How to achieve higher electrical power in a smaller space with same current

[kmarinas86]

Optimal motor configuation for higher electrical power in a smaller space

Favored (because these qualities allow the machine do quick and nimble things for a longer time)
mechanical power
angular acceleration
torque/volume
torque/mass
torque
longevity

Neutral
resistance
voltage
loops, wire
length, wire
charge capacity
area per loop
diameter, wire

Disfavored (because these qualities prevent the machine from do quick and nimble things for a long duration)
current
mass
volume

The chart below consists of the solutions by a Microsoft Excel add-in. What the chart below shows is that in order to follow the criteria above, you have to increase certain parameters at a faster rate than others, while decreasing others in the process. The rate is r, where x=(1+r).

x^9: resistance
x^8: voltage
x^7: mechanical power
x^6: angular acceleration
x^4: torque/volume; wire loops; torque/mass
x^3: wire length
x^1: torque, longevity
x^0: charge capacity
x^-1: current
x^-2: area per loop
x^-3: wire diameter; mass; volume

Consider x=2. We would have:

512 times the resistance
256 times the voltage
128 times the mechanical power
64 times the angular acceleration
16 times the torque/volume; wire loops; torque/mass
8 times the wire length
2 times the torque, longevity
The same charge capacity
50% of the current
25% of the area per loop
12.5% of the wire diameter; mass; volume

The above suggests that while the possible mechanical power is limited by electrical power, its possible have negative relationship between power and volume, power and mass, power per current - SIMULTANEOUSLY. It's only a matter of engineering as to how small, and powerful, and how long lasting the motor can be.

 

[berkeman]

I don't see an attachment. This also looks like coursework, but it's complex enough that I'll leave it here for now instead of moving it to homework help.

 

[capnahab]

In answer to your question, it all boils down to heat. You can put as much power wherever you want but the excess heat has to be removed. Write the general physics forum for more information.