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# Friction Problem

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I've been trying to convert my game's physics system to be frame-independent, but ran into a problem with resistive forces (friction, drag, etc.). Acceleration due to resistive forces always ends up being several thousand times what it should be, overcoming both current velocity and acceleration (ex: if velocity = 10 and standard acceleration = 1, then acceleration due to friction might be in the vicinity of -7000). I've included a copy of my "vehicle" class (written in Java) below, simplified operate in only one dimension. I think I made some sort of mistake either in the way I calculate the vehicle's drag coefficient in the constructor, or the way I integrate resistive force in the "updatePhysics" method, but I'm having trouble working it out. I'd appreciate any suggestions anyone can offer.


class Vehicle
{
float  maxSpeed = 0;
double engineAcceleration = 0;
float  xDragCoefficient = 0;

private float xPosition = 0;
private float xSpeed = 0;
private float xAcceleration = 0;
private float xResistance = 0;

public Vehicle(int newMaxSpeed, int newEngineAcceleration)
{
//This is the maximum speed this vehicle should attain under its own power (per millisecond)
maxSpeed = new Double(newMaxSpeed*0.001).floatValue();

//This is the acceleration caused by the force of the vehicle's engine (per millisecond)
engineAcceleration = new Double(newEngineAcceleration*0.001).floatValue();

//This represents the drag coefficient of the vehicle's "front" cross-section.
//It should keep the vehicle's velocity (xSpeed) from exceeding maxSpeed under
//engine power alone.
xDragCoefficient = new Double(2*engineAcceleration/(2*maxSpeed + engineAcceleration)).floatValue();
}

public void updateVehicle()
{
//The engine is accelerating the vehicle forward, possibly in addition to external forces
xAcceleration += engineAcceleration;

//The motion of the vehicle is resisted by its cross-sectional drag, possibly in addition to other resistive forces
xResistance += xDragCoefficient;

updatePhysics();
}

private void updatePhysics()
{
//Get the number of milliseconds that have passed since the last update cycle
int time = Test.getElapsedTime();

//Temporarily store the initial velocity
float xSpeedInitial = xSpeed;

//Integrate the acceleration due to standard forces (acceleration is constant over a single cycle)
xSpeed += xAcceleration*time;

//Determine the average velocity over this cycle in absence of resistive forces
float averageXSpeed = (xSpeedInitial + xSpeed)/2;

//Determine the average resistive acceleration over this cycle
float resistanceXAcceleration = (-xResistance*(averageXSpeed)*time);

//Integrate the acceleration due to resistive forces
xSpeed += resistanceXAcceleration*time;

//Update the possition by integrating the average speed, now that resistive forces are accounted for
xPosition += ((xSpeedInitial + xSpeed)/2)*time;

//Set Acceleration and Resistance to zero in preparation for the next cycle
xAcceleration = 0;
xResistance = 0;
}
}



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Why not do your updatePhysics function something like this?

private void updatePhysics(){	//Get the number of milliseconds that have passed since the last update cycle	int time = Test.getElapsedTime();			xAcceleration = engineAcceleration - (xDragCoefficient * xSpeed) / mass		xSpeed += xAcceleration*time;	xPosition += (xSpeed)*time;}

That's just using simple euler integration (this may not suffice, it depends upon what you're actually doing, if it's a simple physics simulation you may get away with it) and models the resistive force experienced by the car as F = kv where k is a constant (your xDragCoefficient) and v is the current speed).

You'll also need to calculate your drag coefficient differently and if I've got my maths right (it's been a while since I've done anything like that so I may have got it wrong) you can do it like this:

xDragCoefficient = new Double(mass * engineAcceleration / maxSpeed)

Oh and to convert your acceleration to milliseconds you need to multiply by 0.0012

Also why are xAcceleration and xResistance class variables? Why aren't they just local variables in updatePhysics?

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