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- The__Ghost__Z
Part of my tuning involves using mathematics to aim tires properly with toe and camber angles. Here I will explain the theory behind it. You'll need to have already underderstood a vast majority of tuning to get this, and some linear algebra/calculus, but bear with me if you can. I would also like to use this as a promotional for my tuning garage, to demonstrate tuning skill.
Ghost Tuning Garage
Consider each tire as having a vector. This vector is comprised of the values for rotational speed and direction. For example, a car traveling at, say, 30 MPH has a rotational speed under the front tires of 30mph, and the rear tires at 30mph. Since GT5 does not give us wheel diameters (and rim diameters are different than wheel diameters) we cannot find RPM measurements at the wheels, but that is unimportant.
As a car turns, the angle by which it is traveling relative to the tangent line of the corner changes as well. At low speeds, the car travels as a tangent line to the driving line would, so at apex both the driving line and inside corner, have the same tangent line.
However, you have to remember, that is NOT the angle of the car. That is the angle of the path of travel. The car will be going in that direction when it reaches that point (P). The tires however, will not be pointed in that direction.
Why?
Two reasons. The first is that the car is on a continuum, so the tires need to be pointed in the direction of its ongoing path of travel, not the instantaneous one (which is what that line represents), the second is that the tires actually travel at a small slip angle to their path of travel.
So what ultimately determines that path of travel? Wheel Vectors.
A car has the following wheels:
[Value 1, Value 2]
[30, 0] FR
[30, 0] FL
[30, 0] RR
[30, 0] RL
These wheels are all traveling at 30 mph, with a 0 angle deviation from the tangent line. In other words, the car is traveling straight on a straight road.
As the corner comes up, the car starts to turn. The angle of the front two wheels change (Value 2), the inside one more than the outside to maintain the arc, and try to follow the tangent line. The outside wheel's rotational speed (Value 1) rises and the inside wheel's rotational speed lowers.
The rear wheels, because they do not turn, change rotational speed as well. However, if they cannot change rotation speed quick enough (say, they have an LSD that prevents deceleration, or an engine giving them power that keeps them spinning faster than the angle they are asked to go) then in order for them to travel along the same path as the car, they must slip at a higher angle. We have started the drift.
Now what is interesting is that the new path of the car while drifting is figured by the same basic calculations as before. Except that instead of the wheels being a rectangle that is tangent to the driving line, it is now a diamond that is tangent to the driving line. This means that while the vectors of tire speed and angle determining the path of the car (and how fast) they are in a new shape.
But these are not really 2 dimensional vectors. They are 3 dimensional vectors. Tire Grip is the last one, which is counteracting a large vector of cornering force so the car can maintain the equilibrium in the other two dimensions (speed, angle) if the tires cannot counteract that force, a new equilibrium (a change in angle, aka understeer, or a change in speed) is necessary for the car to maintain its equilibrium.
What is interesting is that the tires grip is not evenly distributed, and additionally, increases almost proportionally as weight over the tire goes up, so you can actually calculate the path of the car using vectors like these:
[V1, V2, V3] FR
[V1, V2, V3] FL
[V1, V2, V3] RR
[V1, V2, V3] RL
Where V1 is the speed of the tire, V2 is the angle relative to the tangent line of the driving line, and V3 is weight over the tire. The maximum cornering speed for a given angle will be found when the tire's relative angels (adjustable by toe) rotational speed (adjusted by LSD and driver input) and grip (adjusted by suspension and driver input) are all in harmony.
This is one of many mathematical models I use to tune with, and it is the one I am most proud of for its creation. Precise calculations are not here because I like to preserve my method, but I see no reason not to, especially after some time now, to share this with the community. If you like the concept or want to know more, you can check out my newly opened tuning garage, here:
Ghost Tuning Garage
Ghost Tuning Garage
Consider each tire as having a vector. This vector is comprised of the values for rotational speed and direction. For example, a car traveling at, say, 30 MPH has a rotational speed under the front tires of 30mph, and the rear tires at 30mph. Since GT5 does not give us wheel diameters (and rim diameters are different than wheel diameters) we cannot find RPM measurements at the wheels, but that is unimportant.
As a car turns, the angle by which it is traveling relative to the tangent line of the corner changes as well. At low speeds, the car travels as a tangent line to the driving line would, so at apex both the driving line and inside corner, have the same tangent line.
However, you have to remember, that is NOT the angle of the car. That is the angle of the path of travel. The car will be going in that direction when it reaches that point (P). The tires however, will not be pointed in that direction.
Why?
Two reasons. The first is that the car is on a continuum, so the tires need to be pointed in the direction of its ongoing path of travel, not the instantaneous one (which is what that line represents), the second is that the tires actually travel at a small slip angle to their path of travel.
So what ultimately determines that path of travel? Wheel Vectors.
A car has the following wheels:
[Value 1, Value 2]
[30, 0] FR
[30, 0] FL
[30, 0] RR
[30, 0] RL
These wheels are all traveling at 30 mph, with a 0 angle deviation from the tangent line. In other words, the car is traveling straight on a straight road.
As the corner comes up, the car starts to turn. The angle of the front two wheels change (Value 2), the inside one more than the outside to maintain the arc, and try to follow the tangent line. The outside wheel's rotational speed (Value 1) rises and the inside wheel's rotational speed lowers.
The rear wheels, because they do not turn, change rotational speed as well. However, if they cannot change rotation speed quick enough (say, they have an LSD that prevents deceleration, or an engine giving them power that keeps them spinning faster than the angle they are asked to go) then in order for them to travel along the same path as the car, they must slip at a higher angle. We have started the drift.
Now what is interesting is that the new path of the car while drifting is figured by the same basic calculations as before. Except that instead of the wheels being a rectangle that is tangent to the driving line, it is now a diamond that is tangent to the driving line. This means that while the vectors of tire speed and angle determining the path of the car (and how fast) they are in a new shape.
But these are not really 2 dimensional vectors. They are 3 dimensional vectors. Tire Grip is the last one, which is counteracting a large vector of cornering force so the car can maintain the equilibrium in the other two dimensions (speed, angle) if the tires cannot counteract that force, a new equilibrium (a change in angle, aka understeer, or a change in speed) is necessary for the car to maintain its equilibrium.
What is interesting is that the tires grip is not evenly distributed, and additionally, increases almost proportionally as weight over the tire goes up, so you can actually calculate the path of the car using vectors like these:
[V1, V2, V3] FR
[V1, V2, V3] FL
[V1, V2, V3] RR
[V1, V2, V3] RL
Where V1 is the speed of the tire, V2 is the angle relative to the tangent line of the driving line, and V3 is weight over the tire. The maximum cornering speed for a given angle will be found when the tire's relative angels (adjustable by toe) rotational speed (adjusted by LSD and driver input) and grip (adjusted by suspension and driver input) are all in harmony.
This is one of many mathematical models I use to tune with, and it is the one I am most proud of for its creation. Precise calculations are not here because I like to preserve my method, but I see no reason not to, especially after some time now, to share this with the community. If you like the concept or want to know more, you can check out my newly opened tuning garage, here:
Ghost Tuning Garage
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