Concerning coil size in relation to target sensitivity I've read that if the coil size is doubled (perhaps to increase depth), the sensitivity to smaller targets falls to 1/8, same as if the target size were halved.
So, it would be something like:
Sensitivity = [target diameter]^3
For instance, if the target size is cut in half the sensitivity is reduced by 1/8, that is (1/2)^3
If it is plotted, the target sensitivity grows rapidly compared to the increase in target diameter.
There is another formula (don't know where it came from) that states the best coil size for a particular target is proportional to two-thirds power of the target size.
The formula would be, K * (Target-size)^2/3 = Coil Size K is a variable correction factor for target shape, composition, orientation, and coil characteristics.
This is how this formula would plot out for constant value for K (same target)
Basically the best coil radius is about half the target size, or coil diameter is loosely correlated to target size.
In relation to depth and coil size, there is a formula that states Max Signal = Radius^3/(radius^2 + depth^2)^3
Don't know where I got the formula, but if you plot it for constant target depth, you get this...
The formula says that the max signal will increase as coil radius increases up to a point, and then the target will become small in relation to coil size and sensitivity will decrease. You can see from the plot that the maximum sensitivity to a small target is given when the coil radius = target depth (where the curve turns at 12" depth and 12" coil radius). Thus, if you were searching for a coin at 15" depth, the best coil would have a radius of 15" (diameter of 30"), beyond this coil size sensitivity would be lost.
Well, this is just speculation and playing around. Try not to take it too seriously.
Johnnyanglo