The Geometry of Cars

Geometry is an essential element of transportation design. Take a moment to write down a few ways in which geometry affects cars and other vehicles. 

Discussion Questions

1. What data is necessary to collect in order to understand the role of geometry in transportation? 
2. What spatial perspectives and/or mathematical planes are relevant? 

The cover of The Geometry of Cars, to the right above, features a car on the road. 

Discussion Questions

1. What angles can be measured on the diagram? 
2. Which angles are most relevant for the vehicle as it travels on the road?  
3. Is any essential information missing from the picture? What is necessary in order to measure that information?

Geometry diagrams featuring automobiles and other vehicles are available in the following book from Schottenbauer Publishing:

Geometry Workbooks

• The Geometry of Cars 
• Paperback
• Kindle Edition

Additional Information

Schottenbauer Publishing

Free Education Resources

Boating in the Lab and on Natural Waterways

Transportation in real life often occurs in conditions which are not ideal. Laboratory studies initiated in traditional classrooms often simulate simple conditions, leaving the more complicated reality for advanced graduate studies and specialty laboratory research.

What are some of the differences between laboratory research and real conditions for transportation? The graphs below, excerpted from The Science of Floating & Boating: Volume 3 from Schottenbauer Publishing, show the differences between a ping pong ball floating in laboratory conditions and in a natural (outdoor) reservoir.

Discussion Questions

1. Which graph shows a sine wave? 
2. Which graph shows chaotic dynamics?
3. In Graph 1, the waves were most likely created by: a) an object moving up and down at a regular frequency, b) natural wind? 
4. In Graph 2, the waves were most likely created by: a) natural wind, b) a boat on the water? 
5. Describe the range of each graph, including the minimum and maximum of each line in each graph. 
6. Which graph demonstrates a larger variation (or order of magnitude) in motion? Why? 
7. On a separate piece of paper, draw the location of the ball as it moves in Graph 1. Include maximum and minimum points. What is the maximum physical distance moved between a consecutive trough and crest?
8. On a separate piece of paper, draw the location of the ball as it moves in Graph 2. Include at least 10 points, including maximum and minimum points on each line in the graph. What is the maximum physical distance moved between a consecutive trough and crest?

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of fluid dynamics, water, and/or boats:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Floating & Boating
• Volume 1: Force & Acceleration
• Volume 2: Force & Acceleration
• Volume 3: Video Analysis
• Fluid Dynamics & The Science of Natural Waterways
• Volume 1: Water Flow Meter & Video Analysis

Anthologies of 28 Graphs

• The Science of Transportation

Additional Information

Schottenbauer Publishing

Free Education Resources

Understanding Translational and Rotational Motion from a Bicycle Wheel

Bicycles are wonderful teaching tools, because they demonstrate the physics of both translational and rotational motion. The free YouTube video, Understanding the Motion of the Wheel from Schottenbauer Publishing, provides graphical analysis of video footage. In the video, spatial analysis of motion (e.g., what does the motion look like to a viewer) is compared to graphical analysis of motion (e.g., what does the motion look like in a graph). This video can supplement traditional lectures on the science of basic motion.

Understanding the Motion of the Wheel

(Free YouTube Video)

The four sets of pictures below are excerpted from the video.

Translational Motion

Axis at Point 1, Time = 0

Rotational Motion

Axis at Center of Wheel

  

Rotational Motion

Axis at Point 1, Time = 0 

Translational + Rotational Motion

Axis at Point 1, Time = 0 

Discussion Questions

1. In each excerpt from the video, what has been traced?
2. What is the pattern of the foot pedal, in comparison to the wheel? Provide an answer for each of the four examples above.
3. On a separate piece of paper, draw each graph as it would appear if the motion had continued for another 20 seconds.
4. In the fourth graph, why is the red line slightly curved?
5. Redraw the fourth graph with a different origin of axis.
6. If you have learned wave functions in class, write an equation for each line shown above.
7. Name several other examples of translational and rotational motion from real-life transportation.
8. Why is graphical analysis different than a video analysis?

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of bicycles:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of the Wheel
• Volume 1: Force, Velocity, Acceleration
• Volume 2: Video Analysis, Force, Velocity, Acceleration
• Volume 3: Video Analysis, Force
• The Science of Exercise Equipment
• Volume 1: Force, Velocity, Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis
• Volume 4: Video Analysis

Anthologies of 28 Graphs

• The Science of Transportation
• The Science of Physical Fitness
• The Science of Summer Olympic Sports

Additional Information

Schottenbauer Publishing

Free Education Resources