# Basic Automobile Physics

By Jim Roal

### Basics of Engines and Ratings

Engine power is a rating of how quickly work can be done. Work is a measure of force times distance. If you lift a 550 pound object 1 foot you have done 550 foot pounds of work (not to be confused with foot pounds of torque which is a force, not work). This ignores inertia affects that would be very large in this example. If you do that work in one second, you have just applied one horsepower (or 746 Watts). The relationship between engine torque and horsepower is:

1HP = ((torque in foot pounds)x(RPM))/5252

If you have either a power or torque measurement, and the RPM, you can calculate the other. If you have only a torque measurement but not the RPM at which that torque is produced, you cannot calculate acceleration. However, if you have only a power rating you can calculate acceleration, if only at the point of that rating. If you want to really understand the acceleration potential of an engine, you need to look at the power curve across the RPM range that the engine will be operating while accelerating.

Torque is a rating or twisting force. A foot pound of torque is 1 pound of force applied perpendicular to a shaft 1 foot from the shaft centerline. Torque can be applied with no motion. A torque rating alone tells you some things about an engine however it does not tell you how much work the engine can do in a given time.

Power (HP or kW) is a rating of the amount of work that can be done in a given time. Power is really the rating you need to determine how fast you can go, how quick you can accelerate, or any other performance aspect of a vehicle, boat, or any powered machine.

Power is conserved in a geartrain except for some loss due to friction. Torque however, is multiplied or divided in a gear train. If you have a 4:1 gear ratio, you will multiply your torque by 4. Applying 200 foot pounds of torque will result in 800 foot pounds on the output. However, if you apply 200 HP to the input, you still get 200 HP (minus some friction losses) out but your output shaft RPM is 1/4 what it was on the input.

Engines with high torque ratings and low power ratings are engines that build power down low, but it quickly drops off at high RPM. These engines usually have a wide, constant power band. They are good for towing where you need to apply power all the way through each gear for long periods.

Engines with high power and low torque are higher RPM engines. These engines do better with more transmission speeds and higher final drive ratios. Their power band is usually not flat but rather slopes upward to a peak and then drops off. If you run these engines much below the peak power RPM, the power is much lower than the peak power. If you can keep the same peak torque rating, but double the RPM at which the peak torque is delivered, you will double power.

Considering that power and torque are just measurements of engine performance, and that power is the measurement of how fast work can be done (such as accelerating a vehicle) in order to really understand the performance of an engine you must really consider the whole power curve across the entire RPM range of the engine. Often people will argue about which is more important, torque or power, but honestly it is the wrong argument to have. The more relavant discussion is about how broad the power curve of the engine is. This is often referred to as "power under the curve" and refers to the area under the power curve of en engine.

### Vehicle Dynamics

Newtons law states that force equals mass times acceleration (F=ma). This equation can be solved for acceleration to show that acceleration equals mass divided by force (a=F/m). Acceleration is the rate of speed change and is expressed in units of length per time squared (typically feet per second squared). Neglecting things like traction, doubling force will double acceleration. Power is required to apply the force at a rate fast enough to do the work of accelerating the vehicle. Doubling acceleration will reduce the time it takes to achieve a given speed by half. Cutting mass in half has the same affect as doubling power. Bottom line: if you want better acceleration, reducing the mass (weight) or a vehicle will have the same affect as increasing power (force).

Weight is simply mass times the acceleration equivalent of gravity (32.2 feet per second squared). If you divide a vehicle weight in pounds by 32.2, you will get the mass in units of slugs. If you divide the weight in Newtons by 9.81, you get the mass in Kilograms (kg).

In high powered vehicles, traction is generally the limiting factor for acceleration. Traction is the force the tires can apply to the pavement. The reaction is an equal and opposite force applied to the vehicle thereby accelerating it. It is governed by friction. There are 2 measures of friction: kinetic (relative motion between surfaces) and static (no relative motion). If your tires are slipping on the pavement you are using kinetic friction. If the tires are not slipping, you have static friction. A car driving down the road at a constant speed is using static friction between the road and tires. Static friction is greater than kinetic. In other words, once you slip the tires, you loose traction force, and thus loose acceleration. Traction equals the weight applied (normal force) to the tire times the friction coefficient. The static friction coefficient is greater than the kinetic friction coefficient. Increasing the weight on a tire will increase the traction, as will increasing the coefficient of friction. Tires will have less traction when slipping.

For off-road vehicles, there is another factor to consider and that is inertia. In soft terrain, such as soft sand, there is very little friction available. As the tire rolls, the sand just shifts under it. In order to propel a vehicle through this medium, you can displace enough sand to force the vehicle forward. This is more like a boat. A boat is propelled forward by pushing water backwards. The off-road vehicle just propels the sand instead of water. This is why paddle type tires are used in very soft terrain.

Gravity has the same affect on a mass as acceleration. When the car is at rest, only the acceleration affect due to gravity is acting on the car to produce weight (force). When the car accelerates, a second force is required to cause the acceleration. These 2 forces are called vectors (each having a direction and a magnitude). Linear algebra is used to combine the vectors into a single resultant vector. This affect is generally referred to as weight shift. What this really means is that the resultant direction of the vector sum of the 2 force vectors is not longer perpendicular to the earth center (gravity only).

The car will have a center of mass located at a point called the mass centroid. This point is different than the geometric center but will typically be somewhat near the geometric center of the vehicle. Because the acceleration force acts right at the tires and is parallel to the road surface, the mass centroid is always located above the traction force vector. This causes the car to lift on the front and squat on the rear whether it is front, rear, or 4 wheel drive, during forward acceleration. This will have the same affect as transferring weight from the front of the car to the rear. When this happens, the rear tires will get a higher normal force (weight applied) while the front tires will get less. This is referred to as weight transfer.

If you design the car right, given the acceleration potential you have you will set it up to just barely lift the front tires off the pavement during maximum acceleration. This will apply all the vehicles weight to the rear tires which will increase traction to its maximum. Adding weight to the vehicle will reduce acceleration just as reducing power would. In order to optimize your weight transfer, you can move your mass centroid up. In other words, raise the vehicle height. If you get too carried away, you will lift the front wheels too far on acceleration and loose control. If that is the case, lower the mass centroid.

As you can see, front wheel drive is the last thing you want for drag racing. Because of the weight transfer affect, you loose traction as you increase acceleration on a front wheel drive vehicle. A rear wheel drive vehicle will increase traction on acceleration.

The traction force on the tires is always parallel to the road surface whether you are accelerating or cornering. Actually, cornering is just another form of acceleration. Any change in velocity is acceleration. Velocity is also a vector. This means it has a particular direction and magnitude. Speed has a magnitude but not really a specific direction. If you change direction of travel, you change velocity (but not necessarily speed), thus you are accelerating. Cornering applies forces just like forward acceleration. For cornering however, you want to lower your mass centroid as much as possible to reduce body roll and keep more even weight on all tires but more importantly to reduce the tendency to roll over.

Someday when I get time I will need to add more to this.....