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The variance in ui can be found according to eqn 4.32, using the law of propagation of
uncertainty.
u2 (U)= u2() +u2( ) 2 ( ) eqn 4.34
The partial derivatives with respect to each variable in eqn 4.33 are expressed in eqns
4.35-4.37.
=sin (P cos + sineqn 4.35
o (p, sin fl cos )eqn4.3
-= cos 2 eqn 4.36
a,8 (cosp-_, sinp)
a-- = cos 2, 1inf-- eqn 4.37
apf (cos/ p sin/)
The expression for the coefficient of friction, pt, is a function of the tribometer
reported forward sliding friction coefficient (tf') and the misalignment angles (J3 and 4k).
The uncertainty in each of those values is evaluated using the same application of the law
of propagation of uncertainty to their formulaic expressions.
4.3.3: Friction Coefficient Expansion
4.3.3.1 (: Pitch misalignment angle
The value of the inclination angle 4 is unknown and since it acts perpendicular to
the direction of sliding it cannot be solved for from the tribometer reported forward and
reverse friction coefficient values (pt', r1'). An estimate of the value of the inclination