what is downbearing?

[Stéphane Collin]

hi Don.

But then, isn't relative error much more important in small angles ?
Or do I miss something again ?

Stéphane Collin.

----- Original Message ----- 
From: "Don Gilmore" <dgilmore@kcmpi.net>
To: "Pianotech" <pianotech@ptg.org>
Sent: Friday, February 20, 2004 8:28 PM
Subject: Re: what is downbearing?


> Hi Jim:
>
> Well, it's true that the downbearing force increases as the angle
increases,
> but not exactly in a geometric fashion.  A geometric progression would
mean
> that the force increases exponentially with the angle...a process which
> continues forever as the angle increases.
>
> In our case the relation is a trigonometric one.  The biggest changes
occur
> in the smaller angle-range.  As I mentioned before, you are already
pulling
> at half the string tension by the time you get to 30 degrees.  As you
> approach 90 degrees, however, the change in downbearing levels off and
large
> changes in angle produce small changes in force on the bridge.
>
> For example, a change from 5 degrees to 10 degrees almost doubles the
> downbearing force.  In contrast, a change from 80 to 85 degrees only
> increases the force by about 1%.
>
> Take a look at a sine wave.  When it starts at zero it is very steeply
> sloped upward.  At the top of the curve (90 degrees) it levels out flat.
>
> Don A. Gilmore
> Mechanical Engineer
> Kansas City
>