Experiments with steering geometry
© Tony Foale. 2000-2018. (The experiments were conducted around 1982/83.)
Rake
The author’s ideas mentioned in other articles in relation to the angle of the steering axis (rake) were subsequently put to the test by modifying a readily available standard production machine – a BMW R75/5. There were two advantages in the choice of this machine.
Firstly, the offset of the wheel spindle from the steering axis is divided almost equally between the offset in the yokes and that of the wheel spindle from the centre line of the fork sliders (figure A.1); the importance of this will become obvious later.
Secondly, the BMW was large and fast enough to make the results meaningful, which might have been less so with a slow, lightweight machine such as a moped. To keep other variables to a minimum, the original frame and suspension were retained and the wheelbase remained unaltered. Two non-standard rake angles were tried, 15 and zero degrees. In each case the trail was kept to approximately the same as the standard value (i.e. 3.5” in.).
Fig. A.1 On the BMW R75/5, the total offset (wheel spindle from the steering axis) is divided approximately equally between that in the yokes (steering axis to fork legs) and that in the sliders (fork legs to spindle. This feature made these forks ideal for the tests as explained in the text.
The first alternative set-up tried was with a rake of approximately 15 degrees and almost nil offset. This was achieved by bolting a superstructure to the frame to support the new headstock (see photo) and reversing the yokes; since their offset is very close to that of the wheel spindle, the overall offset was reduced virtually to zero. For the second setup, the rake was close to zero (i.e., vertical steering axis). This was achieved by reversing the complete front-fork assembly, thus giving the negative offset necessary to maintain the standard trail. The new headstock was supported by an extension of the original superstructure. In both cases the handlebar was pivoted in the usual place and connected to the fork by a ball-jointed link; a side effect of this was an adjustable steering ratio – i.e., for a given angle at the fork the angle needed at the bar could be varied. With the 15-degree rake the bike had full road equipment, including lighting, so that it could be ridden under everyday conditions; indeed, five riders covered nearly 2000 miles between them, including wet and dry going, bumpy country lanes, London traffic and motorway trips. Throughout this period, no steering damper was fitted.
The standard BMW R75/5 used as a basis for the experiments in rake and trail, maker’s figures were 27 degrees rake and 3.5” ground trail.
Although the results of these tests are essentially subjective and might be expected to depend on experience, personal preferences and preconceived ideas, there was in fact no divergence of opinion between the various riders. The initial testing was done on a bumpy, rutted country lane at speeds up to 50 mph. Here the most noticeable effect was the total insensitivity of the steering to ruts and bumps. Not only could the bike be ridden hands-off but at the same time it could be weaved from side to side across the ruts with little effort and no detectable deflection of the steering. In corners, bumps had little effect, which was contrary to the behaviour of this particular machine before conversion, when it had a strong tendency, with no steering damper, to shake its head (sometimes violently) on bumpy corners. This lack of disturbance by longitudinal ruts was also confirmed on smoother roads at higher speeds, when the machine was ridden deliberately on the edge of painted white lines. Though unforeseen, this benefit is easily explained by reference to figure A.2. If we visualize a 90-degree rake (i.e. horizontal steering axis) we can see that the side of the rut gives rise to a moment about the steering axis that tends to steer the wheel back into the rut. With a vertical steering axis, however (zero rake), there is no effect on the steering; instead, the disturbance tends to cause the complete machine to lean into the rut. In this case, though, since the inertia of the whole bike is much higher than that of the front wheel alone, the effect on directional stability is considerably smaller and the rider is less aware of the rut. Thus the steeper the steering axis the smaller the effect.
Fig. A.2 The effect of ruts on steering increases with rake angle, as shown in this exaggerated case. A vertical steering axis reduces the effect.
In the foregoing chapter, we suggested that balance might be enhanced, particularly at low speeds, by steepening the head angle. To verify this, much riding was done at very low speeds and balance was indeed improved by the modifications. The machine could easily be ridden much more slowly than when in standard trim before the rider had to put a foot down. (Of course, champion trials riders can balance a stationary machine indefinitely; but that is exceptional and most of us need to be moving slightly to maintain balance.) In heavy traffic, it was noticeably easier to trickle along slowly on the modified BMW, making it less tiring to ride from one side of London to the other. When, without prior briefing, a novice was asked to try the machine, he commented on the surprising ease of moving off from rest; there was less wobbling than usually seen with a learner and his feet were quickly on the rests. It has been suggested that an unusually steep steering axis might induce wobbles at high speed. Nevertheless, with both the experimental rake angles on the BMW (15 degrees and zero) this was not noticed. With the handlebar released, the machine was ridden from approximately 100 mph down to a walking pace and at no time was there any tendency to wobble or weave. With confidence built by several such runs, the handlebar was knocked to try to initiate a wobble. Whatever the speed, though, the disturbance was damped out within less than one cycle. In standard trim (27-degree rake) this particular machine could develop a pronounced wobble when ridden no-hands at 30 to 40 mph, though it was easily damped out by grasping the handlebar. Directional stability was always excellent and tremendous confidence was instilled in the rider at an early stage.
A further advantage of the steeper head angles was increased sensitivity of the front fork to small bumps. This results from reduced ’stiction’ in the fork sliders as a consequence of the decrease in side loading. (The normal side-load component is approximately halved by reducing rake to 15 degrees and practically eliminated at zero rake.) In addition, this reduction in the side-load component is accompanied by an increase in the spring-load component as the fork is steepened – which gives the same effect as a lower spring rate. The effective rate varies little between zero and 15 degrees rake but is approximately ten per cent higher at 27 degrees. Similarly, the spring-load component of the braking force is reduced as the fork angle is steepened. Moreover, since this spring force acts in concert with weight transfer to compress the fork, the reduction means less nose-diving. For this reason, the effective drop in spring rate was not detrimental and ride comfort was appreciably improved.
The top photo shows the superstructure which gave an unaltered trail with zero offset and rake angle of 15 deg.
The second shows the extended structure, with the reversed forks, giving equal trail with near zero rake angle.
It was under braking, however, that a disadvantage was noticed, in the form of severe shuddering in the fork as the braking force tried to bend it backward. Naturally, this was more severe with the steering axis upright, even though the reversal of the forks converted the twin-leading-shoe brake to much less effective twin trailing shoes. Such juddering was entirely absent with the standard rake, though quite bad at 15 degrees.
Fig. A.3 Steepening the steering head reduces the stiction in telescopic fork sliders, so improving sensitivity to small bumps. Nose diving under braking was also reduced.
This effect apart, one of the most interesting results (mentioned by all the riders) was the surprisingly normal feel of the modified machine, with the steering pleasantly light at low speeds but always totally stable. No special riding technique was required and cornering was accomplished normally. The variable steering ratio mentioned earlier was tried from 1: 1 (equivalent to conventional direct steering) to 1: 2 (steering angle doubled from handlebar to fork). In normal riding (dry roads) it was impossible to detect the difference, only when maneuvering at a standstill, using large steering angles, was the heavier feel of the 1:2 ratio noticeable.
However, since the steeper rakes made the steering lighter anyway, even the effort required with the 1:2 ratio was similar to that with the standard machine. Indeed, the reduced handlebar swing could be a bonus when designing a non-steerable fairing, as handlebar clearance usually results in a bulky shape if steering lock is not to be restricted.
In both experiments the handlebar was connected to the fork by a rose-jointed link providing for steering ratios anywhere between 1:1 (direct) and 2:1 (geared up). This was accomplished by sliding the bar atop the forks toward greater or lesser radii.
With the modified BMW, Tony Foale demonstrates the stability achieved with the 15 degree rake angle.
Trail
Throughout the rake experiments the standard ground trail of approximately 3.5 inches was retained. Yet, it seemed reasonable to assume that the optimum trail (if there is such a thing) might vary with rake angle.
To try trail values between 2 and 4 inches with zero offset this adjustable double wishbone suspension system was made up.
To test this, a double-wishbone front-suspension system was fitted to the BMW (see photo), making it possible to alter the trail by adjusting the wishbone lengths to give variations in rake. There was no offset, and trail values from 2 in. to 4 in. were tried varying the rake angle either side of 15 degrees. Although the machine was perfectly ridable over the full range of settings, the front end proved livelier and the steering more sensitive to bumps as the trail was shortened (steeper rake), albeit never so much as with the standard set-up. In the upper range of trail settings the bike was very steady but could still be manoeuvred quickly. At about 3 in. trail there was a tendency for the machine to lift itself out of a bend when cornered at moderate banking angles (say, 15 to 20 degrees), though no such effect was detectable at higher cornering speeds requiring, say, 35 to 40 degrees of lean. When a machine is banked into a bend, trail gives rise to two opposing effects: (1) directional stability, tending to make the machine run straight and (2) the self-steering effect (also dependent on rake and wheel diameter) mentioned in Chapter 3, tending to steer the machine into the bend. To achieve neutral handling, these effects have to be properly balanced (in concert with several other parameters), and the problem just mentioned, whilst not properly understood, is thought to have been caused by an unsuitable combination of these effects for that particular machine at a critical rake or trail. It is thought that at the greater bank angles, the self-steering effect would have outweighed the straight-ahead tendency.
Conclusions
The scope of our experiments was limited by time and money. Nevertheless, the results indicate a need for more exhaustive and quantitative testing. These tests indicate that currently favoured geometry may be far from “optimum”.
Rake
From our experiments it seems there is nothing magical in the conventional rake angle of 27 to 28 degrees. Indeed, balance, stability and lightness of steering were all enhanced by steepening the angle. The greater improvement came from the first change (from standard to 15 degrees), the subsequent move to near zero rake producing only minor differences. Many effects of castor angle are approximately dependent on the cosine of that angle, the cosine of 15 degrees is 0.97 which is little different from the value of 1.00 for a vertical steering head. At 27 degrees the cosine reduces to 0.89, a more significant difference.
The only drawback noticed – juddering under braking – is a consequence of the poor structural integrity of the telescopic fork as a type. It is not suggested that machines should be built with a steep steering axis, using a headstock mounted fork, whether telescopic or leading/trailing link type, because the consequent high, forward location of the headstock causes structural and styling problems. Much better to consider some form of hub-centre steering or other wishbone layout, such as that used in the trail experiments.
Trail
Apart from the need to avoid the critical situation mentioned, there seemed no obvious optimum value. Results were satisfactory throughout the full test range, so making personal preference the decisive factor.
