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#1
10-17-2011, 05:17 PM
 Anaerin Senior Member Join Date: Feb 2009 Location: Regina, SK, Canada Posts: 279
Heavy Mathematical magic - Calculating Acceleration from Torque

Okay, so I have a wheel of radius r (Meters), attached to a vehicle of weight M (Kilograms). If I apply a constant torque T (Newton-Meters), how much acceleration do I get?

My shaky math comes out to:

Inertia I=W*rē
Therefore Acceleration = (T/I)*r (In Meters/secondē)

Right?
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My thoughts on EVs, in preparations to making my own... http://evthoughts.blogspot.com/

Last edited by Anaerin; 10-17-2011 at 05:19 PM. Reason: Adding metric units, to save confusion
#2
10-17-2011, 06:47 PM
 dtbaker Senior Member Join Date: Jan 2008 Location: santa fe, nm Posts: 3,616
Re: Heavy Mathematical magic - Calculating Acceleration from Torque

Quote:
 Originally Posted by Anaerin Okay, so I have a wheel of radius r (Meters), attached to a vehicle of weight M (Kilograms). If I apply a constant torque T (Newton-Meters), how much acceleration do I get? My shaky math comes out to: Inertia I=W*rē Acceleration = T/I (In Radians/sec) Therefore Acceleration = (T/I)*r (In Meters/secondē) Right?

there's lots more involved.... real wheels are not solid discs which means that the 'r' for moment of inertia is not the rim. and then you are assuming that there is nothing attached to the wheel? you'd have to figure ALL the rotating weight you are accelerating AND the F=ma for accelerating the non-rotating weight thru space.
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Dan
http://www.envirokarma.org/ev - '97 Suzuki Swift
http://www.envirokarma.org/ev2_mx5e - '94 Mazda MX5 Miata
#3
10-17-2011, 07:22 PM
 Anaerin Senior Member Join Date: Feb 2009 Location: Regina, SK, Canada Posts: 279
Re: Heavy Mathematical magic - Calculating Acceleration from Torque

I was trying to simplify things, and just assuming you had to move what was effectively a M-massed weight on the end of a r-length arm (Effectively, the force necessary to move the wheel against the ground). Essentially I need to calculate the force created by the motion of the wheel against the ground, and use that as the F in an F=Ma (Rearranged to solve for a, so F/M=a). Yay, more equations!

Could I use the size of the wheel as a ersatz "Gear", and if so, how would I calculate it's ratio?
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My thoughts on EVs, in preparations to making my own... http://evthoughts.blogspot.com/
#4
10-17-2011, 08:44 PM
 tomofreno Senior Member Join Date: Mar 2009 Posts: 1,958
Re: Heavy Mathematical magic - Calculating Acceleration from Torque

The wheel torque is equal to the cross product of the force the wheels apply to the road (tangential to the wheel contact area) and the wheel radius, here simply equal the product r*F since the angle between r and F is 90 degree. The force F = m*a = T/r where m is the mass of the vehicle and a is its acceleration, so a = T/r*m. The product of this force and the distance the vehicle moves is the work done by the motor to move the vehicle against the drag and Rolling Resistance forces. It does not include the work done to increase the energy of rotating parts, or losses in the motor, controller, batteries, and friction in the drive train. The wheel torque equals the product of motor torque and overall gear ratio (trans plus rear end).
#5
10-17-2011, 08:53 PM
 dtbaker Senior Member Join Date: Jan 2008 Location: santa fe, nm Posts: 3,616
Re: Heavy Mathematical magic - Calculating Acceleration from Torque

Quote:
 Originally Posted by tomofreno The wheel torque is equal to the cross product of the force the wheels apply to the road (tangential to the wheel contact area) and the wheel radius, here simply equal the product r*F since the angle between r and F is 90 degree. The force F = m*a = T/r where m is the mass of the vehicle and a is its acceleration, so a = T/r*m. The product of this force and the distance the vehicle moves is the work done by the motor to move the vehicle against the drag and rolling resistance forces. It does not include the work done to increase the energy of rotating parts, or losses in the motor, controller, batteries, and friction in the drive train. The wheel torque equals the product of motor torque and overall gear ratio (trans plus rear end).

this all handles the non-rotating parts.... I was just trying to point out that to be accurate you would need to find moments of inertia for all the rotating parts too to predict the acceleration. Not insignificant with the wheels plus brake rotors, all the gears/clutch/flywheel in the drivetrain, and the guts of the motor itself.
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Dan
http://www.envirokarma.org/ev - '97 Suzuki Swift
http://www.envirokarma.org/ev2_mx5e - '94 Mazda MX5 Miata
#6
10-17-2011, 09:05 PM
 Anaerin Senior Member Join Date: Feb 2009 Location: Regina, SK, Canada Posts: 279
Re: Heavy Mathematical magic - Calculating Acceleration from Torque

Quote:
 Originally Posted by tomofreno The wheel torque is equal to the cross product of the force the wheels apply to the road (tangential to the wheel contact area) and the wheel radius, here simply equal the product r*F since the angle between r and F is 90 degree. The force F = m*a = T/r where m is the mass of the vehicle and a is its acceleration, so a = T/r*m. The product of this force and the distance the vehicle moves is the work done by the motor to move the vehicle against the drag and rolling resistance forces. It does not include the work done to increase the energy of rotating parts, or losses in the motor, controller, batteries, and friction in the drive train. The wheel torque equals the product of motor torque and overall gear ratio (trans plus rear end).
Okay, let's throw some numbers in here.

Example car: 2010 Chevy Malibu, stock weight, with a Warp9 in direct-drive through a 4:1 differential.

Vehicle weight: 1556KG
Motor torque: 321N-m

So, Final torque at-the-wheel is 1284N-m (4x mechanical advantage from the differential, 1/4 the speed. Right?)
acceleration = 1284/(0.3345 * 1556) = 2.4669. If that's in Radians/sec, then acceleration = 2.4669...*0.3345 = 0.82519 m/s^2

Either way, that's not much acceleration at all. 0.25G? Definitely not going to be winning any drag races with that. So where's my math wrong?
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My thoughts on EVs, in preparations to making my own... http://evthoughts.blogspot.com/
#7
10-17-2011, 09:14 PM
 dtbaker Senior Member Join Date: Jan 2008 Location: santa fe, nm Posts: 3,616
Re: Heavy Mathematical magic - Calculating Acceleration from Torque

hence the need for 'a better lever' with a transmission.... besides a warp9, even at plasma-inducing amps isn't going to win any races in a 3000+# vehicle.
__________________
Dan
http://www.envirokarma.org/ev - '97 Suzuki Swift
http://www.envirokarma.org/ev2_mx5e - '94 Mazda MX5 Miata
#8
10-17-2011, 09:39 PM
 tomofreno Senior Member Join Date: Mar 2009 Posts: 1,958
Re: Heavy Mathematical magic - Calculating Acceleration from Torque

That's 2.47 N/kg or meters/second squared, which is 5.52 mph/second, or a bit under 11 seconds 0 to 60 mph - if you maintain that value of torque, which of course is not constant over the entire rpm range for either an ICE or electric motor/controller. The torque falls off at higher rpm for the electric motor/controller, that be the problem.
#9
10-18-2011, 12:15 AM
 Anaerin Senior Member Join Date: Feb 2009 Location: Regina, SK, Canada Posts: 279
Re: Heavy Mathematical magic - Calculating Acceleration from Torque

Well, here's the end result: http://evthoughts.blogspot.com/2011/...2now-with.html

Do let me know if you spot any problems. I'm sorry about the Javascript being all on one line, but apparently Blogger loves to insert br tags everywhere. :/
__________________
My thoughts on EVs, in preparations to making my own... http://evthoughts.blogspot.com/
#10
10-19-2011, 07:11 PM
 gor Senior Member Join Date: Nov 2009 Posts: 416
Re: Heavy Mathematical magic - Calculating Acceleration from Torque

Quote:
 Originally Posted by Anaerin Well, here's the end result: http://evthoughts.blogspot.com/2011/...2now-with.html Do let me know if you spot any problems. I'm sorry about the Javascript being all on one line, but apparently Blogger loves to insert br tags everywhere. :/
nice little thing : )
just add fields filling exaples, note or comment in rpm field: torque up to given rpm - constant, also may be a title - calculated theoretical constant acceleration; constant torque model as opposite to contant power (ideal CVT model), where torque and acceleration decreases wile speed increases

may be specify (to be clear) - accel calc. w/o taking into account resistance (wind, rolling)

Last edited by gor; 10-19-2011 at 07:21 PM.

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