Page 38 - Rotating Machinery Pratical Solutions to Unbalance and Misalignment

Rotating Machinery: Practical Solutions

Referring to Figure 2-5 the length of the ladder is the radius,
or 20 feet, and the X distance is 10 feet. Since the cosine of an angle
is defined as X/R, it follows that:

Cos a = X/R (2.3)
In this example:
Cos a = 10/20 = .5

20 Foot
ladder
?
R

10’

Figure 2-5. Using the Sine and Cosine Functions

Using the trigonometric table in Appendix C, the angle that
has a cosine equal to .5000 is 60 degrees. Next look up the sin of
60 degrees, since the sine of an angle is defined as Y/R. The sine
of 60 degrees is found to be .866025.

Sin (a) = Y/R (2.4)

For this example:

Sin(60) = Y/R = .866025
By rearranging the equation,
Y = .866025 × 20 or Y = 17.325 feet.