13 replies to this topic

[OO7]

Assuming a 600kg F1 car can negotiate a particular corner at 150mph, would a 1200kg F1 car need to generate twice the amount downforce to take the corner at the same speed?.

Thanks
obi

[red300zx99]

More info is needed on the corner, or more specifically the lateral g's the car is moving. If the 600kg car is going 150mph around the corner yet only going 1g then the 1200kg car could probably do the same thing with no downforce at all, but if the car is travelling at 2g(which usually requires downforce) then yes the 1200kg would need about 2x the downforce of the 600kg car.

[OO7]

Originally posted by red300zx99
More info is needed on the corner, or more specifically the lateral g's the car is moving. If the 600kg car is going 150mph around the corner yet only going 1g then the 1200kg car could probably do the same thing with no downforce at all, but if the car is travelling at 2g(which usually requires downforce) then yes the 1200kg would need about 2x the downforce of the 600kg car.

Thanks for your reply red300zx99.
My original post wasn't very clear. Firstly I'm assuming the cars are identical in every way with the exception of weight and the corner is taken in the fastest method possible, i.e entry, apex and exit points at the cars limit.

1) If the 600kg car produced zero downforce, relying totally on mechanical grip to negotiate the corner at 150mph and it's maximum lateral g-loading, the 1200kg car would need twice the mechanical grip to do the same right?.

2) If the 600kg car negotiated a corner 150mph at it's maximum lateral acceleration and was producing 2000lbs of downforce, an identical car at 1200kg would need 4000lbs of downforce to round the corner at 150mph. Is this correct?.

Cheers
Obi

[seryt]

Originally posted by Obi Offiah

Thanks for your reply red300zx99.
My original post wasn't very clear. Firstly I'm assuming the cars are identical in every way with the exception of weight and the corner is taken in the fastest method possible, i.e entry, apex and exit points at the cars limit.

1) If the 600kg car produced zero downforce, relying totally on mechanical grip to negotiate the corner at 150mph and it's maximum lateral g-loading, the 1200kg car would need twice the mechanical grip to do the same right?.

2) If the 600kg car negotiated a corner 150mph at it's maximum lateral acceleration and was producing 2000lbs of downforce, an identical car at 1200kg would need 4000lbs of downforce to round the corner at 150mph. Is this correct?.

Cheers
Obi

(1) would be correct if it refers to the total mechanical load directed to the centre of curvature for the path of the cg of the car. This would only apply in steady state parts of the turn (i.e. const speed, const radius etc).

(2) The effective friction coefficient of the tyres will drop with increasing vertical load so the heavier car would probably need more than double the total vertical load to generate the required side force.

[GregorV]

Imagine at first that the tyres' grip coefficient is load independent, which is of course not the case but it's best to start the discussion from this point of view to more clearly separate the effects. In this case, if there is no downforce, then a 600kg car and a 1200kg car would in principle be able to take the corner at exactly the same speed as the lateral capability of tyres is also doubled since more vertical force is pushing them down. You can also think of this case as the case of really slow corners.

If you now put in downforce, and assume that the car is going so fast that the weight of the car contributes a negligible ammount to the total vertical force (which is in really fast corners), then indeed you need double the downforce on the 1200kg car if you want the tyres to produce twice the lateral force which is needed to make the heavier car corner at the same speed. This is also the main reason why a heavy fueled F1 car is much slower than an empty one, it doesn't have as much to do with acceleration being reduced due to weight but with the inability to corner as fast in the fast corners where downforce is crucial.

The actual situation is of course always somewhere in between the two extremes, so you'll never need more than twice the downforce to make a 1200kg car corner at the same speed as the 600kg car. If you, however, now also include the effects of tyre load sensitivity, which is an effect where the grip coefficient of the tyre drops with the load applied to it, this disadvantages the heavy car in all regimes, be it in slow corners where there's no downforce (a heavy car will never be able to corner with the same speed on the same tyres as the light one) and even more in the fast ones, where the forces and consequently the loads on the tyres are that much more increased.

[Paolo]

Excellent post, GregorV.
About load sensitivity, a 20% grip reduction can be expected for the heavier car.... hardly negligible.

[McGuire]

It might be better to blow up this thread and start over. :

If we double the weight of the car it will not corner at the same rate, in principle or otherwise. The vertical load sensitivity of the tires is not really the problem. We are trying to change the direction of a body in motion, but we just doubled its mass.

[OO7]

Originally posted by McGuire
It might be better to blow up this thread and start over. :

If we double the weight of the car it will not corner at the same rate, in principle or otherwise. The vertical load sensitivity of the tires is not really the problem. We are trying to change the direction of a body in motion, but we just doubled its mass.

1) Assuming theoretical tyres with a linear coefficient of friction would the heavier car require twice the amount of downforce as the lighter car?.

2) Assuming practical tyres with more realistic load sensitivity, can we expect the heavier car to need more than twice the amount of downforce as the lighter car?.

3) Its impossible to say and depends totally on the tyre and the amount of load it was designed to support. E.g put F1 tyres on a GT car and once the load on the tyres exceeds the nominal range observed on an F1 car the amount of grip avaliable would taper of dramatically. Perhaps the GT car in this scenario would need three or four time the amount of downforce as the F1 car, or perhaps the curve that represents friction & load for the tyre is such that the tyre achieves destruction before the necessary loads are acquired.
If the tyre is designed from the outset as an F1 tyre for a GT car, perhaps there are unavoidable compromises which would make it less efficient?.

Also, because of load sensitivity would the aerodynamic load needed to support a 600kg & 1200kg car be divergent?. A 150mph corner would require 2000lbs & 4500lbs of downforce respectively, a 180mph corner 3000lbs & 8000lbs?.

Obi

[McGuire]

Originally posted by Obi Offiah


1) Assuming theoretical tyres with a linear coefficient of friction would the heavier car require twice the amount of downforce as the lighter car?.


Obi

The short answer is yes, theoretically.

[Dmitriy_Guller]

Originally posted by GregorV
Imagine at first that the tyres' grip coefficient is load independent, which is of course not the case but it's best to start the discussion from this point of view to more clearly separate the effects. In this case, if there is no downforce, then a 600kg car and a 1200kg car would in principle be able to take the corner at exactly the same speed as the lateral capability of tyres is also doubled since more vertical force is pushing them down. You can also think of this case as the case of really slow corners.

If you now put in downforce, and assume that the car is going so fast that the weight of the car contributes a negligible ammount to the total vertical force (which is in really fast corners), then indeed you need double the downforce on the 1200kg car if you want the tyres to produce twice the lateral force which is needed to make the heavier car corner at the same speed. This is also the main reason why a heavy fueled F1 car is much slower than an empty one, it doesn't have as much to do with acceleration being reduced due to weight but with the inability to corner as fast in the fast corners where downforce is crucial.

The actual situation is of course always somewhere in between the two extremes, so you'll never need more than twice the downforce to make a 1200kg car corner at the same speed as the 600kg car. If you, however, now also include the effects of tyre load sensitivity, which is an effect where the grip coefficient of the tyre drops with the load applied to it, this disadvantages the heavy car in all regimes, be it in slow corners where there's no downforce (a heavy car will never be able to corner with the same speed on the same tyres as the light one) and even more in the fast ones, where the forces and consequently the loads on the tyres are that much more increased.

I disagree with your analysis of the case where tire coefficient is not sensitive to load. If you assume such theoretical tire, then regardless of how aerodynamically dependent the car is in the corner, it would need exactly twice the amount of downforce to corner at the same speed with twice the weight.

[Dmitriy_Guller]

Originally posted by Obi Offiah


1) Assuming theoretical tyres with a linear coefficient of friction would the heavier car require twice the amount of downforce as the lighter car?.

2) Assuming practical tyres with more realistic load sensitivity, can we expect the heavier car to need more than twice the amount of downforce as the lighter car?.

3) Its impossible to say and depends totally on the tyre and the amount of load it was designed to support. E.g put F1 tyres on a GT car and once the load on the tyres exceeds the nominal range observed on an F1 car the amount of grip avaliable would taper of dramatically. Perhaps the GT car in this scenario would need three or four time the amount of downforce as the F1 car, or perhaps the curve that represents friction & load for the tyre is such that the tyre achieves destruction before the necessary loads are acquired.
If the tyre is designed from the outset as an F1 tyre for a GT car, perhaps there are unavoidable compromises which would make it less efficient?.

Also, because of load sensitivity would the aerodynamic load needed to support a 600kg & 1200kg car be divergent?. A 150mph corner would require 2000lbs & 4500lbs of downforce respectively, a 180mph corner 3000lbs & 8000lbs?.

Obi

I'll take a crack at this as well:

1) Yes.
2) Yes.
3) Yes. The higher the speed, the greater the relative spread would be. If tires have a maximum friction force that they can produce, then that spread would increase without bound, and at some point the car simply won't be able to take the corner at the same speed with twice the weight, no matter much downforce you can muster (you can say that the spread would be infinity, so it is divergent). That's why the effect of changing car weight is magnified in aerodynamic cars.

[GregorV]

Originally posted by Dmitriy_Guller

I disagree with your analysis of the case where tire coefficient is not sensitive to load. If you assume such theoretical tire, then regardless of how aerodynamically dependent the car is in the corner, it would need exactly twice the amount of downforce to corner at the same speed with twice the weight.

You are, of course, correct

[Christiaan]

okay I am very very rusty at this, but if the cars were going through a perfect arc then the centripetal acceleration will be m*v^2/r where m=mass, v=velocity and r=radius of the corner.

Now the required force on the tyres would be equal and opposite and in a shear plane would be F=mu*N where mu=the coeff of friction and N is the normal reaction force. However the Normal Reaction force is made up of the weight of the car and the downforce. So we can say

m*v^2/r = mu (mg + D) and hence the downfrce required to corner at a particular speed through a gven radius would be

D = m*v^2/(r*mu) - mg

or

D = m( v^2/rmu - g)

and from this we can conclude that independant of how mu behaves with changes in velocity, the required downforce is directly proportional to the mass. Doubling the mass will requre double the downforce.

If however, the tyre coeff changes with the load then it becomes

D = m/f(m) wehere f(m) is a function of mass

Er - correct me if I am wrong

[OO7]

Thanks for the answers guys

I actually started this thread because of Michael Fuller's excellent sportscar website here:Mulsanne's Corner The aerodynamic information at the site states that the latest generation of GTP IMSA sportscars could produce 10000lbs of downforce at 200mph. These cars weighed 900kg-980kg assuming a 70kg driver, while F1 cars at the time were 575kg? with the driver and probably created about half as much downforce. Formula 1 cars have always been the fastest vehicles around corners, but its fun pondering over the potential cornering capacity of a GTP IMSA car on F1 style sprint tyres.

Cheers
Obi