Warren said:
I grew up in Wisconsin, but spent the last 39 years in Virginia. My wife and I rode our RANS Screamer tandem for a decade, in the mountains of Virginia. After several knee surgeries, and a knee replacement, she has decided to quit riding. If you have a tandem with a 20" front wheel, and only want to use assist for climbing, there is no point in getting a mid-drive. You are making this way too complicated.
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Get the 12T, in a 20" wheel for an ~15 mph top speed on 52 volts. Get this pack.
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With this setup you will never have a problem climbing the steepest, longest climbs. You will never be tempted to use it for anything other than climbing, and perhaps starting from a dead stop. With the built-in freewheel in this motor, on a tandem, you won't even know the motor and battery are there, until you use it.
The above is really good advice for OP's request. I have a very similar cycling background and age etc to the OP. Generally I am interested in making assisted bikes rather than electric motorbikes. I don't have a tandem but am planning a cargo bike so the question "how do I get my older-weaker self and 150 lbs of compost up the hill to my house without horking up a lung?" has been something I've thought a lot about.
I also own a torque sensing mid-drive factory made bike (the Aerovironment Charger) which really should meet these goals but doesn't. This is a well engineered drive system, much better than the common kits, no bed-rail and u-bolt brackets or under-spec belt engagement or anything problematicly like that. However, it is excessively noisy and requires more maintenance (belt tension, intermediate chain tension and wear etc) than a bike should. I've had it a long time and have fixed some of the issues (replaced SLA with lithium batteries, upgraded components etc) but don't really trust it or enjoy riding it. It will be replaced with a hubmotor in a bike that I already like. I admire the design principle of mid-drive, it seems like a good idea, but all the actual examples I've seen are crappy or annoying or both.
A similar but lower budget, somewhat quieter, alternative to the suggestion from Diamondback that is even slower because it uses lower voltage would be: a 36 or 48V Bafang BPM front motor in a 20" wheel, a 25 amp controller and a 20+Ah battery in the neighborhood of 30-ish volts. You want a no-load speed of around 12-13 mph.
Assuming 440 lbs gross weight, and 250 watts pedaling input total, this combination will climb a 12% grade at 5 mph and is most efficient on a 5% to 6% grade (very common highway slope) around 9 to 10 mph. By 12 or 13 mph the motor is doing nothing which is what you are asking for. For example, with this setup you can climb Rabbit Ears pass (which I still remember from my cross country, 7%, 3000 ft gain) at 8 mph. It would still be a hard climb, but practical, not torture. All these combinations work without overheating the motor according to the simulator.
Get the motor first and measure the speed with a known voltage and then order the battery with the right voltage to get the no load speed around 12-13 mph. A Ping would be a good fit for this as he can make custom sizes, eg 33 volts last I checked. Since it's a tandem you can afford the space and weight. But anything 20+ah around 30-ish volts will work. This application is not going to demand much from the battery as long as it is big enough to be useful.
I think the control issue in this case is pretty simple. Thumb throttle with auto-cruise control, or almost even just an on/off button. Given that you only want it when you have a hill to climb, that the power is limited by the low current, and that it won't go very fast anyway, you are almost always going to want most or all of it. I'm assuming you can accept climbing 7% at 9 mph at full throttle instead of 7 mph at part throttle or 3.5 mph on your own.
Try out the ebikes.ca simulator, it is great for this sort of design exploration. For your criteria I used a 30 V 20 Ah battery, the 25 A controller, 20" wheel and the Bafang BPM motor (this is the 36 V motor, the 48 would be slower yet, you can scale the battery voltage to see some of the effect)