Using a Sine Bar to Inspect a Taper

1. Increase or decrease the size block stack until the indicator reads 0 across the top of the part.

2. Divide the final total block by five. This is for the standard 5" sine bar and will give you the sine of the included angle. The sine is the ratio of the side opposite divided by the hypotenuse.

3. Convert the sine of the angle to the actual angle by using a scientific calculator or a look up trig table. This will be the included angle of the part.

4. Use the formula    to find the Taper Per Foot of the part. Divide this value by 12 if you need the Taper Per Inch.

Example

Step 1.  .0504 this is the block height divided by 5 and is the SINE of the angle.

Step 2. Convert the sine to an angle, in this case 2º 53' 20". This is the INCLUDED angle.

Step 3. Use the formula   to find the Taper Per Foot of the actual part and see if it matches the specification in Machinery's Handbook.

Step 4. If the included angle is 2º 53' 20" then 1/2 A is 1º 26' 40" and the tangent of that angle is .0252 and is used in the formula as follows

  so, by cross multiplication  .6051 equals the TPF.  Machinery's Handbook calls for the TPF of a #3 Morse taper to be .60235 so the tape is slightly steeper than called for so a small adjustment would have to be made to bring it to specification.