Technical Issue Accuracy of Angular Dimensions

[alanc]

Hi,
    I've just come across something strange which I don't understand.

I wanted to know the angle of an 8tpi thread on a 3/4" shaft. In metric terms this is close enough to a thread pitch of 3.2mm on a 19mm shaft diameter so the thread angle can be represented by a right angle triangle with non-hypotenuse sides of 3.2mm and 19mm. Rather than calculate the angle, I initially drew the triangle on deltacad and measured the angle using the angular dimension function. I got an answer of 9.6 degrees. I then checked this using the trig formula:

Tan (angle) = 3.2/19

The answer I got was 10.6 degrees. I think this is correct but I don't understand why the angular dimension function gave me a different answer.

Has anyone got any explanation or have I made a silly mistake somewhere along the line?

Regards,
Alan

[AlwMVMO]

I got Tan (9.46) x .75 = .125 or Tan (9.56) x 19  = 3.2
If you are calculating in radians multiply the angles by pi/180 or .01745329

ArcTan(.125/.75) = 9.4623 or ArcTan(3.2/19) = 9.5601 --- (this would round up to 9.6 using .1 decimal accuracy)
If you are calculating in radians divide the answers by pi/180 or .01745329

Also when I drew it in DeltaCad I got the same answers.

Side adjacent =.75, side opposite=.125, hypotenuse=.7603,      angle=9.4623
Side adjacent=19,   side opposite=3.2,   hypotenuse=19.2676,  angle=9.5601 --- (this would round up to 9.6 using .1 decimal accuracy)

https://www.mathopenref.com/trigtangent.html

I thought most V-thread angles were about 60 degrees.

https://en.wikipedia.org/wiki/Thread_angle

[alanc]

Hi,
     I'm sorry for raising this. It turns out my calculator was set for grads rather than degrees which of course gave the wrong answer. I must be getting old!!
The thread I was looking at was an acme thread on a lathe lead screw and the angle I was after was the angle the thread makes when looking at the screw from the side. I'm looking to make a thread dial indicator and I need to know the angle to set the shaft holding the gear which will engage with the lead screw.
Thanks for the help.
Alan