Have you ever wondered why people say, "You need a Posi," or "A Locker would work the best," but not known why? I have. So I embarked on an analysis see what you can theoretically get from each of these devices. The results may surprise you. (The bottom of this page contains links to several manufacturers.)
First off let me use a simple convention to describe tractive effort. Let us say that each tire has the ability to provide a maximum of one unit of torque to the surface on which it is riding. With four driven tires you can then get a maximum of four units of torque or traction. For this analysis we will, however, assume a two wheel drive vehicle only. This way we are only looking at one axle. I leave it to you to do the simple extrapolation to two axles. Secondly, you must agree with me that a tire which is spinning at a different speed than the ground moving beneath it cannot be applying a full unit of traction. In other words a tire "spinning out" doesn't have as much traction as one moving at ground speed. This holds true also for a sliding or locked tire which is why ABS brakes were developed to keep the tire moving at ground speed but at the threshold of lockup to provide maximum braking effort.
There are basically four types of differentials in use today. This article is not going to describe the mechanics of how each type functions. I am only interested in the effects they produce. There are many implementations of these types of differentials and many sources on the web if you are interested in the mechanics. The first type is an open unit which sends equal amounts of torque to each wheel up to the maximum torque which the lowest traction tire can handle under all conditions. The second is a limited slip which has the added ability to bias or send a higher ratio of torque to the higher traction tire. A locker prevents either wheel from spinning slower than the input drive shaft (more specifically no slower than the input driveshaft divided by the ring and pinion ratio) but will allow a tire to rotate faster. In order to differentiate wheel speed in a corner they allow one wheel to rachet or over run the slower driving wheel. This can cause some handling quirks on the street as they couple and uncouple themselves. In addition since only the inside tire is driving the car in a corner, the car may tend to understeer.The last type is the spool, where I include the ARB and Toyota Electric locker, which keep both tires rotating at the same speed and provides no differentiation.
Now to the analysis. We will look at the following conditions and analyze the tractive effort produced from each type. Driving in a straight line, driving around a corner, driving on an uneven surface where one tire has more traction, cornering on uneven surfaces and finally driving with one wheel off the ground. A table is provided at the bottom of this article to make comparison easier.
Driving in a straight line (Maximum traction available is 2 units.) Ok, it sounds silly but lets all make sure we understand what is going on. Both tires are spinning at the same speed so the differential is not doing any speed differentiation. In all types of diffs. we are applying 2 units of traction to the ground; 1 unit from each tire.
Driving around a corner (Maximum traction available is 2 units.) Here is where it starts to get interesting. I am going to simplify the analysis by ignoring the fact that a tire looses some of it tractive ability by cornering through lateral slip and the fact that one tire becomes unloaded through weight transfer. We will assume that we are cornering slowly. When going around a corner the outside tire must spin faster than the inside due to the larger arc it travels. An open diff. always distributes equal torque to both tires so even though the inside tire is rotating more slowly, it receives the same amount of torque as outside tire. Hence 2 units of torque applied to ground. A limited slip diff. will provide the same type of differentiation as an open diff. in this case since there is no slippage for it to moderate. Also 2 units of torque applied to the ground. A locker going around a corner will not allow the inside tire to slow down. Instead it allows the outside tire to freewheel or ratchet faster. Therefore only the inside tire transmits torque to the ground giving you only 1 unit of traction. If going around the corner you need more than one unit of traction, the inside tire will slip until it is spinning at the speed of the outside tire. Now the outside tire is providing 1 unit of traction. As you recall, a spinning tire provides less traction so the inside tire is might be providing 0.5 units of traction. The total possible tractive effort from the locker would be 1.5 units with one tire howling. A spool going around a corner would scrub both tires equally. The tires are locked together and always spin at the same speed. The outside tire would therefore be spinning somewhat slower than the ground speed and able to transmit maybe 0.75 units. The inside tire would be spinning somewhat faster than the ground speed and able to transmit maybe 0.75 units. The total for the spool would be 1.5 units with the tires howling. An added danger with the spool is that since both tires are already slipping, they are more likely to cause the vehicle to spin out in a turn. This is why spools are illegal on the street. Lockers partially eliminate this danger.
Uneven surfaces (Maximum traction available is 1.5 units with 1 unit on one side and 0.5 on the other.) Again since an open dif. transmits equal torque, if one tire is on a surface where a maximum of 0.5 units of torque can be transmitted, then the other tire will only be provided 0.5 units of torque from the engine even though more is available from the engine and more traction is available at the tire patch. The total usable to an open dif. is 1 unit which is less than the maximum. A limited slip has a bias ratio built in. Let us say that our unit has a ratio of 3:1. This means that it can transmit three times the torque of the low traction tire to the high traction tire. The low traction tire can apply 0.5 units. The high traction tire has 3 * 0.5 units or 1.5 units available from the drive train. But, of course, the tire can only transmit a maximum of 1 unit to the ground before it starts slipping. So the we get a total of 1.5 units which is the maximum. A locker will distribute half the available drive train/engine torque to each tire. This is different than saying it transmits equal torque to each tire. The high traction tire can handle 1 unit and the low traction tire can handle 0.5 units. Since the tires will spin at the same speed, full torque of 1.5 is applied. The spool is identical with a total of 1.5 units. A locker acts like a spool when you are driving straight. In all the above cases if the engine provides more than the maximum traction which the tires can handle, the tires will spin.
Cornering on uneven surfaces (Maximum traction available also 1.5 units.) It should be obvious that both the open dif. and the limited slip will provide the same tractive effort as in their previous cases since both provide speed differentiation while applying torque. 1 unit and 1.5 units respectively. The locker, however will vary depending on several conditions. If the low traction tire is on the inside of the turn then the locker will provide 0.5 units up to the point before it spins up to the outside tire's speed. Then we get 1 unit for the outside tire and half of the inside spinning tire's potential or 0.25 units for a total of 1.25. If the low traction tire is on the outside of the turn then the locker will provide 1 unit to the inside high traction driving tire up to spin. Thereafter it will provide 0.5 units when spinning and the outside low traction tire will then contribute its 0.5 potential for a total of 1 unit. A spool will again only provide 75% of each tire's potential to the ground because of scrubbing so 1 * 0.75 + 0.5 * 0.75 = 0.75 + 0.375 = 1.125. Unfortunately this is a somewhat simplistic way of looking at the situation. Many other things come in to play. The angle of the turn affects how much scrub happen on the spool and how fast the the inside tire spins on a locker. The percentage of losses due to these factors are variable and my choice is purely to illustrate the effect.
One wheel with no traction (Maximum traction available is 1 unit.) Here is where an open dif. really falls on its face. Since it distributes equal torque to both tires up to the maximum that the low traction tire can handle, if one tire can handle 0 units then the other also gets 0. A limited slip dif. has the same problem even though it can bias torque. With our 3:1 bias dif. if the low traction tire can handle 0 units then 3 * 0 goes to the high traction tire. However there is a way to cheat with a LSD. If you apply the hand brake (or foot brake) with, let's say, 0.25 units of braking torque the slipping tire will have 0.25 units of apparent traction as far as the dif. is concerned. It can then transfer 3 * 0.25 or 0.75 unit to the high traction tire. Since the high traction tire is receiving 0.25 units of brake force as well, you have to subtract that from the 0.75 unit to get 0.5 units of tractive effort. Applying more brake will get even more bias to the high traction tire until it has 1 full unit of effort to the ground. A locker and spool will both transfer 1 full unit to the grounded tire by design.
Recap. Open and LSD difs. provide better performance when cornering but have drawbacks when limited suspension articulation unloads a tire. LSD units come in varying designs. Some using clutch plates and some using the angular resistance forces within the mechanism to provide bias. Bias ratios can go as high as 6:1 which will provide near locker characteristics. A locker or spool will always make available at least one unit of torque to the ground in some fashion as long as one tire is on the ground, but will provide less than the maximum traction when cornering. Except for its simplicity a spool has many drawbacks. It is dangerous on the street because it causes the vehicle to understeer (want to go straight in a turn) and provides no differentiation in a turn allowing the tires to keep proper traction. A part time spool such as the ARB or Toyota design allows the best of both worlds. They give smooth action while turning when unlocked and guaranteed traction from at least one wheel when the going gets tough.
The numbers represent the maximum traction available. The first number in each box is the maximum achievable traction without spinning any tires, although the spool will always scrub in turns. The number in parenthesis of the LSD column is the maximum achievable traction using brake biasing to transfer torque. The numbers in parenthesis of the locker column is the maximum achievable traction when the inside tire is allowed to spin up to the speed of the outside tire.
| Traction in units with no spinning tires (maximum possible) |
Max. Avail. |
Open | LSD | Locker | Spool |
| Driving Straight | 2 | 2 | 2 | 2 | 2 |
| Cornering | 2 | 2 | 2 | 1 (1.5) | 1.5 |
| Uneven surface | 1.5 | 1 | 1.5 | 1.5 | 1.5 |
| Cornering + | Slippery inside Uneven surface | Slippery outside |
1.5 | 1 | 1.5 | 0.5 (1.25) 1 (1) |
1.125 |
| One wheel with no traction | 1 | 0 | 0 (1) | 1 | 1 |
One other traction system worth mentioning is traction control. Traction control is an electronic system that modulates the brakes in low traction conditions. It uses the ABS (Antilock Brake System) sensors to take speed measurements of each wheel. If one wheels is spinning significantly faster than the others, more than is possible by just going around a corner, the traction control system applies brake pressure to the wheel. Just like in an LSD, this effectively redirects torque to the other wheel on the axle and puts drive to the ground. This system works better than manually brake biasing an LSD, as described above, because it applies brake force to only one wheel on an axle. If the vehicle has a center dif in the transfer case, and both rear wheels slip, it can brake both rear wheels to shift torque to the front axle. Traction control is fully adaptable to the conditions but more so than an LSD. A good system should function as well as having two lockers. The disadvantage is that it may overheat the brakes if used in extreme conditions such as slow rock crawling over long periods. Depending on how well the software in the system is written, there might be a delay from when the wheel looses traction and when the system kicks in. Conversly I have seen systems installed on passenger vehicles that spuriously engauge for no reason. This causes the car to bog as it fights the brakes.
http://www.larsdennert.com/4runner to go back to my 4Runner site.
http://www.auburngear.com (A heavy
duty cone type Limited slip)
http://home.off-road.com/~bibelheimer/diffs/diff_info.html
(Different types of Toyota OEM diffs)
http://www.lockright.com (An inexpensive
and easily installable Locker)
http://molmed.umassmed.edu/~kdb/locker/locker.html
(A good site on retrofitting the Toyota Electric Locker)
http://www.powertrax.com (Home of
the Lockright and new Noslip which is a refined version.)
http://reality.sgi.com/georgec_melbourne/george_couyant/diffs/diffs.html
(Diffs for Dummies)
http://www.tractech.com (Detroit
differentials are makers of several Lockers and the True Trac Limited Slip)
http://www.mindspring.com/~audidudi/Torsen.htm
(Torsen Limited Slip White Paper. Same principle as the True Trac or should
I say True Trac is based on this principle)
http://www.arb.com.au (ARB part time
Air Locker. See also
http://www.larsdennert.com/4runner/arb)
http://www.torquecontrol.eaton.com/
(The Eaton Locker is the only automatic Locker that can behave like an open
differential/Limited Slip in a turn.)
6/2/2000