# Computing Wheel Torque From Engine Torque

It seems possible to obtain engine torque and RPM from a truck CAN bus. I'd like to estimate tractive force at the wheels given these two values.

How should I go about computing torque at the wheels? Wouldn't I need gear ratio, which doesn't seem obtainable from the CAN bus?

(also asked this question on physics.stackexchange)

• Are you asking to obtain torque value output at the wheels in any given gear? If so, this would be very hard to do for any given vehicle, because the amount of parasitic loss for any given vehicle is going to be different. There is a general rule of thumb that you lose ~15% hp/tq through the drivetrain of a vehicle with an standard shift transmission, while you lose ~18-20% with an automatic. These are just rules of thumb. The differential gear ratio will be static on any given vehicle, but will can be different between makes/models. Final gear ratio will be different as well. Hard to compute. Jan 13, 2016 at 11:26
• Crossposting in Stack Exchange is highly discouraged. meta.stackexchange.com/questions/64068/… Jan 14, 2016 at 4:09
• Apologies for the crosspost but I appreciate Paulster2's unique perspective. My thinking is that I should be able to create a model that estimates total mechanical advantage from vehicle speed (hence wheel rpm) and engine rpm. My model will also take into account transmission losses etc, to come up with a good estimate for tractive force. Thanks all. Jan 14, 2016 at 10:58

The basics are quite simple.

The motor generates a certain torque `N` and a certain power `P` at a given RPM. Further more, the relation between power and torque is:

``````P = C * N * RPM
``````

where `C` is a constant to convert all that odd units. For `N`, `P` in SI units, it is

``````C = pi / 30
``````

Neglecting any losses, Power is conserved from the motor to the wheels so you can say

``````C * N_motor * RPM_motor = C* N_wheel * RPM_wheel

N_wheel = N_motor * RPM_motor / RPM_wheel
``````

The RPM of the wheel can easily be derived from speed and the rolling circumference of the wheel `R_wheel`. (Keep in mind, the rolling circumference is smaller than the geometrical circumference, as the tire is flexible.

Since you are more interested in the tractive force `F_wheel`, it is

``````N_wheel = F_wheel * R_wheel
``````

and so

``````F_wheel = N_motor * RPM_motor / (RPM_wheel * R_wheel)
``````

As it's also `v = pi * RPM_wheel * R_wheel / 30` (velocity in m/s) you can write

``````F_wheel = N_motor * RPM_motor * pi / (v * 30)
``````

This means, if you really have the torque the motor currently delivers, the RPM of the motor and the speed of the truck, you can calculate the total force applied to the street. It's strange that gear ratios don't appear, but they are hidden in the ratio `RPM_motor / RPM_wheel` or `RPM_motor / v`.

In reality, there are lots of non neglible losses, as Paulster2 wrote in his comment. Every bearing and every gear wheel has some friction, taking away some torque and power. If this torque is constant, the power loss will be linear to the RPM of this part, but usually, torque will increase with RPM, so the power loss grows even faster with RPM.
This means the loss is not constant, it varies with RPM and gear!
One interesting fact: A clutch transfers power / torque by friction. For a slipping clutch, torque is the same on both shafts, but power is lost due to the difference in RPM...

And to make it clear again: You do need the measured torque from the motor, max torque at given RPM is not what you need.

• Fantastic answer, sweber. Two questions: a) There's no way of determining accurate rolling circumference of wheel without say, installing sensors on the wheel, correct? b) Is the torque reading from the CAN bus sufficient for your calculations above? Jan 19, 2016 at 15:19
• a) It's easy to measure the distance when the wheel did... let's say 10 revs. However, the rolling circumference also changes with load and tire pressure. b) I don't know. But as said, there are lots of not precisely known losses up to 20% over the entire transmission line from motor to the wheels. This already makes the calculated value quite imprecise, so what does an imprecise torque reading from the motor matter? Jan 19, 2016 at 19:54
• Can your answer be refactored in any way to cater for the actions of a standard, "open" differential. How would you change it to cater for limited slip or lock diffs and does it assume grip is not exceeded and neither wheel is spinning. On FWD applications, how to you cater for slip angle when the wheels are not at the straight ahead position and could it also cater for differences in wheel angle due to steering geometry design and the effects of differing effective corner weights on load. Jan 29, 2019 at 11:16

Actually guys the ECU it self calculate torque in auto transmission cars, to know how to shifts in a good sequence, This number is accessible, You can read it from live data from obdii scanner device

• Is that "wheel" torque? "engine" torque? which losses are included or not? Jan 29, 2019 at 9:04
• Me no believe. I know my way around Service 01 PIDs, and there's no such animal. Unless you are talking about driver request of engine torque percent or something. Jan 30, 2019 at 4:51