# Calculate wheel torque based on known Weight, wheel size, acceleration data ?

#### soundengineer

I'm trying to calculate Wheel torque in ft/lbs

things I know
Weight lbs or kg
Wheel Diameter inches or meters
acceleration data (I know how fast this wheel is spinning in MPH/kph/meters per second)and I know how much it changes over a given amount of time(meaning I know its going from "MPH1" to "MPH2" in "x" amount of time
I can also get any other data needed

basically I have a vehicle that I am supposed to calculate the torque at the wheels
and I have no Idea of how to get there...

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#### tiny-tim

Homework Helper
Hi soundengineer! ok, you have mass and radius, so you can work out moment of inertia …

you also have angular velocity and angular acceleration …

what equation(s) do you know connecting torque and moment of inertia with angular acceleration? #### rcgldr

Homework Helper
Average acceleration = (mph2 - mph1) / (time period)
I'll use english units:

let t = time period in seconds (or fraction of second)

Average acceleration = (hour / 3600 sec) (5280 feet / mile) (mph2 - mph1) / t (sec)

Average force (lb) = mass of car x (average acceleration)
Average force (lb) = (slug / 32.174 lbf) x (weight of car (lbf)) x (average acceleration)

Average speed (mph) = (mph1 + mph2) / 2

Average power (horsepower) = (average force (lb)) x (average speed (mph)) / 375

Average torque = Average force (lb) times effective radius of tire (ft)

Effective circumference can be measured by driving over a thin strip of water and measuring the distances between strips of water left by the tire. Effective radius is this disance / (2 pi). Slip ratio will reduce the effective radius, perhaps by another 1% or so.

#### soundengineer

Hi soundengineer! ok, you have mass and radius, so you can work out moment of inertia …

you also have angular velocity and angular acceleration …

what equation(s) do you know connecting torque and moment of inertia with angular acceleration? cause I dont know...

I'm actually looking for what formula I need to use.....
I really dont know any of the formulas...

When I look up the Moment of Inertia I get

I = k? * Mass * Radius^2 but I have no Idea what K is supposed to be..

angular velocity is difference in angle/difference in time in radians/second

and angular acceleration is difference in angular velocity/difference in time where I get lost is the units used...and any conversions that need to happen...

so Torque = Moment of Inertia * Angular Acceleration can somebody show me units I need to use

T = (k? * Mass * Radius^2)* ((∆angle2/∆time2)-(∆angle1/∆time1)]/(Time2-time1))?

is my math right? or did I mess that one up?

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#### rcgldr

Homework Helper
Assume angular inertias are much less than linear inertia of the car to make this simpler and ignore them. Unless you hook up the car to a dyno and do a "coast" measurement, it will be difficult to determine of the angular inertias of flywheel, drivetrain, wheels and this will include friction losses. I'm not sure how engine angular inertia could be calculated since there is significant internal aerodynamic drag in the crankcase.

#### tiny-tim

Homework Helper
Hi soundengineer! (have an alpha: α and a theta: θ and a tau: τ and an omega: ω )
When I look up the Moment of Inertia I get

I = k? * Mass * Radius^2

but I have no Idea what K is supposed to be..
k is a constant which is different for different shapes …

for the values, see http://en.wikipedia.org/wiki/List_of_moments_of_inertia (and preferably, learn the common ones for the exams! )

Uesful tip: don't google! … use PF, or use http://en.wikipedia.org" [Broken] I'm actually looking for what formula I need to use.....
I really dont know any of the formulas...

so Torque = Moment of Inertia * Angular Acceleration
That's the formula! (it's the rotating version of good ol' Newton's second law … F = ma becomes τ = Iα )
can somebody show me units I need to use
what's the difficulty?

torque is force times distance = mass times distance squared per time squared,

moment of inertia is mass times distance squared,

angular acceleration is radians per time squared. Last edited by a moderator:

#### soundengineer

Assume angular inertias are much less than linear inertia of the car to make this simpler and ignore them. Unless you hook up the car to a dyno and do a "coast" measurement, it will be difficult to determine of the angular inertias of flywheel, drivetrain, wheels and this will include friction losses. I'm not sure how engine angular inertia could be calculated since there is significant internal aerodynamic drag in the crankcase.
trying to calculate this all after all forces have been accounted for....

all other forces = 0
all I want is math to do final result of what my vehicles actual force is...meaning I dont even care about gearing or anything...

#### soundengineer

what's the difficulty?

torque is force times distance = mass times distance squared per time squared,

moment of inertia is mass times distance squared,

angular acceleration is radians per time squared. ok...now I'm confused again

(Mass in LBS) * (Distance in radians?)^2 / (time in Seconds)^2

cause angular acceleration is in radians...
do I have to convert back to feet?

would it be easier to never convert to radians? just keep it in ft the whole way?

I guess where I'm having the issue is with the angular acceleration part casue it doesnt match the units of the other stuff in the equation..

and you say Moment of Inertia is Mass * Distance.... but the equation is M*R^2
is R not the Raduis of my drum(the Wheel)
the wheel is on a shaft that holds the weight of the vehicle...so the weight of the vehicle is essentialy the weight that my tire has to push...so my Drum is my vehicle weight..

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#### tiny-tim

Homework Helper
ok...now I'm confused again

(Mass in LBS) * (Distance in radians?)^2 / (time in Seconds)^2
ah, now i see the problem …

no, distance is always in feet, even when you're doing angular stuff …

and angle is in radians, which are dimensionless (just ordinary numbers, like π).

so angular acceleration, for example, has units of radians per second-squared, and dimensions of 1/time-squared. and you say Moment of Inertia is Mass * Distance.... but the equation is M*R^2
No, I said "moment of inertia is mass times distance squared" #### soundengineer

so let me walk through this....
I will need some help...

I'll say my data says my tire is 26" Diameter...circumference of 40.84" or 3.403333 ft
My vehicle weight is 3900lbs which is what I'm calling my wheel weight
My data says
sample 1
0 seconds
100MPH
Sample 2
1 Second
109 MPH

so I have a Difference in time of 1 sec.
I have a difference in velocity of 9mph/sec
9mph converted to ft/sec = 13.2ft/sec

what do I do next?
I know somehow I need to work in angular acceleration and velocity...
but I cant figure out how....

sorry...I'm so confused for some reason...maybe just data overload