Wondering if you run a 16" bar with a 8 pin rim could you put a 7 pin rim on it with a 18" or 20" bar and have about the same power. Just how much power difference is there when you go up or down a tooth % wise.
Changing sprocket tooth count does not change engine power it changes the amount of torque delivered to the chain.
Going from a 16 to a 18" or 18 to 20" will make no noticeable difference in power available for cutting. There will be a small difference in going from 16 to 20"
The prime determination for cutting speed is
chain speed and the
torque available at a give chain speed.
SO:
1) High chain speed with lotsa torque gives fastest cutting
2)
a) High chains speed and low torque
OR
b) Low chain speed and high torque
Means reduced cutting speed.
If the wood is hard then b) is preferable to a)
3) Low chain speed with little torque may not even cut at all.
Increasing the sprocket tooth count increases chain speed but reduces torque and VV
The trick is to have a happy medium that suits a given saws torque performance and the hardness of the wood being cut.
Here is a graph showing chain speed versus RPM for different sprocket tooth counts.
High RPM is desirable to get high chains speed but if there is not much torque available at a given RPM the chain speed will just drop as soon as the chain touches wood.