CHANGES IN SPEEDS OF VEHICLES ON HORIZONTAL CURVES

Transcription

1 STATENS VÄGINSTITUT - STO CKHOLM The National Road Research Institute, Stockholm, Sweden CHANGES IN SPEEDS OF VEHICLES ON HORIZONTAL CURVES by C; Holmquist RAPPORT Nr 104 StOckholm 1970

2 STATEN S VÄGINSTITUT- STO CKHOLM The National Road Research Institute, Stockholm, Sweden CHANGES IN SPEEDS OF VEHICLES ON HORIZONTAL CURVES by C. Holmquist RAPPORT Nr 104 Stockholm 1970

3 Holmquist, C: Changes in Speeds... l. CHANGES IN SPEEDS OF VEHICLES ON HORIZONTAL CURVES An essential part of the model for traffic simulation which is in preparation at the National Swedish Road Research Institute is a description of the variations in the speeds of road vehicles during their passage through horizontal curves. Studies of the speed adaptation on horizontal curves have beenmade at the Road Research Institute on several occasions in the course of the period from 1965 to A common feature of these studies is that they have been carried out under left-hand traffic conditions. It was therefore desirable to examine, among other things, the effect produced by righthand traffic on the speeds of vehicles on curves. It was to be expected that the sight from the inner lanes of the curves would be improved for vehicles equipped with steering wheels on the left-hand side, which are completely predominant in Sweden. In order to study the above-mentioned effect, investigations have been made in 1969 at some places where similar measurements had been performed in left-hand traffic, data were available for these places. so that reference In the first investigations, a study was made of free-moving vehicles. They were defined as vehicles separated by a time gap of at least 6 seconds from the vehicle ahead. The results of these investigations proved to be in close agreement with those of Taragin's tests carried out in It was found, among other things, that the speed adaptation took place in most cases before the curve, and was then maintained constant throughout the curve. Furthermore, the difference in speed between the vehicles moving in the inner and outer traffic lanes was very slight. In another investigation, the variation in the Speed of each vehicle with the distance was determined by measuring the travel time over 8 consecutive road sections. This investigation was carried out on freemmoving vehicles at 25 places in Central Sweden, and covered vehicles in all. In the analysis of the observarions, the Speed variable, in kilometres per hour, was replaced by the travel time, in seconds per kilometre. This made it possible to obtain a Simplified description of the relations between the variables involved in the analysis. The results of the measurements SVT : ort 105:L

4 Holmquist, C: Changes in Speeds Were used to plot travel time rate profiles, and it was found that these profiles were parallel, irrespective of the initial speed of the vehicle at the entrance into the curve.i Fig.l shows the travel time rate profiles obtained at one of the above" mentioned 25 places. sec per km - km per hour' 80 0 N / 70 W 50. WIMML w//au--m WWW / d 40 M / 30 -foo f Curve ' Distance [m] Fig. 1. Travel time rate profiles on a horizontal curve. Deceleration. Each profile covers 5 vehicles. The dashand-dot profile represents the average speed. The parallelism of the travel time rate profiles in fig. 1 implies that the travel time of a vehicle on a curve increases by an amount which is independent of its speed. In other words, the distribution curves of the travel time rate are subjected to a parallel displacement See fig. 2. SVI Rapport 104

5 Holmquist, C: Changes in Speeds Percentage of cars with travel time rate less than t Speed v km per hour I I I I f l V" ' 80 _ Sample size i 35 cars 60 s 40 - Section 2-3 5»6 8-9 ZOr" 0. 1 L L 1 I Travel time rate t sec per km Fig. 2. Distribution curves of the travel time rate Moreover, contrary to the assumptions made by Taragin, among others, it was found that the speed adaption did not cease at the end of the straight road section, but continued after the entrance of the vehicle into the curve. Studies have also been made of the variation in the acceleration of the vehicles with the distance after they left the curve. These studies showed that the deceleration before, and the acceleration after, the curve were mirror reflection of each other. Furthermore, the measurements indicated that the speed was approximately constant along a road section extending over the central part of the curve. The length of this road section was on an average equal to 1/4 of the arc length of the curve. The variation in the speed of a vehicle passing a curve can be represented in an idealised form by the travel time rate profile shown in fig. 3. ' For cars, the Speed level, to, (the maximum.travel time rate) on a curve with good visibility and without speed limits, was found to be.., x... closely correlated Witn tne degree of curvature ) The relation obtained for the mean value of to was E'0 = 1,5 D + 36 sec per km x) The degree of curvature is defined as the centre angel of a Circular arch which is limited by a 100 feet Chord. SVI Rapport 104,,.

6 Holmquist, C: Changes in Speeás Travel time rate sec/km Maximum travel time rate on curve 'C 1 e Approach travel time rate tl *wmmüummwmsuu Deceleration Con- stant Speed Acceleration ;e L/4 Distance [En] Fig 3. Travel time rate profile. Idealised behaviour on a horizontal curve. The speed level, tl, (the approach travel time rate) on the attached parts of the road has been calculated on basis of an another investigation made at the Institute. The mean value of t l was 't = /(K-2,5) sec per km 1 where K is the width of the road, in m. In addition, the results obtained from the measurements at the 25 sites of observation showed that the variations in the deceleration and in the acceleration corresponded to approximately linear travel time rate profiles (See fig 3). The slope, k, of these linear profiles was calculated from the formula nu.. /k 2 0,27 to.. 7,8 The increase in the travel time caused by the curve is represented in fig. 3 by the area of the surface which is bounded by the travel time rate profile and by the dash line. This surface area can be calculated SVI Rapport 104

7 Holmquist, C: Changes in Speeds...v 5. when t to and k are known. Tue model for the calculation of the increase 1) in the travel time, AT, due to tne curve is AT=O,24-L(t..t.,)+ - O where AT = the increase in the travel time, in sec, L - the length of the curve, in m, to 3 the maximum travel timerate on the curve, in sec per km, t = the approach travel time rate, in sec per km. The object of the measurements dealt with in the present paper was to find simple models for the calculation of travel times. Moreover, tne results obtained from the above-mentioned investigations will be used in evolving a first draft of a model for traffic simulation. In the subsequent work on this subject, it is intended to devise a more precise model by studying the cumulative effect of an increased number of variables on the speed-distance relation. The data to be used for this purpose will 9 bemore extensive tnan those which have been utilised before. SVI Rapport 104

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