Fun With Math: Bicycle Edition

Bikes are a surprisingly effective way to teach tricky physics.

For instance, did you know you wouldn’t be able to steer a bicycle in zero g?

When you were learning to ride a bicycle you thought gravity was your enemy, trying to make you fall over. But without gravity, you wouldn’t be able to steer, say Cornell engineers. To demonstrate the concept, they built a hybrid vehicle they call a “bricycle” – a cross between a bicycle and a tricycle – that demonstrates what it would be like to ride a bike in zero-G. (Assume you have magnetic wheels to keep you on the floor.) (via)

Watch the video for a full demonstration on just how hard it would be to steer a bicycle in zero g.

You might also find this interesting. If you were to pull straight backwards on the lower pedal of a bicycle which way would the bicycle go?

Seems simple…right?  Think you know the answer? Click here to see a demonstration. Did you guess correctly?

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PI(e) Day Ride

Got this from MassBike. Bikes, math and pie can’t go wrong here.

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Pi(e) Day Bike Ride: March 14, 2009 (3/14)

If there is one thing that we’ve learned through rigorous scientific study here at MassBike, it’s that bicyclists love their pi(e). Be it the quintessential numerical misfit or the flaky, delicious treat. To celebrate our fascination with mathematics and dessert, we’ll be going for a pleasant, afternoon bike ride. Let your inner geekiness and hunger out for a short ride on Saturday, March 14th. Plan to meet in Boston Common near the Brewer Fountain (corner of Park and Tremont) at 12:45pm. We’ll go in plenty of circles and end with some delicious pie. Petsi Pie in Somerville will be giving out free small pies starting at 1:59. They’ll also give you a 10% discount for every 10 digits of pi you can recite. That’s right, 100 digits means a free pie. And you thought all that memorization as a kid was never going to get you anything! Led my Massbike’s own Shane and James. Extreme weather will cancel. RSVP to [email protected].

Here’s a head start on your free-pie pi memorization: 3.1415926…

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Filing Pedals For Greater Performance

Tommymoose over at Bostonfixed has come up with some fun information about pedal strike (anyone who has ridden fixed knows that when you make sharp turns this is a danger). His solution, file some metal off the pedals! Not only that but he went through the trouble of calculating EXACTLY how much you need to take off to get the performance angle you need. His handy work is reposted below by permission. Way to go tommy!

I’ve got 170mm cranks (nothing out of the ordinary) and my pedals have made contact with the pavement a few times when pedaling hard and turning (I know this happens to almost everyone at some point). They only grazed the ground enough to shoot sparks, not enough to buck me or anything, so I got an idea. I took a file and just shaved down the edge that makes contact to allow a little more clearance when turning. I’m new to road bikes, so this might be common, but I felt like nerding out wanted to know exactly how much “harder” this lets me pitch my bike while turning.

I took some measurements, did some trig, and came to the conclusion that with the crank in the fully verticle position, my un-modified pedal makes contact when the bike is at a 65.5 degree angle to the ground. I took off about 4mm from each edge at an angle and found that the bike now 63.8 degrees before there is contact… a gain of 1.7 degrees. Its not much, but this is a ~2.5% increase in bike pitch angle. This doesn’t really matter at all for the type of riding I do, but maybe, just maybe it’ll prevent me from slapping the road a few times(I guess I won’t know!)

To get a baseline for what angle your bike needs to make contact with the ground, stand your bike up straight with your cranks vertical and take your X and Y measurements, then the equation is –

angle = 90 – tan^-1(Y/X)

tan^-1 is inverse tan… 2nd Tan button for anybody that still has their TI-83’s haha
Y = vertical distance from ground to bottom corner of pedal.
X = horizontal distance from center of bike to bottom corner of of pedal

Then to get your new angle, ADD the distance of how much material you took off vertically to Y and SUBTRACT what you took off horizontally from X. The result should be a smaller angle than last time, which is good. If you want to know how much tilt that represents from vertical, just subtract it from 90.

He even went so far as to send me this awesome table of data that shows various angles of strike for various pedal lengths. (download the Excel file here)

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