Maximum possible acceleration of an F1 car?

[Przemator]

Hi all,

I am trying to make a simple 2D F1 game. I am trying to use realistic physics, but some numbers just don't add up. I want to calculate the maximum possible acceleration of an F1 car (how fast can it accelerate without losing grip, disregarding engine power). To do this, I'm using a couple of formulas.

1. The acceleration:

acceleration = traction_force / car_mass

2. Traction force (maximum):

traction_force = friction_coefficient * car_weight

3. Car weight:

car_weight = g * car_mass * weight_distribution

So this gives us:

acceleration = friction_coefficient * g * weight_distribution

I am using these values, not sure if correct:

car_mass = 800 kg
friction_coefficient = 1.7
g = 9.8 m/s^2
weight_distribution = 0.56 (engine force only delivered to rear tyres)

So this gives us:

acceleration = 1.7 * 9.8 m/s^2 * 0.56 = 9.33 m/s^2
max_traction_force = acceleration * car_mass = 9.33 m/s^2 * 800 kg = 7464 N

With this acceleration, it would take the car 3 seconds to reach 0-100 km/h (28 m/s). It seems very low.

Please note, that it would also take 3 seconds for the car to stop from 100-0 km/h.

I have omitted aerodynamics, because I think the wings + diffuser begin their magic at much higher speeds that 100 km/h.

downforce = downforce_coefficient * velocity^2 = 1 kg/m * (100 km/h)^2 = 772 N

Can you please tell me if my calculations are right? It seems like I am missing something. I would appreciate your help.

[PlatinumZealot]

2.8 seconds.

[user001]

2.6 secs with kers: http://www.youtube.com/watch?v=h31A4vuhtRI

[machin]

one thing you've not taken account of is the effect of the CG being above ground level... when accelerating this means that there is more than the static weight on the rear tyres... therefore the rear tyres have more traction...

add in that effect and your numbers will be pretty close to reality I reckon.

[Przemator]

Let me just stress it, that I'm looking for the maximum acceleration (or deceleration) that F1 tyres can handle without losing grip.

You are saying 2.6 sec, but does it mean that if Alonso had a bit more torque in his car and tried to do it in 2.5, his wheels would start skidding? Obviously F1 drivers have to be careful when accelerating, because a few years back they had Traction Control enabled.

one thing you've not taken account of is the effect of the CG being above ground level... when accelerating this means that there is more than the static weight on the rear tyres... therefore the rear tyres have more traction...

add in that effect and your numbers will be pretty close to reality I reckon.

Thanks for your reply. I read somewhere that F1 car has an extremely low CG of 15 cm above ground! Plus it has a very hard suspension which does not allow for the weight transfer to alter much.

[machin]

The effect happens irrespective of the compliancy of the suspension... it happens if you have solid suspension, or soft suspension, and the magnitude is the same, it is simply the application of moments about the tyre contact patches. It is NOT the physical movement of mass as a result of suspension compliancy as this effect is very small.


CG of an F1 car is likely to be higher than 0.15m in my opinion, but happy to be proven wrong if someone can provide a good link.

[ChipAyten]

Without TC its not often you see 0-100 in the 2.6 range much anymore. Keep in mind that when TC was legal the tyres were not slick but treaded. Im pretty sure they don't cancel out but it is something to consider.

[clipsy1H]

2.6 on with full tank... probably will be under 2.1->2.3

[machin]

2.6 on with full tank... probably will be under 2.1->2.3

The interesting thing is that on an F1 car the weight of fuel makes very little difference to the low speed acceleration... the reason is that at low speed the car is traction limited.. adding extra fuel means you have to accelerate more mass, but it also means that you have more traction (more weight pushing down on the driven wheels), so the two basically cancel out.

The same is NOT true of a FWD car with the fuel tank in the rear... in this case the extra fuel means that you have to accelerate more mass and it doesn't contribute to traction because its over the rear wheels.....

Its also not true of a light-weight, front engined, RWD car in which case the extra fuel is generally right over the rear wheels, that actually means that the car may have relatively more traction (since there is the extra weight AND the cg is moved backwards) compared to the increase in mass and therefore the car may actually accelerate (at slow speeds where it is traction limited) faster with more fuel in it!

[user001]

what was the highest ever topspeed? I don't know as i recall Montoya with ~357 kph in monza. don't know the year. maybee 2004 or 2005?

Sergio Perez was 348 kph fast in monza i think last year.

does anyone have torque curves/diagramms of straight line tests?

[PlatinumZealot]

2.6 on with full tank... probably will be under 2.1->2.3

The interesting thing is that on an F1 car the weight of fuel makes very little difference to the low speed acceleration... the reason is that at low speed the car is traction limited.. adding extra fuel means you have to accelerate more mass, but it also means that you have more traction (more weight pushing down on the driven wheels), so the two basically cancel out.

The same is NOT true of a FWD car with the fuel tank in the rear... in this case the extra fuel means that you have to accelerate more mass and it doesn't contribute to traction because its over the rear wheels.....

Its also not true of a light-weight, front engined, RWD car in which case the extra fuel is generally right over the rear wheels, that actually means that the car may have relatively more traction (since there is the extra weight AND the cg is moved backwards) compared to the increase in mass and therefore the car may actually accelerate (at slow speeds where it is traction limited) faster with more fuel in it!

Agreed. If we were talking quarter mile though... that would be interesting.

[Belatti]

what was the highest ever topspeed? I don't know as i recall Montoya with ~357 kph in monza. don't know the year. maybee 2004 or 2005?

Sergio Perez was 348 kph fast in monza i think last year.

does anyone have torque curves/diagramms of straight line tests?

The top speed ever acheived by a formula one car during a race was 369.9 km/h (229.8 mph) set during the 2004 Italian Grand Prix at Monza, Italy by driver Antônio Pizzonia of the BMW Williams F1 team driving the FW26 powered by a BMW 3.0 litre v10.

[Lurk]

During a race it is Pizzonia, otherwise it is Montoya the year after: 372.6km/h. It was on private testing at Monza 1 week before the GP.

There is also a BAR which reach 400km/h but the car was specially prepared for the occasion and it wasn't an F1 track.