In the metalworking books, when you see a picture of a sinebar in use, the

stack used to form the angles is generally composed of gage blocks, the

accuracy of which is measured in millionths of an inch. Are gage blocks, a

moderately expensive item for the amateur, really needed? Or is it possible to

get by with a homeshop-made stack that's only accurate to a thou?

The equation for a sinebar is:

sin(A) = S/L

where:

A = desired angle

S = stack height

L = sinebar length (i.e., roller center-to-center distance)

With a little bit of differential calculus, it's possible to write the error

equation for the angle due to errors in the stack height.

dA = (1/cos(A)) * dS/L

where:

dA = the error in the angle due to an error of 'dS' in the stack height.

(For purposes of this discussion, we'll ignore the effect of any error in 'L'.)

Let's plug in some numbers...

A = 10 deg

L = 5 in

dS = 0.005 in

Then:

dA = 1.01543 * 0.005 / 5 = 1.01543E-3 rad = 0.0582 deg

or about one milliradian error. That's pretty small. Think about it this

way...If I make a one milliradian error pointing my rifle at a target 100 yards

away, I'll miss the bullseye by 3.6 in.

If I'm any kind of machinist, I should be able to machine the block I'm using

for the stack to within 0.001 in, which would reduce the error to 0.2

milliradian, or a target miss of 0.72 in at 100 yards.

The error depends on the angle for which the sinebar is set. For:

L = 5 in

ds = 0.001 in

it looks like this:

5 0.0115029

10 0.0116359

15 0.0118634

20 0.0121946

25 0.0126438

30 0.0132319

35 0.013989

40 0.0149589

45 0.0162057

50 0.0178273

55 0.0199784

60 0.0229183

65 0.0271147

70 0.0335043

75 0.0442748

80 0.0659906

85 0.131479

where the first column is the angle, A, in degrees and the second column is

the error in A, dA, in degrees.

Since a sinebar is seldom used for angles greater than 40 degrees, we can

count on an angle error of less than 0.015 deg (0.25 mrad) if we can machine

the stack block to an accuracy of one thou. Unless you're making highly

critical components, don't be afraid to machine your own blocks for setting

the sine bar.

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