Inside fronts heating up mid corner?

[Tim.Wright]

I think a case can be made for anti-Ackerman. With the outer tire more heavily loaded, it will determine the cornering arc. By pointing the inside tire at other than the Ackerman arc a drag force will be generated to help turn the car. This is particularly true at courses with low speed U-turns. So what being seen is perhaps an incidental artifact of the low speed set up.

Ant-Ackerman is more desirable since the camber more favorably presents the tire from the inside out than from the outside in during the dragging event.

The ackermann effect is is insignificant at such low steering angles. The condition of the tyres (w.r.t. slip angles) is largely dictated by the static toe setting when we are talking about small steer angles.

If we take the model above and assume its a neutral steer, then the average steer angle of the front wheels is only 0.546deg (assuming 3m wheelbase, 1G latacc and 200km/h).

If we also assume a 1600mm track width, the dynamic toe-out required at this steering angle to reach 100% ackermann is only 0.0028deg. So basically nothing at all.

Also, due to the low lateral acceleration its also not correct to assume the outside tyre is setting the trajectory. When you are far under the limit, the trajectory is influenced a lot by both the inside and outside wheels.

[olefud]

You may well be right –I’m working from the whole cloth as to what the actual setup maybe. However, with so many low speed, greater than 90° corners negotiated sans aero down force, anti-Ackerman could prove useful. Rather substantial anti-Ackerman seems to be evident in when negotiating such slow, tight turns. If so, with more downforce at the higher speed sections, more steering lock would be necessary for sustained turning since the anti-Ackerman is more effective for turn-in than during sustained turns where the tires would be fighting each other a bit. It’s just a theory.

[Tim.Wright]

To be honest Ackermann is something that I don't have a deep understanding of on a theoretical level.

On road cars Ive seen changes made to the ackermann which supposedly changed the on centre response but I find this pretty hard to accept since, as Ive shown above, the difference between ackermann and parallel steer is measured in thousandths of a degree in the on centre range.

For racecars, I can imagine it has an effect on turn in (with modest steer angles) but Im not sold on the theory that it attempts to allow the left and right tyres to follow the change in "optimum" slip angle as the wheel load changes. When the front tyres are at the limit they are saturated so the subtlties of slip angle mods induced by the ackermann wont change the cornering force much. I could be wrong though. It something I will investigate one day

[Lycoming]

For racecars, I can imagine it has an effect on turn in (with modest steer angles) but Im not sold on the theory that it attempts to allow the left and right tyres to follow the change in "optimum" slip angle as the wheel load changes. When the front tyres are at the limit they are saturated so the subtlties of slip angle mods induced by the ackermann wont change the cornering force much. I could be wrong though. It something I will investigate one day

But even if it doesn't change the cornering force of the inside tire much, if it's saturated, isn't it still preferable to get the same lateral force at a lower slip angle?

[marcush.]

I've done a few calcs and I'm sure its the static toe...

Whats happening is that the lateral acceleration is so low that the slip angles at the tyres that are required to do the corner are about the same as the slip angle imposed by the static toe setting. This results in the inside wheel having a slip angle about double of the static toe value and the outside wheel has zero slip, so is generating no heat.

Here is my justification:

Consider the car driving straight on the entry to the tunnel. In this condition, the slip angles on the front tyres are equal to the static toe angles but opposing left to right.

Assuming 1mm of toe = arctan(1mm/13") = 0.35deg.

Using the ISO convention, that means left and right slip angles of:
Left = +0.35deg // Right = -0.35deg

...occur from driving in a straight line.

During the light curve in the tunnel, the car turns right and the slip angles move in a NEGATIVE direction for both tyres. You can see already that the right (inside) wheel is already negative so it will increase its slip angle. The outside wheel is positive so first it must decrease its slip angle. So its possible that the outside wheel can have zero slip angle while the car is cornering.

To see if this is realistic for the case of the Monaco tunnel we can make a little model (concentrating on the front axle only)...

Input data:
mass = 650kg
distribution = 45%f
driver: Alonso
laptime: -0.6s
LatAcc = 1G (guesstimation of lateral acceleration through the tunnel)
Front cornering stiffness = 4830N/deg per tyre [Milliken F1 tyre c. 1993]

Assumptions:
Tyres are in the linear range
No lateral load transfer

This results in a front axle slip angle of -0.296deg

Note, this is very similar to the static toe value. If we then superimpose the slip angle from the static toe to the axle slip of -0.296deg we get the individual wheel slips:
Left slip = 0.35 - 0.296 = 0.054deg
Right slip = -0.35 - 0.296 = -0.646deg

So we can see that the left (outside) wheel has very little slip angle compared to the inside one which is doing pretty much all the work.

If we use the cornering stiffness then to find the indiviual wheel Cornering forces we get:
Left = 0.054deg x 4830N/deg = 241N
Right = -0.646deg x 4830N/deg = -3111N

Which confirms the outside wheel is not only doing nothing but its lateral force is slightly towards the outside of the turn. This is not a problem because this corner is not grip limited.

If we assume the car is doing 200km/h at this point we can calculate the power input to the tyre which creates the temperature increase that we see from the onboard camera:
P_left = Vel * SlipAngleL * ForceL = 11 Watts
P_right = Vel * SlipAngleR * ForceR = 1943 Watts

So this is why you see the temperature increase on the inside wheel. It is receiving approx 2kW of heating while the outside wheel receives only 0.011kW.

In conclusion, its the static toe angles which are causing an offset to the left and right slip angles. In a low acceleration corner, the slip angles are so small (due to the high cornering stiffness tyres) that the slip angles are just barley enough to cancel the static toe slip on the outside wheel.

Why don't you see this in other corners? In a normal corner which is grip limited, there is significant lateral load transfer which means the outside wheel has a much larger cornering stiffness than the inside wheel. Also, your slip angles will be significantly more than the static toe so there is no chance that the outside wheel is running at zero slip.

Tim at those Speeds aero has a significant influence on vertical force already so the work of the outside wheel is not Zero ,far from it.No ?

[Tim.Wright]

If the outside tyre has practically zero lateral and longitudinal slip then how can the work/energy imparted in it be far from zero?

Downforce doesnt impart a huge amount of work to the tread in my opinion. Its a largely static force but no displacement. To transfer energy to the tyre you need force and displacement in the direction of the force. The only movement in the direction of downforce is that of the suspension and tyre movements. These movements are pretty small and most of the energy from them is dissipated in the damper. Energy dissipation from tyre vertical dynamics would be mainly due to internal damping and hysteresis. I imagine the energy dissipated here is of course non zero but still small compared to the cornerin forces.

[Tim.Wright]

For racecars, I can imagine it has an effect on turn in (with modest steer angles) but Im not sold on the theory that it attempts to allow the left and right tyres to follow the change in "optimum" slip angle as the wheel load changes. When the front tyres are at the limit they are saturated so the subtlties of slip angle mods induced by the ackermann wont change the cornering force much. I could be wrong though. It something I will investigate one day

But even if it doesn't change the cornering force of the inside tire much, if it's saturated, isn't it still preferable to get the same lateral force at a lower slip angle?

Possibly, but I suspect that reducing the slip angle on the inner wheel will result in an increase on slip on the outer wheel... Need to check that hypothesis...

[olefud]

It would seem that the wild card is aero, and possible aero trim, which would determine the relative tire loading. But there would be some inertia weight transfer from the inner to outer tires, though this would probably be a relatively lesser tire loading relative to the aero loading. Still the outer tire would be the more heavily loaded to some extent and thus be dominant in determining the cornering arc. Thus the car would moving through its primary turning arc while each tire would be moving through an arc with the same center as the primary arc though each tire will likely be pointed in a direction other than the primary car arc, i.e. with a slip angle. With likely differing pointing directions and slip angles each tire will develop an overall side thrust which is again likely not through the car’s turn center. The tire thrusts can be resolved into vectors through the cars turn center, i.e. cornering thrust, and a drag component. With substantial pro or anti Ackerman, the more heavily loaded outer tire will travel an arc truer to the cornering arc and generate the primary cornering centrifugal cornering force, while the more lightly loaded and mispointed inner tire will be mostly dragging and heating up.
Of course if the tires are equally loaded the drag component would also be equally distributed.

[thisisatest]

i like the idea of the inner tire dragging while turned in farther, creating a yaw moment and helping the car rotate.
which sends me off topic for a sec...
a while ago there was a forum topic on front toe-out and the idea that it improves turn-in. Jersey Tom suggested that it only seemed like it was improving turn-in because the end steady-state result was greater understeer. i'm thinking that the toe out introduces an inside tire drag, rotating the car about its yaw axis. thoughts?

[Tim.Wright]

There seems to be a common misconception that a "dragging" inside tyre is going to heat up more than the outside tyre. My opinion is this can't be the case in the Monaco tunnel because the lateral load transfer is too low. The inside wheel is still too heavily loaded for it to be simply dragged around following the chassis.

Anyway, I will put some numbers on it again to avoid a lot of handwaving getting out of hand.

Considering a steady cornering situation with no braking or acceleration, the power dissipated by the tyre from the interaction with the road is:
Power = LateralForce x Velocity x SlipAngle

I will recreate Olefud's condition with the outside wheel doing most of the work and the inside wheel being dragged around.

Input data:
Mass = 650
Dist = 45% f
Tyre mu = 2.0

Lets put some aero downforce too:
Cl = 2.0
Balance = 40%f
Frontal Area = 1.5

Cornering condition:
Lateral load transfer = 80% (near the limit, inside wheel is lightly loaded hence the dragging)
Velocity: 100km/h

And the calculations:
At 100km/h in a straight line we have 1435N of mass force plus 289N of downforce on each front wheel so a total of 1724N of vertical load.

Then while cornering with the assumed 80% lateral load transfer this adds 80% of this load to the outside wheel and subtracts it from the inside wheel:
Vertical force outside wheel = 1724N + 80% x 1724N = 3103N
Vertical force inside wheel = 1724N - 80% x 1724N = 344N

With the vertical force and coefficient of friction we can calculate the lateral force:
Lateral Force outside wheel = VerticalForce x mu = 3103 x 2 = 6207N
Lateral Force outside wheel = VerticalForce x mu = 344 x 2 = 690N

Let assume first perfect ackermann so the inside and outside slip angles are the same and are say 4deg which is not unrealistic. This gives us thermal power dissipations of:
Power outside wheel = LateralForce x Velocity x SlipAngle = 12.0kW
Power inside wheel = LateralForce x Velocity x SlipAngle = 1.3kW

So of course here with the same slip for inside and outside wheels, the outside wheel will dissipate more power and heat up more.

Now lets increase the slip angle of the inside tyre to recreate the condition of it being dragged around. Lets double it. So the slip angles are now 4deg out/8deg in. This gives us power dissipations of:
Power outside wheel = LateralForce x Velocity x SlipAngle = 12.0kW
Power inside wheel = LateralForce x Velocity x SlipAngle = 2.7kW

So clearly the outside wheel is still doing all the work here. The conclusion is that dragging a lightly loaded wheel around won't heat it up more than the heavliy loaded outside wheel. To heat up a tyre it need slip AND force acting together, not just one.

So then, why does this example give a higher power on the outside wheel and my last example gave a higher power on the inside wheel? The reason is the load transfer and the level of lateral acceleration were different. In the first example there was a low level of lateral acceleration and no load transfer. This means the slip angles developed are small and comparable in size to the static toe.

In the second example, the lateral acceleration is high and is causing larger slip angles which drown out the small static toe settings. This also causes a larger lateral load transfer to the outside wheel. With little load on the inside wheel, its not possible to heat it up more than the outside wheel.

[Jersey Tom]

i'm thinking that the toe out introduces an inside tire drag, rotating the car about its yaw axis. thoughts?

If you want yaw moment you will get a larger one by pointing the tire's force laterally, acting on half the wheelbase, than you would pointing it backward acting on half track width.

[olefud]

If you want yaw moment you will get a larger one by pointing the tire's force laterally, acting on half the wheelbase, than you would pointing it backward acting on half track width.

That’s a rather compelling point. I’d just move on if it weren’t for some people I respect stating as an empirical fact that toe-out and TOOT –a form of pro-Ackerman by bump steer- were effective band aides for poor turn in.
So, during turn in the tire thrust won’t be at 90° to the car as the tire will be turned and will run at a slip angle. Some of the tire thrust will resolve into drag, which is bad at the more heavily-loaded outer tire. Also, as load shifts to the outer tire it generates yet more drag opposing turn in. The more the tires are turned the worse the useful tire thrust gets as a sine function of the tire thrust to the direction of travel. And drag increases more as the load shifts to the outer tire. So there are some substantial drag forces and force vectoring compromising turn in.
The more lightly loaded inner tire won’t generate as much thrust but, in general, will maintain maximum thrust at high slip angles. By substantially under turning the inner tire rather high drag can be generated to aid turn in. The point being that inner tire thrust forces of such magnitude could not be developed at 90° to the car’s direction of travel.

[Lycoming]

i'm thinking that the toe out introduces an inside tire drag, rotating the car about its yaw axis. thoughts?

If you want yaw moment you will get a larger one by pointing the tire's force laterally, acting on half the wheelbase, than you would pointing it backward acting on half track width.

The yaw center isn't always exactly halfway between the axles is it? Actually, this may be a relevant question, but at the instant when you begin to turn in, would it not be approximately at the rear axle?

[craigp46]

Ok guys, don't post much on here but this was interesting for me to see.

For me this phenomenon is down to suspension geometry. Red bull and other teams are most likely running upright mounted pushrods, meaning it is possible to move weight to the inside wheel when turning the steering wheel, and shift it in large quantities (more than maybe required for certain points on the track). The dallara f3 car runs the same system and I have experience with this type of setup. This weight transfer takes opposite effect at rear axle. Now, if you go back to the start of the race you will hear Riciardos engineer tell him 'no excessive steering inputs when the lights go out' this for me retierates the upright mounted pushrod (ump) because this causes a loss of rear grip and thus traction.

So I don't think Ackerman or Toe angles are playing a part here, I think the inside tyre is actually doing more work than what we are lead to believe.

As for the advantages of UMP that is a different topic altogether.

[bhall]

This might help. It's the front-left of the FW36 in Melbourne as its tires are being warmed up on the parade lap.