two batteries with different voltages

Hi I have one hypothetical question.
Let's say I have ebike and two batteries, one is 36v 10Ah and another 48v 10Ah.
Now, my trip is devided into two parts one flat and another uphill.
My question is, on uphill part of the trip which battery is better to use, same for flat part?

You'll get more power out of the 48V battery (VA=W), so it would make sense to me to use it on the uphill portion of the ride.

There's not definitive answer. It would depend on the motor, load, controller, gearing (wheel size), etc. The higher voltage is capable of more power, but it will also need to get to higher rpm for the same efficiency.

There is the school of thought that with the 48V battery at some percentage of throttle the performance will be identical as the 36V at full throttle. I'm not much of a believer, because I've seen how controllers respond to partial throttle on hills...lot's of heat and numberous controller failures.

One thing is certain though, the motor is only capable of a given amount of torque regardless of voltage. Also, if you get bogged down on a hill the higher voltage can create too much motor heat faster.

Unless you really only need and want leisurely pedal type speeds with your system, then you'll be happier at 48V. If performance is what you're after, then volt up and gear down is what I always recommend. Run the smallest wheel you can live with, and then use whatever voltage achieves the top speed you want on flat road.

if you have two, 12S and 16S, then why not rebuild the two packs into a single 14S pack by taking two off the 16S and adding them to the 12S and build the pack with all of them in parallel and use 14S BMS. you can use a 16S BMS and hack it down to 14S and then you will have the optimal usage of the available packs.

Bike is 26" with front hub motor. I'm asking this question because, primary battery on my bike is 16s, if I want to go further I'll use 12s battery in backpack. The question I allready asked is which battery is better to use on uphill and wich on flat. I agree to that, about heating up more with higher voltage, but if there is higher voltage used for uphill, it will be higher speed and therefore higher efficiency, meaning less heat produced (maybe same amount as at the lower voltage), but also less time to get on top of the hill, so there I'm thinking I'll consume less sharge.

i explained you will get the most efficiency by making the two batteries into one 14S pack. it is always better in terms of the amount of power you get from the stored charge to take the power out at the lowest C rate and highest voltage available.