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Effect of insufficient clearance time.

Insufficient clearance time between conflicting green phases of traffic signals is a major cause of car-bike collisions. Car-bike collisions caused as motorists start or speed up on a new green constitute 5.9% of urban car-bike collisions (quoted from Forester, Bicycle Transportation, using the data from Cross, A Study of Bicycle/Motor-Vehicle Accidents), ranking number 3 of the motorist-caused types. If the car-bike collisions caused by obviously foolish mistakes on the part of cyclists are eliminated from consideration, it is likely that car-bike collisions caused by insufficient clearance time are 15% of the car-bike collisions incurred by cyclists who possess the minimum standard of traffic skills. This cause of car-bike collisions is the largest identified facility-associated cause of car-bike collisions.

There are also complaints from bicyclists about signals with inadequate duration of the green phase, typically expressed as "Too little time to get across the street before the green ends and conflicting traffic starts." These persons ask for longer minimum-green phases. While traffic engineers understand that the duration of the green phase should not be determined by the time required to cross the intersection, the typical driver does not. However members of the public word this complaint, it refers to inadequate clearance interval and is a symptom of conditions that cause the type of car-bike collision found in the statistics.

The typical situation is when a cyclist is crossing a multi-lane street from a minor street that carries infrequent and slow traffic. The traffic signal provides a green phase for the traffic on the minor street whose duration depends on the number of vehicles waiting in the queue (or on the time for the queue of waiting traffic to clear). If only one vehicle is in the queue a minimum-duration green appears, which is then followed by the yellow, which in turn is immediately followed by the conflicting green. If the single vehicle is a bicycle, the cyclist may well be only half-way across the intersection when the green appears for the main-road traffic. The typical car-bike collision occurs between a cyclist and a motor vehicle from the cyclists' right. The motor vehicle is in one of the lanes nearest the curb while vehicles still stopped are in the lanes nearest the center. The vehicle that becomes involved in the collision has started up, or speeded up, at the new green when the cyclist is hidden from the sight of its driver by the vehicles still stationary in the number one lane. Unquestionably, the colliding motorist has disobeyed the law by entering an intersection on a new green without seeing that traffic already in the intersection has cleared. However, because these accidents occur it is important to understand why they occur and to devise the appropriate countermeasure.

The duration of the yellow phase for the minor-street traffic is commonly determined by the speed of the traffic on that street. Its legal meaning is specific. It shows that the red signal is about to appear, so that any driver who sees it must stop lest he enter the intersection on red. However, because it is impossible to stop instantaneously the duration of the yellow is calculated such that the driver who, upon first seeing a new yellow, is so close that he cannot stop without entering the intersection is allowed sufficient time to enter the intersection on the yellow. Any driver who is further away (and traveling at a legal speed) has sufficient distance to stop before entering the intersection. The conflicting green appears when the last vehicle to lawfully enter the intersection is within it. This system produces few collisions between motor vehicles for three reasons.

1. Motor vehicles are typically large and easily seen.

2. The motor vehicle in the intersection rarely is close to the fronts of the vehicles waiting to start from its right, so their drivers have both a better angle of view and some distance to correct a mistake.

3. Because the motor vehicle still in the intersection is moving relatively rapidly it gets within view, or leaves the intersection altogether, before the waiting drivers have reacted to the new green and started their vehicles.

This system fails to provide the required safety in the case of bicycles for three opposite reasons.

1. Bicycles are small and are harder to see. In particular, the most visually impressive part of the bicycle and rider is low down where it is easily shielded from view by the hoods of motor vehicles. Sometimes the only part of the cyclist that can be seen by drivers waiting at the stop line with other vehicles on their left is the head of the cyclist.

2. The cyclist crossing a typical intersection is close to the fronts of the line of cars waiting at the stop line on the cyclist's right. This is not good judgement on the part of the cyclist, but so much emphasis has been put on staying far right that this position is typical.

3. The cyclist who is traveling slowly, or, more importantly, is starting from a minimum-duration green, is barely into a wide intersection when the conflicting green appears.

The result is a car-bike collision as one of the vehicles in the lanes nearest the curb starts up, or speeds up, and hits the cyclist who suddenly appears in front of it.


Present methods of alleviating the situation.

Two methods are frequently advised or requested to handle this situation and prevent these collisions: increasing the minimum-duration green and increasing the duration of yellow. Neither of these meets the requirements of controlling traffic in the way required by traffic law. While increasing the minimum-duration green helps those cyclists who have been waiting, by allowing extra time to allow for the time lost in starting, it doesn't assist those who have been approaching, perhaps slowly in the hope that the signal will change before they come to a complete stop. These may still lawfully enter the intersection on either green or yellow, so that the situation is much the same as before except that the bicycles don't have to start from a stop. At the speeds typical of urban cyclists they will still move through the intersection slowly, and are likely to be in the position of danger when the conflicting green appears. A lengthy yellow is likely to be met with the same response. Traffic may still lawfully enter an intersection on a yellow, and once cyclists learn that a particular signal has a long yellow they are likely to take advantage of that permission to avoid coming to a stop. Then they will still be near the position of danger when the conflicting green appears.

Changes in traffic law.

Of course, entering an intersection on a stale yellow is undoubtedly unwise. It is not so unwise for someone traveling fast, because that person may well clear the intersection before the conflicting traffic starts. It is much more unwise for someone traveling slowly, but it is done and it is lawful. Originally the law said that drivers shall stop before entering the intersection upon seeing the yellow unless it was unsafe (or, of course, impossible) to do so, and it also said the driver who was still in the intersection when the yellow phase ended was violating the law. Under that law it was reasonable, indeed proper, for engineers to extend the yellow phase to allow slow vehicles to clear the intersection. However, that law produced many difficulties in enforcement and in determining liability. Therefore, in 1962 (for the Uniform Vehicle Code), the law was changed to require a positive decision point, the time when the signal changed from yellow to red, as the time after which it was unlawful to enter the intersection. That change in traffic law required a change in the logic and duration of the clearance interval, a change that has frequently not been made. Extending the duration of either the green or the yellow to allow intersection clearance time does not meet the requirements of the law as now phrased.

The phasing sequence that is required by current traffic law is as follows:

1. Green, which may be very short when only one vehicle is waiting

2. Yellow, of only sufficient duration to allow a stop from maximum legal speed before entering the intersection

3. Red (a 4-way red), for sufficient additional time for traffic to clear the intersection before the conflicting green appears

Changes in signal phase timing.

The change in logic that the change in law has made necessary is in some respects disadvantageous because the clearance interval so calculated will often be longer than the extended green plus yellow of the former system, and the total proportion of green will be reduced in accordance. However, the change in green time may not be as severe as might appear, because the greatest effect is when a single vehicle is in the queue, which is when the green is extended even though there is no vehicle present to use the additional green time. In any case, the change in the law was adopted to eliminate the collisions and the resulting difficulties that the former system caused.

Clearance time for bicycle traffic.

The calculation of clearance time, as it relates to bicycles, must consider two different situations in which bicycles are concerned:

1. One or more bicycles and less than three cars are waiting in the queue.

2. A bicycle is the last vehicle approaching a green signal and is just unable to stop before entering the intersection when the yellow appears.

In the first situation the cyclist must start at the new green, which will be short. Just as a motorist loses about 2.5 seconds when starting, the cyclist will lose some time. This amount of time may be estimated either by adding a single time allowance for starting, or by calculating the acceleration of the cyclist across the intersection.

In the second situation, the cyclist who just can't come to a stop before entering the intersection is likely to be closer to the intersection than a comparable motorist when the green changes to yellow. He will thus have a shorter distance to travel to clear the intersection, but will do so at a slower speed than a motorist. If there is a marked crosswalk, the traffic engineer also may consider that the stop line for the cyclist is the far side of the crosswalk. The cyclist who comes to a sudden stop in a crosswalk can easily clear the crosswalk for the pedestrian traffic that may start to use it.

The following factors are proposed for performing the calculations required by the above considerations.

Braking deceleration and stopping distance of bicycles.

Use the typical automobile formula of 1 second reaction time plus deceleration to stop at 12&nbspft/sec/sec. This is 0.37 g, which is conservative for bicycles with 2-wheel brakes. This produces a stopping distance of:

S = V*1 + V*V/24 (V in fps).

Distance to clear the intersection.

This is calculated by first determining the closest point at which the cyclist can stop before crossing the actual intersection boundary. This is the actual intersection boundary less the stopping distance calculated from above. The distance to clear the intersection is the distance from this point to the center of the furthest lane carrying through traffic. If the cyclist (actually, his front wheel) reaches this position he should be well visible to drivers in the furthest lane, who will therefore delay their start, or slow their approach, to allow him to complete clearing the intersection. This distance is therefore:

D = S + W

Starting allowance.

It would be possible to calculate the position of a cyclist during a specified set of steps of acceleration, but this is probably not necessary. For one thing, the starting accelerations of cyclists are less variable than their sustained speeds. Consideration of a small number of data points (collected by Alan Wachtel from Palo Alto) suggests that the typical cyclist requires about 5 seconds longer to cross an intersection from a standing start than from a moving start. This is probably sufficiently accurate. Some further measurements could be made to see whether a more accurate allowance, either a single allowance or different allowances for different types of cyclists and different widths of street, would materially reduce the calculated clearance time for some installations.

Clearance time from a moving start.

This is:

Tm = (S + W)/V = S/V + W/V = 1 + V/24 + W/V = D/V


Clearance time from a standing start.

This is:

Ts = 5 + W/V

Since Tm = S/V + W/V and Ts = 5 + W/V,

Ts > Tm unless S/V > 5.

Since S/V = 1.38 for 9 (6 mph) and 2.25 for 30 (20 mph), Ts will always exceed Tm. Therefore, whenever a cyclist starts from a standing start his clearance duration will exceed the clearance duration of a cyclist approaching, but continuing, when the yellow appears. The magnitude of this difference will vary from 3.6 seconds for a slow cyclist to as little as 2.75 seconds for a fast cyclist. If the duration of the green has been short, then the clearance time from a standing start must govern, but if the duration of the green has been long, then the clearance time for a rolling start may govern. The dividing line between the two algorithms is specified by whether the green time has exceeded 5 - (1 + V/24), simplified to (96 - V)/24. The ability to specify two different clearance intervals, depending on the duration of the last green, is likely to save up to 2 seconds on clearance interval for some cycles. The ability to specify a clearance interval that is computed from the difference between the green duration and a pre-specified constant will save more time on a greater proportion of the cycles.

Selection of cyclist standard speed.

The other factor that needs to be considered is cyclist speed. Note that this is the normal sustained speed of a cyclist approaching a green signal, because the 5-second start-up increment is the time difference to clear the intersection between starting from red and starting from green. Of course, the difficult decision is how slow a cyclist should the clearance phase allow for. From study of the data collected by Wachtel I suggest a time that is 1.5 times the average for clearing the intersection after approaching on green, or a speed that is 0.67 times the average speed for that movement. (The data I have received from Wachtel refer to the distribution of times for starting from red. The factor may be altered when the distribution for approaching on green is studied.)

The average speed or time for approaching on green and clearing the intersection may be obtained either by measuring at the actual intersection or by estimation from other measurements. The speed will probably vary from location to location depending on the type of cyclist that uses the intersection. Obviously, the fastest cyclists will clear the intersection handily; what is required is a judgement of the standard speed for calculation that will provide adequate clearance time for nearly all cyclists using that intersection. I suggest that for average adults a standard speed of 8 (12 fps) be used, based on an estimated average speed of 12and the 0.67 factor. I suggest that for intersections that are typically used by cyclists who are either extremely young or extremely old the standard speed be reduced to 6 (9 fps). At intersections where nearly all the cyclists are fast cyclists, the standard speed may be raised to 12 (18 fps). In any case, whenever actual observations have been made that information should be used.

Formulas for clearance interval.

The formula for clearance interval then becomes:

If the controller can allow only one clearance interval:

Ci (secs) = 5 + W/V

If the controller can allow two different clearance intervals:

If the green duration has been less than (96 - V)/24 secs:

Ci (secs) = 5 + W/V

If the green duration has been more than (96 - V)/24 secs:

Ci (secs) = 1 + V/24 + W/V

If the controller can compute a clearance interval:

Ci (secs) = the larger of:

1 + V/24 + W/V or

5 + W/V - duration of green

where W ft. is from intersection boundary to half-way across the last lane carrying through traffic and where V = 12 fps for locations with average adult traffic, V = 9 for locations with child or elderly traffic, and V = 18 for fast adult traffic.

Adjustments for hills.

The formula probably need not be adjusted for descending or ascending roads because in all cases the clearance time is calculated from a standing start and the intersection that is being crossed will probably be substantially level. Therefore the crossing speed from a standing start will not change appreciably for the distance, even though the crossing time from approaching a green changes greatly. The speed of approach will differ, but on descents the cyclist should not exceed the speed limit and on ascents he won't be able to do so. Therefore the duration of yellow will not normally need to be changed.

Checking and refinement of formula.

This suggested procedure for calculating intersection clearance time needs to be checked for adequacy and accuracy by some further measurements in different locations.

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