# Pendulum dynamics

1. Feb 25, 2010

### leylah

I'm trying to model a sling load under a helictoper as a simple pendulum.

As the helicopter flies forward, drag causes the mass on the pendulum to swing backwards.

If I have the maximum force (drag), the length of the pendulum, and the mass, then how do I find the maximum angle at which the pendulum is displaced with respect to the equilibrium position? I'm not too concerned with the time history of the pendulum after it has swung to the maximum angle though.

2. Feb 25, 2010

### jfy4

well, here is my stab at it, and heres the math i did so someone can correct me.

$$T$$=Tension in sling
$$\theta$$=angle
$$F_{\mbox{gravity}}$$=the force of gravity on the load

$$T\sin\theta=F_{\mbox{drag}}$$
$$T\cos\theta=F_{\mbox{gravity}}$$
Then I divide these two equations to get
$$\tan\theta=\frac{F_{\mbox{drag}}}{F_{\mbox{gravity}}}$$
then take the inverse trig function
$$\theta=\arctan\left(\frac{F_{\mbox{drag}}}{F_{\mbox{gravity}}}\right)$$

and there it is. Note that this angle is made from the vertical between the sling and the y-axis under the helicopter.

Hope this is right and helps you...

3. Feb 26, 2010

### Bob S

First, the drag force is probably both Stokes drag (low turbulence) and viscous drag (high turbulence) depending on velocity. See

http://en.wikipedia.org/wiki/Drag_(physics [Broken])

Assuming this is a "snatch" with the helicopter moving at a constant horizontal velocity v and hooking onto the mass, this can be most easily modeled in the inertial frame of the helicopter.

Bob S

Last edited by a moderator: May 4, 2017