"Z Line" - 2 - Limits on Vision

The following is from material written by Stephen Prower, formerly Research Officer for the BMF:

In a typical intersection accident the motorcycle will be on the major road (Faulkner 1975: 91% of accidents; Olson 1989: 90% of accidents).

For most of its approach the motorcycle will also usually be perceived by the other driver in head-on view. So the other driver must base his or her estimate of the motorcycle's speed upon its rate of change of angle subtended. Only when the motorcycle commences its final traverse past the other driver's position will the other driver be able much more reliably to base his estimate upon the rate of angular motion of the motorcycle across his retina.

Correspondingly in most intersection accidents that are caused by the other driver's making an error of estimation of the motorcycle's speed, the error in question will be an error that is made in estimating the speed of the motorcycle in head-on view.

An important prediction to be investigated was that, because of the lack of visual information as to the speed of approach of a motorcycle in head-on view, subjects' estimates would be biased towards some 'expected' figure of the speed of approach of the motorcycle.

So subjects would 'dangerously' underestimate faster speeds of approach of the motorcycle above the expected figure, but 'safely' overestimate slower speeds of approach below the expected figure.


Angular motion & Rate of change of angle subtended

I use the term 'Rate of change of angle subtended', by contrast with the term 'Angular motion', to describe the difference in the perceptual information that is available to a driver with which to estimate the speed of an approaching vehicle according to whether he views the vehicle in head-on (or rear-on), or oblique, view.

The terminology is loose, but chosen to make the distinction more clear to the ordinary reader.

When an observer views a moving object that is pursuing a course of travel that projects in front of, rather than 'through', the position of the observer, namely when the observer views the object in oblique, rather than head-on', view, the observer will--in the form of the angular motion of the object across his retina--have:
* Identical visual information upon which to base his estimation of the object's speed of travel, be it, as I say:
'A fly, cannonball, or elephant -- or, more particularly, a motorcycle, or a motorcar'.

Further, as the object, in its course of travel, approaches the point where it makes a right angle to the position of the observer--ie as, in the case of an approaching vehicle that a driver observes from a junction, the object departs more and more from 'head-on' view--, the observer will have:
* Increasingly accurate, to very accurate, visual information upon which to base his estimation of the object's speed of travel.

By contrast, when an observer views a moving object that is pursuing a course of travel that projects through the position of the observer, namely when the observer views the object in head-on view, the observer will have neither of the two 'advantages' in estimating the speed of travel of the object. Instead he must rely for the purpose of estimating the speed of travel of the object upon the visual information of the rate of change of the angle that the object, as a matter of the visual size and shape of its outline, subtends, or makes, to him, ie upon the rate of change of angle subtended of the object.

The visual information will thus be less for an object with a small outline, or silhouette, such as, in the case of vehicles, a motorcycle and rider, or a pedal cycle and rider, than for an object with a large, or extensive, 'outline', such as a motorcar. And since, by comparison with 'oblique' view, the rate of change of the angle that the object subtends to him in 'head-on' view will be very small, the visual information will be correspondingly very small -- indeed, for a small object, it will tend towards the minuscule.

The simple picture of a motorcycle and rider that, by comparison with a motorcar, affords the observer less visual information of its speed in head-on view is complicated by the fact that, although the silhouette of the motorcycle and rider may be smaller and narrower than the silhouette of the motorcar, it is also taller.

Given the fact, Williams 1976 (and Williams & Hoffman 1977) assumed, without discussing the matter, that other road users attempt to estimate the speed of a motorcycle by the rate of change of the angle that the height of the motorcycle makes to them.

However, since:
* Motorcars are the predominant vehicles on the road
* Motorcars are more wide than they are tall
* It is more difficult to estimate the height, than the width,
of a motorcar, because of the confused outline of the bottom
of the motorcar
* The road scene is more 'confusingly' striated, in terms of
the contrast of the background against which a moving
vehicle is viewed, horizontally, than vertically,
I would argue that it is more plausible to suppose that other road users attempt to estimate the speed of all vehicles on the road, including motorcycles, by the rate of change of the angle that the width, rather than the height, of the vehicle makes to them.

But I do not know of any study that has investigated, or otherwise sought to resolve, the point.

Accordingly, I must formally leave the matter open.

Threshold angle

The rate of change of the angle that a moving vehicle subtends, or makes, to an observer in 'head-on' (or 'rear-on') view is so small that the figure of the change of angle between two successive fixations of the vehicle by the observer may fall below the figure of the minimum angle, or Threshold angle', that the human eye is capable of detecting.

If so, given the same:
* Viewing conditions
* Interval of time between successive fixations,
a 'small' vehicle, such as a motorcycle and rider, will 'slip' much 'sooner' below the threshold figure than a 'large' vehicle, such as a motorcar.

And the observer will find himself much 'sooner' unable to estimate the speed of approach of the motorcycle and rider.

To explain why a threshold figure for the detection of small changes of angle exists, per Hills 1980:

'At its most basic, the human visual system is a photon detector and it is inevitably limited by "quantal fluctuations" and the need for certain levels of "signal-to-noise" ratio to be achieved for signal detection. Whether or not an object is detectable to a normal observer is therefore dependent upon a number of interacting conditions. The most significant of these are the visual size of the object; its luminance and colour contrast with its background; the luminance level of the background; and the proximity and intensity of any glare sources in the field of view. These factors have been studied extensively in the laboratory but there have been relatively few field studies using dynamic driving conditions.'

Further, to give a measured value of the threshold figure, per Hills 1980:
'Two types of movement of a vehicle relative to an observer can be distinguished:
a. Tangential or angular movement which occurs when the vehicle moves across the field of view without changing distance from the observer. In this case there is no change in the visual image size of the vehicle.
b. Longitudinal movement or movement in depth in which the vehicle is either coming directly towards or going directly away from the observer [ie observed by the observer in 'head on', or 'rear on', view]. In this case there is no change in visual direction, only a change in visual-image size.

Laboratory measurements suggest that for 2 s exposures the threshold angular movement is approximately 2-3 min arc and the threshold longitudinal movement is about 1 min arc (Hills 1975b). (These values are obviously influenced by the conditions of the test.) Despite the greater sensitivity to longitudinal movement, it is generally believed that it is the longitudinal movements of vehicles that pose the greatest problems of detection and judgement. This is because the same physical displacement of a vehicle has a much greater effect tangentially than longitudinally. For example, consider a small car, a Mini, at a distance of 200 m. If it moves 10 m directly towards the observer, its visual diameter increases by 1 min arc. On the other hand, a lateral movement of 10 m by the car would result in a visual movement of 170 min arc across the background against which it is seen; it would only have to move 6 cm laterally for a movement of 1 min arc. It is the very small changes in visual-image size associated with directly oncoming vehicles that is thought to be the basic problem in judging their speeds, leading to difficulties in overtaking, right turning, and similar situations involving oncoming traffic.'


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