Why is my car acceleration not matching the calculated force?

[Jonsson]

Hello there,

Just got an old car, and I was looking at the specifications, and trying to teach myself Newtonian physics. But I cannot get it to work out correctly. Please tell me where I go wrong.

The car weighs 900 kg. The engine has 200nm of torque, it accelerates from still to 27.7 m/s in 8 seconds. The radius from the center of the drive axle to the outside of the tire is circa 0.3m.

$F = m\,a$

Assuming constant acceleration:

$F = m\frac{v}{t}$

$F = 900\mathrm{ kg}\frac{27.7\mathrm{ m/s}}{8\mathrm{ s}}$

$F = 3116\,\mathrm{ N}$

So, to go from zero to 100km/h in 8 seconds takes 3116 N. This is not taking aerodynamic drag and drivetrain friction into account.

This is where I go wrong I think. The car has 200 Nm of torque:

$\tau = 200\,\mathrm{Nm}$

I have an arm of 0.3m (the distance from the centre of the wheel to the outside of the tyre)

$F = \frac{\tau}{r}$

$F = 666 N$

The problem is $3116\,\mathrm{ N} >> 666\,\mathrm{ N}$

And this is without even taken aerodynamic drag and drivetrain losses/friction and all of that jazz into account.

How come my maths is off by so much?

Thank you for your time.

Kind regards,
Marius

NOTE: Looks like my numbers may be off by a factor of 2∏ ? Not sure where it should go though.

 

[mfb]

You have to take the gear into account, it can increase the torque (and reduce the rotation frequency).

Quick check: a typical wheel has a diameter of ~50cm. At 30m/s, it rotates with 1200rpm. That is not the range where you operate the engine to accelerate.

 

[Jonsson]

These are the gear ratios of the car:


1st 3.80 : 1
2nd 2.06 : 1
3rd 1.26 : 1
4th .89 : 1

final drive ratio 4.125 : 1

Do you think I am right in multiplying the ratio of the gear with the differential final drive ratio?

F = 200Nm * gear ratio * final_drive_ratio/0.3m

Thank you for your time.

Kind regards,
Marius

 

[SteamKing]

That's what a gearbox is for. You have a higher overall gear ratio when starting in first gear to keep the engine from stalling. Once the car is moving, you change gears to reduce the overall ratio until you reach the point where the wheels are rotating at a speed which won't cause the engine to stall, and the engine is turning at sufficient RPM to keep the car moving at a constant travel speed.

When you are accelerating to speed, unless you do it in a single gear, the analysis in the OP is not valid.

 

[PJC01]

Hello Marius,

It seems like you have done a great job in trying to understand the physics behind your car's acceleration. However, there are a few factors that could be contributing to the difference between your calculated force and the actual acceleration of your car.

Firstly, the calculation you have done assumes that the engine's torque is being directly transferred to the wheels without any losses. In reality, there are various losses, such as friction in the drivetrain and aerodynamic drag, that can significantly reduce the amount of force that is actually applied to the wheels. This can result in a lower acceleration than what is predicted by your calculations.

Additionally, the specifications of your car may not be completely accurate or may not take into account external factors such as the condition of the road surface, tire pressure, and other variables. These can also affect the acceleration of your car and may explain the difference between your calculated force and the actual acceleration.

Furthermore, your calculation assumes constant acceleration, which may not be the case in real-life situations. Factors such as the weight distribution of the car, road conditions, and the driver's actions can also affect the acceleration of the car.

In conclusion, while your calculations are a good starting point in understanding the physics behind your car's acceleration, there are many other factors that can affect the actual acceleration of the car. It is important to keep in mind that real-life situations are often more complex than theoretical calculations and your car's performance may not always match your calculations exactly.

I hope this helps in addressing your question. Keep exploring and learning about the physics of your car, and don't be discouraged by small discrepancies in your calculations. It takes time and practice to fully understand and apply these concepts. Good luck!

Best regards,