotating frame is here:
https://en.wikipedia.org/wiki/Rotating_reference_frame#Newton's_second_law_in_the_two_frames