| Topic: |
Science > Physics |
| User: |
"Footer" |
| Date: |
06 Mar 2005 07:22:16 PM |
| Object: |
Applied torque & driving force |
I am currently designing an electric car for my physics class and I
have a few questions about torque and acceleration. Assuming I know the
(instantaneous) applied torque to the rear wheels from the motor, and
the mass of the vehicle and wheel radius are known, how do I determine
the linear acceleration of the vehicle (assuming no slipping)? I was
thinking that since t = F*r i could find the driving force and then
divide by mass to get the acceleration, but the more I think about it,
it seems that the moments of inertia of the wheels should be involved
somehow. Any help would be appreciated.
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| User: "CWatters" |
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| Title: Re: Applied torque & driving force |
07 Mar 2005 01:24:55 PM |
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"Footer" <footer105@yahoo.com> wrote in message
news:1110158536.220349.23500@z14g2000cwz.googlegroups.com...
I am currently designing an electric car for my physics class and I
have a few questions about torque and acceleration. Assuming I know the
(instantaneous) applied torque to the rear wheels from the motor, and
the mass of the vehicle and wheel radius are known, how do I determine
the linear acceleration of the vehicle (assuming no slipping)? I was
thinking that since t = F*r i could find the driving force and then
divide by mass to get the acceleration, but the more I think about it,
it seems that the moments of inertia of the wheels should be involved
somehow.
Yes but the effect is likely to be insignificant. The reason is that the
mass of the wheels is usually much smaller than that of the whole car. Might
be different if you plan to put the motors and/or batteries in the wheels. .
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| User: "John OFlaherty" |
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| Title: Re: Applied torque & driving force |
07 Mar 2005 06:58:52 PM |
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CWatters wrote:
"Footer" <footer105@yahoo.com> wrote in message
news:1110158536.220349.23500@z14g2000cwz.googlegroups.com...
I am currently designing an electric car for my physics class and I
have a few questions about torque and acceleration. Assuming I know the
(instantaneous) applied torque to the rear wheels from the motor, and
the mass of the vehicle and wheel radius are known, how do I determine
the linear acceleration of the vehicle (assuming no slipping)? I was
thinking that since t = F*r i could find the driving force and then
divide by mass to get the acceleration, but the more I think about it,
it seems that the moments of inertia of the wheels should be involved
somehow.
Yes but the effect is likely to be insignificant. The reason is that the
mass of the wheels is usually much smaller than that of the whole car. Might
be different if you plan to put the motors and/or batteries in the wheels. .
I tried to run some numbers, to get a feeling for it. I used energy
totals to make it simpler.
Car Mass: 3000 lb, about 1363 kg
Wheel radius: 15", about 0.381 m
Wheel mass: 50lb, 22.7 kg
Wheel moment of inertia: 1/2 MR^2, or 1.65 whatchacallits
Wheel angular velocity: 70.4 radians/sec
(2PI*car velocity/circumference = car velocity/radius)
Assumed car velocity 60mph, about 26.8 m/s.
Car stored energy due to linear motion
1/2mv^2 = 490,500 joules
Wheel stored energy due to rotation
E = (moment of inertia) * (angular velocity)^2
8175 joules/wheel
total E for wheels: 4 * 8175 = 32,700 joules
fraction wheel rotation / linear motion:
32,700 / 490,500 = .066
So the wheel rotation has taken up about 6.6% of the engine power. It's
not real big, but not quite insignificant, either.
--
john
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| User: "Dave Baker" |
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| Title: Re: Applied torque & driving force |
06 Mar 2005 09:00:37 PM |
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Footer <footer105@yahoo.com> wrote in message
news:1110158536.220349.23500@z14g2000cwz.googlegroups.com...
I am currently designing an electric car for my physics class and I
have a few questions about torque and acceleration. Assuming I know the
(instantaneous) applied torque to the rear wheels from the motor, and
the mass of the vehicle and wheel radius are known, how do I determine
the linear acceleration of the vehicle (assuming no slipping)? I was
thinking that since t = F*r i could find the driving force and then
divide by mass to get the acceleration, but the more I think about it,
it seems that the moments of inertia of the wheels should be involved
somehow. Any help would be appreciated.
You need to take into account the inertia of all the rotating components
which will include those in the engine itself and the transmission as well
as the wheels. The crankshaft and flywheel of a normal car absorb a large
part of the engine's power output during high rates of acceleration. In fact
when you rev your car engine on the driveway with the car stationary the
inertia of the engine components absorbs the entire power output. Think
about this for a bit. If you apply full throttle briefly then the engine is
running at full power output. It still takes a certain amount of time for
the engine to reach maximum rpm, maybe one to two seconds. That is the
fastest that engine will ever rev because none of the output is going
towards accelerating the vehicle itself. Regardless of the vehicle weight or
gearing you can never make the engine rev faster than it will with the car
stationary.
This principle can actually be used to measure engine output if the inertia
of the components is known or if the acceleration rate of a comparison
engine at full throttle is known. The technique is used in some racing
series to check for illegally modified engines. A computer controlled timer
plugs into the ignition system and measures the engine acceleration at full
throttle by timing the rpm from the ignition pulses. If the engine
accelerates faster than normal then either the internal components have been
lightened or the power output has been increased. Of course if you increase
the component mass by the right amount to offset the extra output from
tuning modifications you can fool the device :)
The inertia effect depends on gearing and some of the relevant factors and
equations are discussed in the flywheel article on my website and also in
the article on the computer simulation of vehicle performance.
--
Dave Baker - Puma Race Engines (www.pumaracing.co.uk)
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| User: "John OFlaherty" |
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| Title: Re: Applied torque & driving force |
06 Mar 2005 08:07:48 PM |
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Footer wrote:
I am currently designing an electric car for my physics class and I
have a few questions about torque and acceleration. Assuming I know the
(instantaneous) applied torque to the rear wheels from the motor, and
the mass of the vehicle and wheel radius are known, how do I determine
the linear acceleration of the vehicle (assuming no slipping)? I was
thinking that since t = F*r i could find the driving force and then
divide by mass to get the acceleration, but the more I think about it,
it seems that the moments of inertia of the wheels should be involved
somehow. Any help would be appreciated.
You do have to take it into account. When the vehicle accelerates,
energy is stored in the forward motion of the vehicle and wheels, and in
rotational motion of the wheels.
Torque = moment of inertia * angular acceleration
Force = mass * linear acceleration
To get the net unbalanced force accelerating the vehicle, you have to
consider the torque at the circumference of the wheel, which is lessened
by having to increase the wheels' rotational velocity. To find the
summation, you have to relate linear acceleration to angular acceleration.
If the wheel is a simple disk (unlikely), you can look up a formula to
find its moment of inertia. Otherwise, you may be able to measure it by
applying a torque and seeing what the angular acceleration is.
--
john
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| User: "" |
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| Title: Re: Applied torque & driving force |
06 Mar 2005 07:54:44 PM |
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Footer--
Quincy-Lynn Enterprises developed several electric cars for Mechanix
Illustrated in the early 80's. One was called the Urba Town Car--a
hybrid electric car you build yourself. Google can get you a phone
number--they sell plans-- but all you need is the booklet that comes
with the plans--it will walk you through all the calculations you'll
need to make a great science project ie battery performance, required
HP, top speed, range, etc.
Good luck!
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