The Optics Of Bicycle Reflectors

The humble bicycle reflector works on the principle of corner cube retro-reflection. Incident light bounces off the orthogonally placed, reflective plastic surfaces and emerges in the opposite direction, parallel to the incident ray. Its totally and internally reflected. I have shown this for you in the following image. Additionally, you can play around with this cool applet from a Taiwanese education website to simulate corner reflection.

I call it humble because it is cheap and sustainable. Think about it. You hardly need an external power source to make this thing work. As long its clean and there is a good source of light shining on it directly behind, it signals back its presence faithfully. And if you have three wide paneled reflectors, you can extend the range of the light horizontally.

Courtesy : John S. Allen

This simple concept was so beautiful to scientists that an array of 100 of these corner cubes were left on the moon as part of the Apollo Moon mission of 1969. The idea? By shooting laser pulses from an earth based telescope, you can measure the round-trip travel time and hence the earth-moon distance to an accuracy of mere centimeters!

Most people may think all Neil Armstrong left on the moon was a U.S flag and his footprints. Not quite. In addition, there's also these corner cubes and it has served scientists with lunar laser ranging for over 35 years! If you want to learn more on lunar laser ranging, read this.

Speaking of which, I hear now they have found water on the moon's surface after the whole "bombing mission" last month. I think in a few years, the Giro d'Italia should dream bigger and hold its first stage on the moon instead of sticking to earth. Hey, there's water for aid stations!

P.S : Don't forget to catch the Leonid Meteor shower on Nov 17! I'm going to be headed out in the wee hours of Tuesday morning on my bicycle to see if I can spot any.

ADDITIONAL READING :

Bicycle Reflector Performance By John Allen

What Neil and Buzz left on the moon

Multiple Reflections From Two Plane Mirrors - Applet

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DIY Electronic Shifting Bicycle Part II

Hi folks. Here's little more background behind what was shown in Part I.

Norbert Ladenburger hails from Schwäbisch Gmünd, a little town near Stuttgart at the northern foot of the Swabian Jura Mountains. By trade, he's a goldsmith and owns a small factory there. While one of his big hobbies is building full size kitplanes from America and flying his own machines, Norbert loves getting his hands dirty with bicycles.

The idea of building a DIY electronic shifting bicycle started in 2007 when his son was unemployed. So they conjured up this plan to keep them both busy with something. But then his son moved on after having found a job and he tinkered on with the project.

Norbert tells me that he built his bicycle using carbon fabric and aircraft quality epoxy at home. Obviously, since he's into building kitplanes, he used materials he already had. For the wheels, he made a negative mold from wood. He laminated a half wheel, then the other half and finally glued the left and right parts both together. He tells me that this wasn't an easy process and that there's lots of little things to talk about regarding gluing, tensioning of spokes and the final finishing process but for a basic overview on the wheels, he left it there.

A sample bike and prototype wheels. Photo credits to 'Deichradler' & Lght-bikes.de

The servo is a cheap standard model and the electronics was a kit from a servo-tester. He removed the springs from the derailleur to fit the servo in for push and pull motion. He bought both from a model shop. This site sells the servo and this site sells the electronics.

Here's a small image of what he used.


Now here's the problem. Because its a simple analog circuit, it has been difficult for him to get to steer the rear derailleur with a potentiometer as the gears must be first searched and found with the pot. The front is a double chain-ring for which the servo apparently shifts fine with a simple toggle switch. Norbert thinks a digital circuit is the solution and apparently is looking to reconstruct the setup in the rear.

There was a rumor on the WW forums that he built his setup for 50 Euros. That may be the case for the servo mechanism, couple of electric wires and switches, but the entire bike building project, he estimates, cost him around 500-1000 Euros. But as said before, he did use a lot of materials he already had from the kitplanes hobby side.

For most of us, this may take us down memory lane. Back in the early 1990's, MAVIC experimented with a servo controlled rear derailleur powered by batteries in the handlebars with the shifting relying on the motion of the jockey pulleys. But the idea didn't last long. However, some people contend that Mavic put more of their marketing attention into wheels and rims and such which ultimately diverted resources from the electronic shifting project, in the end killing it altogether. It could have been developed and refined, if not limited to what they last had before the idea collapsed.

If any of you readers have a note of insight, electronics advice or general help for Norbert, it can be noted in the comments section on this blog and he will be reading it. As and when I get more information from him, I'll update the subtler details of the project here.

RELATED READING :

Homemade Electronic Shifting Bicycle From Germany
An All-Automatic CVT Based Bicycle

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Homemade Electronic Shifting Bicycle From Germany - Part I

Here's a toast to cheap.

Rumor has it that this German person named 'Norbert' made this rig under 50 euros (ha!). Not only did he make all the servomotor associated shifting mechanism himself, he also built the aero bike from bottom up including the wheels.

Pay close attention to this servo setup. Here are the pics, obtained from WW Forum. Credits to you guys out there.

What looks to be an 8 speed Dura Ace rear derailleur combined with a servomotor!

Norbert. One question. When will you start your cycling company? :)

Please read about how he made this setup in Part II.

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Some Probability And Statistics On The Individual Time Trial

The Tour de France (TDF) is the marquee cycling event on the calender for any top international pro cyclist as well as their squads. Everyone wants to do well here because its arguably the biggest and most glamorous stage for displaying athletic talent. The competition is tough, the fans are many, the stages are epic and the prize money is fat.

In this post, I'm trying to figure out what kind of a statistical distribution is seen in the finishing times from this year's prologue TT (Tour de France). I will also try to quantify the probability of getting close to the fastest time trialist in the world. Alberto Contador tried pretty darn well. How well?

Only one way to find out these things.

So here's what I did.

Step 1 : I obtained Cyclingnews.com data for the TDF Prologue TT on July 4, 2009. I obtained 180 data points corresponding to all the competing cyclists.

Step 2 : To make sense of this data clutter, I put them into Microsoft Excel 2007 and ran a descriptive statistics analysis on it. Here's what I obtained. What you're about to see is powerful.

Fig 1 : Descriptive statistical figures for the finishing times of a sample set of 180 cyclists from the Tour de France 2009.

So is my sample set taken from a normal distribution or something different? Let's try to answer that reasonably with the table above.

The mean, median and mode are very close to each other which MAY indicate its normally distributed. The average of the average deviation of each cyclist from the mean was 0.63 min or 37.8 seconds. The minimum time belonged to Fabian Cancellara, with a blitzy 19.53 mins whereas the maximum time belonged to Yauheni Hutarovich. I also have a Kurtosis and Skewness of 0.558 and -0.068 respectively.

Positive Kurtosis indicates a relatively appreciable peak which makes me suspect the distribution is leptokurtic (too tall instead of normally high). The book Using Multivariate Statistics (Tabachnick & Fidell, 1996) explains that if my Kurtosis statistic is more than 2 times [sqrt(24/180)] = 0.73, the data is not normally distributed. Since 0.558 is less than 0.73, we're ok.

Negative Skewness indicates that my data is left skewed. The same book mentioned above explains that if my Skewness statistic is more than 2 times [sqrt(6/180)] = 0.365, the distribution is not normal. Since -0.068 is less than 0.365, we're ok here as well.

Step 3 : The above only gives rough indications of the type of distribution. Nothing beats setting up a visual of the spread. So I made a histogram, with a chosen bin width of 0.20 min.

Fig 2 : The histogram for the data set. Please see source of data on CyclingNews.

The graph agrees with the skewness and kurtosis statistics. The data has central tendency but is ever so slightly skewed towards the left. This is the data for the best cyclists in the world. Not really a Gaussian, but not too far away from it either. What kind of distribution it is will take more analysis and tests for goodness of fit, which I'm going to tackle some other time.


So What Does All This Mean?

Looking at the data and Fig 2, we can say that the course conditions in Monaco on that July day were such that nearly 48% of all 180 cyclists managed to get times below the average, which might mean they were pretty fit and came well prepared (or something else worked in their favor which I can't quantify). Thus, the 48th percentile is the average time, i.e 21 min and 30 seconds.

To put it in another fashion, the probability of a world class cyclist racing on this course in a time less than the average time is 0.48.

52% of the 180 performed under par, with about 8% of those 52 giving exactly average times. The probability is 0.52 that a cyclist is at average time or above it on this course.

We can also say that 72% of the 180 cyclists lie between one standard deviation on both sides of the average, 93% lie between two standard deviations about the average and 99% lie between 3 standard deviations. Pretty close to the 68-95-99 rule obeyed by normal distributions eh?


Alberto Contador Vs Fabian Cancellara As Time Trialists

Our last question is the most interesting. So if you're a top pro at the peak of your abilities, what are you chances of ever getting close to Fabian Cancellara's blitzkrieg results? Then the next question would be, how close do you want to get to 'Spartacus'? Within 2%? 3%?

Let's do 2% as a start. Within 2% is 23 seconds difference. Now that's probably the limit of what a time trialist can accept to cap the gap, so to speak!!

Let's look at what Contador obtained that day from the data. Bert raced the course 18 seconds slower than Cancellara for an amazing second place. In other words, there was a mere 1.54% time difference between the best all round cyclist in the world and the fastest time trialist in the world. Just 4 cyclists managed to come within 2% of Cancellara's time - Contador, Wiggins, Kloden and Evans. 4/180 = 0.02 = 2%.

In other words, just 2% of the 180 cyclists got a time less than or equal to 19 minutes and 55 seconds (this 2% window we're talking about).

Put in another way, this is the 2nd percentile. This is where the glory is at. And the money. And the kisses from the long legged European girls.

The probability that you're in this 23 second window from the best man on the bike is low. Just 0.022 or 1 in 45 chance. Keep in mind this is for the best in the world.

Now you know why you and I are not racing in the Tour de France. Let's just scratch our butts and cheer these beasts on.

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2009 Weblog Awards - Nominate & Vote For The Bee!

Hey everyone. So a little about me again. I'm a mechanical engineer currently dabbling in electro-optics full-time after quitting my previous job in the petroleum industry. On the side, I survive through a rabid fascination for cycling and its many aspects, from tech and history to culture.

For the past 3-4 years, this blog has given you varied articles that many of you love and use as reference/research. Some are so controversial they are discussed on forums to the point where people trade barbs with each other. Popular posts such as Serious Cycling=Serious Legs, Power to Weight Ratio, Lore of The Victory Salute, Church Of Lance Armstrong, The Ideal Weightweenie and numerous others are staples of this blog.

Even though I'm not as HUGE as some of the other blogs people read, I will tell you one thing right away. No individual cycling blogger might come close to the variety of topics I write about in depth or the quality of links I pollinate. I say that pretty proudly unless you show me another.

In fact, the kind of readers I get stands testimony to the site's popularity and strength of content. I receive periodic attention from MIT Engineering and Design, U of Delft, Cornell, and various other American universities who use my blog to even engage students in the classroom.

Bikers who work with Lockheed Martin and the Boeing Company have conversed with me in the past. Two big cycling companies approached me soliciting employment offers after the blog, safe to say, impressed them. Not to exclude, authors of best-selling cycling books and inventors of cycling products are also in this company of readers. The average time spent by a reader is about 3 mins and 6 seconds. Now I consider that PLENTY for the fast paced, attention deficit disorderly world we live in today.

For the folks among you who aren't so technical minded, I write quite a number of general articles and share my perspectives, both on the serious and the funny side of things. I make great efforts to make articles readable by all, regardless of nationality. In fact, over the past one year, I have been attracting lots of readers from South America, India and China who share an equal love for cycling but may not be very talented at the English language. I'm pretty sensitive to that issue. I think English by far is the hardest language to master. Anyone disagree?

While content is free to all, I haven't always felt that I'm not doing a thankless job (I'm human afterall). Now you can get to show your annual appreciation by nominating and voting for Cozy Beehive towards the 2009 Weblog Awards. Turns out, there's no prize money or medals offered, but the recognition will go a long way. Last year, I was a finalist in the category of Best Sport Blog but didn't go any further as the competition was just too stiff out there.

All relevant details on how to nominate and vote can be found on the Weblog awards website. See Nominations FAQ and the list of nominations page where you may vote for my blog against what you feel I deserve! See you all there!

Meanwhile, any of you who are serious about blogging and pay attention to content must join the party too!! Ok ok, I'll cut out the sales pitch now.



ADDITIONAL RESOURCES :

CompetitiveCyclist.Com : Cozy Beehive Blog Review (Top 2)
2009 Weblog Awards Voting Page - Nominations Master List

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