Car acceleration force required to size a DC motor torque

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Homework Help Overview

The discussion revolves around calculating the torque required for a model car to accelerate from a stop to a speed of 1.22 m/s within one second. The subject area includes concepts of acceleration, torque, power, and motor selection for a small vehicle, with considerations for various resistive forces and mechanical setups.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the necessary torque and power for the car's acceleration, raising questions about the role of angular momentum and the appropriateness of their power calculations. Some participants suggest considering additional factors such as friction and the motor's power output at different speeds. Others inquire about the design of the motor and gear system, expressing uncertainty about how to proceed with motor selection.

Discussion Status

Participants are actively discussing various factors that influence the power and torque requirements for the model car. There is a recognition of the need for a safety factor in motor selection, and some guidance has been offered regarding the influence of motor characteristics on the overall design. Multiple interpretations of the acceleration requirements and motor configurations are being explored.

Contextual Notes

Participants note that the calculations are preliminary and do not yet account for all resistive forces, such as wind resistance and friction. There is also mention of the need to consider the effects of gear ratios and the potential for back EMF when reversing motor direction.

Mike Gaffer
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I'm working on making a model car, and am trying to calculate the torque required to accelerate the car from a stop to 1.22m/s in 1 second, so I can pick out the right DC motor...

The acceleration required is 1.22m/s/s (~ 4ft/s)
The weight of the car is 0.85 kg
The drive wheels diameters are 0.03175 m (1.25") [wheel circ 0.099746m]

I do not have to take into account wind resistance, frictional resistance, gear box ratios (yet), drive train friction, etc. (this is still a preliminary calculation)...

I WOULD like to take into account the angular momentum ... and am going to have to have some worm gear or gear box reduction (didn't get that far yet)...

So far, I did:
velocity (final) = 1.22m/s (in time = 1s)
= 1.22 m/s^2 acceleration

rpm of wheel = (velocity of car) / dist wheel travels in 1 rotation [circum.]
= (1.22m/s) / 0.099746 m
= 12.22 rps
= 733.4 rpm

ω = rpm x 2pi / 60
= 733.4 x (2pi / 60)
= 76.80093 rad/s

P = W/t = KE / t = 1/2 mv^2/t [power = work/time]
= 0.632 watts?
= E[J] = P[watts] x t[sec] = 0.632 Joules... ? <---- where does ω come into this?

ALSO, 0.632 watts seems like way too little power required... did I miss something?

THANKS IN ADVANCE!
 
Last edited:
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Accelerating a small car doesn't take much power. Things to consider, however:
- power requirements will increase over time, your maximal power is not the average power. For uniform acceleration, it is larger by a factor of 2.
- friction can be significant
- the power output of a motor depends on its speed / you need enough torque to accelerate the car, maximal power alone is not sufficient.
- the rotating parts in the car need some additional energy as well
 
mfb:
How would you recommend I start?
I actually wanted the MAX speed to be closer to 4.5m/s (10mph)...
I was going to take a regular gear on the rear axle (no differential) -- and use a worm gear on the motor directly coupled to the straight gear...
Just pick a motor that "looks" about the right size? I was considering modeling the drive loosely a model train engine's drive...
Any recommendations on how to start? I'm willing to do a 2nd revision if I get too small/big a motor :)
 
Use a sufficient safety factor, and check which motors are available.
The motor will also influence the mass of the car, of course.
Mike Gaffer said:
I actually wanted the MAX speed to be closer to 4.5m/s (10mph)...
How long is your acceleration track?
 
The acceleration track (including space for it to decelerate) will be about 25 feet long...
AGREED re safety factor... I was hoping to calculate exactly what I needed... then assume about 85% friction for gears and double whatever I calculate to size the motor...
 
To reach 4.5 m/s in ~8 meters you need a faster acceleration, and certainly more power.
 
good point... maybe 2m/s is more realistic...
That would give a terminal velocity needed of 4.5m/s in 5m and 3m to stop (reverse current).
 
Last edited:
I'm confused on how you wanted the DC motor to stop? Like reverse the current so that it runs in the opposite direction, or a way to increase the resistance so that it slows down like that?
 
Reverse the current... However this will kick lots of back EMF that must be dealt with...
 

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