Will An Ebike Motor Lose Power Under Stress?

If we imagine a road that has a steady incline of say 10% or thereabouts, for many miles, would a hub motor tend to become less powerful as it (presumably) heats up, and would it eventually grind to a halt before the battery is flat?

yes. This is down to voltage sag.

The battery has an internal resistance. When you climb a hill, the motor draws a lot more power than on the flat, that can be as much as 7 times on a steep hill. The voltage drops more than when you ride on flat road, you can see this on the battery indicator. The indicator loses a bar or two 200m-300m into the climb, then recovers when you come out of a climb.

The second effect is battery drain. A full battery shows 41.5V, a completely flat battery 31.5V. The torque of the motor is proportional to the square of the voltage. A freshly charged battery gives more lively climb (23% more torque) compared to a half full.

So a bike will climb very well at the beginning of the climb and slacks off at the end, it's normal behaviour. A big capacity battery lessens the effect though.

Thanks very much indeed!

 

As you are probably aware, the island is rather hilly and, just this morning, I rode one of the most feared ones: from Shanklin to Ventnor.

 

Towards the top (one might even say summit!), I was on first gear, with maximum assist, but I made it, much to my surprise, delight and respect for the new bike (Woosh). Also, considering the bike is quite heavy, I weigh a good twenty stones and I was carrying panniers with my toolkit and foot pump, I wasn't greatly out of breath.

So a bike will climb very well at the beginning of the climb and slacks off at the end, it's normal behaviour. A big capacity battery lessens the effect though.

Well written, great description - just like a human heart.

St Boniface in ventnor is a big old hill. I get two descents and two ascents in turbo out of my 500w Bosch CX.