What does it do ? - Limited Slip Differential home
Overview

The differential is arguably the single most powerful setup adjustment parameter in GPL. GPL is the first racing simulation to accurately incorporate a limited-slip differential and allow the user to adjust its parameters.

This feature presents a great learning opportunity and a challenge. A basic understanding of the differential's characteristics is essential to developing effective setups for GPL.

Basic Concepts

The differential which appears in almost all road cars is known as an open differential. To reduce tire wear, the open diff permits the rear wheels to rotate at any speed with relation to each other. As the car goes around a corner, the inside wheel goes more slowly, and the outside wheel goes faster.

This works great as long as the tires are not near their limits of adhesion. However, when one tire loses traction (as on a patch of ice) that wheel can spin uselessly while no torque is applied to the other tire. Since race cars operate on the limits of grip, an open differential can be a severe detriment. Cornering transfers weight away from the inside wheel. Applying power exiting a corner while the inside tire is lightly loaded is an invitation to wheelspin.

Some race cars, including karts, deal with this by using a spooled rear axle. This simply means that the rear wheels are locked together and can't rotate with respect to one another. In a kart, they are attached to a solid axle. In some race cars, a "spool" - some type of solid component - is placed within the differential housing to lock the wheels together.

A limited slip differential provides a mechanism which operates between these two extremes. The wheels are not locked together solidly, but neither can they spin freely with respect to one another. Instead, the differential permits the wheels to rotate with respect to one another, but it provides resistance to this relative rotation, or slippage.

CUTAWAY VIEW - A 45/45-3 Salisbury [pronounced Sawlsbri] limited-slip-differential only works as any ordinary differential when no torque is applied. Under power and when coasting the cross-shaped bracket that holds the pinion-wheels seen in the cut-away will move slightly inside the two shells that surrounds the crownwheel-and-pinion-gear.

Because of the angled slopes (ramps) seen on the stub-axle protuding from the pinion-wheel, the two shells will move slightly apart and lock the differential in accordance with the number of clutch plates used (in this case: 3)

The power- and coast-angles are the angles of the slopes on the stubs (in this case: 45/45) and these will convey a locking force at tan(angle)

To change the angles and number of clutches the differential has to be removed from the transmission, the stubs and clutch plates replaced and the whole thing assembled again.

The Salisbury Differential

The differential fitted to the cars in GPL is a Salisbury-type limited slip differential. The Salisbury differential is designed to allow the race engineer to adjust the resistance it provides to slippage between the rear wheels. Resistance to slippage under power (the "power side") can be adjusted independently of resistance to slippage under lift throttle or braking (the "coast side").

The Salisbury diff provides ramp angles for the power side and the coast side. These affect the amount of limiting of slippage as torque is applied. The rule is: the steeper the angle, the less limiting effect. These adjustments only impact resistance to slippage when torque is being applied to the rear wheels by the engine or the brakes.

The Salisbury diff also provides clutch packs. These affect the power side and the coast side equally. The more clutch packs you put in, the more slippage is limited under any conditions.

Impact on Handling

By limiting the slippage between the rear wheels, the differential can have a profound impact on the car's handling. The rule of thumb is: the more the diff limits slippage, the more the car will tend to go straight or understeer (the condition in which the front tires are sliding more than the rear. The car is tending to go straight on, no matter how much we turn the wheel. It's also known as "tight" or "pushin'". The opposite of oversteer) - up to a point. On the power side, if enough torque is applied to spin both wheels, the car will snap into oversteer.

RAMP ANGLES - The yellow figure symbolises one of the four pinion-wheel stub-axles. On the part of the axle where the pinion-wheel runs, it is round, but the protuding end is shaped as shown.

This enables it to apply a splitting force on the two surrounding shells. The force is a projection of the force from either the power- or coasting torque.

45/90 will only apply lock under power

45/45 will apply similar lock under power and coasting

50/75 will lock quite a lot during power but less during coasting

Coast Side

On the coast side, limiting the slippage between the rear wheels provides a sort of poor man's ABS effect. By preventing one rear wheel from locking while the other is turning, the car is made more stable under braking, and brake balance can be moved farther aft. This permits shorter braking distances and makes the car more stable when turning in when braking (aka trail braking: the technique of continuing to brake after turning into a corner, gradually easing off the brake before turning in and continuing to ease off - "trail off" - the brake as the car rotates toward the apex. The intent is to fill the friction circle, thus using as much of the tires' available grip at all times. Not the same as Left-Foot Braking, although the two are not mutually exclusive; you can trail brake with either foot. See Going Faster or Drive to Win for more details).

Limiting slip on the coast side also makes the tail less prone to step out if the throttle is lifted in mid-corner. One of the most important characteristics of a race car that the novice race driver must adjust to is trailing throttle oversteer (refers to the oversteer induced when the throttle is closed or reduced in opening. If the throttle is closed abruptly, the car can spin due to TTO). This is snap oversteer which occurs when the throttle is suddenly closed while cornering. Close the throttle in a car with an open diff (such as a Formula Ford) and the tail will step out or come around with a vengeance. Putting in coast-side limited slip promotes understeer in lift-throttle conditions, and it helps tame this tendency, making the car much more forgiving.

On the downside, limiting slip on the coast side can cause excessive understeer during corner entry, especially for drivers who don't trail brake.

Since I learned car control in a kart, which has a spooled axle, I am most comfortable with maximum slip limiting on the coast side. Therefore, I always use a 30 ramp angle on the coast side (except on ovals, which are a special case). I use the maximum number of clutches that I can deal with on the power side, which also helps the coast side stability.

I've experimented with 45 and 60 ramp angles on the coast side, which are used by many of the fastest GPL drivers in the world, but I always wind up coming back to 30. This feels more comfortable to me, and I'm more consistent and therefore faster over a race distance with it.

However, if you want to train yourself to drive real small Formula cars, you would do well to use less locking on the coast side.

Power Side

On the power side, limiting the slippage helps get the power down by sending more torque to the heavily loaded outside wheel, and less torque to the lightly loaded inside wheel.

With an open diff, if the inside wheel is spinning, and the outside wheel is delivering most of the torque, the thrust from the outside wheel will tend to turn the car's nose towards the inside of the corner. This is called power oversteer (Oversteer is the condition in which the rear tires are sliding more than the front. The car's tail is coming out; if we don't correct with some opposite lock, the car will spin. This is also known as "loose". The opposite of understeer). You see it on cop shows as the big Ford sedan barges away from a corner with smoke pouring from the inside wheel, the driver putting in armfuls of lock to keep the car from going completely sideways.

As we add more locking, the inside wheel is less prone to spin, which means that it is delivering more power to the pavement. This reduces power oversteer, and helps acceleration. It means we're doing a better job of "getting the power down".

However, if the driver applies too much power, so that the grip of the outside rear tire is overcome and the outside rear wheel starts to spin, the car's lateral grip at the rear will go away, and the car will snap sideways into full power oversteer. A spooled axle in a very powerful, very light car such as GPL's Grand Prix cars makes the car almost undriveable because the slightest touch of the throttle will light up both rears and break the tail loose.

The trick is to find the optimum amount of slippage so that we get as much of the power down as possible while still giving the driver some warning of the approaching limit. To some degree, this is impacted by the relative roll stiffness between front and rear suspensions. The stiffer the front, the less weight transfer there is between the rear tires, so the more locking we can use on the power side. However, going to an extreme can result in a car that has a knife-edge breakaway under power.

I've found that I'm most comfortable with an 85 ramp angle on the power side and 3 or 4 clutch packs. Any more locking than this makes the car snap into oversteer too abruptly for me; any less, and the car spins its inside wheel too much. (Others disagree; see below.)

Interdependence

Many of my other chassis settings fall out from my differential settings. Roll stiffness, spring rates, brake balance, even toe and camber choices to some extent are affected by the differential choices made by the race engineer.

Many people use quite different settings. I've heard of people using 60 and even 45 on the power side, and 45 or 60 on the coast side is common. These can work well. But you can bet that other aspects of their setups are also quite different, to cope with the less stable characteristics imparted by these diff settings. Also, the people who do well with less stable cars tend to be the most talented - those with the fast reflexes, good coordination, and smooth driving style necessary to cope with a less stable car.

Other Voices

My opinions about which ramp angles and preload work best are far from the last word. Below are the thoughts of two experts whose views differ from mine - and from each others'.

Steve Smith

For a long time now, many of the fastest drivers have been using and advocating setups based on differential settings other than the 85/30 settings that I've almost always used. I've tried a number of times to work up setups that I'm comfortable with using different ramp angles, but I've always wound up coming back to the old trusty 85/30 setups.

Now Steve Smith has changed my mind. He sent me a few setups with a 60 degree ramp angle on the power side and 60 or 45 on the coast side, along with an explanation of why they work better, and where. In this article, Steve says:

"A 60/60 setup is better. First, it kills the traditional Papy understeer, dead. The car now turns in more quickly. Indeed, it transitions so fast it feels like a dramatically lower polar moment. Mid-corner, it tracks along like a train. Unlike push, you can position the car--into any conceivable angle...and some that ain't--with the throttle. Easily.

The problem comes at the exit. You have to learn a whole new driving technique: squeezing on the throttle as you come off the turns, not mashing it. You have to modulate the throttle until the car is pretty much pointed straight before it will (in Doug Arnao's words) "accept the power." It requires great concentration...at a time when you normally Alpha out. And once you've mastered it in solo Training sessions, you have to learn it again in the heat of competition; it's all too easy to spin out on the last turn of the last lap in a "Red Rage."

But 60/60/1 setups are a whole lot easier to drive for extended spells. Particularly if you like to dirt-track around--they like *lots* of Wellie...but not timidity. Quite the opposite; they reward exuberance. Slides seem very controllable, you feel more self-confident. I find I have far fewer 'offs' at slippery tracks like Kyalami. True, my lap times have improved trivially, if at all. But, overall, 60/60/1 is simply more fun, more rewarding to drive."

It only took me a few laps with his Cooper setup for Kyalami to be convinced. He was right; once I got used to treating the throttle with a bit more restraint, it was easier and more fun. Slides are more progressive, more controllable.

Now all my new setups use a 60 degree ramp angle on the power side. The secret seems to be in the use of stiffer dampers at the front, and stiffer damping in bump than rebound, to help stabilize the car in transition. An additional benefit of running stiffer dampers in bump is that I can run somewhat lower ride heights without bottoming. So far I've only tried 45 on the coast side, with one clutch, but I'll be experimenting with other settings as well.

Carroll Smith

In "Drive to Win", Carroll Smith says:

"Since we want minimum lockup under braking, especially trail braking, typically we use an 80 or 85 degree ramp on the coast side with a 45 degree ramp on the power side.

"For faster corners with more download some teams use 60/30 ramps. I have never been happy with 45/45 (too much corner entry and mid-phase understeer), but I know some very successful people who are - in the UK [where courses are smooth]. I don't know anyone who likes them in slow corners or on bumpy courses. Personally, I cannot conceive of using any ramp of less than 80 [eighty!] degrees on the coast side.

"I usually run no preload at all. I run either 45/85 or 80/80 ramps depending on the car and track."

For what it's worth, note that GPL doesn't model bump steer (Bump steer refers to a change in toe-in as the wheel moves up or down. It's common to set up the rear suspension for a small amount of toe-in under bump to help make the more car stable when trail braking. GPL doesn't model bump steer). In setting up a car for trail braking, I believe it's normal to dial in a little toe-in under bump at the rear, to give a little understeer as the car rolls. Since we can't do this in GPL, using a little extra rear toe or some extra locking in the diff on the coast side does make sense to me.

Ricardo Nunnini

GPL setup guru Ricardo Nunnini says,

"I (and others) are absolutely sold on the 60/30+1 differential. It makes the car so much more, erm, like a car. It all sort of clicks into place.

"At first, you'll find that it punishes bad driving, but in a "fair" way (I called the earliest 60/30+1 setups 'Yoda'). But after correcting the wild compromises necessary to make a setup work with all that nasty preload (mostly the dampers) I'm now setting personal bests almost every time I go out on the track. Driving is much more relaxed, less extra input spent fighting the car. (And I am not a talented driver, just a thoughtful ordinary one.)

"You can generally adapt an existing setup by slapping on the 60/30+1 diff and then setting the dampers to something calm like 2+2/3+3 (instead of, say, the more squirrelly 2+3/3+4). I've found it takes about 50-100 laps to make the transition; far less than for force feedback, but with more immediate performance results. Today, without trying especially hard, I've set new Lotus personal bests at Silverstone, Monza and Zandvoort.

"I really believe this is for everyone. I think David Kaemmer is right about this: 85/30+3 differential is an abomination!"