# ROV stability analysis

1. Apr 21, 2010

### andesam

Hi.

Im designing an ROV and need to know it will be stabile during "flight".

I am considering the (imaginary) line between the center of flotation, CF, and center of mass, CM, as a pendulum. Where the tourqe around CF = -mgl*sin(theta). Theta being the angle between the pendulum and the direction of g (the ground).

Alsow, the pendulum is dampend. Tourqe = (ohmega^2)*konstant. Ohmega = rad/s, konstant is calculatet using computer CAD software. (Edit: im not shure if ohmega skould be squared or not here. By definition, the damping ratio is not squared (Ff=-c*v), but for drag force, velocity is squared (Fd=K*v^2).

Now, how can i calculate the time needed for the system to settle (thetha = 0), given a initial angel and angular velocity? Anyting else i should calculate to determine system stability?

- Thanks

Last edited: Apr 21, 2010
2. May 4, 2010

### andesam

OK. so i have found a formula wich describes a damped pendulum:

I*Theta''(t)+m*g*L*Theta(t)+Gamma*L^2*Theta'(t)=0

Assuming small variations in theta (-10 - 10 degrees) and that damping force is propotional to gamma.
I being the inertia (m*L^2) and Gamma the damping coff.

Now, i am wondering if its possible to determine Gamma. From the solidworks model i can calculate a formula for drag force (with respect to the water velocity), perpendiculary on to the vessle. Is it possible to calculate Gamma from this information?