Bob,
You are right in saying that the winding process determines the amount of wire that can fit. As long as the winder conforms to the "layer" winding technique, you can come quite close as follows;
Turns per layer = length/OD wire.
No of layers = radial hight/OD wire.
Total turns = Turns per layer * No layers.
Length Mean Turn = ((ID coil + OD coil)*Pi) / 2.
Length of wire = Total turns * Length Mean Turn.
Note:
1 Use the covered diameter for the wire.
2 Round answers down to iteger.
3 This is based on the assumption that the layers are aligned as follows;
O O O O
O O O O
The winder will usually wind as below which means that you could get a bit more on;
O O O O O
O O O O O O