Okay, I went ahead...
More than likely, your Nexus hub has a 19-tooth sprocket on its hub. Underdrive gear is 1.36:1 and overdrive is .73:1...
The 19t/36t chainring relationship = .528:1...
10t/44t chainring = 4.4:1...
10t/17t jackshaft = 1.7:1...
Standard engine gearing = 4.1:1...I think...
Soo, 4.1 x 1.7 x 4.4 x .528 = 16.192:1...
We'll keep (4.1 x 1.7 = 6.97:1) as a constant value that we won't change.
Multiply 16.192 by 1.36:1 = 22.02:1 underdrive. Okay for flat road, not good for huge hills...similar to running a Happy Time 54-tooth rear sprocket...
16.192:1 x 1.00:1 = 16.192:1 in second...similar to a 39-tooth sprocket...
16.192 x .73 = 11.82:1...similar to a 29-tooth sprocket...
LET'S DO SOME CHANGES!
Change your rear hub sprocket to a 23-tooth. Then 23/36 = .639:1...
6.97 x 4.4 x .639 = 19.6:1...
19.6 x 1:36 = 26.66:1, similar to a 65-tooth sprocket...
19.6 x 1:1 = 19.6:1...similar to a 48-tooth sprocket...
19.6 x .73 = 14.31:1...similar to a 35-tooth sprocket...
Good improvement, but for huge hills, here's my recommendations...
For AWESOME hillclimbing, switch your chainring to a 72t sprocket in 8mm chainsize, along with an 11t sprocket on the jackshaft. That gives you a 6.45:1 ratio, up from 4.4:1...
Switch the hub sprocket from 19t to 23t. 23/36 = .639:1...
6.97 x 6.45 x .639 = 28.73:1...
In underdrive, 1.36:1 x 28.73 = 39.07:1, similar to using a 95-tooth sprocket...
Your 1:1 ratio is 28.73:1, similar to a 70t rear sprocket...
In overdrive, gearing is 20.97:1, akin to a 51t Happy Time rear sprocket...
Of course, your cruising speed will suck...
Sooo, if wanting decent cruising with excellent hillclimbing...
Use 63t chainring with 11t in 8mm chainsize = 5.73:1...
Use 23t rear hub sprocket and 36t chainring = .639:1...
6.97 x 5.73 x .639 = 25.52:1...
Underdrive = 25.52 x 1.36 = 34.71:1, similar to a 85t rear sprocket...
1:1 = 25.52:1, similar to a 62t sprocket...
Overdrive is 25.52 x .73 = 18.63:1, akin to a 45t rear sprocket.
For starters, you could just change the 19t hub sprocket to a 23t sprocket. Gear ratio would lower from 16.192 to 19.6:1.
Underdrive ratios would change from 22.02:1 to 26.65:1. This is like swapping a 54t sprocket to a 65t sprocket.
The 1:1 ratio is like changing a 40t sprocket to a 48t sprocket...
Overdrive gear is like swapping a 29t sprocket to a 35t sprocket...
Some stuff to think about. There IS a way to improve your performance. Just realize that super-low gears will help you climb huge hills. However, they will lower your cruising speed.
All this should cost you about $50. Changing the 23t sprocket only costs $9.00.
