slip angle for maximum traction
04-03-2006, 11:17 PM
#16
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I'm getting dizzy!
I now have no clue how I get around the track at all.
I now have no clue how I get around the track at all.
04-04-2006, 02:10 AM
#17
Nordschleife Master
When a car enters a corner, all the tyres are turned with respect to the ground. Due to the elasticity of the pneumatic tyre, the tread in the contact patch will resist the turning action because there is friction generated between the rubber and the road surface. As a result, the treads on the contact patch will be distorted, whose direction always lags behind the direction of the wheel ( See figure in below ). We call the angular difference between the treads and the wheel's direction as Slip Angle.
Note : the car is turning left
In which direction the wheel is running ? It is the direction of the tread, not the direciton of the wheel. I am not saying the tread has any ability to force the wheel to travel in its direction. On the contrary, the tread is only a sign showing how an arbitrary point on the tyre surface travels. If the arbitrary point travels in that direction, so does the wheel which is the summation of thousands of those points.
Now you must think the existence of slip angle must reduce the car's steering angle thus leads to understeer. In fact, it is not so if everything else are perfect. Because both the front and rear tyres have more or less the same slip angles, they counter each other thus the resulting steering angle remains unaltered.
However, if the front and rear wheels have different slip angles, then we get understeer and oversteer :
Understeer : Front Slip Angle > Rear Slip Angle
Oversteer : Front Slip Angle < Rear Slip Angle
Neutral steer : Front Slip Angle = Rear Slip Angle
Note : the car is turning left
In which direction the wheel is running ? It is the direction of the tread, not the direciton of the wheel. I am not saying the tread has any ability to force the wheel to travel in its direction. On the contrary, the tread is only a sign showing how an arbitrary point on the tyre surface travels. If the arbitrary point travels in that direction, so does the wheel which is the summation of thousands of those points.
Now you must think the existence of slip angle must reduce the car's steering angle thus leads to understeer. In fact, it is not so if everything else are perfect. Because both the front and rear tyres have more or less the same slip angles, they counter each other thus the resulting steering angle remains unaltered.
However, if the front and rear wheels have different slip angles, then we get understeer and oversteer :
Understeer : Front Slip Angle > Rear Slip Angle
Oversteer : Front Slip Angle < Rear Slip Angle
Neutral steer : Front Slip Angle = Rear Slip Angle
04-04-2006, 02:17 AM
#18
Nordschleife Master
Non-neutral steer due to Tractive Force:
Car magazines often prefer the handling of rear-wheel-drive cars. They say FWD cars usually understeer while RWD is easier to provide power oversteer. Now, we use the concept of Slip Angle to explain this.
Consider a driving wheel, which is under cornering and has created slip angle. If tractive force (that is, the pulling force from the engine) is applied, the slip angle will increase (See Figure in below). This is because the tractive force applied between the tyre and ground will distort the tread on the contact patch further.
Now the scene is clear.
FWD cars has the front wheel's slip angle > rear wheel's. This result in Understeer.
RWD cars has the front wheel's slip angle < rear wheel's. This result in Oversteer.
4WD cars, if the front / rear torque split is equal, has equal F/R slip angles, thus result in Neutral steer.
(Remind you, understeer, oversteer and neutral also depend on suspension design, weight distribution etc. So we cannot say all FWD cars must understeer or all RWD car must oversteer. In fact, car makers usually design the suspension geometry to compensate the non-neutral steering generated by FWD / RWD and weight distribution.)
Power Oversteer and Lift-off Oversteer
The more tractive force we apply, the larger slip angle is created in the driving wheel. Therefore, for the RWD cars, we can use the throttle to control the degree of oversteer. When the car is entering a corner too fast and seems likely to run wide, we can correct its direction by increasing the throttle (not to do this before reaching the mid corner !), then the car oversteers. If we find the correction is too much, we can ease the throttle and let the car returns to neutral steer or even mild understeer, depends on the suspension design and weight distribution.
Only RWD cars or rear-biased 4WD cars can do this ! In the same situation, the driver in a FWD car has nothing to do other than easing the throttle, slow down the car thus reduce the centrifugal force, and hope the car can overcome the corner. There are many disadvantages :
You lose time during slow down.
You lose engine rev during slow down, thus the engine takes longer to rise back to the useful power band once you exit the corner.
Very often, if you miscalculate, you are unlikely to have sufficient road ahead for you to slow down, especially in tight corner.
.
Therefore we always say RWD car is superior than FWD car in handling. There are, however, some well-sorted front-driver (especially some GTi) can play "lift-off oversteer", which is actually the reverse of "power oversteer" - a degree of permanent oversteer is built into the car but is only accessible when the car is pushing to the limit and with throttle disengaged. Step down the throttle again will reduce the oversteer and even back to understeer. Anyway, obviously this is still not as controllable as "power oversteer". While power oversteer can extract a lot of oversteer - actually depends on throttle - lift-off oversteer is rather limited, simply because it is impossible to build a lot of permanent oversteer to the chassis without deteriorating handling in lower speed or straight line.
Once again I have to emphasis that the power oversteer must be highly controllable by the driver, otherwise the car may lose control and spun. To make a good power oversteer car, the secret is to match the power and cornering limit perfectly at the speed concerned. If the cornering limit exceeded the power, the rear wheels will grip hard and refuse to slip. In contrast, if the cornering limit is too low or the engine torque is too high at the speed concerned, the rear end will slide severely once the throttle is pressed. Therefore, the cornering limit must be set at a level where the engine output, at the speed and road we normally want the car to power oversteer, has just sufficient power to exceed. To implement it , choose a suitable set of tyres, applying suitable amount of downforce and an adequate front / rear weight distribution is very crucial.
RWD versus 4WD
Basically, 4WD does not introduce power oversteer. However, most people still prefer it simply because it provides superior cornering grip thus improve cornering speed. As I have promised earlier in the Cornering Grip section, here I'll explain how 4WD improve cornering grip :
Consider a driving wheel running in a corner. Due to the frictional force applied from the road surface, the tread in the contact patch distorts and creates slip angle. The faster the car corner, the more centrifugal force generates thus the larger the slip angle becomes. You can interpret this as the elastic distortion of the tyre generates a counter force to keep the car fighting with the centrifugal force. When the car is accelerated fast to the extent that the elasticity of the tyre reaches its limit, it could not distort anymore, thus more speed will lead to the tyre slide, and the car lose grip. This point is what we call "Cornering Limit".
A FWD or RWD car has already a lot of tyre distortion (slip angle) in the driving wheel because the tractive force is shared by only two wheels. Therefore there is not too much space left before the tyres running into their cornering limits. On the contrary, 4WD cars distribute tractive force to all wheels, thus each wheel shares considerably less tractive force thus create smaller slip angle in cornering. The car can corner at higher speed before the slip angle reach the cornering limit.
* * *
Grip aside, we concentrate back to our current topic - steering tendency.
There is always argument that whether the neutral steer of 4WD is better than RWD's oversteer. Although neutral is more favourable in the entry phase and mid corner phase during cornering, it doesn't provide the "correctability" of power oversteer in the exit phase. Remember, no driver could avoid miscalculation, no matter Mrs. Robinson or Michael Schumacher. Normally we need to feel the car's attitude and the road condition every moment before deciding how to control the car in the next moment. In this sense, RWD's controllable power oversteer is what we want.
Moreover, power oversteer of RWD ask the driver to intervene the throttle during cornering. This let him feel more involving and that he is mastering the car. In contrast, 4WD cars let the tremendous grip, the limited-slip differential and even the computer to rule the car's cornering. Therefore we always hear road testers said RWD is more fun to drive.
I am not saying 4WD cannot have power oversteer. Bugatti EB110, with its 30/70 front-to-rear torque split, did that beautifully while providing tremendous grip. Even though a 50/50 4WD car like Mitsubishi Lancer Evo V could achieve slightly power oversteer by means of well-sorted suspension geometry. For example, if the suspension is setup such that to introduce rear outside wheel positively cambers when subjective to body roll, the contact patch area decreases thus slip angle increases, then power oversteer is also available. However, you cannot set the suspension to provide power oversteer as much as RWD car since there is a trade-off in total grip and straight line stability.
Car magazines often prefer the handling of rear-wheel-drive cars. They say FWD cars usually understeer while RWD is easier to provide power oversteer. Now, we use the concept of Slip Angle to explain this.
Consider a driving wheel, which is under cornering and has created slip angle. If tractive force (that is, the pulling force from the engine) is applied, the slip angle will increase (See Figure in below). This is because the tractive force applied between the tyre and ground will distort the tread on the contact patch further.
Now the scene is clear.
FWD cars has the front wheel's slip angle > rear wheel's. This result in Understeer.
RWD cars has the front wheel's slip angle < rear wheel's. This result in Oversteer.
4WD cars, if the front / rear torque split is equal, has equal F/R slip angles, thus result in Neutral steer.
(Remind you, understeer, oversteer and neutral also depend on suspension design, weight distribution etc. So we cannot say all FWD cars must understeer or all RWD car must oversteer. In fact, car makers usually design the suspension geometry to compensate the non-neutral steering generated by FWD / RWD and weight distribution.)
Power Oversteer and Lift-off Oversteer
The more tractive force we apply, the larger slip angle is created in the driving wheel. Therefore, for the RWD cars, we can use the throttle to control the degree of oversteer. When the car is entering a corner too fast and seems likely to run wide, we can correct its direction by increasing the throttle (not to do this before reaching the mid corner !), then the car oversteers. If we find the correction is too much, we can ease the throttle and let the car returns to neutral steer or even mild understeer, depends on the suspension design and weight distribution.
Only RWD cars or rear-biased 4WD cars can do this ! In the same situation, the driver in a FWD car has nothing to do other than easing the throttle, slow down the car thus reduce the centrifugal force, and hope the car can overcome the corner. There are many disadvantages :
You lose time during slow down.
You lose engine rev during slow down, thus the engine takes longer to rise back to the useful power band once you exit the corner.
Very often, if you miscalculate, you are unlikely to have sufficient road ahead for you to slow down, especially in tight corner.
.
Therefore we always say RWD car is superior than FWD car in handling. There are, however, some well-sorted front-driver (especially some GTi) can play "lift-off oversteer", which is actually the reverse of "power oversteer" - a degree of permanent oversteer is built into the car but is only accessible when the car is pushing to the limit and with throttle disengaged. Step down the throttle again will reduce the oversteer and even back to understeer. Anyway, obviously this is still not as controllable as "power oversteer". While power oversteer can extract a lot of oversteer - actually depends on throttle - lift-off oversteer is rather limited, simply because it is impossible to build a lot of permanent oversteer to the chassis without deteriorating handling in lower speed or straight line.
Once again I have to emphasis that the power oversteer must be highly controllable by the driver, otherwise the car may lose control and spun. To make a good power oversteer car, the secret is to match the power and cornering limit perfectly at the speed concerned. If the cornering limit exceeded the power, the rear wheels will grip hard and refuse to slip. In contrast, if the cornering limit is too low or the engine torque is too high at the speed concerned, the rear end will slide severely once the throttle is pressed. Therefore, the cornering limit must be set at a level where the engine output, at the speed and road we normally want the car to power oversteer, has just sufficient power to exceed. To implement it , choose a suitable set of tyres, applying suitable amount of downforce and an adequate front / rear weight distribution is very crucial.
RWD versus 4WD
Basically, 4WD does not introduce power oversteer. However, most people still prefer it simply because it provides superior cornering grip thus improve cornering speed. As I have promised earlier in the Cornering Grip section, here I'll explain how 4WD improve cornering grip :
Consider a driving wheel running in a corner. Due to the frictional force applied from the road surface, the tread in the contact patch distorts and creates slip angle. The faster the car corner, the more centrifugal force generates thus the larger the slip angle becomes. You can interpret this as the elastic distortion of the tyre generates a counter force to keep the car fighting with the centrifugal force. When the car is accelerated fast to the extent that the elasticity of the tyre reaches its limit, it could not distort anymore, thus more speed will lead to the tyre slide, and the car lose grip. This point is what we call "Cornering Limit".
A FWD or RWD car has already a lot of tyre distortion (slip angle) in the driving wheel because the tractive force is shared by only two wheels. Therefore there is not too much space left before the tyres running into their cornering limits. On the contrary, 4WD cars distribute tractive force to all wheels, thus each wheel shares considerably less tractive force thus create smaller slip angle in cornering. The car can corner at higher speed before the slip angle reach the cornering limit.
* * *
Grip aside, we concentrate back to our current topic - steering tendency.
There is always argument that whether the neutral steer of 4WD is better than RWD's oversteer. Although neutral is more favourable in the entry phase and mid corner phase during cornering, it doesn't provide the "correctability" of power oversteer in the exit phase. Remember, no driver could avoid miscalculation, no matter Mrs. Robinson or Michael Schumacher. Normally we need to feel the car's attitude and the road condition every moment before deciding how to control the car in the next moment. In this sense, RWD's controllable power oversteer is what we want.
Moreover, power oversteer of RWD ask the driver to intervene the throttle during cornering. This let him feel more involving and that he is mastering the car. In contrast, 4WD cars let the tremendous grip, the limited-slip differential and even the computer to rule the car's cornering. Therefore we always hear road testers said RWD is more fun to drive.
I am not saying 4WD cannot have power oversteer. Bugatti EB110, with its 30/70 front-to-rear torque split, did that beautifully while providing tremendous grip. Even though a 50/50 4WD car like Mitsubishi Lancer Evo V could achieve slightly power oversteer by means of well-sorted suspension geometry. For example, if the suspension is setup such that to introduce rear outside wheel positively cambers when subjective to body roll, the contact patch area decreases thus slip angle increases, then power oversteer is also available. However, you cannot set the suspension to provide power oversteer as much as RWD car since there is a trade-off in total grip and straight line stability.
04-04-2006, 02:18 AM
#19
Nordschleife Master
New Trend for RWD cars
In the past 2 decades, we saw car makers gradually increases understeer in RWD cars, making them more "secure" to drive. Porsche 996 is a good example. Its predecessor 911 used to offer hell a lot of oversteer, now the 996 becomes a very civilised GT.
This is partly due to the market orientation ( it seems the wealthy customers tend to love secure rather than excitement), partly due to the use of wider tyres. In the past 2 decades, tyres of sports cars had been widened for about 50%, in addition to the growth in diameter, the contact patch area had been largely increased. Of course this is intended to increase the grip. However, increased contact patch area means every square inches of the contact patch carries less cornering force, so the tread distort less and the slip angle is reduced.
It is known that for the range of slip angle we concern (normally less than 20°), tractive force has less influence to the narrow slip angle than the wide slip angle, as illustrated in below :
Therefore, when apply the same power, the rear wheel slip angle increases in a lesser rate in wider tyres. In other words, power oversteer is less obvious.
This explain why the 115 hp version BMW Z3 1.9 has virtually no power oversteer ability. Its engine lacks the power to generate sufficient slip angle to the wide 205 rear tyres.
If it get considerable more power, like the M Roadster, power oversteer would have come back. But then again the car maker is very likely to install even wider rear tyres in order to cope with the increased performance, as did in the M Roadster. So once again the power oversteer is quite limited.
In my opinion, this trend is quite frustrating to the front-engined RWD cars. It makes them having less and less fun to drive, although the increased grip will ultimately improve cornering time. To mid-engined cars, whose rearward weight bias used to create some undesirable oversteer, the adoption of wider tyres could actually improve the handling and driving fun.
In the past 2 decades, we saw car makers gradually increases understeer in RWD cars, making them more "secure" to drive. Porsche 996 is a good example. Its predecessor 911 used to offer hell a lot of oversteer, now the 996 becomes a very civilised GT.
This is partly due to the market orientation ( it seems the wealthy customers tend to love secure rather than excitement), partly due to the use of wider tyres. In the past 2 decades, tyres of sports cars had been widened for about 50%, in addition to the growth in diameter, the contact patch area had been largely increased. Of course this is intended to increase the grip. However, increased contact patch area means every square inches of the contact patch carries less cornering force, so the tread distort less and the slip angle is reduced.
It is known that for the range of slip angle we concern (normally less than 20°), tractive force has less influence to the narrow slip angle than the wide slip angle, as illustrated in below :
Therefore, when apply the same power, the rear wheel slip angle increases in a lesser rate in wider tyres. In other words, power oversteer is less obvious.
This explain why the 115 hp version BMW Z3 1.9 has virtually no power oversteer ability. Its engine lacks the power to generate sufficient slip angle to the wide 205 rear tyres.
If it get considerable more power, like the M Roadster, power oversteer would have come back. But then again the car maker is very likely to install even wider rear tyres in order to cope with the increased performance, as did in the M Roadster. So once again the power oversteer is quite limited.
In my opinion, this trend is quite frustrating to the front-engined RWD cars. It makes them having less and less fun to drive, although the increased grip will ultimately improve cornering time. To mid-engined cars, whose rearward weight bias used to create some undesirable oversteer, the adoption of wider tyres could actually improve the handling and driving fun.
04-04-2006, 02:30 AM
#20
Nordschleife Master
04-04-2006, 01:17 PM
#21
Hmmmm.
So the article states that slip angle is the difference between the treads and the wheel's direction. So, let's say the wheel's direction is the 0 degree mark, and the treads are being force twisted to 3 degrees, according to the article, the slip angle is 3 degrees. Now, because of cornering forces, add to that 3 degrees of twist another 2 degrees of actual slippage of the tire tread on the pavement. What is the slip angle? According to the article, it's still 3 degrees? According to the past few decades of theory, would it not be 5 degrees? 5 degrees would be the addition of the 3 degrees of tire tread distortion plus the 2 degrees of tire slippage, making the wheel point 5 degrees off the direction of travel of the wheel (and thus the car) itself. This article doesn't take into consideration the tire slippage, which I think is necessary when discussing "slip" angles.
So the article states that slip angle is the difference between the treads and the wheel's direction. So, let's say the wheel's direction is the 0 degree mark, and the treads are being force twisted to 3 degrees, according to the article, the slip angle is 3 degrees. Now, because of cornering forces, add to that 3 degrees of twist another 2 degrees of actual slippage of the tire tread on the pavement. What is the slip angle? According to the article, it's still 3 degrees? According to the past few decades of theory, would it not be 5 degrees? 5 degrees would be the addition of the 3 degrees of tire tread distortion plus the 2 degrees of tire slippage, making the wheel point 5 degrees off the direction of travel of the wheel (and thus the car) itself. This article doesn't take into consideration the tire slippage, which I think is necessary when discussing "slip" angles.
04-04-2006, 02:24 PM
#22
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Originally Posted by shiners780
Hmmmm.
So the article states that slip angle is the difference between the treads and the wheel's direction. So, let's say the wheel's direction is the 0 degree mark, and the treads are being force twisted to 3 degrees, according to the article, the slip angle is 3 degrees. Now, because of cornering forces, add to that 3 degrees of twist another 2 degrees of actual slippage of the tire tread on the pavement. What is the slip angle? According to the article, it's still 3 degrees? According to the past few decades of theory, would it not be 5 degrees? 5 degrees would be the addition of the 3 degrees of tire tread distortion plus the 2 degrees of tire slippage, making the wheel point 5 degrees off the direction of travel of the wheel (and thus the car) itself. This article doesn't take into consideration the tire slippage, which I think is necessary when discussing "slip" angles.
So the article states that slip angle is the difference between the treads and the wheel's direction. So, let's say the wheel's direction is the 0 degree mark, and the treads are being force twisted to 3 degrees, according to the article, the slip angle is 3 degrees. Now, because of cornering forces, add to that 3 degrees of twist another 2 degrees of actual slippage of the tire tread on the pavement. What is the slip angle? According to the article, it's still 3 degrees? According to the past few decades of theory, would it not be 5 degrees? 5 degrees would be the addition of the 3 degrees of tire tread distortion plus the 2 degrees of tire slippage, making the wheel point 5 degrees off the direction of travel of the wheel (and thus the car) itself. This article doesn't take into consideration the tire slippage, which I think is necessary when discussing "slip" angles.
04-04-2006, 09:45 PM
#23
Racer
Thread Starter
OK, even though I started this thread, I"M TIRED OF DAYDREAMING AND READY TO DRIVE!!!!!!! 
I've signed up for enough events to test out every theory. Let the driving begin!!!!! Oh, I forgot. I'm in wisconsin and we haven't started yet. 
Keep talking. It helps me sublimate.
I've signed up for enough events to test out every theory. Let the driving begin!!!!! Oh, I forgot. I'm in wisconsin and we haven't started yet. Keep talking. It helps me sublimate.
04-04-2006, 09:53 PM
#24
King of Cool
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Originally Posted by Bull
Both. Remember, a small amount of "slippage" and noticable sliding are two different things.
You mean my avatar is optimal slip angle for maximum traction ?
04-04-2006, 09:59 PM
#25
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Originally Posted by Flying Finn
Bob,
You mean my avatar is optimal slip angle for maximum traction ?
You mean my avatar is optimal slip angle for maximum traction ?
