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I am doing my best to figure out the effects based of equations alone, and not taking my car in for a dyno test. Sadly, I am having difficulty with some equations

I really hope someone out there can help me.

**These are the things I would like to determine:**

1) If my car is traveling on a flat road at a certain speed, what is the force of the car?

2) If my car is traveling on a flat road at a certain speed, what is the torque that is being generated by the axle shaft?

3) If my car is traveling on an uphill road at a specific angle at a certain speed, what is the force of the car?

4) If my car is traveling on an uphill road at a specific angle at a certain speed, what is the torque that is being generated by the axle shaft?

5) How much torque is being generated by the transmission at a certain engine RPM value?

**So far, this is what I have come up with, assuming the engine speed is 3000 RPM and I am only in 1st gear:**

Vehicle Speed (MPH) =

(Engine Speed (RPM) x Tire Radius (in)) / (168 x Axle Ratio x Trans Ratio)

Vehicle Speed (MPH) = 21 MPH

Transmission Speed into Axle (RPM) = Engine Speed (RPM) / Trans Ratio

Transmission Speed into Axle (RPM) = 669 RPM

Wheel Speed (RPM) = (Vehicle Speed (MPH) x 5280 x 12) / (60 x PI x Wheel Diameter (in))

Wheel Speed (RPM) = 242 RPM

Axle Shaft Torque to Wheels (lb-ft) =

Trans Torque into Axle (lb-ft) x Axle Ratio

Axle Shaft Torque to Wheels (lb-ft) = ??

Trans Torque into Axle (lb-ft) = Engine Torque into Trans (lb-ft) x Trans Ratio

Trans Torque into Axle (lb-ft) = ??

(I know the Max Torque at a given RPM value, but I want to find the torque at any RPM value)

Torque of Axle Shaft (lb-ft) = radias of shaft (ft) x Force (lb)

Torque of Axle Shaft (lb-ft) = 0.125 (ft) x ??

Torque of Wheel (lb-ft) = radias of wheel (ft) x Force (lb)

Torque of Wheel (lb-ft) = 1.209 (ft) x ??

From a free body diagram, I have determined the summation of forces in the X and Y direction:

FY = N - mgcos([itex]\vartheta[/itex]) = 0

Fx = F(car) - F(friction) - mgsign([itex]\vartheta[/itex]) = ma

N = mgcos([itex]\vartheta[/itex])

F(friction) = [itex]\mu[/itex]N

F(car) = ?

m = weight of car

These are a few calculations I have determined and a few I am having a problem determining theoretically. I would like to find out these values for any engine RPM value and any given speed.

Here are some specs of my car:

Max Torque: 250 lb-ft @ 4500 RPM

Max Horsepower: 265 HP @ 6250 RPM

Weight: 4078 lb

Axle Ratio: 2.77

Trans Ratio:

1st: 4.484

2nd: 2.872

3rd: 1.842

4th: 1.414

5th: 1.000

6th: 0.742

Rev: 2.882

Wheel Diameter: 29.02 in

Vehicle Performace: 0-60 mph in 7.4 seconds

I'd really appreciate any help anyone can offer.

Thanks!

Mike