“Torque wins races” is a very often repeated but inaccurate saying, even though it seems right and is very often repeated in the popular press. The equation of motion of a vehicle is:
Acceleration is proportional to [power at the wheels] / [(vehicle speed) x (vehicle mass)]
This is just physics and is derived from Force = Mass x Acceleration. Power at the wheels is proportional to power at the engine, but torque at the wheels is not; because the transmission multiplies torque (gearboxes do not multiply power!). This means that at any instant in time, the amount of acceleration you can feel will be proportional to the power available from the engine. I am assuming relatively constant transmission efficiency. Of course it also means that the more a vehicle weighs the more power you need, and that it takes twice as much power to feel a certain level of acceleration at 40 mph as 20 mph. The ultimate determinant of vehicle performance is the area under the power curve between the usable rpm limits. This is not equal to the area under the torque curve.
You can make up for a lack of torque (or low-end torque) with gearing, you cannot make up a lack of power with optimized gearing. Of course, for 2 different engines with the same peak power, the one that has higher peak torque (or low-end torque) will have more area under its power curve and be faster, except at power peak.
If you are restricted to a particular gear, the peak acceleration will occur at the peak torque speed of the engine but will only occur at the vehicle speed corresponding to that speed. At any speed, you will find that the peak acceleration will occur by selecting the gear that will get you as close to peak horsepower, and choosing a gear that brings you closer to peak torque will be slower. That is why race drivers shift after hitting peak power.
Derivation of Equation of Motion:
Basic Vehicle Equations:
•Force = Mass x Acceleration
•Force at the wheels = Torque at the wheels / Radius of wheel •Therefore: Accel = [Torque(w) / R(w)] / Mass
•T(w) = Torque at the Engine x Overall Gear Ratio
•Accel = [Torque(e) x OGR / R(w)] / Mass
•Which means that as long as the overall gearing is fixed (within a gear in a manual transmission vehicle), the acceleration that you feel will be proportional to the engine torque.
•Does this mean that all that counts in vehicle performance is Torque to weight ratio?
•No, because: You also need to know the tire diameter and all of the gear ratios
•There is another formula that describes vehicle Acceleration.
•What if we take this equation; Force at the wheels = Torque at the wheels / Radius of wheel and put in terms of Power?
Derivation as follows:
Fw = Tw/R
= Pw/R x Ww substitute (Tw = Pw / Ww)
= Pw/Vw (Vw=Ww x R)
- Fw is force at wheels = force accelerating vehicle
- Tw is Torque at wheels = Engine torque X overall gear ratio
- Ww is the wheel rotational speed
- Pw is the power at the wheels
- Vw is the linear velocity at the wheels
- R is the drive wheel radius
Derivation as follows:
Fw = Tw/R
= Pw/R x Ww substitute (Tw = Pw / Ww)
= Pw/Vw (Vw=Ww x R)
- Fw is force at wheels = force accelerating vehicle
- Tw is Torque at wheels = Engine torque X overall gear ratio
- Ww is the wheel rotational speed
- Pw is the power at the wheels
- Vw is the linear velocity at the wheels
- R is the drive wheel radius
•Acceleration = Fw / Mass = Pw / (Mass x Velocity)
