# Science, Technology, and Society

## Bicycles

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After viewing our curriculum units, please take a few minutes to help us understand how the units, which were created by public school teachers, may be useful to others.

## Motion

Speed is the distance travelled by an object in a unit of time, or said another way, speed is the rate at which an object covers a given distance. Speed is given by the formula:

### Speed— distance / time

Although the terms speed and velocity are used interchangeably in everyday speech, they have different meanings. Speed is a scalar. Since speed is a scalar, it describes magnitude only. Speed tells us nothing about the direction in which the object is moving. Velocity is a vector. Because velocity is a vector, it measures speed and direction. Our equation for speed can be rewritten for average velocity:### Average velocity = distance / time

I used this equation extensively. My class had measured a course of one hundred twenty yards in increments of thirty yards. In order to find the average velocities, we took the yard distance, multiplied it by 3 to change it into feet, and divided the product by the total elapsed time. These calculations are presented in the two page spreadsheet “David Coasting Down a Slight Incline” which is located at the end of the unit.We then plotted these points and connected them using a French curve. Each drawing took approximately an hour. The graphs that are presented, again found at the end of the unit, are done with straight lines on graphs produced from Lotus 1-2-3. I have submitted these graphs because they are much more legible.

The results are what we would have expected. The average velocity increases rapidly in the first twenty yards. It continues to increase but at a slightly slower rate over the next forty yards. At this point, the average velocity approaches a limiting value. The graphs have points at the ten and twenty yard line because I redid the experiment with my wife, my son and my son’s friend David. I had wanted to see how the slopes started out in more detail at t = 0.

I used the term average velocity because in most instances an object does not travel at a constant velocity. If you ask a student to describe his ride to school, he will tell you about slowing down for traffic lights and speeding up to pass cars. Thus, we arrive at an average velocity. I also mention average velocity to get the student to realize that his velocity can increase or decrease. This leads into acceleration.

### Acceleration is any change in velocity. Acceleration is given by the formula:

Acceleration = change in velocity / time required for change Acceleration is measured in units of distance/time/time, such as miles per hour per minute or feet per second per second. We have discussed how a moving body has a velocity and can have an acceleration. Therefore, change in velocity is computed by subtracting the initial velocity from the final velocity.Finding the acceleration was a little more involved. I first used the average velocities, but the results didn’t look right. Also, average velocity doesn’t seem to fit right in the equation. So, we went back and found the instantaneous velocities at each yard marker. We did this using the formula:

### Instantaneous Velocity = (Change in Distance)/(Change in Time)

These calculations were fairly straight forward. We went back to our recorded values, found the differences and then the quotients. The results still didn’t look right; I had again forgotten to multiply by the three to change the yards to feet.Now we were ready to find the acceleration. We took the instantaneous velocity and divided it by the change in time. The overall results were good. The acceleration starts off slowly, quickly hits a maximum, and then decreases towards zero as long as the rider is maintaining his velocity. If the rider slows down, a negative acceleration is produced.

We spent two class periods collecting data for velocity and acceleration. Again, I feel that since it was the individual’s own times, the concepts were grasped easier. An account of the class actually performing the experiments is described later in the paper.

Friction is the force that opposes or slows down the motion of a body. Otherwise, by Newton’s first law, you would be able to coast on your bicycle forever.

In bicycling, air is both your enemy and your friend. It’s your friend because it is your main method of cooling. When a bicycle is equipped with fairings, the rider quickly can overheat. It’s your enemy because it is the air resistance that slows you down.

The coasting experiment shows the effects of air resistance quite vividly. When a person rides in a normal manner, he is sitting upright and his body offers a lot a surface area. This is a limiting position. To counter this, ten-speeds have their handlebars curled downward so that the rider can pedal in a streamline position. In this position the body is compact and offers less resistance.

New studies are now showing that the streamline position can be improved upon. When a rider is in the streamline position, his elbows are flexed out producing a “parachute” effect. New handlebars have been designed so that now the rider is in a tucked position like a downhill skier. In our experiment, I had the riders place their hands as close together as possible on the handlebars.

The results were convincing for the narrow position. It had the fastest velocity, followed by the streamline and then by the normal position. To dramatize the effects of air resistance, I had the riders coast wearing my winter parka. These times were slower.