How Does Math Help Build a Car?

by Richard Rowe
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The usual perception today is that mathematics only came into auto manufacture in the 1980s, when computer-aided design and modeling hit the scene. But in reality, every car ever produced has been a machine made of numbers -- from beginning to end.

Product Planning

Automobile bodies might be born in the imagination of designers, but the car itself starts out with market analysis. Every car sold has to fit into a certain niche, and compete with others in that niche if there are any. A product planner's job is to analyze market data, figure out what's selling, where it's selling and for how much. Product planners have to look at horsepower, weight, fuel economy, and dimensional data and send their ideal specifications the engineering and design departments. In a very big way then, it's the product planner's heavily math-intensive market analysis that dictates almost every critical dimension and specification of the finished product.

Chassis Engineering

An engineer's primary job is to build a chassis and components to meet the product planner's specifications -- which is a tad more involved than it sounds. Computer-aided modeling has done a lot for chassis engineers, who can now digitally "build" a chassis in a computer, and "crash test" it over and over again using sophisticated calculus and physics algorithms. Physics modeling has become a field of mathematics and science in its own right, and the results of that modeling affect every aspect of chassis design and material use. Geometry and trigonometry are all-important elements of suspension design, as they are pretty much everywhere else a load-bearing component has to bolt to another one.

Exterior Design

You'd think that exterior design was a purely artistic process -- but it's a type of artistry heavily blended with science and math. You may have heard the phrase, possibly derogatorily that a car "looks like it was designed in a wind tunnel." Designers these days will often take advantage of tremendously sophisticated computer fluid flow modeling to figure out how the air will flow around, under and even through a car's body. They'll make tweaks to the car's design to enhance its aerodynamic characteristics in the computer before ever producing a scale model of it. Again, like computer-aided crash-testing in the chassis department, advanced algorithms and calculus play a critical role in the way the finished product looks and behaves.

Interior Design

Interior design is another area where you might think artistry and aesthetic design were first and foremost, but nope. A lot of geometry and trigonometry goes into the science of "ergonomics," or interior layout. The placement of every gauge, switch, dial and readout in the vehicle is precisely calculated within a certain set of parameters so that they fall easily to eye or hand for drivers and passengers of certain measurements. Those measurements also play a role in the placement of pillars, supports, dashboards and steering wheels because of the airbags. And all of these elements have to work together to make for an interior layout that's safe, convenient, comfortable and hopefully good looking.


After all of the design elements are in place, the car's off to the assembly line. With all of the robots involved in today's manufacturing process, there's scarcely a point in it that isn't absolutely reliant on computer calculations, geometry, trigonometry, welding and material physics to measure, machine and assemble components. With today's manufacturing processes, everything has to be measured to the nanometer, finished and fit precisely in. Mathematics even come into play in workflow analysis, as manufacturers are always looking for ways to make the most efficient use of their workers' and robots' time. Toyota is famous for this; its "kaizen" system of continuous improvement by constant analysis has long been an industry standard in production.

Completion and Delivery

A car's not through with math once it is built. After production, a certain number go into product testing or quality control. Some are sent off to be crash tested, where physics has the final say on the production run. Others are road-tested on a test track, where precise measurements are taken of the car's acoustic qualities, ride, handling, power output and emissions. It takes math -- a lot of math -- to gather and correlate all of these results. Finally, a car has to go through a logistical process for delivery. Here, time and distance tables are calculated, delivery costs are tabulated, and the car becomes just another tracking number in a vast system until it finally arrives on the dealership lot. Once there the owner takes possession and drives away, never knowing that his newest prize is a machine made of numbers from beginning to end.

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