How to convert an inch dimension to arc minutes for precise measurement?

[SevenToFive]

How can l convert an inch dimension to arc minutes? We have a customer who requires a 3 foot diameter roll not move more than an 1/8 inch. I need to convert the 1/8 inch to arc minutes to compare to the backlash in our gearing.

Any help is greatly appreciated.

 

[russ_watters]

How can l convert an inch dimension to arc minutes? We have a customer who requires a 3 foot diameter roll not move more than an 1/8 inch. I need to convert the 1/8 inch to arc minutes to compare to the backlash in our gearing.

Any help is greatly appreciated.

1/8" is a fraction of the circumference and arc min is the associated angle.

 

[Let'sthink]

18" is radius and the angle is [1/(8*18)] rad = [{(180*60)/(8*18)}/π] arc min = 75/π = 23.87 arc min

 

[Tom.G]

I get a different answer, by a factor of π.
D =36"
Allowed Move = 1/8" = 0.125"
Circumference = π⋅D = 113.1"
Circum/Allowed Move = 113.1/0.125 = 904.8 (the fraction of a revolution req'd to move 1/8")
Allowed Rotation = 360°/904.8 = 0.3979° = 23.87 arc min

 

[Let'sthink]

I get a different answer, by a factor of π.
D =36"
Allowed Move = 1/8" = 0.125"
Circumference = π⋅D = 113.1"
Circum/Allowed Move = 113.1/0.125 = 904.8 (the fraction of a revolution req'd to move 1/8")
Allowed Rotation = 360°/904.8 = 0.3979° = 23.87 arc min

I am sorry I had committed a calculation mistake,now I also get the same answer.

 

[Baluncore]

For small angles, a quick estimate can use the navigational offset rule of “1 in 60, per degree”.
So 1/8” on a radius of 18” = 1 in ( 18 * 8 ) = 1 in 144.
Apply the 1 in 60 rule, then multiply degrees by 60, to get ( 60 * 60 / 144 ) = 25 arc min.

The 1 in 60 navigation rule comes from 1 radian ≈ 57.29578 degrees.
Mathematically we have ( 60' * 57.29578° / 144 ) = 23.8732 arc min.

 

[SevenToFive]

Thanks everyone for the replies. Greatly appreciated.