Module 3 — Sciences applied on trucks provides the physical and mechanical foundations needed to understand how heavy goods vehicles behave on public roads. The module covers three interconnected domains: the kinematics of rigid bodies, which describes the position, velocity, and acceleration of objects moving through space; the physics of energy conversion, which explains how force, power, and thermal efficiency govern fuel consumption; and vehicle dynamics, which characterises the stability and maneuverability of truck combinations under real operating conditions. These principles underlie engineering standards, safety regulations, and the technical performance limits imposed on heavy vehicles by transport authorities worldwide.
Kinematics is the branch of mechanics that describes the motion of objects without reference to the forces that cause that motion. In road transport engineering, kinematic analysis provides the tools to model how vehicles — and their individual rigid components — move through three-dimensional space.
Describing the position of any moving object requires a reference frame: a mathematical construct that defines the origin point and the axes against which positions and displacements are measured. In automotive mechanics, the standard choice is an orthonormal Cartesian frame, consisting of three mutually perpendicular unit vectors — conventionally denoted i, j, and k — forming a direct (right-handed) basis in which the following cross-product relations hold:
$$ \vec{i} = \vec{j} \land \vec{k}, \quad \vec{j} = \vec{k} \land \vec{i}, \quad \vec{k} = \vec{i} \land \vec{j} $$
A reference frame (or référentiel) extends this concept by anchoring the coordinate system to a specific origin point O, producing a full spatiotemporal system R(O, i, j, k) capable of locating any point in three-dimensional space at any instant in time. Transport engineering typically employs an inertial (Galilean) reference frame — one in which an isolated body subject to no net force remains either at rest or in uniform rectilinear motion, with constant velocity in both direction and magnitude.
The position of a point M in reference frame R is expressed as the vector from origin O to M:
$$ \vec{OM}(t) = x_m(t)\cdot\vec{i} + y_m(t)\cdot\vec{j} + z_m(t)\cdot\vec{k} $$
All distances are measured in metres (m) under the International System of Units.
The trajectory is the path traced by point M through space over time — the complete set of positions OM(t) as t varies. For a heavy vehicle, the trajectory of key reference points (such as the rearmost axle or the outer corner of a trailer body) has direct practical significance: it determines the swept path and the road space the vehicle requires to complete a given maneuver.
Velocity characterises how rapidly the position of a point changes over time. Two definitions are operationally relevant. Mean velocity over a time interval Δt is the ratio of the displacement vector to the elapsed time:
$$ \vec{v_i} = \frac{\Delta\vec{OM}}{\Delta t} $$
Instantaneous velocity is the limiting case as the time interval approaches zero — the time derivative of the position vector:
$$ \vec{v}(t) = \lim_{\Delta t \to 0} \frac{\Delta\vec{OM}}{\Delta t} = \frac{d\vec{OM}(t)}{dt} $$
The instantaneous velocity vector is always tangent to the trajectory at the point in question and directed in the sense of motion. Velocity is measured in metres per second (m/s).