## PSN-L Email List Message

Subject: Re: Ball Pivots
From: ChrisAtUpw@.......
Date: Sat, 23 Nov 2002 20:07:33 EST

```In a message dated 23/11/2002, rpratt@............. writes:

> In pondering this issue, it would seem to me that as 2 convex surfaces roll,
> the contact point would move in the same direction as the mass.  This would
> put the pivot off center and effectively shorten the boom.  Depending on
> the radii involved the geometry with respect to the upper pivot will also
> be affected.

Hi Randall,

The contact point will certainly shift, but the boom angle changes at
the same time. There will be some axis lying under the curved surface about
which the mass rotates.

The effects would be magnified on a small instrument because the boom angles
of
> motion for the same displacement will be larger.

If the bearing sizes are scaled with the boom length, the angles for a
given boom deflection should be the same.

In addition the small instrument is operating at a much finer angle between
the
> upper and lower pivots so again the effect will be more pronounced.
> Possibly the ball is more stable because the period is in effect lessening
> with displacement from center.

The major difference between a large instrument and a small one lies in
the period lengthening required. A 1 metre boom has a natural pendulum period
of 2 sec. To get it to give a 20 second period (1/10), you have to suspend it
at an angle to give a restoring force of g/100 -> 0.573 degrees.
A 25 cm boom has a natural pendulum period of 1 sec. To get it to give a
20 second period (1/20), you have to suspend it at an angle to give a
restoring force of g/400 -> 0.143 degrees.
The smaller boom will be more difficult to set up and will give four
times the deflection for any given ground tilt. It will also be
proportionately more sensitive to any springyness in the suspension and to
any frictional effects.

In response to Steve Hammond's problem with wire suspensions rusting,
you can buy nickel plated piano wire. This should give additional protection.
D'Addario list several ranges of strings which are widely available

Regards,

Chris Chapman
In a message dated 23/11/2002, rpratt@............. writes:

In pondering this issue, it would seem to me that as 2 convex surfaces roll, the contact point would move in the same direction as the mass.  This would put the pivot off center and effectively shorten the boom.  Depending on the radii involved the geometry with respect to the upper pivot will also be affected.

Hi Randall,

The contact point will certainly shift, but the boom angle changes at the same time. There will be some axis lying under the curved surface about which the mass rotates.

The effects would be magnified on a small instrument because the boom angles of
motion for the same displacement will be larger.

If the bearing sizes are scaled with the boom length, the angles for a given boom deflection should be the same.

In addition the small instrument is operating at a much finer angle between the
upper and lower pivots so again the effect will be more pronounced.  Possibly the ball is more stable because the period is in effect lessening with displacement from center.

The major difference between a large instrument and a small one lies in the period lengthening required. A 1 metre boom has a natural pendulum period of 2 sec. To get it to give a 20 second period (1/10), you have to suspend it at an angle to give a restoring force of g/100 -> 0.573 degrees.
A 25 cm boom has a natural pendulum period of 1 sec. To get it to give a 20 second period (1/20), you have to suspend it at an angle to give a restoring force of g/400 -> 0.143 degrees.
The smaller boom will be more difficult to set up and will give four times the deflection for any given ground tilt. It will also be proportionately more sensitive to any springyness in the suspension and to any frictional effects.

In response to Steve Hammond's problem with wire suspensions rusting, you can buy nickel plated piano wire. This should give additional protection. D'Addario list several ranges of strings which are widely available http://www.daddariostrings.com/products.asp

Regards,

Chris Chapman
```