Saturday, June 26, 2010

The Potential Kvale

I am planning on having a bicycle built for me by Chris Kvale next Fall. I could have a frame made by a number of up and coming builders, the young turks do beautiful work. Though they are fine craftsmen, Chris is too, and the following is what sets him apart from the less experienced builders. I was going to just post a piece of this and a link, but I just love this stuff. So pardon the length. 

A Fresh Look at Steering Geometry 
By Chris Kvale and John Corbett

The following is a revision of an article publishing in CYCLING USA, February 1981. Although the references are dated, the basic concepts are still valid.

It's the motor that counts, of course, but a bicycle frame that gives optimum handling characteristics for a given event will increase efficiency and, therefore, performance. One area of frame design which has often been misunderstood because of lack of information, misinformation, and general confusion is front end design--specifically the relationship between head angle and fork offset. With the advent of high-quality American-made frames available throughout the country, it is important for the rider to understand some of the factors which will affect his choices in geometry. The following discussion, based on several years of original and secondary research, will illustrate the complexity of the problem and lead to some tentative conclusions.

Current References

The most frequently repeated myth regarding head angle and fork offset is the notion that "neutral" steering, thought to be ideal, could be described by a formula which relates them to trail, resulting in a frame that neither rises nor falls as the wheel is turned. (Rising or falling, in the following discussion, refers to the front of the frame, specifically the top of the head tube.) The alleged upshot is called "neutral" steering and is thought to be ideal. This formula was developed by A.C. Davison in CYCLING in 1935. He had discovered that when rake (offset) equals trail, the frame does not rise or fall when the wheel is at 90°; he assumed that the frame was not rising or falling while the wheel was being turned. However, the frame does rise or fall while the wheel is being turned to the 90° position, and this can be proven mathematically. At 73°, the Davison formula would give an offset of 50.8mm; with this offset, the frame would drop 3.65mm at the 60° point. In fact, the front of the frame will always drop unless the offset is far longer than would ever be used; i.e., at 73°, an offset of 104mm would be required--at this point, the frame doesn't fall, it rises. With all steering geometries of practicable design, the frame will drop as the wheel is turned. However, the most important point to understand about the Davison formula is that its relationship to "neutral" steering is purely coincidental. In the 1930's, head angles were flatter and the Davison formula seemed to give a satisfactory explanation for a very stable-feeling frame. For example, for a frame with a head angle of 71° and an offset of 57mm, the trail of 57mm would give this frame a very stable feeling which some might describe as "neutral." However, with 74°, a fork offset of 48mm yields 48mm trail, and most riders would find this a little on the sensitive side and far from what would be described as "neutral." The fact is that the amount of trail by itself seems to be the primary operative factor affecting steering and the Davison formula would vary the trail much more than experience indicates, especially with steeper head angles.

The fact that bicycle design is an incredibly complicated business is well-illustrated by David Jones in PHYSICS TODAY (April 1970). Using a computer and advanced mathematics, Jones has probably produced the most accurate and authoritative formulas governing bicycle design and, amongst other things, disproved the myth of the magic formula for head angle and fork offset which results in a frame which neither rises nor falls as the wheel is turned. He also makes the point that it is impossible to attempt to isolate one factor of frame design from the others and predict changes in performance and handling by dealing with that single factor.

In their authoritative book, BICYCLING SCIENCE, ERGONOMICS AND MECHANICS (MIT Press 1974), Frank Whitt and David Wilson treat steering geometry with a page and a half and one table, an indication of the paucity of information on the subject. However, they do stress the extremely important point that the person-machine relationship is so complex and so variable that mathematical models and absolute statements are, at the very best, only a rough guide.

Unfortunately, myths die hard. The Davison formula continues to pervade recent references on frames and frame designs. Some authors mention it by name, others by referring to it but without discussing it at all. Adding to the confusion surrounding the topic, some authors have introduced the ill-defined terms "understeer" and "oversteer." Generalities abound: "...steep head angles and short fork rake result in quick and nervous handling...," "...if the angle is too steep and the rake is very short, the steering will be ultra-sensitive..," and "...a longer rake will also tend to be more stable..." A lot of the current references seem to be repetitions of long-held but unsupported beliefs. However, the fact that something is amiss is recognized in that at least two of the current authorities realize that "neutral" steering does not seem to fit today's frames: one suggests that "oversteer" is desirable for a racing frame and the other observes that "the trend is away from the neutral or near-neutral steering geometry of the past."

Original Research

The reader should keep four important points in mind during the following discussion: (1) The research and conclusions are based on middle-sized frames, about 52 to 62 cm, and that frames towards the ends of this range are more difficult to design to accommodate the rider's body while maintaining desired handling characteristics. (2) As some of the far-sighted authors have noted, this is a complex situation and no one factor should be totally isolated. (3) The conclusions are made for normal riding speeds; at very low speeds, the trail does not seem to have the same effects. (4) The research and conclusions are based on unloaded frames (racing frames) and do not apply to loaded touring frames.

As indicated by the trend of previous research, the relationship between head angle and fork offset, resulting in trail, is probably the most important factor in determining the steering characteristics of a frame. The other factors which appear to have some effect are, in no particular order, bottom bracket height, front wheelbase (bottom bracket center to front axle), overall wheelbase, and the resulting weight distribution.

One of the first things Corbett and I (Kvale) did was to accurately measure six frames with which I was intimately familiar. Three were Italian--a Cinelli road frame, a Masi road frame, and a Cinelli pursuit frame; three were American--a custom track frame, a custom criterium frame, and the first frame I built. I found that the two frames which gave the greatest hands-off stability and still responded quickly were the track bike and my frame; both of these frames have a fork trail in the low sixties. The Cinelli and Masi road frames, with trail in the high forties, steered lightly and easily, but neither was exceptionally easy to ride no-hands. The Cinelli pursuit frame I rode several years on the road as a five-speed time-trial bike; it was extraordinarily stable no-hands, but was very heavy in the corners--seeming to require actual physical steering rather than mere leaning. It is important to note that this bike handles perfectly in its event--steady track time-trialing; it has a large amount of trail which makes it easy to stay right on the pole line without wandering around the sponges. Although the American-made criterium frame had the right amount of trail to predict stability and ease of no-hands riding, it was squirrelly--even hands-on. The problem was, I think, that the top tube was too short and the short front wheelbase moved the center of gravity so far forward that it had an adverse effect on steering. 

From these and many other bikes I've ridden, I've come to the conclusion that the optimum trail for a racing or sport frame should be in the high fifties to low sixties. I would describe this trail as giving stability which enables the bike to be ridden easily under the most adverse conditions--crosswind and uneven road surface--but still allows a feeling of agility in steering. The rider will not be riding no-hands, but this kind of stability tends to keep the front of the bike from wandering around, which requires energy to correct regardless of whether the rider is aware of it and this would contribute to fatigue in a long road race. This stability also enables the rider to easily take a hand off to reach into a pocket, grab a bottle, look over his shoulder at traffic, and so forth, while keeping the bike in the same line.

Since constant trail can be maintained while juggling the head angle and fork offset, it is necessary to understand what effects those two factors have with constant trail. Flatter head angles (72-73°) require a longer fork offset to maintain trail; this combination is more comfortable on rough roads, but does not seem to sprint or climb as well as a steeper head angle-less offset combination since the wheel is farther in front of the rider. In out-of-the-saddle sprints, the front wheel seems to go farther side-to-side with each leg thrust than with the latter combination. On the other hand, the steeper (74-75°) head angle-less offset puts the wheel more underneath the rider. In a violent sprint, this combination seems to have a feeling of pivoting and going less far from side-to-side with each leg thrust. The trade-off, of course, is comfort. The steeper head angle-less offset will transmit more road shock to the rider's body with consequent fatigue. For the rider who wants a frame for most road events, a compromise of 73-1/2° seems to be adequate for criteriums without being unnecessarily fatiguing in long road races. Many riders specializing in shorter events feel that compromises for the sake of comfort are unnecessary, but they should remember that a frame which contributes to fatigue probably diminishes performance.

Although head angle and fork offset combinations affect comfort, it is also important to realize that the type of materials with which the frame is made have a great effect on feel and handling, especially on rough roads or in a sprint. For instance, a fork made of Reynolds 531 narrow oval tubing (old style) with a standard forged fork crown would probably flex much more side-to-side in an out-of-the-saddle sprint than would a fork of identical geometry made of Columbus SP (comparable wall thickness) with an investment cast crown.

It is a mistake to attempt to judge the amount of fork offset by sighting the fork from the side. Many Italian frames made with Columbus tubing appear to have little fork offset, but this is an optical illusion caused by a very gradual curve of the fork blade as supplied by the Columbus factory. Some of the curves in the Reynolds blades supplied by the factory are much sharper, and a fork built with these could appear to have much more offset but actually have significantly less.

The question then is, why do the Italians build frames with steep head angles and relatively large fork offsets with consequent little trail? (Colnagos are typically 74-75°, 50mm fork offset, and 42mm trail.) It seems that the bottom bracket height contributes to--and complicates--the problem of stability. Most Italian racing frames have medium-low bottom brackets, usually around 70mm drop--about 10.55 inches from the ground, and it is probably this fact which helps compensate for the relative lack of trail. Nonetheless, most of these frames are still a little on the nervous side and tend to wander a bit when one's attention is taken off the front. Most of them are more difficult to ride no-hands under adverse conditions than many American frames, which tend to have shorter top tubes and less fork offset. This again illustrates the interdependence of all aspects of frame geometry and raises another important question: how does a frame with solid no-hands steering stability still handle quickly? Keeping the overall length of the frame down, especially the front wheelbase, seems to promote quick handling, It is very important at this point to distinguish between "light" feeling and responsive handling. A frame with fork offset in the forties will often feel very light and quick-steering; a frame with fork offset in the high fifties to low sixties will be more stable yet still very responsive without being nervous if the top tube is relatively short in proportion to the rider's torso.

An interesting illustration of this point was made with a homemade frame which Corbett repaired. Since the front triangle had to be removed from this frame, the owner decided that this was the time to shorten the top tube, and Corbett shortened the top tube 4.5cm! The head angle and fork offset were maintained, but the new shorter frame differed markedly in its handling, becoming more responsive.

One of the other experiments Corbett performed was to build and ride a fork with an adjustable wheel position. By fixing the head angle and changing the fork offset in 18mm increments, he was able to ride one of his bikes with trail from -27mm to 110mm and to evaluate its steering characteristics. He found that the steering characteristics fit into the pattern described above: i.e., with trail of less than forty, the bike felt nervous; with a trail of 53mm, it began to exhibit the sort of hands-off stability which seems desirable yet still turns easily; and, with a trail of 72mm, it had a very heavy feeling. Again, it is important to note that the weight distribution will change as the wheel is moved in the fork, and this probably has an effect in addition to the difference in trail.

With all this in mind, are there any conclusions which can be drawn which would be useful? The answer is probably yes; it seems to be that for middle-sized frames, the head angle-fork offset combination which gives a trail in the high fifties to low sixties will give a no-hands stability which is desirable for a racing or sport frame. The angle will be chosen for the event, but it is quite possible to make an entirely satisfactory compromise.

The authors: Chris Kvale raced from 1965 through 1987 and has been building custom racing, sports, and touring frames since 1975. John Corbett, who teaches mathematics at the University of Minnesota, built a number of custom frames and studied frame design intensively at the time this article was written, in 1980.

1 comment:

Unknown said...

A quick note I will follow up with numbers later, my young daughter is learning to ride sans training wheels. I was given by my sister the bike I had purchased for her in 1977, a Raleigh Mountie, same basic design as I had learned to ride in 1964 and I am sure predates that, it has a slack head angle and generous rake. She did not like the styling, and got as a gift a new 20" wheeled bike, steeper head angle and visually less rake, much more nervous overall. I have here riding the older bike, after much explaining that it would be easier to learn on, she is riding. I will report back with the real numbers, but I find it interesting that the styling precedes function on many of these kids bikes that will be their first experience on two wheels.