Speed of sharpening surface - 10” vs 8”

[BradGE]

A question over on the Tormek Facebook group about whether an 8" CBN wheel could be used instead of a 10" one got me thinking about angular velocity.   In practice the 8" wheel would work (ie would fit) on a T7/T8, but the grinding surface would be passing the edge at a slower speed due to the smaller radius.  So all other things being equal, a 10" CBN wheel (or diamond wheel, or SG) will cut more efficiently than an 8" one because it's passing more quickly by the edge.   I was familiar with that concept, but it's been more than two decades since I looked at the relevant formulas, so I did a bit of a refresher this morning and turns out it's simpler than I thought... Angular velocity is directly proportional to radius - so the grinding surface of a 10" wheel is travelling 25% quicker past the edge than an 8"one.   That's relevant information for the person considering the 8" CBN wheel, but probably also for those considering at what point their SG is worn enough to replace...  As the diameter shrinks, more time is required to achieve the same result... 

[Ken S]

Brad,

The only time I would think it makes sense to use a new eight inch wheel instead of a ten inch wheel on a T8 would be if the particular wheel was only made in eight inch size. An example would be an eight inch Norton 3X wheel in 46 or 80 grit.
The calculation is different comparing a ten inch wheel on a T8 with an eight inch wheel on a T4. Since Surface Feet per Minute equals circumference times RPM, the 120 RPM of the T4 essentially cancels out the smaller diameter.

Ken