ROV Stability Analysis: Calculating Time for System to Settle

AI Thread Summary
The discussion focuses on designing a stable ROV during operation by analyzing the dynamics of a pendulum system formed by the center of flotation (CF) and center of mass (CM). The torque equations are presented, incorporating damping effects, with uncertainty about whether angular velocity should be squared in calculations. A formula for a damped pendulum is introduced to model the system's behavior, assuming small angular variations. The user seeks to determine the damping coefficient (Gamma) from drag force calculations based on their SolidWorks model. The conversation emphasizes the need for accurate calculations to ensure the ROV's stability during flight.
andesam
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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: I am 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
 
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OK. so i have found a formula which 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?

(Please notify me if you need more information)

- Thanks
 

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