Design of a kids play structure that is mathematically beautiful – based on the logarithmic spiral.

I’ve been wanting to build a play structure for the kids that I could also have some fun on.  Looking at the parkour structures on pinterest, I didn’t find any that were inspiring or aesthetically pleasing enough to put in the backyard.  Plus, the local parks will always have better monkey bars.  I was challenged on my trip to Vancouver (see post about Terra Nova Park) to design something more meaningful.

Being an engineer, I took my inspiration from math and the beauty of the logarithmic spiral.  It’s a shape that can be observed in nature from nautilus shells to galaxies and can be represented through some elegant equations.  So I thought it would be cool to design a balance beam structure that grows in a logarithmic spiral. Of course, the fact that it will be made from 4x4s from logs is a nice coincidence. As my beams will be straight, I tried using an 8 sided structure on paper but decided that six sides would be enough to look good.

The next step was to build a scale model. We’ll, this brought me back to my balsa model airplane days as a youngster. I don’t know where the model shops are anymore but there was a Michaels on the way to the cottage so we stopped for some supplies along with some stuff for the kids of course :).  I used 1/4 inch square balsa wood sticks which works out to a 1:14 scale.

Photo of balsa wood play-structure model

Balsa wood model of my logarithmic spiral play-structure design

The model helped me to work out a lot of issues like whether to spiral up or down as it grows outwards and which segment to start and end at to get a good sized structure at the right height.  Here was my initial mock-up.

Now that I had the concept, time for some real dimensioning and calculations.  After reading the Wiki posts and refreshing myself on the equations, I popped open an excel sheet and started plotting spirals (using x-y co-ordinates) and playing with the growth parameter (b).  I liked the shape of b=0.2 and like my model, I broke it down into 60 degree arc segments to get the lengths of each beam.

Photo of Logarithmic spirals plotted in excel

Logarithmic spirals plotted in excel

Ok, have some time off in July, let’s see if I can build it!

Kids Learning Opportunities:

  • With young kids, chat about what shapes in nature they can name that look like the spirals.  If you set up the sheet, let them change the parameters and see what happens.  What shapes do they like best?
  • Teenagers – challenge them to plot these spirals in excel – test their math and spreadsheet skills!




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