What is your best recommendation to optimize the torque/speed relationship of a motor?

Question

I'm a engineering student currently taking Thermodynamics and we have this project for our finals which is a sort of reeling /towing device, the assignment consists in a reeling motor that has to tow a small car up along a slope, loaded with a certain weight, the team that is able to reel in the most weight in the shortest time will win the competition and have the maximum grade and extra credits for the semester.

The rules are:

You can only use 1 Peltier thermoelectric generator module that will deliver 12 volts to the motor of my choosing. No capacitors or energy storage devices. I could use a voltage regulator to rise the voltage but speaking to one of my professors he said that due to the fact the power is just a relationship between current and voltage, rising the voltage wouldn't really make a difference as the current would drop, so my best shot was to shop for a motor with good torque that would surely work under 12 volts in case the peltier module does not deliver its full capacity.

I had 2 options, and because I need to move the biggest load in the shortest amount of time, I had to look for a motor with a good speed/torque relationship that would work under 12 volts in the worst case scenario, but I read somewhere you can make a speed reduction arrangement to help torque like the one below:

Reducing Engine

So I went and bought two different motors,

One with high speed and comparably low torque (to see if I the reducing arrangement can help me get a better torque in the end.

BEMONOC Small DC Motor 12V High Speed 12000 RPM High Torque PMDC Motor for DIY Parts  (0.135 N.m)

And one with low speed and high torque, to test both.

Greartisan DC 12V 200RPM Gear Motor High Torque Electric Micro Speed Reduction Geared Motor Centric Output Shaft 37mm Diameter Gearbox (0.2157463 N.m)

But I was wondering if you have any suggestions as to how to improve this torque/speed relationship and get the best out of it, I really want to win this competition.

I would truly appreciate any information you can share with me in contribution to my project.

Thank you in advance and sorry for my grammar, English is not my first language.

Answer 1

With such a limited power supply, the key metric that you should be concerned with, is efficiency, i.e. how much of the energy supplied to the motor can actually be used for lifting the weight. For a typical Permanent Magnet DC Motor, peak efficiency occurs at at approximately 90% of the motor's 'no load speed', and 10% of its 'stall torque'.

Therefore, you will find that using a "low speed and high torque motor" which is able to reel in the load without 'struggling' at all (i.e. the motor itself, before the gearbox, is able to turn at approximately 90% of it's no-load speed), then your system will run more efficiently.

You say that the winners will be able to lift "the most weight in the shortest time" - this is an ambiguous scoring system. Is it:

1. the most weight lifted over a certain distance wins, but if there are two teams lifting the same weight, then the faster team wins?
2. Teams get a score base on the weight they lifted and the time it took - something like $\frac{Weight}{Time}$?
3. Something else?

Without that information, you can't make an informed decision regarding which motor is likely to be best.