Hi, I was wondering if I could have some help with implementing pacejka longitudinal friction, I have successfully implemented pacejka lateral friction and it works how I need it to now its just longitudinal friction I need for doing burnouts in vehicles and I don't know how to implement it with the formulas I have found on the internet.

This is my pacejka function

pacejka = function(slip, surface)
	if surface then
		local x = slip
		local b = surface.Stiffness -- Stiffness
		local c = surface.Shape -- Shape
		local d = surface.Peak -- Peak
		local e = surface.Curve -- Curve

		return d * math.sin(c * math.atan(b * x - e * (b * x - math.atan(b * x))));
	end
	return 0
end

And here's a snippet of my implementation of lateral friction

local WheelVelocity = self.GetPointVelocity(self.Engine, attachPosition + attachDirection)
local RelativeWheelVel = force.WorldCFrame:VectorToObjectSpace(WheelVelocity)
		
self.angularVelocity[force.Name] = (RelativeWheelVel / (math.pi*2) * self.WheelRadius)
		
local lateralVelocity = RelativeWheelVel.X
local longitudinalVelocity = RelativeWheelVel.Z
		
local slipAngle = math.deg(math.atan2(lateralVelocity, math.abs(longitudinalVelocity * self.stopWheels)))
--local slipRatio = ((Weld.Part1.RotVelocity.Z * self.WheelRadius) - longitudinalVelocity) / math.max(math.abs(longitudinalVelocity), 0.00001)
		
local pacejkaLatValue = self.pacejka(slipAngle, self.wheelSurface[force.Name]);
--local pacejkaLongValue = self.pacejka(slipRatio * 100, self.wheelSurface[force.Name]);
		
local totalTireLoad = Length * (Mass * Grip)
local tireLoad = math.clamp((1-(-self.springLength[force.Name] / 6.9*(2.5))) * (Mass * Grip), 0, totalTireLoad)
		
--local longForce = (tireLoad* (pacejkaLongValue / 2)) / 4
local lateralForce = (tireLoad * pacejkaLatValue) / 4

drivForce.Force = Vector3.new(-lateralForce, 0, longtitudinalForce.Z)

Yes I have clamped my lateral friction so it doesn't have any weird behavior but just for the sake of keeping it short i have slightly edited my code to not include it

also, the longtitudinalForce shown in the code snippet is just my power calculation

the friction graph is displaying the friction only for the front left wheel.

Any help implementing longitudinal friction is appreciated!

Welcome, new person. Did you look for discussions on Pacejka functions in the forum? This one is about lateral velocity, but it might contain some nuggets for you: https://gamedev.net/forums/topic/711781-vehicle-physics-pacejka-lateral-velocity​

@bmarci I think the problem with the movement is where I'm applying the force because I'm applying it in the same place as where I'm applying my suspension force, I will look into changing that to the contact point of the tires as you suggested.

I Have managed to get longitudinal friction working by using the torque from the engine in the slipRatio formula and then doing the same as I did with lateral, One problem I have rn is using slipRatio for the visual wheels and making them spin based on the slip ratio, Rn I'm using the relative velocity for the spin of the wheels.

local DistanceMoved = ((RelativeVel.Z) / (self.WheelRadius / 0.5)) * dt -- dt is delta timing
if DistanceMoved ~= DistanceMoved then
	DistanceMoved = 0
end
local WheelRotation = self.wheelRot
WheelRotation = WheelRotation + DistanceMoved / (self.WheelRadius * 0.5)
WheelRotation = WheelRotation % (2 * math.pi)
self.wheelRot = WheelRotation

Yea for Tireload I couldn't find much this is definitely a better formula than my lousy formula.

If you have any idea on how I would go about that please let me know

bmarci said:
angular_velocity

But wouldn't the angular velocity just keep adding up with each cycle of the loop, Also another thing to note is I have my Torque capped to the first value on my torque curve table

bmarci said:

IdleBrick said:
But wouldn't the angular velocity just keep adding up with each cycle of the loop

Yes, as long as it gets positive torque, as soon as you step off the throttle or start braking or just leave it free rolling the acceleration will be negative and the angular velocity will decrease as well.

This mostly works until the vehicle is stopped by a wall or span out, Then the angular velocity will stay the same and be out of sync with how the car should be

@bmarci Yea I have just tried looking it up and I can't find much, Managed to find a Wikipedia page on it but that's about it. Following the formula from Wikipedia I have been able to calculate cornering stiffness

local slipAngle = math.deg(math.atan2(lateralVelocity, math.abs(longitudinalVelocity * self.stopWheels)))
local slipRatio = ((self.angularVelocity[force.Name] * self.WheelRadius) - longitudinalVelocity) / math.max(math.abs(longitudinalVelocity), 0.00001)
		
local corneringForce = RelativeVel.Z / TurnRadius
local corneringStiffness = corneringForce / slipAngle

I haven't found anything on Lateral displacement. I don't know how I would implement both formulas into pacejka to have a force when not moving to stop cars with the same angular velocity as accelerating. It all a bit of a headache :(