Equation for weight?

[djones]

Is there a simple equation or rule for how weight affects the cornering and braking ability (i.e grip) of a car.

For example if you have a car that weighs 1000kg then add 500kg to that exact car is the ability to grip (create G) 50% less???

[RH1300S]

I hope the engineers here will be able to answer fully.

But doesn't this come back to E=mv2?

So to corner twice the mass at the same speed requires 4x the grip? (or - indeed the same mass at twice the speed needs 4x grip)

[Cyco]

RH; E = mc^2 has absolutely nothing to do with this situation (despite a certain car mag promoting it as an explanation for some things). This is for relativistic motion, and while F1 is fast, its not that fast.

A better explanation is to forget Einstein and go back to Newton's equations of motion, mainly F = ma. The lateral force on the tyre comes from the mass and its acceleration (in this case laterally).

A great post about tyre grip and loadings is HERE, by Ciro

[RH1300S]

I know - I must have edited my post when you posted

E=mv2

Newtonian (ish) - wasn't Newton modified from E=mv to E=mv2 by someone else?

BTW - I have hit the limit of my knowledge.............

[Roland Ehnström]

RH1300S, you are correct about that, but it's only the velocity that is squared in E=mv2, not the mass. If you want to double the velocity you must add four times the energy, but if you double the mass you must only double the energy.

Anyway, it is easier to talk about force than energy in this case, so F=ma is more relevant. If you double the mass you must double the side-force from the tires, or else you will crash. However, this does NOT mean that you will only be able to go half as fast, because when you double the mass you will also gain a lot of grip from the tires simply because they are pressed harder to the ground.

Therefore, I would guess that adding 50% mass would only reduce the cornering and braking ability of the car by 10% or so (given that the brakes are still effective enough to lock up the tires).

[xpensive]

Interesting, perhaps one of the moderators can straighten this delicate issue out?

[Belatti]

I can build that ecuation, but it would be soooo big and full of estimated/empirical coeficients that it would be pointless.

[xpensive]

You are way too modest, Gaucho.

[Jersey Tom]

This makes no sense.

Short answer: No.

Long answer: Not even remotely.

Also has nothing to do with E=m*c^2, nor KE=1/2*m*v^2

Really long answer: Not gonna type out just yet. Look up tire load sensitivity...

[Roland Ehnström]

Look up tire load sensitivity...

Yep, that's exactly what I was getting at when I wrote this:

when you double the mass you will also gain a lot of grip from the tires simply because they are pressed harder to the ground.

Jersey Tom and I are completely agreed, but I do think my answer was perhaps a tad more informative.

[RH1300S]

Thanks guys - helped me

Roland - of course the double the mass thing makes sense - all I had to do was THINK (which I did driving home last night)

Tyre load sensitivity was where I was heading next - Carrol Smith explains it well - although I think he was explaining why double the aero load doesn't double the grip (because of tyre load sensitivity).

[xpensive]

Myself, I humbly imagine the following:
- Mass is proportional to centripetal accelleration when cornering, as Lateral force = mass* speed^2/Radius.
- Tyre-force (friction, adhesion or whatever) is not proprtional to vertical load, a wider tyre gives more grip.
- Besides, an increase of mass at the same vertical CoG, will also increase yaw(?) or roll.

[Belatti]

You are way too modest, Gaucho.

Why the sarcasm? Dont you know how the physics of a racing simulation PC game are made? Those are oversimplified versions of this.
It can be made, its not that hard, but it would take a lot of time and like I said it would be a large large ecuation full of estimated and empirical coeficients.

[Roland Ehnström]

Actually, the easiest way to get an approximate answer to the original question would be to test this in a racing simulation (computer game). Hack a game to add 500 kg to the cars and see how much slower you can go through the corners.

[Ciro Pabón]

If:

- circular curve, constant radius
- same grip in all wheels (no weight transfer)
- constant speed

it all boils down to friction factor f (or Gs) being equal to speed V squared divided by radius R minus the sideslope e:



No term for mass, so, the Gs are the same. In principle, a car that weighs 1.5 times more (1500 kg instead of 1000), takes curves with the same friction factor or Gs. That is, the grip is the same.

That's the reason why a truck, that weighs 60 tons can take curves at more or less the same speed of a car that weighs 1 ton.

This equation assumes that the lateral force a tyre can create is proportional to the weight of the car, but that's not true.

So, a first good approximation is through the use of curves for friction factor of a tyre, measured in real life, like Pacejka's, which is what simulators use. Again, in those equations, used by simulators, AFAIK, there is no influence of the mass of the vehicle in its cornering ability. There is influence of mass and suspension on weight transfer, but that, as pointed out, is a much more complex equation. Being complex, it's not what was asked.