Car Physics for Games
by Marco Monster

Physics in Game Maker Studio 2 The following is an introduction demo of how physics can work in Game Maker Studio 2. It will give you an introduction of how you could implement it in your game. Step 1: Create Sprites for Physics Objects. Version 1.9 November, 2003. This tutorial is about simulating cars in games, in other words vehicle physics. One of the key points in simplifying vehicle physics is to handle the longtitudinal and lateral forces separately. Longtitudinal force. Physics provides a wonderful means for allowing a player to immerse themselves within a game. It makes sense that a mastery of a physics engine would be a powerful asset for any programmer to have at their disposal. Optimizations and specializations can be made at any time due to a deep understanding of the inner workings of the physics engine.

Yokogawa dcs pdf. Level: Advanced

Abstract: An introduction to car physics modelling for games.

version 1.9
November, 2003

Introduction

This tutorial is about simulating cars in games, in other words vehicle physics.

One of the key points in simplifying vehicle physics is to handle the longtitudinal and lateral forces separately. Longtitudinal forces operate in the direction of the car body (or in the exact opposite direction). These are wheel force, braking force, rolling resistance and drag (= airresistance). Together these forces control the acceleration or deceleration of the car and therefore the speed of the car. Lateral forces allow the car to turn. These forces are caused by sideways friction on the wheels. We'll also have a look at the angular moment of the car and the torque caused by lateral forces.

Notation and conventions

Vectors are shown in bold, we'll be using 2d vectors. So the notation a = -b would translate to the following code snippet:
a.x = -b.x
a.y = -b.y

Throughout this tutorial I'll be assuming that the rear wheels provide all the drive (for four wheel drives apply the neccesary adaptations).

I'll be mainly using S.I. units (meters, kilograms, Newtons, etc.), but I've included a handy conversion table at the end for those readers more familiar with imperial measures (pounds, feet, miles, etc.)

Straight line physics

First let's consider a car driving in a straight line. Which forces are at play here? First of all there's what the tractive force, i.e. the force delivered by the engine via the rear wheels. The engine turns the wheels forward (actually it applies a torque on the wheel), the wheels push backwards on the road surface and, in reaction, the road surface pushes back in a forward direction. For now, we'll just say that the tractive force is equivalent in magnitude to the variable Engineforce, which is controlled directly by the user.

F_traction = u * Engineforce,
where u is a unit vector in the direction of the car's heading.

If this were the only force, the car would accelerate to infinite speeds. Clearly, this is not the case in real life. Enter the resistance forces. The first and usually the most important one is air resistance, a.k.a. aerodynamic drag. This force is so important because it is proportional to the square of the velocity. When we're driving fast (and which game doesn't involve high speeds?) this becomes the most important resistance force.

F_drag = - C_drag * v * |v|
where C_drag is a constant and v is the velocity vector and the notation |v| refers to the magnitude of vector v

The magnitude of the velocity vector is more commonly known as the speed. Note the difference of data type: speed is a scalar, velocity is a vector. Use something like the following code:

speed = sqrt(v.x*v.x + v.y*v.y);
fdrag.x = - Cdrag * v.x * speed;
fdrag.y = - Cdrag * v.y * speed;

Then there is the rolling resistance. This is caused by friction between the rubber and road surface as the wheels roll along and friction in the axles, etc.etc. We'll approximate this with a force that's proportional to the velocity using another constant.

F_rr = - C_rr * v
where C_rr is a constant and v is the velocity vector.

At low speeds the rolling resistance is the main resistance force, at high speeds the drag takes over in magnitude. At approx. 100 km/h (60 mph, 30 m/s) they are equal ([Zuvich]). This means C_rr must be approximately 30 times the value of C_drag

The total longtitudinal force is the vector sum of these three forces.

F_long = F_traction + F_drag + F_rr

Note that if you're driving in a straight line the drag and rolling resistance forces will be in the opposite direction from the traction force. So in terms of magnitude, you're subtracting the resistance force from the traction force. When the car is cruising at a constant speed the forces are in equilibrium and F_long is zero.

The acceleration (a) of the car (in meters per second squared) is determined by the net force on the car (in Newton) and the car's mass M (in kilogram) via Newton's second law:

a = F / M

The car's velocity (in meters per second) is determined by integrating the acceleration over time. This sounds more complicated than it is, usually the following equation does the trick. This is known as the Euler method for numerical integration.

v = v + dt * a,
where dt is the time increment in seconds between subsequent calls of the physics engine.

The car's position is in turn determined by integrating the velocity over time:

https://treeholiday.amebaownd.com/posts/15438878. Studio one 4 32 bit download. p = p + dt * v

With these three forces we can simulate car acceleration fairly accurately. Together they also determine the top speed of the car for a given engine power. There is no need to put a maximum speed anywhere in the code, it's just something that follows from the equations. This is because the equations form a kind of negative feedback loop. If the traction force exceeds all other forces, the car accelerates. This means the velocity increases which causes the resistance forces to increase. The net force decreases and therefore the acceleration decreases. At some point the resistance forces and the engine force cancel each other out and the car has reached its top speed for that engine power.

In this diagram the X-axis denotes car velocity in meters per second and force values are set out along the Y-axis. The traction force (dark blue) is set at an arbitrary value, it does not depend on the car velocity. The rolling resistance (purple line) is a linear function of velocity and the drag (yellow curve) is a quadratic function of velocity. At low speed the rolling resistance exceeds the drag. At 30 m/s these two functions cross. At higher speeds the drag is the larger resistance force. The sum of the two resistance forces is shown as a light blue curve. At 37 m/s this curve crosses the horizontal traction force line. This is the top speed for this particular value of the engine power (37 m/s = 133 km/h = 83 mph).

Magic Constants

So far, we've introduced two magic constants in our equations: C_drag and C_rr . If you're not too concerned about realism you can give these any value that looks and feels good in your game. For example, in an arcade racer you may want to have a car that accelerates faster than any car in real life. On the other hand, if you're really serious about realistic simulation, you'll want to get these constants exactly right.

Air resistance is approximated by the following formula (Fluid Mechanics by Landau and Lifshitz, [Beckham] chapter 6, [Zuvich])

F_drag = 0.5 * C_d * A * rho * v²

where C_d = coefficient of friction
A is frontal area of car
rho (Greek symbol )= density of air
v = speed of the car

Air density (rho) is 1.29 kg/m³(0.0801 lb-mass/ft³), frontal area is approx. 2.2 m² (20 sq.

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