what is downbearing?

[David Skolnik]

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Stephane-

What sort of errors do you suspect?

David Skolnik



At 01:02 PM 2/20/2004 +0100, you wrote:
>Hi Don.
>
>I would be interested in the maths calculating the relative errors we do=20
>when we measure downbearing with the carpet thread method and with the=20
>Lowell buble gauge method.  I have the feeling that these errors might be=
=20
>enormous.  Right ?
>
>Best regards,
>
>St=E9phane Collin
>----- Original Message -----
>From: <mailto:dgilmore@kcmpi.net>Don Gilmore
>To: <mailto:pianotech@ptg.org>Pianotech
>Sent: Thursday, February 19, 2004 11:13 PM
>Subject: Re: what is downbearing?
>
>Hi Julia:
>
>I won't purport to be an expert on the subjective qualities of=20
>downbearing, but purely from an engineering standpoint, calculating the=20
>force of downbearing is fairly simple.  I haven't been following the other=
=20
>downbearing threads, so forgive me if this information is redundant.
>
>Ideally, downbearing is proportional to the angle that the string bends=20
>downward (toward the harp) after passing over the bridge.  If you can=20
>measure this angle, the downbearing force is simply
>
>F =3D T * sin A
>
>Where F is the downbearing force, T is the string tension and A is the=20
>angle that the string dips downward.  You can see that more tension means=
=20
>more downbearing as does a greater angle.  Note also that a negative angle=
=20
>(upward) means a negative downbearing.
>
>If you don't have an accurate way to measure the angle A, you can also=20
>calculate it by measuring the length of string between the bridge and the=
=20
>next contact point (b) and how far the string has dipped down at that=20
>point (h).
>
>F =3D T * h / b
>
>Obviously, everything is fine until you realize that you need to know the=
=20
>string tension...but how?  Well, believe it or not, you can calculate the=
=20
>string tension theoretically if you know the size of the string and its=20
>musical pitch.  If I did my math right, the formula should be
>
>T =3D 0.0023 * (fLd)^2
>
>Where f is the frequency in Hertz, L is the vibrating length (agraffe to=20
>bridge) of the string, in inches, and d is the diameter of the string,=20
>also in inches.  The answer will be in pounds and the string must be=20
>steel.  The tension should come out to around 100 to 200 lbs or so.  Then=
=20
>you can use the other equation to determine the downbearing.
>
>Hope this helps.
>
>Don A. Gilmore
>Mechanical Engineer
>Kansas City
>>At 11:11 AM 2/19/2004 EST, you wrote:
>> >Greetings,
>> >
>> >           What exactly is downbearing? Does it affect the sound of the
>> >piano or is it a mechanical/ physics measurement for the playability of=
=20
>> the
>> >piano? Why is it important to measure it? Can it be calculated by a
>> >formula(e)? What does it mean?
>> >

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