Formulas/Methods for calculating the torque/power requirements for a vehicle?

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PaperclipGod

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Apr 7, 2003
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I've been messing around with electric motors lately, and I'm wondering if there are any formulas for determining the ideal motor size for a given application.

e.g., If I want to accelerate a given mass, X, at velocity Y, and rolling resistance Z, how much torque would I need?
 
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PaperclipGod

Banned
Apr 7, 2003
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Nice hint. :/

I tried Google already, though, and all of the results are for calculating the torque of a motor; not for calculating the ideal motor size given the requirements of the vehicle.

e.g., for this hypothetical scenario:

You want to motorize a block of metal weighing 100lbs. Your requirements are that it can accelerate at a rate of 5 ft/s/s. By taking into account the weight of that mass, the weight of the motor, the drag on the object, the rolling resistance, etc, how would you calculate the requirements for the engine/motor?
 
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ShawnD1

Lifer
May 24, 2003
15,987
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SunSamurai said:
http://www.google.com/search?q=Form...s=org.mozilla:en-US:official&client=firefox-a
Click to expand...

Ha. The first result I get is this exact thread.


PaperclipGod said:
You want to motorize a block of metal weighing 100lbs. Your requirements are that it can accelerate at a rate of 5 ft/s/s. By taking into account the weight of that mass, the weight of the motor, the drag on the object, the rolling resistance, etc, how would you calculate the requirements for the engine/motor?
Click to expand...
You can't really figure out the torque and gear ratios until you know how much power you're dealing with. Motors are sold according to power, so figure that out first.

The power equation is very simple since it's just a variation of the work equation.
power = (force)*(speed)

Calculate it for worst case scenario - maximum speed.
(power in W) = (force in N)*(maximum speed in m/s)
divide this power number by 746 to get horsepower.

edit:
If you're trying to calculate it according to acceleration, the way to do that is to calculate how much force is required to have that acceleration.
(total force) = (friction) + (inertia)
then from there it's the same as before
(power) = (force)*(distance)/(time)
 
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D

dighn

Lifer
Aug 12, 2001
22,820
4
81
PaperclipGod said:
Nice hint. :/

I tried Google already, though, and all of the results are for calculating the torque of a motor; not for calculating the ideal motor size given the requirements of the vehicle.

e.g., for this hypothetical scenario:

You want to motorize a block of metal weighing 100lbs. Your requirements are that it can accelerate at a rate of 5 ft/s/s. By taking into account the weight of that mass, the weight of the motor, the drag on the object, the rolling resistance, etc, how would you calculate the requirements for the engine/motor?
Click to expand...

massive simplification:

assuming you want to get a block of mass M from rest to speed of V in T amount of time:

ke = 1/2MV^2
energy from motor = int(P(t), dt) = P*T if you assume it is running at full power (which should be areasonable assumption if you have transmission running it at/near full efficiency)
subtract energy lost from friction you have

P = (1/2MV^2 + Efriction(M, Shape etc))/T - Ef is the more difficult part and to solve for it fully itll be a differential equation involving some complex terms (friction is not easy). I say just give it a safety factor of some percentage and try it. e.g P = 1/2MV^2*1.3/T for 30% overhead.

like stated this is a massive simplfiication of the problem and will nly give you an estimate of the figure involved. calculating it precisely is a VERY difficult problem and may not be feasible to do at all because you'd have to obtain detailed characterstics of the involved components.
 
yhelothar

yhelothar

Lifer
Dec 11, 2002
18,409
39
91
Given from what I've learned in college physics...

Torque = Force × radius
Rolling resistance(R)=Coefficient × normal(mg)
g=9.8m/s²

So to answer your question in this very simplified scenario with only 3 variables taken into account, the motor would need just enough torque to overcome to rolling resistance so that there can be a minimal amount of acceleration for it to reach velocity(Y).

Thus we can set the torque equal to the rolling resistance.

T=Cmg

Well this probably didn't do anything to answer your question. But I would guess that gearing has a lot to do with this problem. The same amount of torque that you put into a 10 speed bike at a low gear would be much different than at a high gear.
This is probably the radius component of torque as T=Fr.

Thus in your example problem with a 100g block, and you were to stick in a motor, say in a very simplified system in which the engine is directly connected to the axle of the wheels like in a RC car.

I'm not sure what the radius component of torque would be in this case. I want to say it's the radius of the wheels, but somehow that doesn't sound right.

But anyways, given that it is the radius of the wheels.
Then to solve your problem...

T=Fr
F=ma
T=mar

but then the torque has to work against rolling resistance too.
So you'd have to add the torque created by the rolling resistance to the required output of the engine.
that would be Taccelerateobject+Trollingresistance=Trequirement
Trollingresistance=cmgr

Althought for your purposes, I'd probably assume that rollingresistance is going to be negligible if you have decently round/inflated tires, and especially if your object is less than 100lbs.

So to simiplify this problem, given that I got the radius correctly,
Trequired=mass of object+engine × acceleration × radius of wheels
 
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yhelothar

yhelothar

Lifer
Dec 11, 2002
18,409
39
91
I found a site that explains it.
http://scienceblogs.com/startswithabang/2009/04/what_does_torque_in_a_car_do.php

So mass isn't the mass of the entire car, but just the moment of inertia, which involves the distance of the wheels to the center of mass.

But this torque can tell you a lot about how fast the car can accelerate. Let's turn it into a physics problem. We'll assume that this "500 Newton-meters" is an actual, legit value for how much torque the tires experience. We can estimate that the mass of a typical car is about 1500 kg, and that the typical distance between the center of mass of the car and the wheel's rotational axis is about 20 cm; this gives us a moment of inertia for the car of 60 kg m^2. The car's wheel size plus the sidewall radius of the tire is about 20", or 51 cm.
The acceleration of this car? 4.25 m/s^2, or (more commonly), it can do 0-60 miles-per-hour in about 6.3 seconds. Want a car that can accelerate faster? Here are the things that can help:
more torque (duh),
a lighter car,
a lower center-of-mass (closer to the wheel axle in height),
larger diameter wheels & tires,
and an engine that can output this large amount of torque over a wide range of engine speeds.
Click to expand...
 
JulesMaximus

JulesMaximus

No Lifer
Jul 3, 2003
74,550
940
126
Just buy the biggest SUV you can and make sure it has a gas guzzling Hemi. The jihad needs more money.
 
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