Maths: Proportionality in Fuel Consumption Models

Mathematical modelling lets us describe real-world behaviour with a single equation, then test how well that equation holds up. Here, fuel consumption is modelled as F = k × S² / W, linking fuel use per kilometre to speed and load weight through an empirical constant k. The structure matters. Fuel consumption is directly proportional to the square of speed, so doubling speed quadruples F — a disproportionately large rise. It is inversely proportional to load weight, so heavier loads reduce fuel used per kilometre, making them more efficient per tonne carried. These relationships connect through k, which is fixed from one known test run and then reused to predict consumption under new conditions. That predictive step is where modelling becomes powerful — and risky. If a company treats one measured value as universal, ignoring how speed and weight interact, its emissions reporting can drift far from reality. Understanding proportionality is therefore not just algebraic manipulation; it is about judging whether a model remains valid beyond the data that produced it.