Azimuth Pointing Errors

The effect upon azimuth of the 102m shims is expected to be

daz = ROLL * sin(el) + YAW * cos(el)

with a convention for the signs of ROLL and YAW :

daz = + 1.30 * sin(el) - 3.05 * cos(el) for wheel 1
daz = + 1.30 * sin(el) + 3.05 * cos(el) for wheel 2
daz = - 1.30 * sin(el) - 3.05 * cos(el) for wheel 3
daz = - 1.30 * sin(el) + 3.05 * cos(el) for wheel 4

These formulae yield expected values that may be compared with the 6 measures tabulated above (sect 5.3.3). The difference is -0.06 + 0.41, which appears to validate the formulation.

Alternately these equations might be written

daz = f * ( +- 1.30 * sin(el) +- 3.05 * cos(el))

if there are scaling factors f for each wheel. However, the formal solution (f = 0.32 + 0.45, f = 0.88, f = 0.88, f = 1.5 + 1.7) appears useful only for wheels 2 & 3, and the further assumption of a global value of f yields 0.90 + 0.94, similarly unconstrained by the poor elevation coverage of our data.

If there are factors affecting ROLL and YAW separately, ie

daz = +- 1.30 * fR * sin(el) +- 3.05 * fY * cos(el))

where fR and fY are the efficiencies with which tilts in the A-frame are transmitted to ROLL and YAW, we may determine fR & fY by solving the 6 equations simultaneously.

    
    wheel 1 :   1.30 * fR * sin(62.3) - 3.05 * fY * cos(62.3) =  0.00
    wheel 2 :   1.30 * fR * sin(53)   + 3.05 * fY * cos(53)   =  2.53
    wheel 3 :  -1.30 * fR * sin(63.5) - 3.05 * fY * cos(63.5) = -2.22
    wheel 4 :  -1.30 * fR * sin(49.4) + 3.05 * fY * cos(49.4) =  0.30
    wheel 4 :  -1.30 * fR * sin(68.4) + 3.05 * fY * cos(68.4) = -0.24
    wheel 1 :   1.30 * fR * sin(55)   - 3.05 * fY * cos(55)   = -0.44

. . . give (fR, fY) = (1.00,0.78), with a s.e. of 0.16.

NB: It is problematic to assign any A-frame tilt to one wheel rather than the other. This is of no consequence for del, but clearly impacts the expected value of daz.