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Hi Terry,
OK, here's a more user-friendly method for you that will give you the =
correct position of the rib anywhere along its length. (You can also =
use this method to plot out points on a template. Compute numerous =
points and connect the dots. :-)
Clamp any part of the rib against a flat surface, concave side up =
(soundboard side down). With this arrangement, let:
h =3D the height of the rib above the flat surface
r =3D radius of the rib
d =3D the distance along the rib you are measuring, with respect to the =
clamp point. For instance, if you clamp in at the middle of a 4 ft rib =
and measure at the end, d would be 2. Of course this is approximate. =
More accurately, d would be the distance from the clamp point to the =
position on the flat surface, directly underlying the measurement point. =
(Think right triangles.)
Then:
h =3D r - Sqrt ( r^2 - d^2)=20
So for a rib of 60 ft radius (720 in radius), these would be some of the =
elevations, h, as a function of distance, d, from the clamp point:
d (in)
h (in)
=20
=20
=20
1
0.001
=20
2
0.003
=20
3
0.006
=20
4
0.011
=20
5
0.017
=20
6
0.025
=20
7
0.034
=20
8
0.044
=20
9
0.056
=20
10
0.069
=20
11
0.084
=20
12
0.100
=20
13
0.117
=20
14
0.136
=20
15
0.156
=20
16
0.178
=20
17
0.201
=20
18
0.225
=20
19
0.251
=20
20
0.278
=20
21
0.306
=20
22
0.336
=20
23
0.367
=20
24
0.400
=20
25
0.434
=20
26
0.470
=20
27
0.506
=20
28
0.545
=20
29
0.584
=20
30
0.625
=20
31
0.668
=20
32
0.711
=20
33
0.757
=20
34
0.803
=20
35
0.851
=20
36
0.901
=20
37
0.951
=20
38
1.003
=20
39
1.057
=20
40
1.112
=20
41
1.168
=20
42
1.226
=20
43
1.285
=20
44
1.346
=20
45
1.408
=20
46
1.471
=20
47
1.536
=20
48
1.602
=20
49
1.669
=20
50
1.738
=20
51
1.809
=20
52
1.880
=20
53
1.953
=20
54
2.028
=20
55
2.104
=20
56
2.181
=20
57
2.260
=20
58
2.340
=20
59
2.421
=20
60
2.504
=20
61
2.589
=20
62
2.674
=20
63
2.762
=20
64
2.850
=20
65
2.940
=20
66
3.031
=20
67
3.124
=20
68
3.218
=20
69
3.314
=20
70
3.411
=20
71
3.509
=20
72
3.609
=20
Hope that helps!
Peace,
Sarah
----- Original Message -----=20
From: Farrell=20
To: Pianotech=20
Sent: Thursday, December 11, 2003 7:00 AM
Subject: Re: Rib dimensions
Lots of good methods for calculating the radius of an arc have been =
provided. But there is also the question of whether the curve is a true =
arc or some other shape (this assumes you have a specific shape as a =
target). Most of the provided methods do not address that concern - in =
fact you could have an obtuse angle with two straight sides rather than =
an arc. That's why I suggested making a number of measurements along the =
curve - offsets from a straight line.
Terry Farrell
----- Original Message -----=20
From: Absolute Piano=20
To: pianotech@ptg.org=20
Sent: Wednesday, December 10, 2003 4:40 PM
Subject: Rib dimensions
Hello,
I'm trying to apply some science to my soundboard rib making and I =
am
looking for "tables of static values for the Resisting Moment (W) =
and the
Moment of Inertia (I) for all the possible cross sections of =
sugarpine and
spruce (DIN 1052 Class I will suffice).
What is the formula for converting pounds/inch squared to kg/cm =
squared?
Given a right angle connected to the outside of an arc of a circle, =
how do
you prove the circle is 60'? (I made a jig for crowning ribs that is
adjustable and I want to calibrate it.
Thanks,
Jude Reveley, RPT
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