home                    bicycle engineering

19 November 1989

In accordance with your request I examined, tested, modified and retested a Da Hon Folding bicycle similar to that which was involved in the Westcott accident. The results are reported below.


I examined the instruction booklet to determine how to unfold and fold the machine, and to determine the adequacy of the instructions. I rate the safety instructions as only fair because there are several errors. For example, under the subject of wet weather the rider is cautioned not to apply the front brake too strongly, lest the bicycle "flip forwards." This effect is far more likely to occur in dry than in wet weather, both because the brakes don't grip well against wet rims, particularly against wet chrome-plated rims such as those on the Da Hon, and because the front wheel is more likely to skid on wet surfaces than to flip the bicycle. In my opinion, it would be practically impossible to flip the Da Hon through excessive application of the front brake while it was raining. However, this caution appears only under the wet weather section, not elsewhere.

There is a general warning as to the kind of use for which the Da Hon is designed.

"This bicycle has been designed for general transportation and recreational use. It has not been designed to withstand abuse associated with stunting and jumping or organized competitive events. The user is warned that he assumes risk for injuries, losses and damage from such uses."

This warning conflicts with two other statements in the booklet. The booklet opens with the words:

"Congratulations, you have just acquired a high quality product made of the finest materials and parts....Since this bike has been designed to be light-weight and provide good riding quality to a wide range of people, it is mechanically more complex and thus requires more careful use and maintenance than other bicycles....Pay special attention to items denoted: (caution), (warning), and (note)."

The riding instructions contain a paragraph instructing the rider to get the feel of this bicycle:

"4.3 Getting The 'Feel' of the Bike
DAHON Folder is a high performance bicycle designed for both commuting and recreational use on paved roads. (Warning, fast riding on unpaved areas could result in mechanical damage and bodily injury.) Although DAHON Folder is easily ridden by people of various sizes and ages, it is necessary to first get the 'feel' of the bike to avoid unfortunate mishaps due to unfamiliarity. Take the bike to a flat, uncrowded area and test the steering, pedalling, and balance."

Just what is the DAHON? Is it to be used only gently because of its delicate folding mechanism? Or is it a high-performance bicycle? It is not to be used on unpaved surfaces, yet its wheels and tires are far stronger than those on racing bicycles. It is not expected to withstand what its manufacturer calls the abuses of racing, yet racing bicycles are delicate machines that the riders take great care of and ride very carefully. These conflicting statements in the instruction booklet show that the Dahon's manufacturers do not understand the bicycle business and the characteristics of the various types of bicycle that are available.


I inspected the Dahon bicycle. In that inspection I found the following notable items.
I removed the wheels to get the wheel covers off and inflate the tires. I removed the wheel covers, the reflectors, and the wheel cover clips.

The front hub was much too tightly adjusted, so I readjusted it.

The rear wheel is a beast to remove and replace, a difficult job when you have a flat.
The rear hub had no oil in it beyond the hub manufacturer's (Sturmey Archer) initial application. I oiled the rear hub.

The chain-wheel spider was loose on bottom-bracket spindle. I tightened it.

The rear hub shift cable adjuster was improperly assembled to the shift cable wire, so it kinked the wire badly. I soldered the wire close to its end, cut off its end cap, and reassembled it properly.

The Dahon, except for its unusual folding mechanism, is a typical cheap utility bicycle. The folding mechanism produces an unusual geometry of the front fork, with the upper steering bearing being about two inches behind the centerline of the steering column.

In fact, the Dahon is typical of a general class of bicycles, the small-wheel folding type. These are generally utility-grade bicycles that are a bit more expensive than others of that grade because of the folding mechanism. Their design limits their performance, so that they cannot be considered high-performance bicycles. Their utility and desirability depends only on their ability to fold. No person who had no need of the folding characteristic would consider them to be a good buy. So far as folding is concerned, and use in the folded condition (pushing, carrying, storing, etc.), the Dahon is ingeniously designed. Insofar as its other characteristics are concerned (except one that I discuss later), the Dahon is a typically-crummy utility bicycle.

There is one exception to my generalizations about these machines. The Moulton folding bicycle is an extremely good bicycle because it circumvents the difficulties that the folding mechanism imposes by ingenious and expert design, expensive production methods and good components. It costs about 5 times the cost of the Dahon.

The instruction booklet refers in an oblique way to the one outstanding characteristic of the Dahon (in addition to its folding mechanism, of course).

"Although DAHON Folder is easily ridden by people of various sizes and ages, it is necessary to first get the 'feel' of the bike to avoid unfortunate mishaps due to unfamiliarity. Take the bike to a flat, uncrowded area and test the steering, pedalling, and balance."


I did test the steering, pedalling and balance of the Dahon, first near the Hawkins office in San Jose and, later, near my home in Sunnyvale. The Dahon has the worst steering and balance of any undamaged bicycle that I can remember having ridden. I tried to ride it with my hands off the handlebars and wobbled all over the road. It took extreme wiggling of my pelvis to get any steering response at all, and after a few seconds I had to regrip the handlebars to stay upright. This is improper and unsafe handling behavior for a bicycle. The bicycle that I have ridden that had the next-worst stability to the Dahon was also one that had unexpectedly dumped its rider.


General Stability Considerations

Bicycles, automobiles and airplanes all are supposed to have stable handling characteristics. A stable vehicle tends to correct for the variations in environment or steering that may occur. An automobile should tend to steer straight and, when steered into a corner, should not make the driver's task more difficult by attempting to turn a sharper corner than the steering input that the driver has made. The characteristic that makes a car try to make sharper corners than the steering wheel is set to is called oversteering. The characteristic that makes a car try to straighten out when it is turned into a corner is called understeering. Engineers are universally agreed that safe handling requires a small amount of understeer and that oversteering is dangerous. Similar effects and opinions apply to airplane design. One of the factors that made early driving and flying difficult and dangerous was that early cars oversteered and early airplanes were unstable. In each case, the driver or pilot had to continually fight the machine to keep it on course. The theory of airplane stability was not developed until the 1920s by the NACA of the U.S.

Bicycle stability requires steady steering when going straight, steady steering when cornering, and correcting for undesired sidewards lean. When a bicycle is in a turn, it must lean inwards a precise amount that is determined by the bicycle's speed and the radius of the turn, according to well-accepted laws of physics. When it is going straight, it must remain upright, again according to well-accepted laws of physics. However, those laws also state that the bicycle must start to fall over to one side or the other because, being balanced on two wheels in one line, it is in unstable equilibrium. A cyclist will always start leaning to one side or the other of the proper angle; it is impossible for him not to. A bicycle is stable when it automatically tends to correct for this unwanted lean.

It is easy to ride a properly-designed bicycle without hands on the handlebars because the bicycle itself tries to correct for the inadvertent leanings that are impossible to prevent. When the bicycle leans to the right, the front wheel turns to the right so that the bicycle is again properly balanced, although it will be turning away from the straight course. This works both ways. When the cyclist wants to correct both this rightward lean and the turn to the right, he moves his pelvis to the left, thus tilting the bicycle to the left and persuading it to turn leftwards. This corrects the unwanted deviations in both course and lean. When the correct angle and direction have been achieved, the cyclist moves his pelvis to center position, causing the bicycle to straighten up. This continues until the cyclist notices that the bicycle has started to lean again, either to the right or to the left.

The cyclist feels this self-correcting feature. Because the bicycle tends to turn its front wheel into the correct angle, it pushes against the cyclist's hands if the cyclist is not placing his hands in the correct position. This is what engineers call feed-back. Because a bicycle has a direct mechanical connection between front wheel and handlebars, stability in a bicycle must produce feed-back. You can consider this in another way. Whenever the cyclist tries to turn the handlebars in an inappropriate direction the bicycle fights back by trying to maintain them in the appropriate direction. The ill-informed cyclist looks on this as difficult steering, because when he tries to steer by only turning the handlebars, which of course will make him fall, they feel stiff.

Automotive and aeronautical engineers have developed mathematical formulas by which they predict the stability of the vehicles that they design. However, no useful and accurate formulas have been developed for the bicycle. The formulas that have been developed all have serious deficiencies. This is because both the mathematics that represent what we do understand are difficult and because our understanding is imperfect. One large source of difficulty is that the cyclist, with his perceptions, movements and bodily flexibility, weighs 5 times more than the bicycle. Another is that the flexibility of the bicycle's parts is poorly accounted for. For whatever the reasons, we cannot, today, mathematically predict the stability of any particular bicycle design.

Despite the mathematical difficulty we build stable bicycles. Practically all bicycles on the market are stable, although to different degrees. We do this by the combination of traditional information and adjustment. Bicycle design is far more a matter of craftsmanship than of engineering. Bicycle designers have acquired a fund of information about the designs that work, and the ability to test prototypes and adjust their designs to obtain different degrees of stability.

While other factors must have some importance, the factor that seems most important is called trail, or trail distance. This is the distance that the point where the tire touches the road trails, in other words is behind, the point where the steering axis intercepts the road surface. The trail distance is produced by the interaction between the angle that the steering axis is backward from the vertical (the head angle) [actually, the head angle is measured most conveniently from the horizontal, not the vertical], the amount that the front fork blades are bent forwards of the steering axis (the fork rake), and the wheel diameter.

Since the pivot point is forwards of the place where the tire touches the road, the frictional drag of the tire tends to keep the wheel straight ahead. This is the same principle that keeps caster wheels pointing in the direction that you push an office chair or shopping cart. This trail distance also works when the bicycle leans over. If the bicycle leans to the right, the upward force of the road on the bicycle tire, the force that prevents the bicycle from sinking into the ground, moves to the left side of the bicycle and deviates from the steering axis. This tends to turn the wheel to the right, thus steering the bicycle to the side that is require to keep the bicycle from falling over. The greater the trail distance, the greater this effect. While our mathematics cannot predict the amount of trail that any design will require, we do know that increasing the trail increases the stability and decreasing the trail decreases the stability. Therefore, when a design shows an improper amount of stability, we know that the first corrective measure is to change the amount of trail. The easiest way to do this is to change the fork rake, although the designer may choose to change the head angle or, conceivably, the wheel size.

Changes in trail change only the stability; there is no other criterion that is bettered or made worse by such changes. Of course, when you change the trail by changing the rake (the amount of bend in the front fork blades) you move the wheel forwards or backwards. If you wish to maintain the same wheelbase, or the same distance between pedal and front wheel, then you must also move the head tube the opposite amount to compensate. This change is simple when prototyping a new model of bicycle, but it isn't practical when working on the bicycle that you own. Then changing the fork rake is the only practical way, and it produces a change in wheelbase.

Because steering angles and wheel sizes are pretty generally rather similar, different bicycles have similar trail distances. Trails run between 1-3/8" and 2-3/4". In general, racing bicycles have long trails while utility bicycles have short trails. The difference is that racing bicycles require great stability and are ridden by well-informed and skilled cyclists, while utility bicycles are purchased by less well- informed persons who dislike the feed-back to the handlebars that a stable bicycle produces and who don't like stability because a stable bicycle responds by steering to their inadvertent wobbles. Here is a table of the trail distances for different bicycles that I have measured, most of which I or other members of my family have owned.

 Bicycle Trail Distance
Raleigh Sports Utility 3-speed 1-3/8"
Peugeot touring with 650B tires 1-1/2"
Dahon folding bicycle 1-9/16"
Gitane Hosteller 1-7/8"
Raleigh International 1-7/8"
Holdsworth Italia Touring 2"
Minneapolis Wonder with original fork 2" approx
Viking Tour of Britain tour/racing bike 2-1/4"
Kvale racing 2-1/4"
Raleigh-made Huffy touring 2-3/8"
Minneapolis Wonder with replacement fork 2-1/2"
Ideor track racing 2-1/2"
Holdsworth Italia road racing 2-3/4"
Schwinn Paramount track racing 2-3/4"
 Elliott track racing 3"

Notice that the Dahon folding bicycle has a trail distance almost the smallest of any.

The Minneapolis Wonder has two entries, one for its original fork and one for its replacement fork. That is because with its original fork it developed front-wheel oscillation, one effect of insufficient stability, when descending hills with a camping load. Replacing the fork with one that had 1/2" more trail corrected that deficiency.

The two Holdsworth bicycles are made to almost the same dimensions because the touring bicycle that I first purchased fitted me so well. The only differences are that the racing bicycle has a slightly shorter rear triangle and 3/4" less rake to the front fork, thus producing 3/4" more trail. Both are stable, but the racing one is more so and it feels that it corners just as you think about taking the corner. You don't have to worry about how that bicycle will handle when you round a difficult corner in the midst of a racing pack. The track racing bicycles give the same feeling.

By and large, the bicycles on this list increase in stability as trail increases. Two other illustrations of the importance of trail are the independent experiments of David E. H. Jones and John Corbett. Jones built a series of bicycles that he hoped would demonstrate important factors in stability by being unridable. The one that was most difficult to ride, being almost unridable in Jones' experienced hands, was the result of a series of experiments and had negative trail. As Jones remarks at the close of his paper (Physics Today, April 1970, 34-40):

"It seems a lot of tortuous effort to produce in the end a machine of absolutely no utility whatsoever, but that sets me firmly in the mainstream of modern technology. At least I will have no intention of foisting the product onto a long-suffering public in the name of progress."

Corbett, a professor of mathematics and bicycle frame builder, built an experimental bicycle whose front fork could be adjusted to provide trail from -7/8" to +4-5/16".

"He found that the steering characteristics fit into the pattern described above, i.e., with trail in the low forties [approx. 1-5/8"] the bike felt nervous, with a trail of 55 mm [1-3/16"] it had the sort of hands-off stability which seems desirable yet still turns easily, and with a trail of 74mm [2-15/16"] it was very heavy feeling." (Chris Kvale, A Fresh Look At Steering Geometry, Cycling U.S.A., Feb 1981)

Stability of the Dahon Bicycle

As discussed above, no one can demonstrate by mathematical analysis whether the 1-9/16" trail distance is too little, just right, or excessive for the Dahon bicycle with its unusual geometry. However, it is easy to ride test the Dahon to determine whether it has proper stability and to modify the trail to improve its stability if that proves necessary. Its designers first selected a very small trail which might well cause trouble and then apparently failed to make the necessary tests.

Near the low-trail end of the scale, the Dahon's steering feels very light, but it also feels as if it doesn't know where it is going. It has practically no self-correcting action, so it requires that the rider continually pay very strict attention to it to keep it on a straight course, and it won't respond when the cyclist leans the bicycle. The absence of feedback through the handlebars means that the cyclist has to use some other means to learn which way, and by how much, the bicycle is leaning or deviating from course. This probably means that the cyclist has to do this by using his eyes, which would be effective only when looking ahead. Therefore, whenever the cyclist wants or needs to look in any other direction, he or she is much more likely to let the Dahon steer to one side or the other, an action that, if not immediately corrected, will make the cyclist fall. Chris Kvale makes this point from experience about several Italian road-racing frames that he considers to have too little trail for the type of riding they are used for.

"The question then is, how do the Italians get away with building frames with steep head angles and relatively large fork rakes with consequent little trail. [Colnagos typically have 1-5/8" 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 from the front." (Chris Kvale, A Fresh Look At Steering Geometry, Cycling U.S.A., Feb 1981)

It is my conclusion, based upon my education in physics and engineering, my experience in cycling, my reading, and my test riding of the Dahon, that it is dangerously unstable.


I changed the Dahon's trail distance by changing the rake of the fork blades. This required removing the front wheel and brake and applying a brazing torch to each fork blade in turn while I applied a bending force with a wrench-like tool. I did this in steps and test rode the bicycle at each step.

Original trail distance 1-9/16". Bicycle handled very badly, wobbled all over the road when I tried to ride without hands. Requires extreme movement of pelvis to get any steering response, and then that is uncertain and inconsistent.

Trail increased to 2". Rode much better without hands.

Trail increased to 2-1/4". Rode better still - no longer have to wave hands about to make it steer.

Trail increased to 2-3/4". Almost reasonable handling - almost like a touring bike.

It is quite obvious that the designers of the Dahon either failed to understand the danger of the instability that they referred to as the unusual 'feel' of the bicycle, or did not perform during the design stages the simple tests that I performed on the production model. Had they done so, they would have produced the bicycle with greater trail to improve the stability and handling.

It must be remarked that the Dahon, as I have modified it, will no longer fold properly. This is because the front wheel is now more than one inch rearwards from its original position. Had the designers made the changes in the prototype, they would have lengthened the main structure by this amount, so the wheel would have been in the original position. Then the bicycle would have folded properly even though the trail had been increased.

Respectfully submitted,

John Forester, M.S., P.E.
Cycling Transportation Engineer


Jones, David E. H.; The Stability Of The Bicycle; Physics Today, April 1970, 34-40

Lowell, J. and H.D. McKell; The Stability of Bicycles; Am J Physics, Dec 1982, 1106-1112

Kvale, Chris and John Corbett; A Fresh Look At Steering Geometry; Cycling U.S.A., Feb 1981

Papadopoulos, Jim, Post-Doctoral Associate, Cornell University; Personal conversations concerning the Cornell Bicycle Research Project, to which I am an advisor.

Return to: John Forester's Home Page                                        Up: Bicycle Engineering