Lets assume that the supported weight is the same.

First lets look at spoke loading from the hub end.

The forces on individual spokes will depend on the number sharing the load. It does not matter what the wheel diameter is. From the point of view of strength, you could halve the number of spokes provided that each spoke is twice as strong.

If we now consider the rim loading.

The spokes also have a role in stabilizing the rim. If we look at it from rim strength alone, the first order factor would appear to be spacing so if you halve the rim diameter you could halve the number of spokes (Each spoke would still have to be twice as strong though)

If we consider deflection in the spoke

Assuming that each spoke has the same stress (force / cross-section) then the strain (Deflection / length) will be proportional to length. So if you have half as many short spokes that are each twice as strong and each carries twice the load, they will stretch half as much and you won't need as much preload to prevent movement at the ends of the spokes.

Deflection of the Rim should probably also be consdered but I'm too sleepy to think that through.



The bottom line appears to be that you can use fewer spokes on a smaller wheel but if you do, they each have to be stronger.

David