■How to calculate car acceleration from engine torque

Engine torque is described in automobile catalogs as follows, and the torque transmitted from the engine to the transmission is shown in the figure below.

・ Maximum torque (Nm/rpm)：142/3,600
・ Maximum power (kW/rpm) ：72/5,200

The torque generated by the engine is amplified by two gears (transmission gear, final gear) in the transmission and differential.
While this causes transmission loss, it is eventually transmitted to the tires and becomes driving force.
To calculate the drive force, first calculate the torque of the drive shaft. The formula is as follows.
Inertia is how difficult it is for a rotating body to rotate, and a load is generated in proportion to the angular acceleration and inertia.

Next, calculate the driving force transmitted to the tire.
Dividing the torque of the drive shaft by the radius of the tire gives the driving force. The concept is based on the principle of leverage.
When a force T is applied from a distance of r[m] from the central axis, a force of T・r is applied to the central axis.
If you apply a force at a distance r[m] from the central axis, you need to divide the torque by r.

Finally, the acceleration is obtained from Newton's second law, F = ma, so the amount obtained by subtracting the running resistance from the driving force is divided by the vehicle weight.

■Approximate acceleration from engine torque

In order to obtain the approximate acceleration, the following calculation may be used.
It is a form that omits transmission loss and inertia load.

■Method for calculating vehicle speed from acceleration

However, just because the engine continues to generate torque does not mean that the vehicle speed will increase forever.
The reason for this is, first of all, when the gear stage is low, the engine speed rises quickly and reaches the upper limit of the speed, which automatically limits the torque.
The upper limit of the rotation speed is set so that the engine does not break down.

Next, even if you raise the gear stage before the rpm reaches the upper limit, the upper limit of the vehicle speed will be reached, and the torque will be automatically limited again.
In countries where there is no upper limit on vehicle speed, the higher the vehicle speed, the greater the running resistance.
Eventually, the driving force and running resistance will balance and the vehicle will not accelerate any further.

■Power is not required to calculate acceleration and vehicle speed

As explained so far, only torque was needed to calculate acceleration and vehicle speed, power was not used.
I didn't even use the engine speed. So what exactly is power? I will explain it here.

■Specific example of obtaining acceleration from engine torque

As a specific example, let's approximate the acceleration of the vehicle from the official specifications of Mazda3.
According to information on the internet:

It has been announced that the 0-100km/h time is 8.2 seconds, so we will use this as the answer for the calculation results from now on.

＜Calculation＞
First, calculate the tire radius from the tire specs. The calculation method is explained here.

From the above, we were able to obtain a value that is reasonably close to the official announcement of 8.2 seconds.
One of the reasons why the calculated value differs from the official announcement value is that the gear ratio is calculated on the premise of 3rd gear.
If you want to calculate it more accurately, you need to consider the torque for each rotation, the shift pattern and the gear ratio.

In addition, mazda3 was improved in November 2020, and the torque became 240Nm / 4500rpm.
In order to visualize the change in vehicle speed with respect to torque change, when calculating the time from 0 to 100 km/h when only the torque condition is 240 Nm, it is 8.7 seconds.