Chapter 4. Moving Observer Method. 4.1 Overview. 4.2 Theory

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1 Chapter 4 Moving Observer Method 4.1 Overview For a compete description of traffic stream modeing, one woud reuire fow, speed, and density. Obtaining these parameters simutaneousy is a difficut task if we use separate techniues. Since we have a fundamenta euation of traffic fow, which gives the fow as the product of density and space mean speed, if we knew any two parameters, the third can be computed. Moving car or moving observer method of traffic stream measurement has been deveoped to provide simutaneous measurement of traffic stream variabes. It has the advantage of obtaining the compete state with just three observers, and a vehice. Determination of any of the two parameters of the traffic fow wi provide the third one by the euation = u.k. Thus, moving observer method is the most commony used method to get the reationship between the fundamenta stream characteristics. In this method, the observer moves in the traffic stream unike a other previous methods. 4.2 Theory Consider a stream of vehices moving in the north bound direction. Two different cases of motion can be considered. The first case considers the traffic stream to be moving and the observer to be stationary. If n o is the number of vehices overtaking the observer during a period, t, then fow is n 0 t, or n 0 = t (4.1) The second case assumes that the stream is stationary and the observer moves with speed v o. If n p is the number of vehices overtaken by observer over a ength, then by definition, density k is np n p = k (4.2) Dr. Tom V. Mathew, IIT Bombay 4.1 February 19, 2014

2 Figure 4:1: Iustration of moving observer method or n p = k.v o.t (4.3) where v 0 is the speed of the observer and t is the time taken for the observer to cover the road stretch. Now consider the case when the observer is moving within the stream. In that case m o vehices wi overtake the observer and m p vehices wi be overtaken by the observer in the test vehice. Let the difference m is given by m 0 - m p, then from euation 4.1 and euation 4.3, m = m 0 m p = t k v o t (4.4) This euation is the basic euation of moving observer method, which reates, k to the counts m, t and v o that can be obtained from the test. However, we have two unknowns, and k, but ony one euation. For generating another euation, the test vehice is run twice once with the traffic stream and another one against traffic stream, i.e. m w = t w k v w t w (4.5) = t w k m a = t a + k v a t a (4.6) = t a + k where, a, w denotes against and with traffic fow. It may be noted that the sign of euation 4.6 is negative, because test vehice moving in the opposite direction can be considered as a case when the test vehice is moving in the stream with negative veocity. Further, in this case, a the vehices wi be overtaking, since it is moving with negative speed. In other words, when the test vehice moves in the opposite direction, the observer simpy counts the number of vehices in the opposite direction. Adding euation 4.5 and 4.6, we wi get the first parameter of the Dr. Tom V. Mathew, IIT Bombay 4.2 February 19, 2014

3 stream, namey the fow() as: Now cacuating space mean speed from euation 4.5, = m w + m a t w + t a (4.7) m w t w = kv w = v v w [ ] = v t ( w = 1 v 1 ) t ( w = 1 t ) avg t w If v s is the mean stream speed, then average trave time is given by t avg = v s. Therefore, m w t avg = t w (1 t avg t w ) = t w t avg = t w m w = v, Rewriting the above euation, we get the second parameter of the traffic fow, namey the mean speed v s and can be written as, v s = t w mw Thus two parameters of the stream can be determined. Knowing the two parameters the third parameter of traffic fow density (k) can be found out as (4.8) k = v s (4.9) For increase accuracy and reiabiity, the test is performed a number of times and the average resuts are to be taken. Dr. Tom V. Mathew, IIT Bombay 4.3 February 19, 2014

4 4.3 Proof 4.4 Assumptions Numerica Exampe The ength of a road stretch used for conducting the moving observer test is 0.5 km and the speed with which the test vehice moved is 20 km/hr. Given that the number of vehices encountered in the stream whie the test vehice was moving against the traffic stream is 107, number of vehices that had overtaken the test vehice is 10, and the number of vehices overtaken by the test vehice is 74, find the fow, density and average speed of the stream. Soution Time taken by the test vehice to reach the other end of the stream whie it is moving aong with the traffic is t w = 0.5 = hr 20 Time taken by the observer to reach the other end of the stream whie it is moving against the traffic is t a = t w = hr Fow is given by euation, = 107+(10 74) = 860 veh/hr Stream speed v s can be found out from euationv s = = 5 km/hr Density can be found out from euation as k = 860 = 172veh/km 5 Numerica Exampe The data from four moving observer test methods are shown in the tabe. Coumn 1 gives the sampe number, coumn 2 gives the number of vehices moving against the stream, coumn 3 gives the number of vehices that had overtaken the test vehice, and ast coumn gives the number of vehices overtaken by the test vehice. Find the three fundamenta stream parameters for each set of data. Aso pot the fundamenta diagrams of traffic fow. Sampe no Soution From the cacuated vaues of fow, density and speed, the three fundamenta diagrams can be potted as shown in figure 4:2. Dr. Tom V. Mathew, IIT Bombay 4.4 February 19, 2014

5 Sampe no. m a m o m p m w = (m o m p ) t a t w = ma+mw t a+t w u = t w mw k = v speed u density k speed u fow fow density k Figure 4:2: Fundamenta diagrams of traffic fow Dr. Tom V. Mathew, IIT Bombay 4.5 February 19, 2014

6 4.5 Summary Traffic engineering studies differ from other studies in the fact that they reuire extensive data from the fied which cannot be exacty created in any aboratory. Speed data are coected from measurements at a point or over a short section or over an area. Traffic fow data are coected at a point. Moving observer method is one in which both speed and traffic fow data are obtained by a singe experiment. 4.6 References 1. L. R Kadiyai. Traffic Engineering and Transportation Panning. Khanna Pubishers, New Dehi, Dr. Tom V. Mathew, IIT Bombay 4.6 February 19, 2014

Traffic data collection

Traffic data collection Chapter 32 Traffic data coection 32.1 Overview Unike many other discipines of the engineering, the situations that are interesting to a traffic engineer cannot be reproduced in a aboratory. Even if road