Question

4. [10 pt] An observer moves at a constant speed of v0 and counted the vehicles that passed him and that he passed, derive the formula for the net count (number passed him – number he passed) q0 in one hour if the space mean speed and density of traffic that he was measuring was u and k, respectively.

Answer 1

4 In order to understand clearly Let us consider speed and delay. Study by floating car method. - - - - - -- The above test is conducted for two lane two way road during the congestion period A test vehicle is doiven with approximately avg speed of flow over a given course of travel of length e O A group of four observers sitting in car records various details as follows Observer 1 15t observer records total Journey time and cumulative delay time Using 2. Stopwatches. Observer2 Location and cause of congestion is recorded by 2nd! observer observer3 3 rd observer counts total number of vehicles overtaking the test vehicle and overtaken by test vehicle. vous concern is lurth observer 3 - Lobserver 4 observer 4 counts total number of vehicles travelling in opposite direchon on opposite lane. Derivation - Steph: when test vehicle is stopped and the traffic is running q=ay Tu vzo Py = 97 — Tv.

Step 2: When test vehicle is ruming and flow is stopped. TO Ivo kaas I TUV as = KL (2) Step 3 - When the test vehicle is running in the direction of flow (94-95) =q tw-KL % = at KL (3) Step 4: when test vehicle is running in opposite directon of How aytas a qtatku qa = ata tkL (4) from equation (3 and equation 4 % = qtw-kh +qa - atat kl (90+qa) = q (totta) .: Traffic volumel flow can be written as q=5 20+qa 7 I twtta kiv= lot ag 7 [Ewttal Now from equation , we can write qooq tw-KL qo= qtwta.L - = 9 tw-ah qo=altw-I) or, qo= ku(tw-t ) Hence Journey time of traffic Hlow is writtenas E = [tw-28]

where, tw - Average Journey time of test vehicle when the test vehicle is running with the flow. ta = Average Journey time of test vehicle when the test vehicle is running against the flow. 9. = Avg number of vehicles overtaking the observer-Avg number of vehicle overtaken by the observer da = Aug. number of vehicles travelling on road when the test vehicle is running in same direction. (It is noted by 4th observer of opposite lane test vehicle) Here to may be tre oreve.