Formula Racing Physics in curves (under-steer, over-steer)

Question

I have a working physics code for a -let's say- WipeOut-style vehicle [well, closest approximation]. Some time next year I would like to do a formula game but am struggling to get to tweak my code to behave anywhere near the way the formula (say, like in F1 GP game that ran on 100 MHz Pentiums) behaves in curves.

Visually, think 3D engine and a 3D track (with hills/valleys - but still a track (not a generic heightmap)).

Since the target HW is below 100 MHz and code is written in ASM, we can't use any off-the-shelf physics engines, but it must be written from scratch (initial prototyping will be done in C++ for max productivity and understanding of limitations of the physics component).

Now, I don't have any issue with the following (already working):

• non-linear acceleration (e.g. each gear range has different constants/behavior)
• hill-based acceleration/decceleration (how steep hill is)
• car gets lighter over time (less gas in the tank), affecting acceleration
• each parameter can have an additional modifier (linear, non-linear) applied to it over the time

My greatest issue is I can't seem to get the thing to over-steer / under-steer in curves. I want to allow the player to choose several different levels of physics - from Arcade, through gradually more realistic features, to a full-blown (as far as manageable by me) physics (like in F1GP game). So far, I have these racing physics modes implemented:

• Arcade racing (kinda like in Lotus/Outrun)
• gear-specific non-linear acceleration (each formula has different characteristics)
• hill-based speed-up/down (steepness)
• speed-based drag in curves (how quickly car reacts to turning)
• tire temperature gradually rising (affecting all physics ranges, modifiers and constants)

Through trial&error I found a way how to get the car to turn faster/slower based on current speed. It works pretty well, but it won't realistically skid the car away from the track (like F1GP does).

Also, nowhere in the code, I actually use any vectors. It's all just constants, valid ranges, and type of applied modifier (none/speed-up/down, linear/non-linear) that we use on the desired variable, as that's the fastest possible way on given platform (all these values fit into available CPU's registers, unlike vectors that have to be read from slow RAM).

So, how does one actually get the car to under-steer/over-steer in curves ? What's the actual physics here ? Rigid Body ? I believe it should be perfectly possible to emulate this feature via 2D vectors (car direction + speed) ?

Answer 1

I would add oversteer/understeer control as follows:

• Have different friction settings for the front tyres and rear tyres (against terrain.)
• If front tyres have more friction, your car should oversteer.
• If rear tyres have more friction, your car should understeer.

If that does not work for you, you could play by widening/shorting the track (spacing between the left and right wheels.) I suspect a wider car to oversteer more easily, but you would have to experiment with that. The friction differential is probably a better approach.

Note: that in real-world F1 racing, oversteer can be induced with higher downforce on the front wing.

So if you model downforce in your simulation, you could play with that: shift downforce from the rear to the front for more oversteer.

Lastly, you can also eliminate oversteer by moving from rear-wheel-drive to front-wheel-drive. The latter is typically understeered, the former is typically oversteered.

UPDATE: If you do not use a physics engine, you can fake oversteer by giving the car-rotation some momentum!

So instead of controlling the car's angular velocity with the joystick, you control the angular acceleration of the car with the joystick:

As you move back the joystick to the centre, the car continues its rotation for a while, forcing your players to counter-steer.

pseudo code:

rotvel = rotvel + joystick.x * dt;
rotang = rotang + rotvel * dt;
// bleed off the residual angular velocity
rotvel = 0.80f * rotvel;
// apply the rotation to the car
car.rotation = rotang;