Even though your Car sits quietly at the starting line, it is still packed with energy... a quiet kind of energy called "potential energy". As it sits on the sloping track at the starting line, gravity is tugging at it, trying to pull it down the track. In fact, all the time the Car is on the slope, gravity is tugging at it to make it go faster. Only when all the wheels are down on the flat part of the track does gravity cease to pull the Car faster.
The amount of energy that the Car has as it sits on the starting line is determined by its mass (weight) and its height above the finish line. That height is usually about four feet. But where do you measure? To the front of the Car? The middle? The back?
The answer: Measure the height at the "center of mass" (also called the "center of gravity"). But, where is the "center of mass" when the front of the Car is at the starting line? And, where is the "center of mass" when the front of the Car is at the finish line?
What is this thing called "center of mass"? It is that point on which the Car will balance, no matter how it is oriented. To the physicist, the "center of mass" is important because, for many of his computations, he can ignore everything except the total mass (weight) and the location of the "center of mass".
The greater the "height" of the "center of mass" (relative to its finish-line position), the more potential energy the Car has.
At the other end of the track, the Car has given up all of its potential energy. It is zipping along the track with a kind of energy called "kinetic energy", the energy of motion. The heavier the Car and the faster the Car moves, the more kinetic energy the Car has.
Potential Energy vs. Kinetic Energy.
How does the amount of kinetic energy at the end of the race compare to the amount of potential energy at the starting line? Well, the rules prohibit motors, springs, starting devices, sticky stuff on the front of the car, and so forth, to help add energy to the car as it moves down the track. The only energy available is the potential energy (due to its mass and height) that it started with. To answer this question, the physicist recites the "law of conservation of energy", which says that the "total energy (in a closed system) stays the same".
Now, as I said, the Car can not gain energy as it moves down the track, but what about the other way around? Can it lose energy? Yes, it can, and always does! (At least, it is lost from providing speed.) Friction raises the temperature of the Car and the air around it. Since every bit of lost energy means lower speed on the track, our job is to identify and minimize every source of energy loss.
In this book, I will speak of both acceleration and deceleration. Although they are the same kind of force, we will treat them separately. We will talk of forces that act to speed up the Car and call the result "acceleration". We will also talk of forces that act to slow down the Car and call the result "deceleration".
At this point in the story, we are looking at the forces that cause the Car to go faster. Later, we will look at the forces that cause the Car to go slower.
So, exactly how does acceleration work? Our Earth's gravity is our power source. It exerts a force on every object. If an object is dropped, gravity causes it to gain speed as it falls. In absence of any impediment, the object will gain 32 feet per second every second that it falls. After the first second it will be traveling at 32 feet per second. After the next second, it will be traveling at 64 feet per second.
Components of Acceleration.
But our Car is not falling straight down. The track is in the way! To study the effect of gravity on our Car, we must separate the part of gravity's force which is pushing our Car along the track from the part which is pushing our Car into the track. These two forces are perpendicular to each other and are called "components". Together, they add up to the total force of gravity. But only the part, or component, of gravity which is pushing our Car along the track is causing acceleration. (We will talk about the other component of gravity later when we talk about friction which slows our Car down.)
Relationship to track geometry.
Gravity accelerates the Car more on a steeper section of track. Many tracks start with a slope of about 30 degrees (one third of the way between horizontal and vertical). The slope gradually diminishes until, after about 12 or 14 feet, the slope has reduced to 0 degrees (level). At a slope of 30 degrees, the component of gravity which is accelerating our Car is only one half the total force of gravity.
[Note. For the mathematically inclined, "Force of acceleration = Force of gravity X sin (angle of slope)."]
Relationship to weight distribution.
So far, we have thought of our whole Car sitting of a section of track with a specific slope. However, remember that there are both front wheels and back wheels on our Car. Also remember that the slope is not the same all the way along the track. This means that the slope of the track under the back wheels may not be the same as the slope of the track under the front wheels. To really understand how the force of gravity will act on our Car, we must look at the front and back of our Car separately.
The Car will be accelerated most if the steeper section of track is under most of our Car's weight. On most of the tracks we will race, the slope of the track under the back wheels is greater than the slope under the front wheels. Positioning our Car's center of mass toward the rear of our Car causes greatest early acceleration as well as providing greatest available energy.
There is one type of track on which this detailed inspection is really important. On this type of track the Car rests on a very shallow slope at the starting line. The track slope increases to about 30 degrees and then decreases to zero again.
On this type of track, the available potential energy increases as the center of mass is positioned more toward the back of our Car (placing more weight on the rear wheels). But the Car accelerates earlier as the center of mass is positioned more toward the front of our Car (placing more weight on the front wheels). Where is the best place for the center of mass? The best location is very sensitive to the exact track geometry. Perhaps you can analyze this to help you understand the relationships better. Fortunately for us, this type of track is not used often!
[Some more equations... "Force = mass X acceleration".
Acceleration of Gravity = 32 feet per second per second."]
Figure 2. Comparison of Forces at a Modern Track Starting Line. Note the slightly greater initial forward force when the Center of Mass is toward the rear of the car. Fall further down the track!
Figure 3. Comparison of Forces at an S-Shaped Track Starting Line. Note the slightly greater initial forward force when the Center of Mass is toward the front of the car. Accelerate early!
Friction is one of the causes of energy loss that we want to keep very small. We had so little energy to begin with that every loss is very important. To understand how to minimize Friction losses, we must first understand what Friction is.
Friction happens when two things rub against each other. Friction resists that motion. Motion in spite of Friction releases energy in the form of heat. You experience that result in a beneficial form when you rub your cold hands together. If you press your hands together harder as you rub, the amount of heat produced increases. The friction produces a pleasant warmth. But in your Car, that lost heat energy takes away from your Car's speed. That energy is wasted.
Most Friction forces are proportional to the weight of the car body. This means that as the weight of your Car's body increases, so does the force of Friction which resists the Car's motion. This is not all bad, because your Car's mass (weight) ends up cancelling out in most of the speed and time formulas. (Watch for information about an important exception in the chapter on Air Resistance.)
Wheel - to - track
The friction between your Car's wheels and the track happens several ways:
When a wheel rolls, it compresses the surface that it rolls on and it compresses its own tread surface. When anything is compressed, its molecules rub against each other. Some of the energy used is returned, but some is lost (more heat!). For usual wheels and track surfaces (both rather hard) there is very little compression, so this is not a major loss of energy.
If the surface of the wheel tread or the surface of the track are irregular, then the compressions are greater. (Look for more problems in the chapter on Oscillation.)
If the surface has dust or dirt that gets crushed as the wheel rolls over it, then the picture changes a bit. The crushing is not elastic, and the energy used to crush or move the dust or dirt is not returned. (How does the width of the tread relate to the amount of dust or dirt that the tread encounters?)
If, for any reason, one of your Car's wheel slides on the track, then you have major losses of energy. This can be caused by severe alignment problems and binding between the wheels and axles. Otherwise, this problem seldom occurs.
The last problem is rubbing between the wheels and the guide rail. This occurs rather frequently because it is very difficult for a Car to run all the way from the starting line to the finish line without running into the center guide rail. If the wheels are misaligned so that the Car steers into the center guide rail, then this friction loss increases in importance.
Wheel - to - axle.
The friction between the wheels and the axles occurs as the car rolls. The interior of the wheel hub rubs against the bottom of the axle shaft. The force of this friction depends on the textures of the hub and axle surfaces, the weight of its share of the Car's body, and the nature of the lubricant between them. Smooth, polished, well lubricated surfaces are good.
Avoid enlarging the axle hole in the wheel. It would be advantageous if the size of the hole could be made smaller, so long as friction were not increased. (The chapter on Leverage of Frictional Forces talks about the importance of the size of the hole in the wheel hub.)
Wheel - to - body.
The inner face of the wheel hub will sometimes rub against the Car's body, near where the axle enters the Car. These two surfaces need to be smooth, polished, and lubricated to minimize friction. Some shaping is also helpful to minimize braking torque. (See the chapter on Leverage of Frictional Forces for more information about shaping.)
Since these surfaces are parallel to the direction of travel and to the direction that gravity is pulling, this friction source should be low. However, if the wheels have "toe-in", the wheels will tend to press on the car body as the car rolls because the wheels are steering toward the center of the Car. This will increase the force between the hubs and the Car body. Remember that the force of friction is proportional to the perpendicular force between the surfaces. It is important to keep that force small by properly aligning the wheels.
Wheel - to - Axle-head.
Friction between the wheel hub and the inside of the axle head is very similar in all respects to friction with the Car body.
Relationship to Wheel Alignment.
Wheel alignment is important for two reasons. First, it determines whether the Car will run straight down the track (good) or will try to steer into the center guide rail (bad). Alignment also determines whether the wheels will try to stay centered on the axle (good) or will press toward the inner or outer ends of the axle (bad).
Both of these alignment ills will increase the friction which tries to stop your Car from completing its journey to the finish line swiftly.
4. Leverage (of Frictional Forces)
"Leverage" is the application of a small force moving through a large distance to cause a large force to move through a small distance (or vice versa).
Leverage is applied about a center. The distance from the center and the amount of force applied (perpendicular to the radius) combine to form something called "torque". Torque is a force which produces angular acceleration (or deceleration).
Figure 4. Note that a force applied near the fulcrum (center or rotation), in this case, the top end of the lever, has less effect than a force applied toward the end.
A bicycle caliper brake is a good example of leverage. In this case, the force is friction, and leverage is used to reduce motion. The caliper brake applies friction to the rim of the bicycle wheel to slow the bicycle. If the brake were to be applied halfway between the rim and the hub, twice as much force would be required to stop the bicycle in the same distance. The braking torque from the caliper's pinching force is greatest when it is applied far away from the hub. As the force moves toward the center of the wheel the braking torque reduces.
Our Car's wheels don't have brakes designed into them, but they do have friction around the hub. That friction force acts some distance from the center of the wheel. The friction between the axle shaft and interior of the hub acts at about 1/20 inch from the center of the wheel. Most rules do not permit the hole and axle diameters to be reduced. Just reducing the diameter of the axle does no good, because the interior of the hub is still the same distance from the center of the wheel.
But, look at the sides of the hub where they contact the Car body and the axle head. Normally, the flat inside of the hub will contact the flat side of the Car body. The flat outside of the hub will contact the flat underside of the axle head.
Where is the best place for the contact to occur? Is it better for the friction to occur close to the center of the wheel or further away from the center? Where is the braking torque least? Right! Closer to the center of the wheel.
Now, what can be done to cause the friction between the hub and the Car body or axle head to be closer to the center of the wheel?
Figure 5. Comparison of Braking Torque for Unshaped versus Shaped hubs. Note that when the hub contacts the car's body near the center, the braking torque is significantly lower.
Latest update: 3/17/2006 Fix malformed gif
Copyright 1995, 1997, 1999, 2002, 2006 © by Stan Pope. All rights reserved.