How to build a fixie

Last week I built a fixie.  Here's how I did it.

First I went on Craig's List and looked for 1970s-ish steel bicycles that would make good fixies.  I tried a couple of sellers before settling on the orange Schwinn Varsity, which I bought for $120.  This is what the bike looked like:

I took of the wheels, the chain, the crankset, the rear brake, the front and rear derailleurs, and all the shifters.

From eighthinch.com I purchased an Amelia wheelset with a 16-tooth cog on the rear wheel, which cost $109.50, including shipping.  I also purchased a 44-tooth chainring for a one-piece crankset and an eighth-inch-wide single-speed chain from harriscyclery.net for $31.40, including shipping.  From a local bike shop I bought white Fizik bar tape and a new brake cable (I already had on hand fresh brake pads), which cost about $24.  In total I spent about $285 on the bike and parts.

The first step in reassembling the bike was to install the wheels.  The cog on the rear wheel has right-handed threads, so when you pedal forward, the cog gets tighter.  But on top of the cog goes a lockring that is reverse-threaded, so when you push back on the pedals to stop, you don't unscrew the cog.  The rear stays had to be squeezed together a little bit due to the lack of a freewheel.  Next I cleaned out the bottom bracket, composed of the cups and ball bearings, which was full of grime and grease.  The one-piece crank, which is pretty unique to this old style of bike, looks like this:

I greased up the cups with white lightning grease and put the bottom bracket together, ball bearings and all, this time substituting a single 44-tooth chainring for the double that the bike originally came with.  That extra hole you see that looks kind of out of place fits into the drive pin located on the one-piece crank.

Next it was time to install the single-speed chain.  Getting the chain sized appropriately is important because a fixie has no derailleur to take up the extra slack.  Fortunately the old Schwinn had horizontal drop-outs (the C-shaped indentations in the frame where the rear axle sits), which allow some wiggle room if the chain is not perfectly taut.  I erred on making the chain a bit long, so that I could just move the rear axle back in the drop-outs to make it taut.

Once I had the chain on, the bike was ready to ride, but not necessarily safely.  I installed new brake pads and a new brake cable on the front.  I wrapped the handle bars with white grip tape to make it look flashy.  And unfortunately, the bolt holding the handlebars to the stem was missing, which I didn't know about when I bought the bike, causing the handlebars to wiggle to and fro while you were riding.  After going to multiple hardware stores and multiple bike shops, I still was not able to find a bolt that fit the threads.  I think Schwinn literally invented their own bolt size!  So I used a bolt that was a little too small and tightened it down hard with a nut, which seems to work for now.  Finally, I took off a piece of metal that used to be holding shifters by removing the stem temporarily from the headset.

And that was it!  It's going to take a bit of practice to get used to riding fixed gear.  I didn't realize I coast fairly often, mostly when riding around the city.  With the fixie, you have to keep pedaling all the way up to the red light!  I haven't gone up any giant hills yet, but fortunately they don't exist in Michigan.

  

Gear Ratio Math

This weekend I purchased a 1970s Schwinn Varsity, which this article calls "the single most significant American bicycle."  I am in the process of converting it into a fixed gear bicycle, and I'll have photos and a description of that process soon.  Today's post, however, is on some math with fixed gear bicycles.  On fixed gear bikes, there is one speed, one chainring, and one cog.  What makes a fixed gear different from a generic single speed is that the drivetrain is connected directly to the hub of the rear wheel without a winch mechanism permitting free turning of the wheel while the pedals remain stationary.  You have to pedal continuously on a fixed gear bike as long as you're moving forward!

One of the most important decisions when making a fixed gear bike is choosing which gear you want to be stuck in forever.  I chose to make this decision based on my desired leg revolutions per minute and desired speed.  Since I'll be using the bike for getting around town and maybe a few longer rides, I want to be going about 18 mph when I'm pedaling at 90 revolutions per minute.  Now, how do I figure out what gear ratio to use?

18 mph = 28,962 meters per hour = 482.7 meters per minute

The circumference of my bike wheel (700x23c size) will be 2.09858 meters.  This means the rear wheel will need to turn 230.013 turns per minute.  I want my pedals to be turning at 90 per minute.  This means the gear ratio I'll need is 230.013/90 = 2.5557.  Of course, chainrings and cogs come in limited sizes, and to minimize wear on the chain both should have an even number of teeth.  I've decided on a 42x16 combination, which is actually a gear ratio of 42/16 = 2.625, corresponding to a speed of 18.5 mph at 90 rpm.

Now that we've done some basic arithmetic, how about a little number theory?  As I was reading up on fixed gear bikes, there was much discussion on "skid patches."  Some die-hards believe that adding a break to a fixed gear ruins its sleekness, and so they rely on skidding to stop their bike.  Basically they lean forward to take weight off the back wheel, lock their legs, and then skid to stop.  Since most people skid with their pedals in the same position every time, this causes skid patches to form on the tire at certain locations.  The gear ratio determines how many skid patches you end up with.  For example, if your gear ratio is 45x15, then every pedal stroke corresponds to 3 whole wheel revolutions, and you will have one skid patch.  If your gear ratio is 42x16, as I plan mine to be, you will have 8 skid patches.  How do you determine how many skid patches you'll have?

Theorem.  Let a/b be the reduced gear ratio, meaning that a and b are relatively prime integers (In the above example, 42x16 reduces to 21/8).  Then there are b skid patches.

Proof. First we show that there cannot be more than b skid patches.  If a/b is the reduced gear ratio, then for every one pedal revolution there are a/b revolutions of the wheel.  So for every b pedal revolutions there are a wheel revolutions.  Thus, b pedal revolutions returns us to the original starting location on the wheel, since a is an integer.  So there can't be more than b skid patches.

Now we show that there can't be fewer than b skid patches.  Let's assume that there are fewer than b skid patches.  Then there exist two different numbers of pedal revolutions that correspond to the same location on the wheel.  Let's call these two different numbers of pedal revolutions m and n, with 0<n<m<b.  If m and n pedal revolutions get us to the same spot on the wheel, then their difference, m-n pedal revolutions will get us to the same spot on the wheel.  Now m-n pedal revolutions is equal to (m-n)(a/b) wheel revolutions, which must be an integer in our case.  This means that b divides m-n or b divides a.  But b can't divide m-n because m and n are both less than b, and b can't divide a because b and a are relatively prime.  This is a contradiction, so after every pedal revolution [0,1,2...b-1] we must be at a different location on the wheel, and there must not be fewer than b skid patches.

There are no more or no fewer than b skid patches, so there must be exactly b skid patches.

Some fixed gear skidders are ambidextrous, and can skid with either their left or their right leg forward.

Theorem.  Consider the case of an ambidextrous skidder.  If the reduced gear ratio a/b has an even numerator, then there are b skid patches.  If the reduced gear ratio has an odd numerator, then there are 2b skid patches.

Proof.  Ambidextrous skidders can skid every half pedal revolution, which is equivalent to a situation where we have a single-side skidder using a front chainring half as large.  The gear ratio for an ambidextrous skidder, then, is effectively (a/2)/b.  If a is even, then this can simplify such that a and b remain integers, and as above there are b skid patches.  If a is odd, the gear ratio could only be simplified to a/2b and according to the theorem above we have 2b skid patches.  

Liquid Nitrogen and Helium

This evening we made liquid nitrogen ice cream.  We used a very simple recipe--one quart of heavy cream, one pint of milk, 3 tablespoons of vanilla, and 1/2 cup sugar.  Then we added about half a gallon of liquid N2 to bring the mix down to 77 Kelvin (-321 degrees F).  The ice cream was quite smooth and delicious.

Ned and Liesel enjoying liquid nitrogen ice cream.

I was curious about some properties of extremely cold matter that I remember learning in high school and decided to read up on it.  Other than being extremely cold, nothing particularly exciting happens around the temperature at which nitrogen is liquid.  Liquid helium, however, is considerably colder (boiling point of 4.2 K), and at these temperatures we start to see very interesting quantum mechanical phenomena.  For example, if you cool liquid helium a couple degrees below its boiling point, it becomes a superfluid, with bizarre properties.  Atoms of most elements settle into a solid at cold enough temperatures due to intermolecular interactions.  Helium, however, is so light and has such weak intermolecular interactions that even at absolute zero it remains a liquid.  Since helium stays liquid near absolute zero, it can transform into a Bose-Einstein condensate, in which all the atoms of the liquid move in unison with each other.  Superfluid helium can leak through its container, finding openings between the container molecules that ordinary fluids would not be able to penetrate.  Superfluids also have zero viscosity, which means they can climb up the walls of their container, seemingly defying gravity, and spill over the edge, eventually emptying the container.


More practically, liquid helium is used for cooling superconducting magnets used in NMR and MRI machines.  Superconducting magnets are made from superconducting wire, which when cooled below a critical temperature, exhibit zero electrical resistance.  Electrical current will flow forever in a loop of superconducting material.


Really cool video on superconductors.

As you might expect, it is pretty simple to make liquid nitrogen, since it makes up 80% of air.  All you have to do is compress air, allow it to radiate off its heat, and then let it expand, which will cause the gas to get extremely cold.  This process is repeated several times until liquid nitrogen is achieved. 

Epilepsy Surgery

Two and half weeks ago, I completed my 8-week surgery rotation.  Doing one or two clinical clerkships before starting the PhD is optional at Michigan, but taking this option is one decision I'm very happy about.  For one, I got to see what being a doctor is all about, and I won't be worrying for the next four years about whether I have what it takes.  I also got to see how all the facts I was memorizing for the past two years come into play in real life.  And finally, I got to join my classmates during the most challenging transition of their careers, and I got to work closely with a few classmates that I had not worked with before.  I strongly recommend splitting the M3 year for any MD/PhD student--I actually think it should be mandatory at most schools.

The first month I was on the General Surgery-White service, which is mostly gastrointestinal surgery.  The second month I was on the transplant service, with a one-week stint on the neurosurgery service.  The transplant service was the most enjoyable because the professors and fellows spent a significant amount of time teaching medical students.  We were also required to make a 15-minute presentation on a topic in transplant; I did mine on organ sales.  Some of the surgeries I saw over the two months included laparoscopic cholecystectomy, liver resection, Frey procedure for chronic pancreatitis, bowel resection, peritoneal window for a lymphocele, nephrectomy, and kidney transplant.  Unfortunately I missed out on a liver transplant and Whipple procedure for pancreatic/bile duct cancer, which are big operations also performed on the services I rotated on.  Overall I had a great time on surgery, but I don't think my skill set or  scientific interests are aligned with a career in surgery.

While on neurosurgery, I saw several procedures on the spine as well as a temporal lobectomy for epilepsy. I wondered what sorts of surgery are available for epilepsy, how often it is performed, and how successful it is.  Below is some interesting information I found.

Surgery is considered for epilepsy patients who have not responded to sufficient trials of anti-epileptic drugs (AEDs) and who have a reasonable chance of benefiting from surgery.  What is considered "sufficient trials" is not set in stone, as an estimated 300 years would be required to try all AEDs in all combinations.  Patients who benefit from surgery have what are called "complex partial" seizures, which means that their seizures originate in a defined focus in the brain and cause them to lose consciousness.

Before surgery, a number of tests must be performed.  A brain MRI is taken to assess brain structure.  An electroencephalogram (EEG) is commonly used to diagnose epilepsy but is usually not used to make major surgical decisions.  Neuropsychological testing can determine the patient's baseline attention, concentration, language, visuospatial skills, verbal and visual memory, problem solving, personality, and emotional functioning.  Many of these skills are carried out by distinct regions of the brain, so a patient's performance on the tests can tell physicians where the epileptogenic focus lies.  The intracarotid amobarbital (Wada) test, in which the left and right sides of the brain are anesthetized one at a time, permits determination of language and memory lateralization.  If a patient can accurately recall 75% of items presented during anesthetization, then the hemisphere contralateral to the one anesthetized should be able to support memory after the anesthetized hemisphere undergoes surgery.  If the above non-invasive methods still leave ambiguities in the surgical plan, then invasive intracranial monitoring can be performed by placing electrodes in the space under the dura mater, the connective tissue sheath surrounding the brain.

There are four operations that can be performed for epilepsy:

1. Anteromedial temporal resection (AMTR): Excision of the amygdala (fear conditioning), hippocampal head and body (memory), uncus, entorhinal region (spatial memories), and the parahippocampal gyrus (memory encoding), and a variable portion of the tip of the temporal lobe.  This is the most commonly performed procedure for epilepsy, as the medial temporal lobe is a common location of epileptogenic foci.
2) Corpus callosotomy: Disconnection of communication between the two brain hemispheres.  Usually only the anterior portion of the connection wires are broken.
3) Functional hemispherectomy: One side of the brain is disconnected from all other structures, but the brain remains in place (actually removing one side of the brain increases morbidity).
4) Multiple subpial transection: Cuts are made perpendicular to the brain surface in the epileptogenic focus.  The idea is that the cuts will disrupt side-to-side connections between neurons that cause a seizure to spread, while preserving connections from the outer most layer of the brain to the inner layers.

A 2011 study showed that in a cohort of 615 adults who underwent epilepsy surgery, 52% remained seizure-free five years post-op (excluding small seizures that did not cause the patient to lose consciousness).  Patients with medial temporal lobe epilepsy can benefit from AMTR early in their disease course, even though the average waiting period for patients to undergo epilepsy surgery is currently 20 years.  Corpus callosotomy usually decreases but does not stop seizures, as more than 80% of patients experience a 60-70% decrease in seizures (but 10-15% of patients get no benefit).  Amazingly, cutting off communication between the brain hemispheres has remarkably few side effects.  Occasionally patients have transient paralysis in part of their body or temporary bladder incontinence.  While psychological studies can detect impaired inter-hemisphere communication, this does not interfere with patients' daily living.  Similarly, functional hemispherectomy has a seizure-free outcome in 54-90% of patients, with the only common long-term complication being impaired motor function of the contralateral hand.

One more detail to add from the temporal lobectomy that I witnessed: rather than remove brain tissue en bloc, the surgeons used a suction device.  Brain tissue was sucked up by the sucker, which made a horrible noise, and sent to waste!

In the future, I wonder if epilepsy surgeons will not be removing brain tissue, but possibly modifying it by injecting drugs or stem cells that would stabilize the electrical activity?  Unfortunately we don't know how most epilepsy drugs work (hence the trial and error in selection and dosing), but if we figure that out, perhaps more targeted therapies carried out by surgeons will be possible.

Are progressive reforms un-American?

Some of my friends argue that the culture of the United States prohibits a national health plan, a sound climate change policy, stricter gun laws, and other progressive reforms.  While admitting that such reforms would alleviate much suffering on paper, my friends say they simply won't work in our country.  Is there really something thoroughly un-American about pursuing national goals?  Would enacting these reforms really destroy the United States as we know it?

Unfortunately, the United States is already being destroyed because some of our most upstanding values have been perverted while others have been forgotten completely.  Americans have long valued personal freedom--freedom of religion, freedom of speech, and freedom to make money through a capitalist economy.  Closely tied to this value of individual freedom is the American dream--the idealized story of a person who rises from poverty using their own ingenuity and elbow grease, without assistance from others.  Unfortunately, research shows that inter-generational socioeconomic mobility in the U.S. is substantially less than that in Europe and Canada (see Understanding mobility in America by Tom Hertz: http://www.americanprogress.org/issues/2006/04/Hertz_MobilityAnalysis.pdf).  It turns out that giving people the nominal freedom to make money with low taxes does not imply you are giving them the means to success, no matter how much they work.  Lack of education, jobs, and health care are all huge obstacles that can't be overcome simply by letting people do as they please.  Furthermore, the American ideal of personal freedom has been warped into an exaggerated "I do what I want" attitude, in all aspects of life (larger and larger serving sizes at McDonald's, for example), in which any sort of collective organization or movement by the nation as a whole is seen as undermining one's "freedom."  It's not entirely clear how this came about, but politics certainly played a role.  After all, the idea of a health care mandate originally came from Republicans and was later vehemently opposed for political reasons.  

In any case, the emphasis on individuality comes at a time when going it alone is becoming a poorer and poorer strategy in multiple diverse contexts.  In foreign policy, unilateral military action without support from allies in the 21st century is ludicrous.  In technology, crowd-sourcing and global communication have made it possible to accomplish complex tasks.  In science and medicine, great strides are being made by collaborations among experts in different areas.  We are seeing that modern nations do not survive if they remain divided as millions of individual families trying to make the best of things.  Modern nations thrive when they combine their resources for a common goal.  The big problems of today--health care, climate change, gun violence--require unified action from the entire nation.  The issues we currently face are no less daunting than those faced during World War II, when we came together unified against a common enemy, and we reached the height of our international prowess.  In the 1940s, people prided themselves on making sacrifices for the good of the country, and overcoming today's problems will also require sacrifices.  Unfortunately, making sacrifices is no longer on Americans' value radar, as we've been spoiled by decades of prosperity.


In sum, I believe that American values at their best are in support of the reforms we need to tackle climate change, health care shortages, and other major issues.  What's actually in the way of these reforms is Americans themselves, who have become complacent and oblivious to the loss of respect that the U.S. once commanded on the world stage.  Our political leaders have failed as well to light the fire and rekindle the collective spirit of the nation.  We need them to emphasize the urgency, because today's challenges are insidious, without a "Pearl Harbor" call to arms.  Let's stop being anti-social, America, and come together for the good of our nation and the world! 

UMMS Class of 2014 Music Video

Biorhythms Winter 2012

Here are videos from the two acts I participated in during the University of Michigan Medical School Biorhythms Show Winter 2012.  In the first dance I was a defibrillator.  The second act was with our rap group Phlomax: Internists vs. Pathologists.  This year four professors joined us on stage!


Arryhthmias from UMMS on Vimeo.