Bike frame design — the myth of vertical compliance

The notion of “vertical compliance” is built into bike lore, and everybody knows that frame design and frame materials influence compliance.

But this is a myth.

The conventional diamond frame is a triangulated truss with little opportunity to flex vertically. Allee posted this link that documents an experiment performed by Mike Iglesias showing that a diamond frame is essentially rigid under normal vertical loads.

The tests were confined to conventional frames. It is possible that compromised triangulation – for example a steeply sloping top tube, or maybe unconventionally long chain stays with no additional triangulation, would allow some flex in the structure.

The test also showed that there was some flex in the fork. That makes sense, since the fork is not triangulated as is the rest of the diamond frame. There was even variation among the forks in the test, all of which were chro-mo. The amount of fork deflection was in all cases a significant fraction of the deflection in the tires (probably hard little road racing tires). This would be interesting to pursue further to see if fork materials, tube diameter, wall thicknesses, curve characteristics, total offset, head angle, etc. make a significant contribution to rider comfort. I would speculate that a unicrown fork with 31.8mm diameter blades does not deflect much; a fork with straight blades (angled at the crown) would deflect less than a fork with curved blades; a steel fork with 1.2 mm walls (for disk brakes) would deflect less than one with 0.7 mm walls (Reynolds 953); and more offset and shallower head angles would allow more flex. Determining whether those differences are significant and whether they would make a difference to the rider’s comfort would require some experimentation.

The bottom line is that tires provide more suspension than conventional frame components (with the possible exception of the fork) and are highly tunable. Larger tire volumes provide more suspension travel; lower pressures provide lower spring stiffness; lighter tread and sidewalls may be more effective at absorbing shock because of lower unsprung weight.

The Iglesias experiment examined only vertical compliance. Deflection at the bottom bracket with pedaling and the tendency to keep the head tube and seat tube parallel under the complex loads of cornering and maneuvering, especially while carrying significant baggage mass, can still be changed with frame design and material specification.

Iglesias looked at static loads but did not look at vibrations. It is well documented that vibration causes fatigue, so the intensity of vibration can be a real concern, especially for riding long distances.

The fact that common bike frame materials are used for musical instrument components suggests that none have intrinsic damping characteristics, but there may be differences in resonance or transmission of vibration outside of resonant windows. This also may be worth looking into, but my intuition tells me that if there is no vertical give, there can’t be much damping of vibration, and there should be little or no variation with frame design or materials.

While I was pondering about how one might explore vibration characteristics, I realized that I already own an accelerometer that might be capable of making appropriate measurements – my smart phone. And sure enough, the app world was way ahead of me and there are several apps available for vibration analysis of machinery. So I downloaded an app and started experimenting.

I do not have a fleet of CF, Ti, and Al bikes, but I do have a couple of steel bikes with very different frames, and I know the details because I built them.

For a preliminary proof-of concept experiment, I compared vibration transmission of two bikes over three surfaces. I must emphasize that my methods were crude, so this is preliminary at best, and nearly worthless at worst. However, I think it demonstrates that a smart phone has potential for this application.

Bike 1 is the touring bike. It has heavy-gauge oversize main tubes, heavy and long stays, and moderately heavy fork blades. The tires are Schwalbe Almotion which are not extremely stiff, but not particularly flexible, either. They measure about 45mm wide.

Bike 2 is the rando bike. It has light main tubes, lighter but shorter stays than the touring bike, and Kaisei “Toei Special” fork blades that are claimed to “provide passive suspension that improves both comfort and speed.“ Tires are Rene Herse Loup Loup Pass 38 mm with extra light and flexible casing.

The three surfaces are 1) fresh, smooth asphalt; 2) weathered, pebbly asphalt; and 3) gravel (see photos below).

I ran each surface at 65 psi and at 35 psi. The phone was placed at the back of the top tube to capture the vibrations transmitted through the frame to the seat post, and at the front of the top tube to capture vibrations at the handlebar.

The app generates a tremendous amount of data, but it seems to me that the important part is the vibration amplitude in the vertical direction expressed as root mean squared (RMS) acceleration.

Resonant frequencies were mostly around 8 to 12 Hz, with a few exceptions that I cannot explain. There was an unexpected amount of vibration in the horizontal plane, sometimes almost as high as the amplitude in the vertical direction.

These preliminary results indicate that as far as vibration goes:

• Nothing matters much on smooth surfaces.
• Frame doesn’t matter much.
• Fork doesn’t matter much (I was surprised to see that the vibration amplitude was greater in front in several cases).
• Tire characteristics don’t matter much except on gravel.
• Tire pressure matters a lot, and it matters more as surfaces get rougher.

Let me again emphasize the crude nature of my experiments. I think there is probably some bad data. I did only one run for each situation, and multiple runs would be required to confirm accuracy. I did not control for several variables. But I do think that this approach could provide some insights if the experiment were designed better. And it would be interesting to see different frame materials tested. If I get motivated, I might explore this further.

Smooth fresh asphalt.

Weathered asphalt

Gravel

Crude accelerometer mount.

Other posts on frame design:

Bike Frame Design – the influence of tubing diameter and wall thickness

Bike Frame Design – strength of steel frame tubing

Carrying stuff: weight distribution and frame design

More thoughts on tubing specifications and ride qualities

A Measured Rant – Metrication and Bikes

During the time I  worked in bike shops (1977 until 1987), we had four different standards for bike parts and dimensions to deal with: USA, English*, Italian, and French. There were also variations such as Raleigh and Swiss.

Basic US-made bikes, usually with single-speed coaster brakes, were all fractional inch — tubing diameter, ball bearing size, threading on axles — and they used US-standard fractional-inch wrench sizes. As you went up in price point, more components (hubs, brakes, derailleurs) were used that were manufactured in Europe, and these parts used European standards, usually English. A medium quality American-made 10-speed had a mix of US-standard and English-standard threads and fasteners, requiring both US and metric tools. High-end American bikes were entirely English (or sometimes Italian) standard.

Metrication officially began in the UK in 1965 with a government policy to encourage the switch. That process was not complete when English bike standards were established and frozen in place (and it still is not really complete). In the English bike standard, some bike parts are fractional inches (ball bearings and frame tube diameters; bottom bracket shell diameter and threading; chain pitch and width; pedal axle diameter and threading). But wheel axles used metric diameter and threading specifications, and all the wrenches you needed to work on these bikes were metric (those Whitworth wrenches that were sometimes needed were throwbacks).

The Italians mostly followed the English standard (or evolved to the same place by a different route). The biggest differences were bottom bracket, freewheel, and axle threading that was a mixed-up hybrid of metric diameter and inch-base thread pitch.

French bikes, as might be expected, were almost fully metric – even frame tube diameters were in millimeters. The only exceptions that I know of were those fractional-inch ball bearings and the standard inch-pitch chain.

In the English-speaking world, gear ratios are expressed as gear inches, a dusty old traditional measure that refers to the diameter of an equivalent direct-drive high-wheeler wheel (in inches, of course). The metric equivalent is meters development, the distance traveled with one pedal revolution.

The chaos that is tire and wheel sizing deserves its own discussion (Sheldon is definitive). A good example is the seven different non-compatible tire sizes that can be called 26”*.  This bedlam was further confused when some marketing geniuses created new names for existing tire sizes: 29” (formerly known as 700c or 28”) and 27.5” (formerly known as 650b or 26×1½). In a previous post, I noted that you have to look under at least three different size designations to find 650b (584) tires in various manufacturers’ catalogs.

The International Standards Organization (ISO) made things a little more consistent by designating the English standards as the international standard. This has already occurred in practice when the Japanese bicycle manufacturing industry, which used the English standards, took over the world, eliminating much of the European competition. ISO standardization makes life easier for the mechanic, but it has pretty much eliminated the manufacture of replacement parts for French and Italian bikes, creating a real challenge for anyone trying to fix up an old Peugeot or Bianchi.  The ISO standards recognize the reality on the ground, but if evolution to full metric standards is a goal, they should have adopted the French (or Swiss) standards.

Since I tend to stick with old or old-style parts, I am not up on the recent proliferation in bottom bracket and axle specifications, and I do not know whether they are consistently metric or not. But I suspect that they are as confused as the rest of the bike world.

ISO also established a tire size standard that is simply the tire width and wheel diameter (for example 42 – 584 designates a 42mm-wide 650b tire). Unfortunately, it makes too much sense to be adopted into common usage.

An assistantship in graduate school allowed me to leave the bike shop world behind. At the end of my training as an engineer, I had been working with the metric system for seven years. I was comfortable with meters and liters, hectares and newtons.

When I left the ivy-covered halls, I was reminded that the metric system is not a part of the culture of the US. As a country, we would rather deal with the absurd and cluttered conversion factors of the traditional system —  inch, feet, yard, mile; square foot, acre, square mile; ounce (dry, avoirdupois, or fluid?), pound, cup, peck, gallon, cubic inch. Though a few metric standards are slowly creeping into regular usage, the civil engineering world at the municipal level is still entirely stuck on using US traditional units, though they have made the small simplification of decimal feet (and no rods or chains). I am sure that as a country we waste millions of dollars every year on calculation time and incompatibility with international standards.

The metric system, is of course, much more tractable with its powers-of-ten conversions between different scales/orders of magnitude. Perhaps more importantly, it makes an unambiguous distinction between mass and force. The metric unit of mass is the kilogram; the force unit is the newton. The relationship is as basic as Newton’s first law (F=Ma). In contrast, it is unclear whether you need to multiply a pound by g to get force or divide by g to get mass. This has led to the occasional and inconsistent use of lb_m , lb_f (pounds mass and pounds force) and slugs (mass).

Since most of us don’t do many calculations involving acceleration, the difference between force and mass is still hazy in everyday life. But that does not excuse the abomination of using “kilogram force” for spoke tension measurement. The engineers at Park Tool should be ashamed.

When I write, I tend to use the units I am most comfortable with. To a large extent, that means US customary miles, inches, and gear inches. I frequently find it easier to use millimeters over fractional inches, but millimeter equivalents for fractional-inch standards can be clumsy (1 1/8″ is easier to say than 28.575 mm). In this blog, for clarity (and so I can practice), I will endeavor to include metric or US equivalents in parentheses as appropriate, but I don’t always remember. I will also try to use ISO descriptions for tire size.

*Perhaps more accurately “British” or “UK” but “English” was the common designation.

**Rim diameters of 26” wheels: 1) 559 (mountain bike), 2) 571 (650c), 3) 571 (US hook bead), 4) 584 (650b), 5) 590 (650a, 3-speed), 6) 597 (Schwinn 3-speed), 7) 599 (old US lightweights). Two of these are so old and obsolete that they could be ignored. But still.

Carrying stuff: weight distribution and frame design

 

There are a lot of opinions, and some passion, in the bike touring and utility-cycling worlds about distribution of weight and the best design for bikes intended to carry loads.

I would like to contribute my observations to the discussion. These observations are based mostly on trial and error with little in the way of controlled experiment, but I have been messing around with bikes for decades and have a lot of accumulated experience, anecdotal though it is. I have experienced all of the commonly described problems caused by touring loads front and rear: shimmy, wobble, instability, slow steering, difficult low-speed handling, bikes too unstable to stand up to pedal, and I have found ways to overcome those problems in ways that work for me. Your results may vary.

I would generalize my observations in the following principles for heavy touring and utility loads.

• Rigidity is a critical characteristic for racks. Loads that sway and shift wreak havoc with stability and handling. My current Tubus rear rack (with large-diamater steel tubing) enabled noticeably more stable handling than my previous rack, even though the predecessor was made by a reputable manufacturer (Blackburn aluminum). Inexpensive, flimsy, non-triangularized racks can be a handling nightmare with a significant load (I am looking at you, Pletscher).
• Mounting loads lower is better. I don’t know how important this factor is by itself because I have made other changes at the same time that I lowered the weight, but it makes intuitive sense that it is a good thing.
• For rear loads, longer chainstays are better. The farther the load’s center of mass hangs behind the rear axle, the more it unloads the front wheel and the worse the handling and potential issues with shimmy become. Chainstays on traditional touring frames are usually around 17.5” (444 cm) for a good reason. Longer than that can be even better. Bigger frames should have proportionately longer chainstays, which is not the usual practice.
• Front loads should be close to the steering axis. Every change in course and every steering adjustment to maintain balance is impeded by the inertia of the load. This effect can be minimized by reducing the distance the load travels when the handlebars are turned. The usual American handlebar bag is farther from the steering axis than a rando-style rack-top bag, so the latter has less impact on handling. Low-rider front racks place panniers as close as possible to the steering axis and thereby allow better handling than a rack with a high mount. And front baskets and porteur racks, mounted high and far from the steering axis, create a handling challenge with a substantial load. Low-trail frame geometry helps mitigate the heavy steering caused by front loads but does not erase it, and the above observations still apply.

Departing from Abrams Creek

My current touring/utility bike (link) has extremely long chainstays. I hardly notice a rear load, even 40 pounds or more (except up hill, of course). It has lower-than-average trail (50 mm) and can handle a pretty good front load, too, but it feels best if the front load is limited to 15 or 20 pounds. Other than that arbitrary limit on front load, the ratio of front to rear load does not seem to make any difference.

Groceries

The dead weight of the payload can be hard on rear wheels, though I have never broken a spoke on tour (though I have bent a front wheel on an unexpected obstacle). Wheel specifications are important, and I may get around to doing a future blog on speccing strong rear wheels.

More discussion on the subject.

http://www.cyclingabout.com/best-carry-load-bicycle-touring-front-rear-panniers/

http://www.adventurecycling.org/default/assets/resources/200906_MechanicalAdvantage_Heine.pdf

Other posts on frame design:

Bike Frame Design – the influence of tubing diameter and wall thickness

 Bike frame design — the myth of vertical compliance

Bike Frame Design – strength of steel frame tubing

More thoughts on tubing specifications and ride qualities

In a previous post, I noted that some highly respected people in the bike world assert that the frame tubing specifications make little or no difference to the ride.  However, in my experience, there are some circumstances in which tube choices make a huge difference.

For example, there was a Monark Siver King at Stu’s for repair.  It was an American balloon-tire kid’s bike, the frame of which was made from 1” round aluminum tubing.  If I remember correctly, the bottom bracket deflection could be measured in inches as you pedaled, yet it had a surprisingly lively ride.  My time with it was short, and I did not try it with a load, nor did I dive into any tricky corners; I suspect that with that much flex the handling could have been challenging.

Close to the same time (early 1980’s), I was at a Portland cyclocross race.  Jim Merz, then a Portland frame builder, brought a bike to the race that appeared to be nearly as flexy as the Monark.  The frame was steel (I think), and I don’t know anything about the specifications, but it must have had very thin walls.  He was using the flexibility as a substitute for suspension and he was riding over some of the obstacles that made the rest of us dismount.  He said something at the time about a good competition bike being “on the hairy edge of breakdown”.  I did not ride the bike, and I don’t know how long that frame survived.

I have ridden two tandems that had frames that were clearly too flexible.  Tandems are an extreme example because of the long tubes, double power input, and double human payload compared to a single bike.

One tandem was an American coaster-brake balloon-tire bike with 1” steel tubing, which usually means low strength steel and thick walls.  While riding placidly it was pleasant enough, but anything other than a gentle change in direction would cause the frame to twist, bend, and buck and generally become a challenge to keep under control.  Another tandem, a Gitane of traditional-diameter (unknown wall thickness but possibly tandem gauge) Reynolds 531 was better, but still could be a handful at low speeds and when cornered hard, and there was a lot of flex when accelerating or climbing.  On the other hand, I have ridden tandems built with oversize and presumably heavier gauge tubing that handle just like single bikes.

In this vein, Mr. Weiss, over at  Bike Snob NYC posted a  link  to a magazine article published in 1996 (back when steel was still taken seriously). The article is an account of a blind test of seven bikes with different frame tube specifications but otherwise identical design. It is remarkable that they assembled this group of bikes, but they could have made more of the opportunity.

In fact, they blew it.  This group of bikes could have been ridden by a group of testers whose pooled observations might have yielded some real insights.  And they could have performed some objective testing, like keeping track of lap times and measuring frame deflection.  Instead, one rider/writer recorded his hurried impressions.

The writer, Alan Cote, had a great deal of trouble telling the tube sets apart by their riding properties. With only one observer (contrary to the impression given by the graphics accompanying the article), this could either mean that differences were truly too subtle to distinguish, or there were too many bikes and too little time to sort out all the sensory information, or maybe that Mr. Cote was not a good observer.

Cote reaches some preliminary conclusions, then appears to second guess himself when he is informed of the construction material of each bike. “I think my ride impressions were essentially random”, he says after he discovers that the tubing specifications do not necessarily correlate with his initial ride impressions.

All of these tube sets are steel, so the specific steel alloy (or associated tensile strength) makes essentially no difference in tube rigidity, and the alloy, by itself, should make no difference in ride qualities.  Ride characteristics are determined by a combination of tube diameter and wall thickness.  Of course a higher-strength alloy does allow thinner walls and lighter weight without reducing the total strength, so the alloy characteristics can influence the long-term usefulness of a frame.

Using my  previous analysis  and a subjective analysis of the other frame specifications, most of these frames should have similar characteristics, but there is enough of a range that differences should have been perceptible, at least in the frames at the extremes.

The most flexible frame should have been the one constructed from SLX tubing.  It has the most flexible main triangle and the lightest chain stays, seat stays, and fork blades.  Cote identified this bike as the “softest”, apparently only for power transmission.  I don’t see any reason it would not also be the softest in its over-the-bumps ride.

I am surprised that he could not distinguish the straight-gauge (Aelle) frame.  Unless we have been defrauded about the value of butted tubing over the last 120 years (a possibility I cannot entirely eliminate) there should be a noticeable difference between this and the other bikes.  I found my Schwinn Sports Tourer, with similar tubing, harsher and less lively than comparable butted frames (though I recognize that that perception could have been because I knew it was straight gauge).

The stiffest frame should have been the Thron, with stout oversize tubing and heavier chain stays and seat stays.  This frame should be 30% or more stiffer than the SLX, a difference I would expect a rider to feel both in lateral flex during pedaling and over the bumps.  Cote called this the best at shock absorption, an impression that is surprising.

Cote’s favorite (which he called the “stiffest”) was the Neuron frame, made from tubing that used a complicated elliptical butting pattern.  Based on its specs, I would expect that it should be only incrementally stiffer than the SLX.  It is possible that the unique butting patterns provide a noticeably better ride, but if so, that fact did not save Neuron tubing from being eliminated from the Columbus catalog.

For a wine drinker who is happy with generic white wine, the difference between chardonnay and pinot gris is too subtle to bother with.  But a wine journalist worthy of the name would easily identify the two, wax poetic about the contributing tastes and mouth feel, and maybe tell you what vineyard the grapes came from.  A bike journalist should have a similarly well-calibrated sense of the contribution of frame construction to ride characteristics.  Maybe the differences between these frames were subtle, and maybe any differences really don’t matter when it comes down to the overall riding experience, but I have a hard time believing that the differences were indiscernible.  Bike journalism is driven too much by manufacturers’ (advertisers’) claims rather than educated, calibrated experience.  This was a unique opportunity to improve the writer’s ability to judge ride characteristics (maybe bike magazines should have a stable of test bikes with known and validated characteristics for training aspiring writers).

Or, if a panel reached consensus, this test would have reached a defensible conclusion that frame material really doesn’t matter (at least within this range).

Instead, it was a lost opportunity.

Other posts on frame design:

Bike Frame Design – the influence of tubing diameter and wall thickness

 Bike frame design — the myth of vertical compliance

Bike Frame Design – strength of steel frame tubing

Carrying stuff: weight distribution and frame design

A little more about tires and rolling resistance

Bicycle Rolling Resistance is a website run by Jarno Bierman in the Netherlands.  Jarno* uses a roller to measure tire rolling resistance.  The attraction of Jarnos’s work is that he uses a consistent method for a large number of different tires, and he uses a textured roller in an effort to account for energy loss from vibration as well as tire flex.  The consistent test procedure gives me more confidence in his results than I have in roll-down test of just a few tire models, and the textured roller presumably approximates a real-world road surface better than a smooth roller.

However, he focuses on a narrow range of road tire sizes, staying close to 25 mm width. He treats stouter touring tires as a separate class, and he sticks to tires of around 37 mm for that group.  Road and touring tires are all 700c.  He has not yet directly explored the characteristics of wide light and supple tires.

He has, however, compared the rolling resistance of a particular model of high-performance road tires in different widths and concluded that the widest (28 mm) had the lowest rolling resistance (conti GP link ) .  And he performed a similar test with a touring tire, showing that the 37 mm tire had lower rolling resistance than the 40 mm or 47 mm tire, while the 32 mm version had the highest rolling resistance for this tire model (Marathon link ).

However, the real outlier is in the mountain bike category.  I am a little dubious of the usefulness of this test on knobby mountain bike and fat bike tires (since the knobs are larger than the roughness elements on the test roller — it seems to me that a more pertinent test would involve a rougher roller**), but the relatively smooth tires in this category should behave like road tires.

The best-performing tire in the mountain bike class  has a rolling resistance that is competitive with the best 25 mm road tires, even with each class at inflation pressures appropriate to their widths.  As one might expect, it has a very light tread and casing but measures 47 mm wide.

These results seem to show that wide/light/supple tires can be as fast as their proponents claim.  Jarno has a long list of tires that he wants to test and not a lot of capacity to do the testing, but I would love to see him test some performance-oriented tires in the 38 mm range.

 

*I understand that you go straight to first names in the Netherlands rather than referring to someone with an honorific (e.g. Mijnheer Bierman) as you might in English.  I prefer that informality, but I don’t want to sound disrespectful, and I apologize if I am incorrect.

**I think it might be useful to test tires on a series of rollers with different size roughness elements, comparable to Nikuradse’s experiments with pipes.  This additional experimental data might provide some insight about optimum tires, width, and pressure for different surfaces.

A list of 650b road tires and some general tire observations

As I am sure all of you bike geeks out there know by now, there are two mechanisms by which rolling is resistance is generated. One is the energy consumed by flexing of the tire as it rolls (hysteresis loss). The other is vibration, which converts forward motion to vertical motion and consumes energy within the body of the rider.

Hysteresis loss can be minimized by using a hard tire. As an extreme example, rolling resistance is very low for steel train wheels rolling on smooth steel track. High air pressure in a bicycle tire can minimize the amount of flex.

Two other factors influence hysteresis loss.  A tire with a light and supple construction tends to lose less energy to flex at any pressure.  Thick tread, heavy casing construction, and puncture-resistant belts all tend to increase energy losses.

A wider tire can lose less energy to hysteresis at the same pressure as a narrower tire because of the shape of the contact patch. However, the maximum pressure a tire can handle is limited by the tire’s width.

Historically, many of the measurements of bike tire rolling resistance have been made on smooth rollers. These measurements ignore energy loss due to vibration and have helped encourage an emphasis on narrow, high-pressure tires for most applications. Recent research has used more real-world conditions and has shown that, because of energy losses to vibration, wider tires at lower pressures can be faster on the less-than-perfect surfaces that we are likely to experience in our daily riding lives. In addition, wider tires provide greater comfort and control, especially on rough surfaces and with heavy loads.

It is worth noting that light tire construction, including both thin tread and a light-weight fabric casing, reduce both hysteresis loss and vibration loss. Thus the fastest tires tend to be the lightest tires, and they also provide the most comfortable ride.

There are circumstances in which the best tire is narrow and hard, but they are restricted mostly to competition on good pavement or at the velodrome. Outside of those conditions, it makes little sense to be stuck with skinny tires that ride harshly, require frequent inflation, and can be steered and bounced by surface irregularities. For riders not involved in competition (and many who are), a 28mm tire is the narrowest that is needed, and tire widths of 42 mm and wider are very practical, and can be as fast as narrower tires.

For those of us who are low-performance riders, low rolling resistance still matters. In fact, because we cruise at a lower speed, wind resistance is lower than it is for faster riders, so rolling resistance becomes a higher proportion of total resistance. The difference between a very fast tire and a slow tire result in as much as 2 mph cruising speed on a flat road for a 100-watt rider.

On the down side, light high-performance tires tend to be relatively easy to puncture or cut and are more prone to stone bruises (broken cords with no external damage). And, as one might expect, they wear out relatively quickly. I get between 1500 and 2000 miles from light tires on the back wheel (3000 to 4000 miles for a pair that is judiciously rotated), and wider tires do not seem to last appreciably longer than similar narrower tires (at least in the range of 28 mm to 42 mm). I don’t have a lot of problems with punctures on the roads that I ride on my weekend peregrinations, and I have the skills to fix them easily when I do, so the greater speed (and therefore greater range) and comfort are worth it to me under these circumstances. However, when I do have flats, some are caused by very small objects, such as tiny thorns or miniscule slivers of glass that would not penetrate thicker tread and casing.

I use stouter tires for commuting and utility riding and accept any loss of speed in exchange for the practicality and reliability. City streets are littered with more broken glass and other sharp things than are country roads. When I have to stick to a schedule and when I am wearing office clothes, I really don’t want to repair a flat, and I seldom need to do so when using heavier tires with protective belts. Most of these tires last significantly longer than performance tires, on the order of 2500-3500 miles, even while hauling groceries and other loads. The Schwalbe Marathon currently on the back of my utility bike has about 2000 miles on it and looks like it just getting warmed up. From an economic perspective, a good quality tire that is heavier and more robust can cost half as much as a light tire and last twice as many miles.

For me, touring is more similar to utility riding than it is to sportier weekend jaunts.  Tires wear faster and are more likely to puncture with the dead weight of a load of camping gear.  Light tires are okay for a fast weekend trip, but a journey to the opposite coast would require tire replacements (maybe more than one) along the way, perhaps at an inopportune time, and the risk of tire failure that would leave the traveler stranded would be increased. And repairing flats on a loaded bike is considerably more trouble. I am still not sure how much priority durability should get compared to rolling resistance.

Although the general tendency is for lighter tires to be faster but more fragile, manufacturers seem to be able to do some tricks with rubber compounds and casing design that make some tires behave differently than expected looking at only weight, or at least mitigating the performance impacts of added weight.  Some of the tricks seem to be expensive (tire costs range by a factor of four or more), and it appears that you get what you pay for to some extent if you are discerning about ride quality.  I would recommend doing further research about any tires you are considering.

The renaissance of the 650b tire has paralleled the rediscovery of the advantages of wider tires. The 650b size allows a wider tire to work with a traditional road bike design, whether as a retrofit on an existing frame or on a frame designed for that size. Under the marketing designation of 27.5”, the size has become quite popular in the mountain bike world (and now on fat bikes), but is still not entirely mainstream on road bikes. However, there is now a wide range of 650b tires available, from extremely light tires that roll fast and float over rough surfaces to massive and possibly bullet-proof trekking tires. There is also some bleed-through from the off-roaders, providing road tires that fit those 650b mountain bikes.

I have assembled a list of  650b road tires available as of late November 2016, posted below. I expect that assembling a list like this in the future will become an impractical undertaking because  the number of options will continue to increase. I probably missed a few in my searches, but I hit the major tire manufacturers and marketers of this tire size. I cut off the maximum width for the list at 50 mm because there are few road frames that accept a tire any wider than that and because there are very few road tires that are wider. I did include some all-surface knobbies in the list, up to the 50 mm Continentals.

Finding all of these tires on the manufacturers’ web sites illustrated the lack of standardization for tire size nomenclature. Tires were listed as 27.5 (inches) x width in inches, 650b, 650 x zzb) (where “zz” is the width in mm), zz-584, or 26 x 1 ½ (with some other number to designate the actual width). Even in the same web site, it could take multiple searches using these different designations to locate all of the 650b tires.

Because I am too lazy to add references to the text of this blog, I will leave it to the reader to search out the details.  Here are few links to get you started.

Myths

Roller data

Roues Artisinales

Rolling resistance tests

Velonews

Heine 1

Heine 2

Peterson on 650b

Yet another useless marketing term: Road Plus

 

And here is the table of 650b road and all-surface tires

Manufacturer/ marketer	Model	Width (mm)	Series	Advertised Weight (g)	Comment
Schwalbe	One H 462a	25	Evo	215
Schwalbe	Pro One HS 462	25	Evo	225
Schwalbe	Durano	28	performance	405
Panaracer/ Compass	Cypres	32	Extra Leger	261
Panaracer/ Compass	Cypres	32	standard	285
Panaracer/ Rivendell	Nifty Swifty	34		406
Schwalbe	Kojak	35	performance	410
Schwalbe	HS 159	37	active	580
Continental	Tour Ride	37		580
Panaracer/ Pacenti	Pari-Moto	38		300
Panaracer	Gravelking	38		310
Panaracer/ Compass	Loup Loup Pass	38	Extra Leger	333
Panaracer/ Compass	Loup Loup Pass	38	standard	354
Panaracer/ Soma	B-line	38		380
Maxxis	Detonator	38		480
Panaracer/ Soma	Xpress	38		410
Panaracer	Col de la Vie	38		500
Panaracer	Ribmo	38		520
Schwalbe	G-One HS 473	40	evo	420
Schwalbe	Marathon plus HS 440	40	performance	920
Surly	Knard	41		465	knob
Panaracer/ Rivendell	Fatty Rumpkin	41	green label	480
Panaracer/ Rivendell	Fatty Rumpkin	41	force field	620
Panaracer/ Soma	Grand Rando	42	SL	300
Panaracer/ Pacenti	Pari-Moto	42		330
Panaracer	Gravelking	42		350
Panaracer/ Compass	Babyshoe Pass	42	Extra Leger	362
Panaracer/ Compass	Babyshoe Pass	42	standard	390
Panaracer/ Soma	Grand Rando	42	EX	390
Schwalbe	Marathon supreme HS 469	42	evo	470
Panaracer/ Soma	Cazadero	42		470	knob
Panaracer	Pasela	42	fold	480
Panaracer	Pasela	42	wire	520
Maxis	Overdrive	42		535
Panaracer/ Soma	Grand Rando	42	Blue label	610
Continental	Tour Ride	42		650
Panaracer/ Bruce Gordon	Rock n road	43		520	knob
Schwalbe	Marathon Cross	44	performance	620	semi knob
Schwalbe	HS 159	44	active	645
Schwalbe	Marathon HS 420	44	performance	820
Kenda	Kwick Journey	44		954
Kenda	Kwick Seven.5	45		834
WTB	Horizon	47		515
Panaracer/ Compass	switchback hill	48	Extra Leger	413
Panaracer/ Compass	switchback hill	48	standard	478
Continental	Race King Performance	50		580	knob
Schwalbe	Marathon supreme HS 469	50	evo	600
Schwalbe	Hurricane HS 352	50	performance	670	side knobs
Schwalbe	Big Ben	50	performance	745
Schwalbe	Marathon Almotion HS453	50	evo	750
Schwalbe	Marathon Mondial HS 428	50	evo	780	semi knob
Continental	Double Fighter III	50		845	knob
Schwalbe	land cruiser	50	active	900	semi knob
Kenda	Kwick Seven.5	50		950

Bike Frame Design – the influence of tubing diameter and wall thickness

The usual assumption is that significant part of the ride characteristics of a frame is determined by its rigidity. An excessively flexible frame feels inefficient for power transmission and can be more difficult to control on rough surfaces or with a load. On the other hand, an excessively rigid frame rides harshly, transmits shock and vibration to the rider, and feels less lively.

Custom builders talk about the importance of using the appropriate combinations of wall thickness and diameters for a particular rider and the use to which the bike will be put (but they usually keep their design procedures proprietary). Jan Heine advocates for the improved ride quality and desirable flex in a frame constructed of extra-thin-walled traditional-diameter tubing (Jan’s blog). On the other hand, some influential figures in the business of building steel bikes downplay the importance of tube diameter and/or wall thickness to the ride of a bike (Sachs in forum discussion, Gordon link).

It is difficult to make an objective judgment about the influence of bike tubing. There are design fashions and fads, the power of suggestion, and the placebo effect. There are also confounding effects of frame angles, chain stay length, fork design, individual fit, and tire characteristics. And it is difficult to get a statistically significant sample size, both in the number of human subjects and the availability of bikes that are identical except for the factor being compared.

Without objective experiment, all we have is experience. For decades, the standard high-quality bike frame was made of Reynolds 531 tubing. The usual combination was a 1” diameter top tube with 0.8 mm wall thickness on the ends and 0.5 mm wall thickness in the thinner (butted) section in the middle of the tube (.8/.5/.8) along with a 1 1/8” diameter down tube with .9/.6/.9 wall thickness and a single-butted 1 1/8” .9/.6 seat tube. There might have been millions (I am completely making up a number here) of frames built with these specifications by Peugeot, Raleigh, Schwinn, and a host of competitors. A bike built using this tubing was responsive and reliable, and could win races, tour the world, or get the rider to work in the morning. The comparable Columbus tubing was a little heavier. The Columbus SL sticker designated tubing with .9/.6/.9 top and down tubes, and Columbus SP was 1/.7/1.

Traditional alloy steel tube wall thickness. Numbers separated by a slash are butt thicknesses.

By the late 70’s, Reynolds advertised variations on the basic set of tubes with options for touring and larger frames. Heat-treated Reynolds 753 appeared in 1978, which was offered in wall thicknesses down to a .7/.5/.7 top tube and .8/.5/.8 down tube on road bikes; other tube manufacturers soon followed with their own heat-treated offerings. The mountain bike revolution created a need for steel tubes durable enough for the abuse of off-road riding, and larger-diameter tubing became available to fill the demand. Fat-tubed aluminum frames began to compete with steel. As tubing for mountain bikes and aluminum frames grew in diameter and  this look began dominating the market, the traditional tube diameters started to look oddly skinny by comparison, and road-bike builders began to use oversize steel tubing partly to fit that new aesthetic.

We are currently in a golden age for the hobby frame builder. We can buy quality steel frame tubing for road use in three different diameter standards. Traditional construction, as noted above, uses a 1” diameter top tube and 1 1/8” diameter down tube and seat tube. Oversize (OS) employs 1 1/8” top tube and 1 ¼ down tube; double oversize (2OS) uses a 1 ¼” top tube and a 1 3/8” down tube. The default for all three standards is a 1 1/8” .9/.6 single-butted seat tube, but there are a number of variations available. Wall thicknesses of .7/.4/.7, .8/.5/.8, and.9/.6/.9 are available in all diameters and 1/.7/1 is available in some sizes, along with variations on seat tube, seat stay and chain stay diameter and wall thickness. Fork blades are available from light to stout.

Standard steel bicycle tubing diameters. Red indicates traditional diameters; * indicates oversize (OS); ** indidates optional OS head tube and steerer; and + indicates double oversize (2OS). Sizes larger than 2OS are usually used for mountain bike or tandems.

In spite of all this variety, I have not found any analytical methods for helping choose tube diameter and wall thickness, or even any specific guidance on ride characteristics. Clearly, a heavier-wall tube is more rigid than a thinner-wall tube of the same diameter and same material, but how do tubes of different diameters and wall thicknesses compare?

In order to answer this question, I did some rough calculating. Deflection of a tube in bending is inversely proportional to the moment of inertia (MI) of a tube. The variable part of the MI is (D^4 – d^4) (where D is the outside diameter of the tube and d is the inside diameter). Using that as a basis, I created a stiffness ratio table (Table 1) for a range of readily available main tubes. It is common practice (and this shows in most Reynolds tube sets) to use a thinner-walled top tube than down tube, so there are nuances not shown in this table. However, this seemed like the clearest way to present the information.

Tube diameter is the most important determinant of rigidity, and there was only a little overlap in the rigidity of different diameters (less than I expected). Based on a averages across two tubes, traditional .9/.6/.9 is essentially the same rigidity as OS .7/.4/.7, and OS 1/.7/.1 is very similar to 2OS .7/.4/.7. The butted section of the smaller diameter tubes are relatively more rigid, so calling these as ties is a judgment call — for all I know, this average is meaningless because the ride characteristics are predominantly determined by one factor, such as down tube end thickness.

The heaviest 2OS tubing (1/.7/1) is about three times stiffer than traditional .7/.4/.7. In general, progressing from one rank to the next increases rigidity by 10% to 15%. The Bruce Gordon link above suggests that most of us would not notice a change in one rank level (although Jan Heine might disagree). I would speculate that it would be easier to detect a change in 3 ranks or more—traditional .7/.4/.7 should feel noticeably different than traditional 1/.7/1 or OS .8/.5/.8 with no other design changes.

Relative rigidity of steel tubing with specified diameter and wall thickness, ranked by average relative deflection across two tubes.

A critical piece of information in choosing frame tubes is the frame size. Deflection is proportional to the cube of tube length (based on the equation for deflection where loading is applied to the free end of a cantilevered beam). This should be a conservative approach, since frame tubes are part of a truss and not really cantilevered and torsional deflection is proportional to tube length. However, we still are not including the effect of increased weight of the rider.

The following chart (Figure 1) shows the rank (from Table 1) of top and down tubes that would be used to match the ride of a frame made of traditional tubing of specified wall thickness (everything else being equal) using the cube of the ratio of tube lengths.

If the ride quality of a 58 cm traditional-diameter 7/.4/.7 frame is desired, it is easy to duplicate in larger frames, but smaller riders are out of luck. A lighter seat tube and perhaps  a 1”  down tube might get close. On the other hand, the ride of a traditional 1/.7/1 frame can be duplicated in the full range of frame sizes. Using oversize tubing means that there is no need for lateral tubes or double top tubes on large frames even for applications that require extra rigidity.

Figure 1. Relative rigidity rank (from Table 1) that would approximate ride characteristics of a 58 cm frame constructed of traditional diameter top and down tubes of specified wall thickness.

Other posts on frame design:

 Bike frame design — the myth of vertical compliance

Bike Frame Design – strength of steel frame tubing

Carrying stuff: weight distribution and frame design

More thoughts on tubing specifications and ride qualities

Gearing part III: Gear sequence

The third installment of my gear cogitations addresses gearing systems and how to get low-enough gears without too much compromise.

First, let me opine that the great majority of cyclists do not need gears as high as stock gearing provided on new bikes.  In fact, most don’t need more than 100” ( the old-school 52×14, or with modern hardware, 41×11 ).   A 100” gear allows 27 mph at 90 rpm (27” nominal diameter wheel); most of us only hit this speed going downhill, and if the descent is too steep to pedal with this gear, it is more efficient to tuck.  This even goes for low-level competition cyclists.  As a category 3 rider, I once wore myself out pushing a 108” gear on a long downhill in a race, only to be passed and dropped by some of my teammates who had tucked on the descent and were relatively fresh for the subsequent long climb.  As for top speed and sprinting, a little practice gets a rider’s maximum cadence well about the 90 rpm that is sustainable for long periods — Charles Murphy set his paced record of 60 mph in 1899 on a 104” gear (at 198 rpm).  The 130” gear (52×11; 35 mph at 90 rpm) that comes stock on high-end racing bikes is good only for downhill sprints and for developing bad pedaling habits unless you can keep up with Mark Cavendish.  For touring and town bikes, a high gear of 85” is not unreasonable, though most of us will probably want to stick with 95” to 100” on the touring bike.

So here are my criteria for an all-purpose gearing system:

1)  As explained at length in the last post, with my topography, fitness level, and purposes, I like to have a low gear in the low 20’s or even lower.  People who live in flat places or who are strong climbers (and plan to stay that way) can adjust accordingly.

2) A high gear of 100” or a little lower works for me on the road

3) Gear ratios should be spaced closely enough to allow the rider to maintain a cadence within his/her comfort range throughout the gear range (or at least the most frequently used portion of the gear range).  As a reference, 5% steps are real tight, allowing a cadence that stays between 90 and 95 rpm.  Most of us are happy with steps of 10-15%.

4) There should be a logical shift sequence that is easily executed.  It used to be common for people to have a gear chart taped to their stems so they knew how to get to the next gear.  While it is not a bad idea to give some thought to how your gears are laid out, they should not require a map.

Figure 1. Hayduke diagram of 3-speed internally-geared hub with 44-tooth chainring and 19-tooth cog. 25% steps between gears; 178% total gear range.

Internally-geared hubs (IGHs) (along with single-chainring derailleur systems) have the simplest  shift sequence. 

Three-speed hubs have a relatively narrow range and large steps between gears, which is okay for flat areas, and IMO a lot better than single speeds.  I was happy with a 3-speed commuter bike when I lived in flatter places and had a higher level of fitness (and youth) than I do now.

Seven-speed IGHs have smaller steps and enough range for short trips in hillier areas.  I currently use a Shimano Nexus 7-speed on my commuter/utility bike geared down for the local hills.  High gear is 80″; low gear is 33″.

Figure 2. Hayduke diagram of my Nexus 7-speed internally-geared hub with a 42-tooth chainring and 22-tooth cog. Average 14% steps between gears. 244% total gear range.

The wide-range-double “compact” crank seems to be dominating the market.  This setup has a good range for many situations, though it does not go low enough for my purposes.  For me, the fatal flaw with this approach is the shift sequence.  The shift between front rings is big (30% or so), so usually when the rider make this shift,  it is necessary to correct 2 or even 3 cogs on back to get a reasonable-size step.  This shift is right in the meat of the riding range (50” to 80”) so the clumsy big front shift and rear correction happens frequently.  When I tried a similar arrangement, I hated it because the gear I wanted to shift into always seemed to require this awkward sequence of shifts.

Figure 3. Hayduke diagram of typical compact double with 48- and 34-tooth chainrings and 12-27 tooth 9-speed cassette. Gear range 108″ to 34″ (318%). Three pairs of near-duplicate gears; 13 usable unique gears. 7.8% average step between gears (neglecting duplicates).

Half-step gearing was once common and might still have some applications. In this context, “step” is the average percent steps on the freewheel; a half-step setup has approximately half the percent change between chainrings on the front as there is between cogs in the back. This may seem odd in these days of cassettes with a multiplicity of cogs, but back in the five-speed-freewheel days it made a great deal of sense.

In order to shift a half-step system sequentially, both front and rear derailleurs are used on half the shifts.

If the rider is on the big ring and desires a half-step lower gear, only the front derailleur is used since the front provides the half step.

On the other hand, if the rider is in the small ring and wants to go a half step lower, the rear derailleur is shifted down (one step) and the front derailleur is shifted up (a half step) for a net change of one half step down.

The sequence is mirrored for upshifts. This may seem counter-intuitive at first but becomes second nature with a little practice.

For many years, my touring bike had a 14-28 five speed freewheel and half-step-with-granny gearing with 28-46-50 chain rings. In practice, I stayed in the 46 chainring much of the time, but the availability of the smaller step was a real advantage now and then.

A clearer example of the usefulness of the half-step approach is a wide-range 14-34 five-speed freewheel. Shifts on this freewheel average 25% and the top two shifts are 29% and 28%. With half-step rings, the shifts are about 12%.

Figure 4. Gear chart (gear inches with nominal 27″ wheel) for 14-34 five-speed freewheel and half-step-plus-granny triple chainring gearing. Average step of 12% between sequential gears on large and middle chainrings,  526% total range, 12 usable non-duplicate gears.

Figure 5. Hayduke Chart for 14-34 freewheel with half-step plus granny gearing.

But the best way I have found to meet my gear criteria with more-modern equipment is the step-and-a-half triple with granny.  In this arrangement, the step between the big and middle chainrings is about 1.5 times bigger (in percent) than the steps on the freewheel.  For example, a 9-speed 13-34 cassette averages 11% steps between the cogs; 42- and 50-tooth chainrings are about 16% apart (note that since we are confined to integer number of teeth, this frequently needs some trial-and error to find a combination that works best).

Of course most riders are not likely to shift sequentially through the gears.  Usually, one would still use the chainrings as high-range low-range (with a double) or high-medium-low ranges (triple).  However, the  shift between chainrings is not as big as in a compact system, so you don’t need to correct as often on the cassette when you change chainrings; when you want the next sequential gear, you only need to correct by one cog.  The shift from the middle to small rings is still a big step, but this shift does not happen as often as the similarly large step between rings on a compact, because it is at the extreme of the gear range.

Gear chart (gear inches) for 9-speed 13-34 cassette with triple chainrings selected for step-and-a-half-with-granny gearing. Average step is 5.7%; gear range is 503%.

Hayduke chart for 9-speed 13-34 cassette with triple chainrings selected for step-and-a-half-with-granny gearing.

Gearing Part II: In praise of low gears

I may have mentioned in previous posts that there is some topography around here.  In town, 6% slopes are routine, 10% climbs are common, and there are even some block-long hills around 20%.  Rural roads are usually a little gentler, since lower road density allows routes that avoid the steepest hills, but there is little flat road and still plenty of 6-10% and steeper climbs. 

I am not as young (or as fit) as I used to be.   I don’t alway ride with the express purpose of causing myself cardio-vascular distress in an effort to recapture my lost youth.  I am formerly (I hope) handicapped by a bad heart valve, and occasionally get injured (the knee is healing up nicely, thanks for asking).

I like long rides.  Jamming up hills out of the saddle works for short trips around town or even relatively short rides in the country, but I don’t have the fitness (or probably the potential, much less the motivation, to develop enough fitness) to use this tactic for rides longer than 25 miles or so.

I like to be comfortable and reasonably safe on my rides, so my bikes will never be as light as a stripped-down racing machine. And on tour, I carry appropriate loads, including camping gear. I also like unpaved roads, though there is a lot more rolling resistance on them than on smooth pavement.

I am a spinner.  I tend to stay around 90 rpm on the flats (such as they are) and I feel best when I also maintain this cadence on climbs.  If I go much under 70 rpm it  feels like a grind, beats up my knees, and tires me quickly.

All of this has led me to install very low gears on my bikes and use them frequently.

 I consider myself a 100 watt cyclist (see this previous post) though I probably average closer to 125 watts these days.  Of course I can push it up higher for short periods or for training rides.  But I might also slow down and enjoy the scenery.  Pacing is important on day-long rides, and on a tour, you have to leave enough energy to set up camp, cook dinner, and do it all again tomorrow, and  35 watts gets you down the road.

So how low is low enough?  This table gives speed and gear as a function of slope and rider power output for a 175 lb. rider on a 25 lb. bike.

	100 Watts		200 Watts
Slope (%)	Speed (MPH)	Gear at 90 RPM (inches)	Speed (MPH)	Gear at 90 RPM (inches)
3	7.3	27	12.6	47
4	5.9	22	10.7	40
5	4.9	18	9.2	34
6	4.1	15	7.9	30
7	3.6		7.0	26
8	3.2		6.2	23
9	2.8		5.6	21
10	2.6		5.1	19

The lowest commonly-available low gear is 19 inches (24 tooth front, 34 tooth rear, 27 inch [nominal] wheel).  A fellow 100 watt cyclist runs out of gear (or has to reduce cadence) on a paltry 5% slope even with this gearing that is extremely low by current convention.    Even the 200-watt sportster who wants to maintain a good cadence on a long hill might find the usual 39×27 (39 gear inches)  or “compact” 34×27 (34 gear inches) too high for a mountain ride.   And this chart does not take into account  camping loads or rough surfaces. 

 The lack of low gears in hilly terrain can turn a pleasant rural ramble into a gruelling test of strength and endurance.  While I enjoy a little gruel now and then, it is nice to have options.  It would be difficult to have gears that were too low.

Bikes in the mix: Commuting mode

Transport Politic did an analysis of the latest US Census data on differences in commuter transportation mode between 2000 and 2009.   Their interests were somewhat broader than mine, and they make some interesting observations about how the presence of rail and recent investment in rail seems to have an influence on moving people toward non-auto commutes (I think that non-auto commutes, rail, and the political will to invest in non-auto infrastructure would be difficult to sort out in their cause and effect relationships).

But of course I zoomed in on that bike commute column.  It is interesting to see that Southern cities (TP saw them as “sprawling” cities, but they all happen to be Southern) saw increased auto share and small or negative transit and biking growth; this includes Memphis (no surprise).  Nashville saw an increase in transit use (new commuter rail) but I am surprised to see a decrease in biking with the visible bike activism there.

This makes Knoxville that much more remarkable.  I pulled up the same data for us, and biking increased 325% (if I calculated it the same as they did– percent increase of percent share) in the same period.  That beats everybody on TP’s list!   (I suspect that some of these results are statistical noise from small numbers and small sample size.  I look forward to seeing better numbers for the full 2010 census.)  The Knox TPO Bike Program has seen count increases that support the scale of this increase.

% Change in Mode Share, 2000-2009 in America’s Biggest Cities (from Transport Politic)
	Total Auto	Total Non-Auto	Driving alone	Carpooling	Transit	Biking	Walking
Austin	-5.1	4.5	-1.2	-25.2	12	11.9	-11.4
Baltimore	0.5	-6.6	11	-37.1	-12.7	200.6	0.7
Boston	-11.9	9.7	-10.9	-16.4	6.9	117.7	8.4
Charlotte	-3.7	24.3	-1.6	-16.2	8.5	3.6	59.4
Chicago	-6	4.1	1.4	-31.5	1.6	129.2	4.7
Columbus	0.3	-24	4.3	-29.1	-39.7	107.3	-18.6
Dallas	0.6	-20.8	10.8	-40	-28.1	9.3	-2.3
Denver	-2.4	-3.3	1.7	-23.3	-7.5	89.8	-15.5
Detroit	-3.3	7.8	4.1	-33.1	-12	192.4	58.4
El Paso	-2.4	14.4	4.3	-35	2.5	47.8	26.5
Fort Worth	-1.5	-16.4	4.7	-29.9	1.5	-18.2	-31.5
Houston	0.7	-23.5	5.3	-19.8	-33	-17.9	-0.4
Indianapolis	-0.3	-2.6	3	-21.8	-17.1	129.1	1.1
Jacksonville	-1.1	-11.3	0.4	-10.4	-18.5	-4.1	-4.7
Las Vegas	-0.1	-13.7	5.5	-27.5	-28.5	-10.7	18.7
Los Angeles	-3.6	9.2	2	-28.7	10.7	63.8	-4.2
Memphis	-1.5	-7.9	2.7	-22.2	-7.8	-78.7	-4
Milwaukee	0.9	-10.1	2.4	-7.2	-18.1	90.3	0.4
Nashville	-1.3	-13.4	2.8	-24.9	21.7	-23.3	-39.5
New York	-12.6	3.3	-5.6	-34.3	4	28.8	-1.1
Philadelphia	-3.5	1.2	4.3	-33.5	-2.1	150.7	-4
Phoenix	-1.2	-3.5	3.9	-22.3	-1.4	4.6	-9.8
Portland	-7.2	18.6	-3.3	-28.1	-6.4	230	6.3
San Antonio	-0.6	-9.9	4.2	-24.6	-12	-11.7	-6.2
San Diego	-1.5	-13.2	3.5	-31.4	-12.4	14.6	-19.6
San Francisco	-9.6	6.2	-3.9	-31	2	50.2	10.5
San Jose	-2.1	-2.1	0	-13.3	-21.3	43.1	32.8
Seattle	-7.7	12.5	-6.5	-14.1	10.9	59	4.4
Washington	-12.7	9.3	-5.1	-39.3	12	86.2	-5.9

 

Personal note:  After an MRI, the orthopedist sayst that the knee issue is a nasty bone bruise.  That means no surgery and no long-term problems, but it also means that it will heal slowly.  I don’t know how long I will be off the bike, but I am taking the opportunity to reacquaint myself with the local bus system.