The Fugue Counterpoint by Hans Fugal


Calipers and Science

Just for kicks I dug up the original Jackson/Pollock paper for skinfold measurements for determining body fat percentage. Turns out there's also a 7-point equation that also takes circumference of waist and forearm into account.

Here's a snapshot of the equations for men from the paper ("Generalized equations for predicting body density of men" by A.S. Jackson and M.L. Pollock, 1978. I couldn't find the PDF for the women paper online).
Generalized body density equations

Important notes: skinfolds are in millimeters, circumferences are in meters, and log is the natural log (ln in most computer languages). I plugged my values from two weeks back into a spreadsheet and got the following results:

JP Equation Density %BF
Sum of seven skinfolds
S, S^2, age 1.0518 20.62%
S, S^2, age,C 1.0476 22.51%
log S, age 1.0506 21.15%
log S, age, C 1.0482 22.25%
Sum of three skinfolds
S, S^2, age (5) 1.0607 16.69%
S, S^2, age,C (6) 1.0549 19.24%
log S, age (7) 1.0578 17.95%
log S, age, C (8) 1.0574 18.14%

The most interesting thing here is that there's a large difference between 7 and 3 site measurements, and the 3 site range is significantly larger. Also very interesting to note is that the one-site (suprailiac) AccuMeasure chart is, for me, in line with the 7-site measurement (22.1%). Given other measurements I've taken and just general guesswork based on what I see in the mirror, I think that is a decent estimate.

It's also curious that there are two sets of equations given, one using logs and one using squares.

Moral of the story: more data is better, sometimes not-enough more data is worse than a simpler estimate, and interesting things can be learned when you go to the original source. (This is just a quick note, but the paper is very interesting and reading it will be an interesting exercise that sets proper expectations for, and understanding of, the JP7 skinfold method).


Motorcycle Wheel Alignment

An important part of maintaining a motorcycle is keeping the correct slack on the chain. Usually this involves loosening the rear wheel nut and using two adjustment bolts (one on each side of the wheel) to set the correct tension. Care must be taken to ensure that the front and rear wheels are aligned, or you get bad wear and handling. When you know they are aligned already, you can just count the "flats" and turn the bolts the same amount. But from time to time, or whenever you're uncertain, you have to align them.

The simplest method is just using the marks on the swingarm. This is what I did the first time, but it felt like the rear tire was out of alignment. A little searching of the web confirmed that these marks are both too imprecise and often just plain wrong. What really matters is not the marks the manufacturer put on, but whether the two wheels are actually aligned.

The most common DIY method is to take a string, hold it taught so that it just touches both edges of the rear tire and extends to the ground at the front tire. Carefully measure on both sides, and adjust until the front tire is perfectly centered. I tried this method after I decided I wasn't sure my wheels were aligned. It was a big hassle, especially with just one person, but eventually I got the hang of it. It felt more accurate than the marks but it still felt wildly inaccurate. Something more rigid than string but still nice and straight may have given me more confidence, but I didn't have anything long and straight enough. It could have been placebo, but it rode a lot better after aligning this way.

By this point it had turned quixotic and I would not rest until I found an easy and accurate way to align my wheels. One search led to another and I eventually stumbled across the ProAligner. I was intrigued—how could a ruler be more accurate? Even one with "scientifically designed" red marks. Being the cheapskate engineer that I am I wasn't gong to shell out even $30 unless I knew it would work, and not if I could make my own.

If you search for more details on the ProAligner, you get not a lot of results that fall in two categories: gushing reviews that may or may not be shills, and skeptical curmudgeons that scream SPAM or dismiss even the idea of aligning your wheels. Nobody bridges the two with important details like what the theory is and why it may or may not work, or how it is even used.

Luckily for you anxious wheel aligners (Yes, I realize it is January. I live in California—deal with it! ;-), I have put the jigsaw together and will now help you decide whether to buy the ProAligner.

First, let's discuss the theory on which it works. It's simple geometry. Center front wheel relative to rear tireAlign rear wheel
You are making right triangles and adjusting the wheels until the opposite sides are the same. First you center the front wheel on the rear tire by sighting down each edge of the front tire, then you align the rear wheel by sighting down each edge of the rear tire. Adjust and repeat as necessary until the rear wheel is aligned when the front wheel is centered. Refer to the figure, and reread this paragraph until you get it because it is the key to the whole method, and the thing that ProAligner hopes to hide from all but those who have purchased their ruler. Once you know this tidbit and how it works, it's a slippery slope to realizing you don't need their product to replicate it.

I approximated their design in CAD (the exact spacing is irrelevant, I think I used centimeters and didn't fret whether my printer scaled it slightly), printed it out, and taped it onto some cardboard. Since I don't have a center stand, and my high-quality bike lift is opaque, I needed to do it on the sidestand, so I cut the cardboard to the appropriate angle.

The first time I tried to use it, I put the ruler at the rear wheel and didn't have the whole process figured out. I thought you just sighted along the front tires and soon realized that this alone was super inaccurate unless you could be sure the front wheel was centered perfectly. With the ruler at the rear wheel, it was impossible to read, even with the "scientifically designed" markings.

The second time, I put the ruler just behind the front wheel and had figured out the key idea of centering the front tire relative to the rear wheel, then sighting the rear wheel to read the adjustment. The ruler was easy to read at this distance. I think even a regular school ruler would be—it was 2–3 feet from my eye. The shadow side of my rear tire was hard to sight because it was all just dark. It would have been easier with better lighting, but it was easily remedied with a piece of masking tape on the rear edge to provide contrast. I was pleasantly surprised that it was not only easy to sight and read (aside from having to literally lie on my stomach), but the readings were consistent and reproduceable. It was fairly close to aligned (from the string method) but needed slight adjustment—it turned out I could distinguish one "flat" of the adjusting bolt. This is quite accurate, and easier than futzing about with strings.

As I see it, ProAligner is clever on several fronts. First, coming up with the idea of sighting down the edges of the tires and realizing that this is quite accurate (like sighting a rifle), that was pretty clever. Then, the folding ruler while hardly novel does make positioning it stable and flexible. Finally, I'll concede that the "scientifically designed" markings are easier to read than a regular ruler. So if you're into supporting clever independent companies or would rather spend some money than spend time making your own, then go buy yourself a ProAligner and rest assured that it is accurate and easy.

I have some other ideas for accurate measuring of alignment if lying on the ground isn't your thing. First, a string-based method that I hope would take away most of the frustration: Get a dowel or 2x4 and accurately notch the width of your rear wheel and the center point between the notches. Run the string from the rear tire (hint, wrap around the tire and anchor on a spoke—tape on the tire doesn't stick well) to the notches and wedge it under the centered front wheel. Now you just turn the bolts until the sides of the string just barely touch on both sides.

Second, a laser-pointer method. This isn't unlike this post which was my original tip on the ProAligner, but I think it's easier than his contraption. Attach two laser pointers to straight 2x4s such that they span the rear wheel and point true and level. Bungee them to the rear wheel such that the lasers hit down by the front wheel. Adjust until the front wheel is centered between the laser points. The success of this depends on how accurately you can true the pointers and whether you can keep them on (or have a friend), etc. You could also forego the boards if you have a friend and just sight the laser down the side of the rear tire (a little red on both edges, and also down on the ground by the front tire), have your friend mark with chalk, then measure.

Well, now you have all my thoughts on wheel alignment. My favorite is the ProAligner method—it's faster, simpler, feels most consistent and reliable, and you can even DIY with a ruler, some cardboard, a utility knife, and some tape.


Baldness Genetics

Coincidentally, less than an hour after I cut my hair to one inch all around because of androgenic alopecia, a link to this article came up in my feed reader this morning. Apparently they have found the genetics that cause it. As I understand the article, there are two genetic variants (which they just discovered) on chromosome 20, which when combined with the one they already knew about on the X chromosome (which you get from your mother), increases your chances of going bald sevenfold.

If you have both the risk variants we discovered on chromosome 20 and the unrelated known variant on the X chromosome, your risk of becoming bald increases sevenfold."

Does this mean you have to get genes from both parents to be bald? What if you don't have the one on the X chromosome but you get the ones on chromosome 20 from your dad? Well, as you can see this report of the findings isn't very enlightening, but it does tell us that yes if your mom's dad and brothers are bald you have increased "risk" (so no, contrary to what you might have read (but probably haven't), it's not a myth), but just because your mom's dad isn't bald doesn't mean you might not be.