Caster angles for a revolve

Greetings everyone. This is my first post! I'm happy and thankful to have a resource like this available for us technical folk. So, I am making a revolving platform (8'x8') and a revolving circular platform (6'6" diameter) that sits on top of that.

It has been a while since shop class, and I can't remember the best way to determine the angle of the fixed casters. Does anyone have a solution or equation?

Thank you all!
 
I attached casters to boards and screwed the boards in at 90 degrees from hub...double checking by measuring the distance of the ends of the boards to one another...as they should be equidistant. I then placed additional boards with casters in between those and measured them on both ends to make sure that they were equidistant from the nearby boards ala casters. I had decreased the size of the boards, and thus the amount of casters, the further I went in putting boards between so that the distance between the casters on the out side of the concentric circles where not so far apart and that the casters all didn't end up just around the hub. Because the casters where mounted on boards....they all where going the same direction on that board and thus hit the right angle anywhere on the revolve...make sure you put the casters in concentric circles so that when you bolt your revolve together the bolts can be placed to not hit a caster that would otherwise be in a random place. Admittedly I had to place an additional block/caster in between each board at the furthest edge of the revolve as it became squishy on the outside edges of the revolve. caster layout.jpg
 
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