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.

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.

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). Traditional 1/.7/1 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). I might note that traditional 1/.7/1 is not readily available, probably because of that redundancy.

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 13% to 19%. The Bruce Gordon link above suggests that most of us would not notice a change in one rank level (although Jan Heine would 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 OS .7/.4/.7 with no other design changes.

Table 1. Rigidity index relative to traditional .9/.6/.9 tubes

Table 1. Rigidity index relative to traditional .9/.6/.9 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.
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.

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.

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.

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A new bike for me

My touring frame is a bit long in the tooth, having been built in 1978.  It was the first frame I built. It has never gotten a proper paint job and is suffering some from rust, although not as much as one might expect. Damage and changes over the years make it less reliable for a long trip. It also has a few design quirks that I would like to correct.

So I built this new frame. It has a standard touring design of 72° head angle and 73° seat tube angle. It has a fairly low bottom bracket for stability. Tubing is on the stout side for durability and rigidity with a load on rough surfaces. There is plentiful clearance for 42 mm tires.

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The Rohloff 14-speed hub with Paragon sliding rear dropouts is one feature that is a little out of the ordinary, but the biggest deviation from standard design is the long chain stays.

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Most production touring bikes have chain stays no longer than 18” (460 mm) or so (for comparison, a competition bike’s chain stays tend to be about 16” (406 mm) or a little shorter).

The longer stays on a touring bike allow the panniers to be mounted far enough behind the rider to provide clearance between the rider’s heels and a loaded pannier while pedaling without forcing the weight of the load too far behind the rear axle. It is possible to mount a rack and panniers on a bike with short stays in a manner that allows the rider to pedal without kicking the luggage on every stroke, but a load cantilevered out in space behind the bike tends to pick up the front wheel. This messes with the weight distribution, which results in vague, unstable, and/or wobbly steering. At best, this change in handling is something the rider has to get used to; at worst, it is downright dangerous. I would theorize that the tendency for Americans to try to tour on bikes with short chain stays had a lot to do with the shift in fashion from rear loads to front loads.

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The 21” (535 mm) chain stays on this frame place the center of a loaded pannier about an inch in front of the rear axle. There is almost no change in handling when a 50 lb. load is placed in the bags.  The stout Tubus rack also contributes to this loaded stability.

I went for a classic British three-speed aesthetic.  Most made it to the US in black, though several other colors were available. A steel VO stem and a steel Campagnolo Sport crank (manufactured briefly in the early 1970’s) fit in with the “all steel bike” theme, as do the SPD pedals styled to look like rubber pedals. The road handlebars spoil the look somewhat.

The bike hit the road in August, 2014, and it has been in regular use as a commuter/utility bike since. I have ridden it regularly on weekend excursions and two camping trips.  I am very happy with the design and, for the most part, the components.

More details than anybody cares about will follow.

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A few photos

Cades Cove on a bike camping trip last fall; a back road on an early spring day; and a new frame for Hayduke.

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A Few Changes

In the last year, I have had two significant career changes.  In February of 2011, I was assigned to work on a nearby environmental clean-up project.  I don’t want to be coy about this, but I don’t want to give the impression that I speak for my employer (now former employer), nor is this the appropriate forum to describe the internal workings of the project, since there are several law suits pending.

The project is located about 45 miles from home, so cycling to the site was out of the question, at least on a daily basis, so I did more driving than I have for years.  Fortunately, I only needed be at the site two or three days a week and I mostly worked out of my downtown office.  I eventually got access to an assigned car, and the ride to pick it up was an opportunity to add a few commuting miles.

Somehow this change in routine, along with the mental exercise of tackling work that I was not all that familiar with, took much of my mental energy.  Blogging frequency suffered, as did other volunteer commitments. Even though I spent much of my transportation time thinking about writing, it seldom made it on the page.

The cleanup project was a great professional experience.  I learned a lot and worked with some great folks.  However, I was not that passionate about the work, and it was a temporary assignment.  At its close, I would have to find a new niche and develop new skills to match.

This was not to be, as it turned out, because a new employer offered me a job with significantly increased responsibilities and an opportunity to work on issues that I really care about, and even to have significant impact on those issues locally.  I started the new job just last week.

This job will consume my mental energy to a much greater extent than the last job change.  I have lots of stuff to write about, including a frame building project and a bike camping trip, along with the new challenge of bike commuting to a coat-and-tie kind of job.  But I suspect that the demands of the job will make me scarce in the blogosphere.

One of the original excuses for starting this blog was to pass on the experience of heart valve replacement and recovery.  Almost two years out, I feel fully recovered, although my sternum still feels less than whole sometimes.  Because of injuries and illness, I have not had a good season of training (to the extent that you can call what I do “training”) since the surgery, so I do not yet have a complete before-and-after comparison of speed and endurance.  The best comparison I have so far is the fall century that I completed this year right at seven hours, about six weeks after the orthopedist let me back on the bike.  The last time I did the ride before surgery, I did it in 7 1/2 hours.  The surgery did not make me 25 again as I secretly hoped (I could have done it in five hours or so back then), but there is a definite improvement in performance and energy level.

The broken arm is not yet completely healed.  I have full mobility and good strength, but the latest x-rays show that the bone is not entirely fused.  I need to be somewhat careful with it, so the mountain bike is still off limits, even though there has been an incredible growth in  trails available with connections only about a mile away from my house.  A piece of advice here: don’t break your arm

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An Experiment in Frame Geometry

My utility bike is a 1974 Schwinn Sports Tourer. It has a straight gauge chromo frame with fillet-brazed joints. The frame design could have come out of the Rivendell catalog: low bottom bracket, moderately long chain stays, and 73 degree head and seat tubes.

I bought it off Ebay in 2003 or so. I converted it to a 7-speed internal hub and added fenders and lights and other utilitarian stuff. It has averaged more than 1500 miles per year since then, commuting to work and running errands.

The bike has a few faults. One is that a 35mm tire is a tight fit laterally in the fork – the sides of the tires tend to rub on the fender and/or fork blades if everything is not set just so.

The second fault is that it rides harshly over bumps, even with 35 mm tires. I would ascribe this to the relatively stout straight-gauge tubing used in the frame. My sportier bike,  with steeper angles, shorter chain stays, and narrower tires but built with standard-gauge butted tubing, is much more forgiving. It is unclear from the information out there whether the Schwinn fork is chromo, but the rear triangle is reportedly plain carbon steel.

And the third problem is that the bike cannot be ridden no-hands at any speed because of a serious shimmy.  This shimmy damps out even with light hand contact on the bars, but it is a significant annoyance.

My theory (at least I have not found anybody who states it exactly this way) is that shimmy in bikes, at least in many cases, is a harmonic phenomenon something like a torsion pendulum, with the trail of the fork, which tends to make the bike go in a straight line, acting as the spring. In a torsion pendulum, the frequency of oscillation is determined by the stiffness of the torsion spring and the moment of inertia of the system.

Bikes are a little more complex than the simple torsion pendulum example, because there are two mass/moment of inertia systems influencing the oscillation. The first is the obvious one: front wheel, tire, any luggage on the front — everything that pivots around the steering axis. The second mass and moment of inertia system is not so obvious. Because the head tube moves side to side as the as the fork is turned, all of the mass of the bike that does not pivot around the steering axis pivots instead around the contact point of the rear tire. This means that the frame, rider, rear luggage, back wheel, and any other paraphernalia influence any oscillation, with mass closer to the front of the bike or extending behind the back wheel (and thus farther from the pivot point) having greater moment than weight directly over the back wheel.

In this conceptual model, shimmy occurs when the front (pivoting around the steering axis) moment of inertia/trail system has a similar natural frequency of oscillation as the back (pivoting around the rear tire contact point) moment of inertia/trail system. Since these two systems are so different, it may also be that oscillation will occur when harmonics are similar.

I don’t know a definitive way to test this theory, but if it is a good model, changing weight distribution should affect a shimmy, as should changing fork trail without changing weight distribution. I have had experiences when changing weight distribution seemed to cause or eliminate shimmy, though other times the shimmy seemed to be insensitive to changes. The Schwinn does not have racks or baskets on the front, so I can’t change loads there, but the shimmy does not respond much to a wide range of loads on the back. I have tried added damping by adjusting the headset too tight with no change. The shimmy persists with tires from 28mm to 35mm and different front hubs.

I decided what I needed was a new fork. The fork crown would be wide enough that there would be no problem with the 35mm tires. The blades would be mid-weight chromo to see if the over-bumps-ride ride would improve over the unknown material of the original fork. And I would try a low-trail design, as championed by Jan Heine of Bicycle Quarterly (here, for example).

Here are the results.

Problem 1: Solved. There is now plenty of clearance.

Problem 2: With the new fork, the bike rides only marginally better over bumps (based on subjective observation), even with the greater offset. Maybe a fork built with lighter fork blades would have enough more give to make a difference, but I think that would be inappropriate for a bike that gets this much abuse. Then again, maybe I will try it someday just to see how much difference it does make. Anyway, the bike got a new sprung Brooks saddle to handle some of the jarring, but that does not help my hands.

Problem 3: The finished fork results in about 25mm of trail, which is at the low end of accepted practice. Somewhat to my surprise, the handling did not change all that much. It feels quick and maneuverable at low speeds and it feels a little twitchy at downhill speeds, but it still in the range of what I would call normal.

The bike now has much less tendency to shimmy – reducing the trail seems to have worked in that regard. If the above theory is correct, increasing the trail should have also worked.

And for a bonus, I discovered that brazed-on centerpulls do indeed have a nice solid feel. But this mounting did not make enough difference in braking to make up for the trouble of making the mounting studs.

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A Visit to Portland

Portland is a wonderful place. Everybody knows it is the one of the best (link) cities if not the best city (link) in North America for cycling. The relatively compact development patterns (for a US city) means that distances between trip generators and destinations are small enough to make cycling practical for a lot of people. And there has been a lot of effort expended to create bike-friendly infrastructure.

It’s also one of the best cities for mass transit (link), and includes real trolleys (with real steel rails) in the transit mix.

There is a little bit of a potential conflict here, as I discovered on a recent visit.

My wife and I visited Portland recently, arriving May 19 for a two week visit to various Oregon destinations. I grew up Oregon, and some of my old friends have ended up in Portland, so I was planning to do some visiting, in addition to getting reacquainted with the city.

The first full day there, my wife was suffering from the remnants of a sinus infection and jet lag, so I left her at the hotel (recommended) and took the trolley to walking distance from the nearest bike rental shop . They set me up with a serviceable hybrid, and I took to the streets.

It was a short ride to the river. After rolling along at the riverfront MUP for a while, I got onto the street again. I made a left turn onto a one-way street, looked over my right shoulder to check traffic before getting into the right lane, and Crunch! I was down hard. I failed to notice that there was a trolley track in the street that I just turned onto. I somehow made it to the sidewalk and called 911. It was clear that my left arm was broken.

Surgery to install plates and screws and two nights in Good Samaritan (also recommended if you have the misfortune of needing their services) later, I was back on the street. The rest of the Oregon visit was less active than originally intended, but visits with family and friends (through the pain-med fog) meant that it was far from disappointing.

The hard cast came off July 11, the eighth week after the incident, and I wore a brace and did physical therapy for few weeks. I got permission to get back on the bike after eleven weeks (August 5). I am now in the 16th week of recovery, and things are getting back to normal. The arm still ain’t quite right, but it’s getting there.

I love Portland, and I even love the trolleys.  The bike/trolley conflict is an open issue. For a first step, a little more warning would be nice.  A few more signs like this might have saved me some pain and suffering.  If you visit (or if you live there) just be real aware of where the tracks are.

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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 what comes stock on bikes these days.  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 team mates 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 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 and 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 than I do now. 

Seven speeds 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).

The best way I have found to meet the criteria I laid out above 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 12-27 cassette averages 10% steps between the cogs; 39 and 46 tooth chainrings are about 15% 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).

Figure 4. Hayduke chart for step-and-a-half-plus-granny gearing system. 20-36-45 chainrings and 12-36 nine-speed cassette. 15" low gear to 101" high gear (675% range). 7.4% average step between gears on middle and large chainrings; 14% maximum step. 24 usable non-duplicate gears.

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.

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