# Homework Help: Need help combining rotation and translation

1. May 12, 2006

### SkitSystem

Hello, I'm trying to build a submersible, however for some reason the two propellers attached to opposite sides of the submersible, rotate at different velocities. I figure i might be able to use accelerometer data to help it go straight. My problem is trying to describe the curving almost spiraling motion mathematically. This is my first year of physics, and all i know is about rolling motion but i'll keep trying to derive a formula based on rolling logic, if no one can help me

2. May 13, 2006

### Gokul43201

Staff Emeritus
Given a large enough tank with still water, your submersible (unless it is a perfect sphere) will execute circular motion in the steady state (after executing a number of outward spirals).

The difference in propeller RPMs results in different forces acting on the submersible at the positions of the two propellers. This results in an unbalanced torque about the center of mass.

You can represent the force on the sub (from the props) in terms of a net force acting through the CoM and a net torque about the CoM. The net force causes a linear acceleration, and the net torque results in a rotation (more accurately, an angular acceleration). As the linear and angular velocities increase, so does the viscous drag force (and torque) from the water.

In the steady state, the linear viscous drag equals the provided force, and the net force on the CoM is zero. The submersible will hence have a terminal speed determined by the linear drag coefficient (C1). Also the rotational drag will equal the supplied torque about the CoM and the angular velocity will hence remain constant thereafter, and its value will depend on coefficient of rotational drag (C2). At any point of time, (before or after the steady state is reached), the ratio of linear to angular velocities will give you the radius of curvature.

If you want your submersible to go straight, you must either change the speed of one of your two props or adjust its position a little bit. Incidentally, how are your props driven ? Are they not both running off the same motor ?

Last edited: May 13, 2006
3. May 16, 2006

### SkitSystem

I think i've become a bit more confused. Drag requires that i know the force of the propellors, however i'm not sure if i can attain that value. Also when your talking about viscous drag your referring to F=-bv right? Also as i said before i have an accelorometer, and we are currently trying to build a velocity meter using Bernoulli's equation, however I'm not at all sure how i can obtain angular velocity.

Also i know this is very simplistic but i have tried to derive an answer using what little physics i have mastered. I figured after a while that at the terminal velocity the sub will move in a perfect circle. However i believe we might be able to get this value using r=v^2/radial acceleration. Am i wrong in thinking this? also could i use the accelerometer on the same axis of the propellors to measure this radial acceleration? Or would that be another value entirely?

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