A case for family tandems

Did you enjoy my previous embedded WolframCloud project?  Yes?  Great!  Let's do it again, this time with a tandem bicycle.

One of the nice things about tandems for kids is that they are (theoretically) never outgrown.  To show how this works, I put together another wolframcloud project.

I made a rough model for a kid growing over time.  Mathematica has data for childrens' sizes (== girls growth chart, or just go to wolframalpha.com and type the same).  I scaled all body parts linearly for the graphic.  Our kids' thighs are relatively a bit short compared to Jill's, but this is pretty minor.  All other bike-related body dimensions scale quite linearly.

I'm drawing the frame using an extension of the code I wrote last time.  Somehow, Mathematica doesn't have bike frame geometries built in.  I'm sure we'll address this oversight soon.  Perhaps we could use image processing methods (accounting for image distortion away from the center of the image) to grab the numbers.

In the tandem embedded graphic, the kid's age can be adjusted, from tiny 4 year old to 14, or basically fully grown.  Note that Clara's face doesn't age along with her digital age.  We don't have a function for that built in (yet!), and anyway it would freak me out to see the results. Also, my apologies for not giving her a helmet.  As digital kid gets older, you can adjust the saddle height and position of cranks to find a nice fit.

You may find some combinations that cause the kid's knees to bend the wrong way.  I didn't specify which solution for the quadratic equation (someday I might fix this), so Mathematica sometimes grabs the nonphysical one.

The handlebars can be either a swept back bar (current) or drop bars.  As the kid gets bigger, drop bars enable the kid to stretch out more comfortably, especially if you use the drop position (3).  If you do that when the kid is very young, she can't reach all positions on the bars.  That would be really dangerous in the real world!

If iframe isn't working try our cloud directly.


One other fun thing about tandems is that daddy and kid have to pedal at the same cadence ( technically not true, but changing this requires using different sized chainrings on the timing cranks.  This is a bad idea because either (a) the kid pedals slower, but needs to push harder or (b) the kid pedals faster.  Neither is a good idea in my opinion.).

Despite having the same cadence, our foot speeds are different.  Right now, the kid's cranks are 120 mm long, while daddy's are 170.  This means my feet are moving about 1.4 times faster than the kid's.  When the kidback cranks are no longer needed, both sets of cranks will be the same length (not modeled).

Check out more information about the Wolfram Cloud.