Car tuning in Ultimate Stunts

Introduction

This document describes how the physics of cars in Ultimate Stunts can be tuned. You may want to tune a car when you add a new car, or for instance when you are not satisfied with the default settings.

You have to be aware of the fact that Ultimate Stunts is not made for physics realism. If you want realism, pleas take a look at simulators like Racer. If you just want to have fun with self-made tracks and lots of stunts, then Ultimate Stunts is the game for you. Within the limits of the Ultimate Stunts physics engine, you can make your cars as good or as bad as you want, and as realistic or unrealistic as you want. The philosophy of Ultimate Stunts itself is to give gameplay top-priority. Cars should be fun to drive in the first place. Realistic settings are only used where that contributes to the driving fun. Cars that are too difficult to drive are bad, and too easy cars are bad too. This makes car-tuning something like an art.

Getting information from the real-world car

In many cases, you want to make your Ultimate Stunts car similar to an existing car. For most cars, specifications can be found on the internet, and they can be realy useful. If possible, try to get as many of the following items as possible. Don't forget to look what kind of units are used: miles per hour is different from kilometres per hour.

Top speed
Max. power, max. torque + their RPMs
Gear ratios + the final drive ratio (= differential ratio)
The traction type (front wheel / rear wheel / four wheel traction)
The mass of the car
The weight distribution between front wheels and rear wheels
The height of the center of gravity above the ground

Before using them in Ultimate Stunts, you should know that Ultimate Stunts internally uses SI units everywhere. So, you should convert everything to SI units. This table gives some multiplication factors:

Non-SI units		SI units
1 km/h	=	0.2778 m/s
1 mile/h	=	0.4469 m/s
1 hp	=	735.5 W
1 kW	=	1000 W
1 RPM	=	9.549 rad/s

The 3D models of the car

The 3D models of the car body and wheels have some influence on the physics of the car, so if you want to make the car realistic, then the sizes of these models should be correct. Especially the radius of the wheels and the positions of the wheels are important. However, making the 3D models is not covered in this document: here, it is assumed that you already have the 3D models and a working .conf file for the car, and that you only make modifications to that .conf file.

Important properties of a car

In this section, some physics properties of cars are described.

Top speed

A car cannot accelerate forever. As the speed increases, the friction forces increase, and at a certain speed, the engine power is no longer sufficient to compensate the friction forces. At high velocities, aerodynamic drag is the main friction force, so the aerodynamic drag setting cwa is important. A higher cwa setting means a lower top speed. Also, engine power and torque are important. Increasing them increases the top speed. Also, don't forget the gear ratios. If you want high speed gear settings, then the highest gear should be such that the engine reaches maximum power at the top speed. Some formulas:

#Symbols:
v = speed of the car
cwA = aerodynamic drag parameter
Fdrag = aerodynamic drag force
Pdrag = power required to compensate drag
v_max = top speed
P_max = maximum power of engine

r = radius of wheel
ratio_g = rear ratio of highest gear
ratio_d = differential ratio (final drive ratio)
w_wheel = rotation speed of wheel
w_engine = rotation speed of engine
w_engine_P_max = rotation speed of engine @ max power point

#Calculating the top speed
Fdrag = cwA * v^2
Pdrag = Fdrag * v = cwA * v^3
v_max = (P_max / cwA) ^ (1/3)
cwA = Pdrag / v_max^3

#Calculating optimal gear ratios
w_wheel = v / r
w_engine = w_wheel * ratio_g * ratio_d = v * ratio_g * ratio_d / r
ratio_g * ratio_d = w_engine_P_max * r / v_max

If you have a car with a certain amount of power, and you want it to have a certain top speed, then you can calculate the gear ratio / differential ratio combination, and then fine-tune the top speed by changing the cwa value.

acceleration

At velocities near the top speed, cars have a very low acceleration, but at low speeds, some cars can accelerate very fast. At low speeds, acceleration is not limited by aerodynamic drag. Instead, it is limited by the amount of force that can be supplied by the engine, though the tires, compared to the mass of the car. A higher car mass means a lower acceleration, and a higher traction force means a higher acceleration.

With the right first gear ratio, any engine can generate enormous traction forces. A higher gear ratio means a greater traction force. I can hear you asking: "why don't cars have infinitely high gear ratios, if that gives greater traction forces?". Besides the fact that there are technical limitations to gear box technology, there are several reasons for this. One reason is that with high gear ratios, an engine will very soon reach high RPMs, so that the traction force will start to drop, so you will only have an advantage of the gear for a very short time, and then you'll have to switch to a higher gear. Another reason is that tires can only apply a limited amount of force to the ground. If this force is exceeded, then the tires simply start skidding, instead of generating extra force. So, for fast acceleration it may be smart to match the first gear ratio with the maximum traction force that can be applied by the tires.

The maximum amount of force that can be applied by the tires depends heavily on the vertical force on the wheel (here called the normal force). In a neutral situation, this is simply a part of the weight of the car: the weight distribution of the car describes how much of the weight goes to the front wheels and how much to the rear wheels. This distribution can be changed in Ultimate Stunts by moving the centerofmass forward or backward. When accelerating, decellerating or turning, this distribution can be different from the neutral situation. When the car accelerates, it leans more on the rear wheels, so the normal force on the rear wheels will be higher than in the neutral distribution. As a higher normal force allows for a greater traction force, this effect is good for rear-driven cars and bad for dront-driven cars. Aerodynamic downforce from spoilers also has an influence on the normal force, but for acceleration this is less important because downforce is only generated at high speeds, and acceleration requires the highest forces at low speeds.

Because the high number of effects, no exact description will be given here, especially because the situation is different for front-wheel and for rear-wheel cars. An exact description is possible, but would take an extra page of formulas. Here is a description for the situation where the acceleration generates no weight transfer, and no aerodynamic downforce is present.

#Symbols
m = mass of the car
g = gravitation constant (9.81 m/s^2)
Fz = gravity force
wfrac = fraction of weight on the traction wheels (= percentage / 100), 4WD: wfrac=1
Fn = total normal force on the traction wheels
mu = static friction coefficient of traction tires
Ftr = maximum traction force
a = acceleration
a/g = acceleration in G-forces
M_engine = maximum engine torque
M_wheel = maximum total torque applied to traction wheels
ratio_g = rear ratio of first gear
ratio_d = differential ratio (final drive ratio)
r = radius of the traction wheels

#Neutral situation normal force
Fz = m * g
Fn = wfrac * Fz = wfrac * m * g

#Traction force
Ftr = mu * Fn

#Acceleration
a = Ftr / m = mu * Fn / m
a/g = mu * Fn / Fz

#Neutral situation acceleration
a/g = mu * wfrac

#Gear ratios
M_wheel = ratio_g * ratio_d * M_engine
Ftr = M_wheel / r = ratio_g * ratio_d * M_engine / r
ratio_g * ratio_d = Ftr * r / M_engine = mu * Fn * r / M_engine

braking

The brakes add a torque to the wheels that will decrease the speed of the car. A brake torque that is too high is useless because the tires will simply start skidding instead of generating more braking force. As braking also takes place through the tires, braking foces are limited in the same way as traction forces. Modern cars usually have four-wheel braking, but the braking torque on the front wheels is usually a bit stronger, because braking generates some weight transfer from the rear wheels to the front wheels, so the front wheels can usually generate more braking force. Aerodynamic downforce can add more grip to tires in braking situations, especially at high speeds.

#Symbols
M_brake = maximum braking torque on a single wheel
F_brake = maximum braking force on a single wheel
Fn = normal force on a single wheel
mu = static friction coefficient of the tire
r = radius of the wheel

F_brake = mu * Fn
M_brake = r * F_brake = r * mu * Fn

jumping

Jumping is more important in Ultimate Stunts than in any other racing game. While jumping, there is not much that a car can do, however: it is simply not designed to be airborne. You cannot steer or brake, as the wheels don't make contact with the gound. There is only one thing left in the air: aerodynamics. In theory, you could make a car that starts flying at high speeds by giving it a negative downforce, but this is not really useful. A more useful purpose of downforce is to make sure that the nose goes down in a jump, so that you can see where you land with the in-car camera view. To do this, you need to increase the front downforce and/or decrease the rear downforce. Note that this will also affect the steering behavior.

steering

The way how a car behaves when taking corners is essential in how the car handling is experienced by a driver. Unfortunately, this is a complicated subject, and it is not described easily.

If a car needs to follow a circle-shaped path, then it needs to accelerate towards the center of that circle. This means that the tires need to generate sideward forces. Also, the car needs to rotate, so that it remains aligned with the circle. About the sideward forces, you already guessed it: they are limited by the tires, just like engine and brake forces. Also, if engine or brake forces are applied on a certain wheel, then there is less force "left" for steering. Weight transfer effects are extremely important in corners. Because of the steering, the outer wheels get more weight, and the inner wheels less. Also, if the rear wheels get more grip, then the car will understeer, and if the front wheels get more grip, the car will oversteer. The distribution of normal force between front and rear wheels depends on a lot of things, so it can also be tuned in a lot of ways. The weight transfer due to accelerating and braking can be increased / reduced by putting the center of gravity lower or higher, the neutral weight distribution can be changed by moving the center of gravity forward or backward, the distribution at high speeds can be changed with the front and rear downforce, and the grip can be tuned by changing the static friction coefficient of the front or rear tires a little bit.

Another thing that needs to be tuned is how fast the car rotates. When turning into a corner, the front wheels' rotation is changed, so that a sideward force is generated on the front wheels. As this force is initially not present at the rear wheels, the car starts rotating. How fast it starts rotating depends on many things, one of them being the moment of inertia of the car. The moment of inertia is to rotations what mass is to linear motions. If the moment of inertia is extremely high, then the car will respond very slowly to steering forces: it takes a long time before the car starts steering, and after the corner it takes a long time before the car drives in a straight line again. If the moment of inertia is low, then the car will respond very quickly to changes: small changes in steering, gas or braking will cause an overreaction in the orientation of the car.

The following formulas give some general information on how fast corners can be taken with a given tire quality.

#Symbols
R = radius of a corner
v_max = maximum speed in this corner
m = mass of the car
g = gravitation constant (9.81 m/s^2)
F = maximum total sideways force of the tires
Fn = total normal force on the tires
mu = static friction coefficient of the tires

F = m * v_max^2 / R = mu * Fn = mu * m * g
vmax = sqrt(R * mu * g)