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Make a square wheel car

You will need:

  • A cardboard box
  • Scissors, a ruler, a pencil, paper and tape
  • A box of water bottles
  • 2 wooden kebab sticks and 1 plastic straw
Square wheel car made out of cardboard rolling across taped together water bottles
Square wheel cars are great for STEM!

Instructions

  1. Line up the water bottles in a row and then tape them together.

    lining up water bottles
    Lining up the water bottles
     
  2. Measure the diameter of the base of your water bottle.
     
  3. Multiply that number by 1.2 (we'll go through "why" in mathematics further down the page).
     
  4. Using the scissors, cut out 4 squares with a side length of the number calculated above.
     
  5. Draw 2 lines on each of your square wheels by connecting the opposite corners together (it should look like a cross on each wheel). This allows you to find the center of each wheel.
     
  6. Poke a wooden kebab stick through one of the crosses on a wheel where those two lines intersect.
     
  7. Tape the wooden kebab stick onto the wheel to make the connection strong.
     
  8. Test that you can roll one of the square wheels along the taped together water bottles.

    Spinning one square wheel along the water bottle row
    Testing to see if the square wheel rolls into the bottle gaps
     
  9. Measure the width of your water bottle row where the sides are straight (avoid the neck of the bottle). Whatever the width, subtract at least 30mm off that number so that your square wheel car has enough room to move along the water bottle track.
     
  10. Cut out a cardboard rectangle for the base of your car. You need to use the width of the water bottles minus 30mm as calculated above for the width of your rectangle. For the length you need enough it would be worth making it the side length of the wheels multiplied by 3 so you have lots of clearance for both sets of wheels to spin next to each other.
     
  11. Cut your plastic straw in half.
     
  12. Slide one of the plastic straw halves over the kebab stick attached to a square wheel.
     
  13. Push a second square wheel onto the kebab stick through the middle of cross you made earlier.\
     
  14. Place the newly made axle on your cardboard car base and slide the square wheel along the kebab stick until the two wheels are almost the same width as the car base but can still spin freely.
     
  15. Tape the straw on the axle to the base of car securely.

    Half a square wheel car
    One axle secured to the car base
     
  16. Repeat for the second axle and you are done!

    Square wheel car ready for action
    Square wheel car ready for action!
     
  17. You might want to push another kebab stick through the middle of your car base and tape it so that you have a handle to use when moving your square wheel car along the water bottle track.

    Square wheel car moving along the track
    Square wheel car on the starting line

What is going on?


There is a fair bit of mathematics hidden behind this experiment. You'll also have seen that the car base didn't move up and down but rather moved along the track at the same height the whole time. This is because the square wheels followed the dips and rises of the curved water bottles exactly, making the axles of the car not move up and down vertically at all. The line that each edge of the square wheels were following is called a catenary curve.

As your square wheel moves along the curved track you'll notice that the sides of the square follow the curve of the water bottle without jamming into the bottles. This is the same issue engineers have to sort out when meshing gear teeth together.

The mathematics can be daunting for younger kids but great to follow through with high school math students. The Exploratorium has done a neat summary of the mathematics. Note that l is the side of the square wheels and d is the diameter of the water bottles.  


math for square wheel cars by Exploratorium
Math on square wheel cars done by the Exploratorium 
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