Calculating acceleration characteristics

[thehitchhiker]

Ok so I'm working on a preliminary report for a BAJA vehicle that my team and I are building and I need to find out stuff like torque at wheels, traction force and acceleration.

All the data that I have now is this:
Max. torque - 19Nm @ 3000rpm
Max. Power - 11bhm @ 4400rpm

How would I go about finding the stuff and what else might I need? I have the gear ratios of the transmission. Can I calculate the wheel radius from this or is wheel radius required to be able to do the calculations ?

 

[Mech_Engineer]

Torque at the wheels (max) is relatively straightforward, you just need to take the max torque the engine produces, and multiply it by the gearbox/drivetrain ratio you have. Keep in mind some will be lost to efficiency, so you might have to make an estimate at drivetrain efficiency.

Traction force is going to be more than a little tricky- traction on what surface? You'll need to know what surface is being considered, and the coefficient of friction for the tires on that surface. Since this is an off-road vehicle, traction in dirt will probably be you surface of interest, but I doubt you'll be able to find a regular "coefficient of friction" for it since dirt is such a loosely packed material... You may need to design a test rig that can measure the static and dynamic coefficients of friction for the specific tries you plan to use on varying surfaces.

Acceleration (max) will depend on the two above, friction will be your big ticket item here. Once you've got your max aceleration and torque values, the next step will be calculating the torque at the wheels as a function of engine speed, and therefore the acceleration of the vehicle as a function of engine speed (and therefore time).

 

[thehitchhiker]

Torque at wheels is calculated by multiplying the engine torque by gear ratio or is it dividing? And how will I get max acceleration once I do have torque at the wheels?

And finally, how would I calculate the acceleration and torque as a function of engine speed?

Thanks in advance!

 

[xxChrisxx]

You can't calculate anything as a function of engine speed as you only have two fixed values.
You'd need either a torque or power output at every rpm (ie a dyno readout). You'll need the wheel radius.

Also it might be a good idea to learn how gears work and the relationship between torque and power before you do anything else.

Power = Torque * Angular Velocity

Power must be constant (for calculation), so a gear ratio will alter the the torque and angular velocity by a proportional amount.
An output gear double the size, rotates half the speed as the drive gear. As such torque must double.

 

[thehitchhiker]

Ok so here's what I've done so far,
The cap on top speed for the vehicle is 60km/hr.
I assumed the max speed that we will reach to be40km/hr

Following that I used the relationship
V (km/hr) = pi * D * N * 60
Where V is velocity of the wheels, D is diameter which is 21in or .5334m and N is rpm

So I found N to be 397.83.

I then used this and equated P(engine) = P(wheels)
P= 2 * pi * N * T

Thus,
N(engine) * T (engine) = N(wheels) * T(wheels)
3000 * 19 = 398 * Tw

Tw = 143.21Nm of torque.

Would this be right? And how much would it decrease by when considering losses?
Also, the assumption in speed of wheels is probably wrong...

 

[jack action]

You can find what will affect the performance of your vehicle http://hpwizard.com/car-performance.html" (check out the theory at the bottom of the page);

And the tire-road characteristics http://hpwizard.com/tire-friction-coefficient.html" .