Matthew Sill

In the early days of the auto industry, a car was a carriage without a horse. The first cars were designed without regard to aerodynamics, center of mass, or many safety features that we take for granted on modern cars. Since the first cars became available in the early part of this century, automotive engineers have made a number of changes that have improved the handling, speed, and survivability. In 1909, Henry Ford sold the first of many 22 horsepower Model T's, today, almost 100 years later; a host of carmakers offer 300 horsepower super cars, as well as affordable, practical cars for the daily driver. In the auto industry today, our understanding of physics is constantly improving our ability to create cheaper, safer, and more enjoyable cars for the consumer.



When you think of performance vehicles, speed is often an attribute that comes to mind, but what factors actually contribute to the speed of the car, and what barriers to carmakers have to overcome? Drag force and Horsepower, these are the most important factors influencing the speed of a performance vehicle. A designer can make a car faster by building a bigger engine, like the 2000 Lamborghini with it's 575 hp engine, but there is nothing they can do to get rid of the drag force. This becomes a problem because drag force increases by the square of the velocity, so the faster a car is traveling, the higher the forces are that oppose movement. Because of this, even the most powerful production sports cars max out at about 200 mph. In addition to drag force and Horsepower, other important information is torque, other factors, such as aerodynamic lift at high speed, and handling, are obstacles that can be overcome by correct engineering.

Drag Force:
Drag force= (1/2)Crav^2, In the drag formula, the area facing the drag force is the only real tool designers have to change, in essence, the density of air, and the coefficient of friction are set, and do not change much, the velocity on the other hand, changes frequently through the life of the car, but for testing purposes, is constant. This leaves cross sectional area for designers to tweak with. This is often reduced by lowering rooflines, and angling all body surfaces away from the oncoming drag force. An extreme example of this would be the land speed record cars such as the spirit of America, ( which can top 800 mph. As you can see, the Spirit of America is little more than a jet plane without wings, and almost all of the surfaces have been swept back to minimize drag force on the body.

Horsepower is measures how much force the engine can apply to car in a given amount of time. It is a measurement of power, which is measured in Joules per second, or Watts. The equation for instantaneous Power is P=FV for an object moving in a straight line. IN addition, F=MA, so P=MAV with the result being in Watts. To find the horsepower, this formula must be divided by 746 because there are 746 watts in one Horsepower.

This formula is the reason an engine can be rated for a specific Horsepower, despite being mounted in a number of cars, with varying masses. You might think that an engine removed from a heavy car and placed in a light car might produce more horsepower, in fact, because A=F/M the acceleration will increase at the same rate as the mass is reduced, resulting in a constant horsepower.

The placement of the engine is another important consideration in designing a hot car. The best configuration is what is called "mid-engined" where is engine is as close to the center of the car as possible. This is good because the engine tends to be the center of mass for the automobile, and forces act on the center of mass. If you have a car with the center of mass in the front or the back, forces acting on that point will have more success breaking the tires grip on the road, since the force will only have to overcome the friction of two tires, rather than four. For example, a car turning around a curve has a number of forces acting on it. Friction acting on the tires in the form of centripetal force keep the car moving in a circle, while the momentum of the car, which is the force that is trying to go in a straight line, opposes the centripetal force. The sum of these forces must be equal, or the tires would start sliding. If the Cm for the car is near the center of the car, the momentum will have to oppose the friction forces on all four tires. ON the other hand, if the Cm is over the rear tires, the momentum will only have to break the friction force of the back two tires. Thus, a mid-engined car is less likely to slide in a corner, making such a car more stable and safe than a front or rear engined car.


In the past few years, carmakers have been looking at ways to make cars cheaper and more affordable to own. The best way to do this is to reduce the size of the engine, while at the same time, keeping performance, and comfort to the level demanded by consumers. Several ways to do this are, improving the engine itself, allowing a smaller power plant to do the same amount of work, design the body better, so that less force is required to keep the vehicle in motion, and reduce the overall weight of the car, so that less work is needed to move it.

Engine Efficiency:
The special metals used in the new engines can be understood through a physics approach, for example, when parts such as pushrods and pistons are made of a light weight material, we can think of the parts in terms of Momentum. Momentum P is equal to Mass times Velocity. When the weight of a part is reduced, the impulse force required to change the momentum of the part is reduced. Thus, a lighter part, will require less force to move around, energy wasted in making the engine go can now be used to drive the vehicle.
Reducing the friction inside the engine is another way that engineers use science the improve today's cars, however, most of the improvements such as low viscosity synthetic oils, specially coated cylinders and cylinder walls come from an understanding of chemistry, not physics, and while significant, these improvements are outside the bounds of this paper.

Drag Force at low speeds:
Drag force= (1/2)Crav^2 Assuming that V and A are constant, note what happens when C, the Coefficient of Friction decreases. The total drag force decreases, meaning that a car with a low drag force will be able to accelerate and travel faster than one with a high drag force. This means a smaller engine is required to drive such a car, which means a gas savings for the owner, and a "greener" more efficient car. So Drag force is not just important to speed freaks and adrenaline junkies, real cars, driven by real people, utilize a working knowledge of drag force to design more efficient, cheaper cars, that still drive as well as gas hogs with square bodies. The only problem, from the buyer's point of view, is that many car designers have become slavishly dependent on low drag numbers that many cars end up looking like slugs or salmon, and no matter how efficient a car is, an ugly car is still an ugly car.

Car Weight:
As with the parts inside the engine, when the entire car is made lighter, through the use of lighter materials or better designs, less force is required to move the car. This is based on F=MA or more accurately, A=F/M, so as mass of the car decreases, the acceleration increases, or less force is required to accelerate the lighter car.

In the early days, cars were designed with reckless disregard towards physics; early autos were boxy and poorly designed for high speed. Small heavy engines pushed boxy containers down the road while guzzling gas at an alarming rate. Later on, in the 50's and 60's designers created beautiful cars but even these smooth modern-looking cars were not designed as well as they could have been from physics point of view. Today, armed with knowledge of physics, automotive engineers can design cars to best reduce drag, increase horsepower output, increase acceleration and safety. This means lower ownership costs, and better performance for the consumer. In reaching compete automotive nirvana however, there are several obstacles. First, it would be nice to reduce the coefficient of friction of the car body to zero, would bring the drag force down to zero, in which case car speed would be only dependant on Power of the engine. On the other hand, designers would like to increase the friction between the tires and the road, allowing for better stopping and safer cornering, unfortunately, tires having infinite friction are a long way off, and even if they were available, the stresses on the occupants would be too high. Another stumbling block is the low efficiency of the gasoline engine, which utilizes roughly 15% of the power produced to propel the car. In conclusion, the automotive industry has come a long way since the first engine was fitted into a carriage, but the perfect car is still a long way off, and we still have many more years of tinkering with physics to improve the way in which our automobiles work.

Variables used:

  • M = Mass
  • r = Rho. which is the density of air.
  • V = Velocity
  • C = constant, coefficient of friction.
  • A = acceleration
  • a = area
  • Cm = Center of Mass


  • Physics for Scientists and Engineers: 3rd Edition, Serway, Raymond. Pub: Saunders College Publishing 1990.

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