To go the same speed in top gear I see little logic in overdriving through the joey box to then just gear down in the chain ratios.
You can get essentially identical lowest and highest overall drive ratios from either the overdrive or underdrive setup, and thus similar acceleration at low speed (without a push truck) and similar speed at the top end. Either approach, you can juggle sprocket teeth here and there (within space limits) to get the desired overall ratios. I should not have stipulated specific tooth counts; ratios are the important aspect. Underdrive system advantage is less lossy at the top end, which is very significant, and also you have developed a clear route to implementation. Overdrive system advantage is closer ratios at the top end and a bit wider at the low speed end. I was just exploring and questioning to understand the options.
Thanks for the kind words guys.
I agree that you can get the same top and bottom ratios regardless of whether you overdrive or underdrive.
What I was trying to say was I can't see why I would overdrive the secondary only to underdrive it again it again to get the rear wheel speed back down again, I was just trying to show what I was talking about using the those numbers.
Eg: if you want a wheel speed of 4000rpm and the output shaft is 6000rpm and the main to joey 1:1 (easy maths) as a underdrive/direct you could have 20/30 sprockets on the rear chain(1:1.5 ratio)
If you went direct overdrive the joey output shaft is now 7620 rpm so now need a 1:1.9 ratio to get the rear wheel back close to 4000 rpm so you can either make the back sprocket bigger and have 20/38 or make the front sprocket smaller 16/30.
The bigger rear sprocket increases the chain speed, the smaller front sprocket makes the chain rollers move more to get around a smaller radius.
Both those are undesirable IMHO.
If you wanted to run the back wheel faster than the existing output shaft rpm the case may be different.
Thanks
jon