S1 used a viscous differential. This had a bad quality to it in that the more the difference in speed between driven tires, the higher the locking factor between driven tires. The result was that if one driven tire started spinning while under excessive throttle input, the increase in locking force would soon cause the other driven tire to start spinning as well, reducing stability.

A limited slip differential has the exact opposite behavior. The greater the difference in speed between driven tires, the lower the locking factor. This helps increase stability when a tire starts spinning due to excessive throttle input.

The reason for this behavior is that the coefficient of kinetic friction varies with speed, and is not constant as is often taught in early physics courses. Starting from almost no speed, kinetic friction increases to a peak, which occurs at a very slow speed, then decreases as speed increases.

With a standard clutch, the higher the speed differential between the plates, the lower the coefficient of kinetic friction. In a street car, trying to launch at high rpms by slipping the clutch doesn't work well, because of this. It's better to just drop the clutch at medium low rpms and let the tires spin, which is what magazine testers do when drag testing showroom stock cars.

There are two common methods used for drag racing clutches to overcome this effect. Sometimes both are used. One is to use weights and springs to increase pressure on the clutch plates as engine rpm increases, but this means the driver has to use more foot pressure on the clutch pedal to compensate for the increase in plate pressure, or some type of launch control is needed that doesn't require the driver to manually resist the plate pressure. The other method is to simply use a clutch with a higher initial coefficient of kinetic friction, so that even at high differences of speed between the plates, the clutch friction is still higher than the grip provided by the tires, so the driver can always keep the tires at the limits.

In the case of a motorcycle clutch, or a limited slip differential, this effect can also be controlled by the number of clutch plates used. Adding more clutch plates reduces the difference in speed between plates, and increases the overall kinetic frction. In the case of a limited slip differential, using more clutch plates requires an adjustment to the ramp rates to reduce plate pressure to end up with the same locking factor. If a limited slip differential has indepently settable locking factors for engine acceleration versus engine braking, more clutches will smooth the transition between the locking factors.

I don't know if S2 models this behavior of a limited slip differential, and I haven't thought of a good experiment to verify this.

Nice.


And your point is?

Quote from AndroidXP :

Nice.
And your point is?

My point is actually a question.

Does S2 model limited slip differentials in the manner described?

One of the advantages of this limited slip differential's behavior to decrease locking factor when speed differential between driven tires increases, is that the result is positive stability. If excessive throttle is used, one tires starts to spin and then increases it's rate of spin. Meanwhile, the other tire is getting less and less torque applied to it as the spinning tire continues to increase rpms. It's sort of self stabilizing as long as the excessive throttle input isn't too extreme, or the initial locking factor isn't too high. It gives the driver enough time to hear that the engine rpms are accelerating too fast and lift on the throttle a bit to stop the single tire spinning without losing control of the car.

I suspect that the modelling of preload, or clutches, is incomplete. The reason I say that is because I am sure that if they were fully modelled, we would be able to adjust them.

This may be one of the reasons that the clutch-pack diff in LFS at the moment still seems a bit wierd to some people.

I've actually had some real life experience with this. A long time ago, I bought some even longer time ago used hot rods. One was a 1969 Chevelle SS396 that didn't have a limited slip differential (a bit strange that a hot rod didn't have a limited slip differential). I could floor it in first gear with the result that the right rear tire would spin and smoke like crazy, yet the car just kept going in a nice straight line, not accelerating very quickly because all the engine speed was going to the spinning right rear tire. Donuts were not possible with just one rear tire spinning. One other unusual feature is that the Chevelle had coil springs front and rear (no leaf springs).

Later I got a 1969 Dodge Charger 440 R/T with a limited slip differential. One good test to confirm this was to get one tire wet and see if the car would still spin both tires (it did). When spinning both rear tires, it would get squirrely and require control inputs to keep it aimed in the right direction. Donuts were very easy to do. Unlike the Chevelle, the Charger had no coil springs at all, it had leaf springs in the back, and torsion bars in the front (sort of like sway bars, but attached to the frame and pointed forwards and attached to the front A arms).

Saying a Sailsbury type clutch pack LSD is the exact opposite of a viscous coupling is incorrect. Viscous diffs are (wheel) speed sensitive, whereas Sailsbury diffs are torque sensitive (e.g. the more you put your foot down (for any given gear), the more locked the diff is). I assume the locking factor in LFS to be the maximum.

Also vicous diffs don't transfer any torque until wheel slip occurs, so there is always some lag in the process. Clutch diffs transfer torque as wheel slip happens, so there is no lag.

The diff preload (the passive bit) is currently unadjustable, so we've no idea what it is, so as Colcob speculates it might well not be modelled yet.

I'd really like to see the number of clutches and ramp angles like GPL, rather than the locking factor. Since that is what you are actually adjusting.

Quote from Bob Smith :

Saying a Sailsbury type clutch pack LSD is the exact opposite of a viscous coupling is incorrect. Viscous diffs are (wheel) speed sensitive, whereas Sailsbury diffs are torque sensitive (e.g. the more you put your foot down (for any given gear), the more locked the diff is).

This is true unless one of the tires breaks loose and starts spinning. The more the one tire spins (compared to the other), the less the locking factor, because there is less overall torque being applied to the now faster rotating differential (due to the faster spinning tire), and because kinetic friction decreases with speed. These are minor factors, since the initial locking factor (such as number of clutches, and pressures), can be adjusted to compensate for these factors. The main point here is limited slip, one tire can spin without the other tire spinning.

I found this to be true in my old 1997 Trans-Am. With a certain amount of throttle, I could get just the right rear to spin while taking off on a straight line. With less throttle, neither tire would spin, and with more throttle, both tires would spin. I could get the same thing to happen while cornering hard (except it would be the inside rear tire that spun first).

With a limited slip differential, a certain amount of throttle pressure will result in a one tire spin, and more throttle pressure will result in a two tire spin. The higher the locking factor, the less the difference between these two throttle pressures for one tire spin versus two tire spin. The lower the locking factor, the more the difference between these two throttle pressures.

GPL models this. A lower locking factor will be easier to drive, giving you more warning, since there's more margin between the throttle pressures for a one tire spin versus a two tire spin. A higher locking factor will be harder to drive, because the margin between the two throttle pressures is reduced, but will give you more acceleration out of a corner because you can use more throttle pressure without the inside rear tire breaking loose.

I think of a limited slip differential as a positively stable setup, because there is a margin of throttle pressures between a one and two tire spin. This margin gives a driver a warning that throttle pressure is approaching the limits of what the tires can deliver, indicated by a single tire spinning, by either the sound of the tire spinning, or by the sound of the increased engine rpms.

A viscous differential is not stable. At a specific throttle pressure, the inside rear tire will break loose and initially spin, but once it's starts spinning, the locking factor increases, and the momentum of the inside tire and fluid in the differential may be enough to break the outside rear tire loose, without any change in throttle pressure by the driver. Even if it doesn't cause the outside tire to break loose, the inside tire will cycle between spinning and not spinning with the locking factor following the same cycle. Neither of these situations are stable. A viscous differentinal may be ok for front/rear differentials on a 4 wheel drive vehicle, but it's a bad choice for a rear end differential.

I think if you're spinning one side of the diff so fast that you're getting a reduction in locking due to a reduction in kinetic friction, it's probably way too loose to begin with.

OK fine. So what is the point of this thread? Its a statement which leaves little to be discussed. At least my thread on diffs back on RSC was to prompt some discussion about the development of LFS.

wasnt there a big discussion on this not too long ago also?

yup. bob's post:dunce:

Quote from Bob Smith :

OK fine. So what is the point of this thread?

Hmm, one of my posts never made it into this thread, my fault, should have checked.

I wanted to know what type of limited slip differential was being modeled by LFS, and if anyone here that races in IRL think the differential model is correct yet, but as posted it's still in development, so it's probably not there yet.

The point about kinetic friction reducing with speed would probably have some effect on a single pair of clutch plates type differential, but it would be minor. I went a bit off track here, sorry about that.

Similar to your thread at RSC, I wanted to ask if differentials with multiple clutch plates, and selectable ramp rates could be implemented.

Quote from JeffR :

Hmm, one of my posts never made it into this thread, my fault, should have checked.

I wanted to know what type of limited slip differential was being modeled by LFS, and if anyone here that races in IRL think the differential model is correct yet, but as posted it's still in development, so it's probably not there yet.

The point about kinetic friction reducing with speed would probably have some effect on a single pair of clutch plates type differential, but it would be minor. I went a bit off track here, sorry about that.

Similar to your thread at RSC, I wanted to ask if differentials with multiple clutch plates, and selectable ramp rates could be implemented.

Jeff, Scawen appears to have done the new LSD model properly. Your comments about decreasing friction coefficient with velocity at the clutch mechanism in the differential is probably correct to some extent, but is most likely a very minor thing. Any graphs I've seen on torque bias ratio on such differentials indicate it to be a constant anyway. I'd be very surprised if the variation was large enough with velocity to notice a difference. The variation in what the tires are doing when the slip ratios are vastly different would probably overpower this to the point where you'd not notice the difference between modelling or not modelling that.

My guess, and it's just a guess, is that the torque bias ratio in LFS's LSD model is a constant.

But it isn't a passive clutch pack, it's Sailsbury type (IIRC). Isn't the locking of those diffs torque sensitive? In which case it can't be a constant TBR.

Quote from Bob Smith :

But it isn't a passive clutch pack, it's Sailsbury type (IIRC). Isn't the locking of those diffs torque sensitive? In which case it can't be a constant TBR.

The locking torque is indeed variable and controlled by the combination of wheel torques coming into the unit. The torque bias ratio itself is constant, however. Both are correct

Quote from ussbeethoven :

This thread is pretty old, but my questions will probably fit into this topic. To my comprehension a viscous LSD doesn't have a locking factor and basically behaves like a indefinitely variable open diff, i.e. if one wheel starts to slip (thus increasing rotation), more torque is transferred to the other one - I also understand the fact, that using higher settings (whatever Nms/rad means) in LFS's setup screen will reduce the time necessary to redirect torque....so probably less difference in speed between the tyres is allowed.

Regarding my current lack of reference points, how can those numbers be compared to the power/coast side of a progressive clutch-pack (preload shouldn't apply, right?) resp. how would e.g. 30% power 'translate' into Nms/rad - and what would RL production cars probably use?

/Edit: Probably in the wrong subforum by now.

You can't really compare viscous and clutch-pack diffs easily. They operate in very different ways. For one, viscous diffs operate completely independently of input torque from the drive shaft, much like an open diff. It is open when the wheels are spinning together and progressively locks as the difference in angular velocity between the wheels increases. A clutch-pack, on the other hand, is open when the net input torque is zero (given zero preload) and progressively locks depending on how much torque is applied at the input shaft in either direction.

Nms/rad is read as Newton-meters seconds per radian. It can also be written as Nm/rad/s, or Newton-meters per radian per second. It's a measure of torque (in Newton-meters) transmitted from one wheel to the other given a particular difference in angular velocity (radians per second). Clutch-pack diffs deal only with torque and ignore angular velocity.

Bikes don't have to deal with any of this crap.

The locking factor of any differential can ultimately be measured in Nm, i.e. the amount of torque required to give slip. However, the ramp angles, % locking or preload don't actually tell you this difference. That could be measured though by using strain gauges on the driveshafts to deduce the torque loading of each shaft.

The viscous diff units are given in Nm/rad/s, and so a torque difference is quoted. Whether this is the torque needed to provide slip I don't know, but it's probably. But strain gauges would give you numbers.

Or just drive it and see. As they work in such a difference manner (one torque sensitive, the other speed sensitive) that you'll end up just as accurate with trial and error as you will with most numerical analysis.

Take two cars and drive them around the same corner at the same speed with two different differentials: a viscous and clutch-pack. Set the differentials up so that, at one particular throttle setting, the outside wheel receives the same amount of torque on both cars, and likewise for the inside wheel.

Now increase the throttle. As a result, the torque on the driveshaft increases in the forward direction. On the clutch-pack diff, this results in the differential locking up more. On the viscous diff, this results in no change in differential locking. As long as the car maintains grip and turning radius, the difference in angular velocity between the drive wheels does not change. However, as soon as the inside wheel breaks loose, the difference becomes greater and then the diff locks up more.

The point is, there is no translation of settings due to totally different response characteristics.