5.3 Survey results
5.3.4 Speeds
5.3.4.1 Entering speeds Standard entering processes
At saturated approaches or coordinated approaches with vehicles regularly waiting at the stop line during the onset of green, Entering Type 1 is the standard entering process (cf. Figure 8). This process is a variably accelerated movement. Distance, speed, and acceleration depend on the interval since the start of movement.
For the calculation of intergreen times, the distance from the stop line to the present location of a vehicle is known (or assumed), while the time to cover this distance has to be calculated. The entering movement has, hence, to be described by a function relating time to a distance. The distance, of course, has to be corrected by the systematic and random error∆le.
Derivation of the entering speed function
Accelerations cannot be measured directly in the present context, therefore a rapid succession of speed measurements was undertaken. Furthermore, the time precision of the used device of one second is insufficient for an accurate estimation of the movement functions. Speed and distance, otherwise, are recorded with satisfactory precision (one kilometre per hour and 10 centimetres respec-tively).
Therefore, the average movement of the entering vehicles is described based on distance/speed measure-ments. These measurements were cumulated and a logarithmic function fitted using the least squares method. This approximation describes the speed as a function of the distance. As compared to power functions, a logarithmic function could achieve a better fit. Since such a function is strictly increasing, the approximation is only valid as long as the vehicles accelerate. However, the acceleration process takes commonly significantly longer distances than the entering distances of ordinary signalised intersections.
Thus, this approximation holds true for the described problem.
To derive entering times from a speed-distance-function of a variably accelerated movement is only possible by dividing the movement into small steps with assumed constant accelerations. The move-ment functions for accelerated movemove-ments can then be applied to these steps, and the time can be determined incrementally as a function of distance. Details on this procedure are provided in Ap-pendix A.4.
Variance of the acceleration behaviour
Data was collected at five urban intersections. A two parametric logarithmic function (Eq. 37) was fitted to the data sets for each survey individually as described before. The optimum parameters are given in Table 13 together with the number of data sets on which the function fitting is based (sam-ple size). The last column gives the sum of the squared errors. The resulting functions are shown in Figure 25.
v(s) = c1ln(c2s+1) (37)
5.3 Survey results 87
Intersection Peak Sample Size
c1 c2 Squared error (km/h2)
1 A 018 AP 118 2.8 0.96 0.75
2 A 019 MP 387 2.6 0.96 2.09
3 A 019 AP 186 2.6 0.96 0.99
4 A 020 MP 118 2.8 0.96 0.75
5 A 020 MP 73 2.8 0.94 0.86
6 A 046 AP 427 2.5 0.95 0.67
7 A 046 MP 279 2.4 0.95 0.10
8 A 098 MP 193 2.8 0.95 0.50
Table 13:Survey details and results of the entering speed measurements
The results show that
• the logarithmic function can be well fitted to the data,
• the second parameter of the function is more or less constant for all survey intersections,
• there is only a weak indication that morning peak (banded rows) and afternoon peak may differ, and
• the data of three intersections coincides quite precisely.
The lower accelerations at intersection A 019 and even more A 046 cannot be explained without further scrutiny. The results, however, give an indication of the range of possible entering behaviour. The results coincide quite accurately with the results obtained by driving measurements conducted by HOFFMANN
and NIELSEN(1994). HOFFMANNand NIELSENshowed, furthermore, that the maximum speed of the first vehicle is commonly only reached after more than 150 m, which justifies the use of a strictly increasing function for common entering distances.
Entering time difference
The entering time depends on the entering speed and the entering distance. Because the entering speed is the decisive factor in this context due to its greater variability, its impact on the intergreen time difference is highlighted here.
The German Guidelines for Traffic Signals (RiLSA) assume a moving start (Type 2) with a constant speed of 40km/h and no crossing time. The entering time calculated in this way can be compared to the ef-fective entering time based on theequivalent entering speed as explained in Section 3.3.2 on page 44 f.
Theequivalent entering speedve,eff is defined as the speed with which an entering vehicle would have to travel the entering distance as to arrive at the same time as it arrives with the real accelerated move-ment.
The equivalent entering speedve,eff as a function of the entering distance is shown in Figure 26 with the entering speed according to RiLSA indicated in grey. The difference between the effective entering time and the entering time calculated according to FGSV (1992) as a function of the entering distance is illustrated in Figure 27. In the graph shown, the entering distance is assumed constant (no entering distance variation).
Figure 25:Entering speed functions
Figure 26:Equivalent entering speeds as a function of the entering distance
5.3 Survey results 89
Figure 27:Entering time difference with reference to RiLSA as a function of the entering distance
Moving starts
As has been explained before, moving starts (Type 2 or 3 according to Figure 8 on page 44) are a rare exception (cf. JAKOB 1980). The survey supports this statement. The number of moving starts was too small to obtain significant information. Moving starts have, hence, been discarded from the entering speed assessment.
Particularly for coordinated approaches a thorough individual evaluation is recommended. It has to be checked whether moving starts can frequently be expected. Entering crossing times and entering speeds have to be obtained to compute accurate capacity estimates. The results will depend siginificantly on the realisation of the coordination (lead time for turning traffic, offset etc.). This procedure was not followed further, because these observations cannot be generalised.
5.3.4.2 Clearance speeds
During the clearance process, vehicles rarely change their speed significantly. As part of the speed measurements, several clearing vehicles were measured successively. However, a significant change of speed could not be observed. For safety considerations, the rare situations, where clearing vehicles accelerate before arriving at the intersection and decelerating after crossing the stop line have to be considered. For capacity considerations these situations seem to be negligible.
The clearance speed depends noticeably on the approach speed and the saturation degree. In saturated cycles, vehicles clear the intersection as a platoon. The clearance speed, thus, is determined by the slowest vehicles in the platoon. For saturated, non-coordinated approaches with short green times, the maximum speed of the platoon remains well below the speed limit. This coincides with the clearance speeds assumed by the German Guidelines for Traffic Signals (RiLSA). Even for approaches with aver-age green times around 40 s the clearance speed remained lower than the speed limit. An apparent correlation between green time duration and clearance speed could not be observed. This effect could, nevertheless, be superimposed by the influence of coordinated approaches.
Well coordinated approaches lead to significantly higher clearance speeds. Figure 28 shows the clearance speed distributions of the five intersections where speed measurements have been conducted. The details
are given in Table 14. The observed approaches of intersections A 019 and A 98 are coordinated and have been summarised, as have the remaining intersections A 018 and A 20. While the speed limit is50km/h, free flowing vehicles sometimes reach speeds of up to70km/h.
Figure 28:Clearance speed distribution (n=711)
As the average clearance speed varies according to local conditions, the distribution varies, too. For approaches with high pressure on the drivers (high saturation degree, short green times), the distribu-tion tends to be negatively skewed. Higher speeds during yellow as reported by CHANG ET AL. (1985) have not been in evidence. Due to the chosen methodology a systematic assessment, however, could not be realised. For saturated conditions vehicles always clear during yellow. Therefore this dependance is not of particular importance. Surveys conducted by TANG (2008) at coordinated and non coordi-nated intersections in the same city showed higher clearance speeds (50km/h averaged over all three survey intersections for through traffic). The clearance speed, hence, seems to vary significantly among intersections.