Sine bar errors

[mklotz]

The equation for the angle error resulting from an error in the sine bar length, i.e. distance between roll center-lines, is:

dA = -(S/cos(A)) * (dL/L^2)

If we substitute the sine bar relation, S = L * sin(A), into this we obtain:

dA = -tan(A) * (dL/L)

Using

A = 10 deg
L = 5 in
dL = 0.005 in

we have:

dA = -tan(10) * 0.005/5 = 0.000176 rad = 0.01 deg

An error of 0.005 in 5 inches is a rather big error in this application and, as you can see from the above, causes a relatively tiny error in the angle.

If you have access to a precision angle plate, you can calibrate the value of 'L' for your sine bar. Mount the angle bar on the sine bar in such a way that placing a stack under the sine bar will bring the angle plate horizontal. (In effect, you're using the sine bar to "cancel out" the angle of the precision plate.) Once this is achieved, measure the stack height, 'S'. Then the value of 'L' for your sine bar is:

L = S/sin(A)

where 'A' is the angle of the precision angle plate.