1. Introduction to Transportation Engineering 1 Instructor Dr. Norman Garrick Tutorial Instructor: Hamed Ahangari March 2016

2. Traffic Stream Analysis 2

3. 3 Basic Concepts Flow Rate Headway Density Spacing Speed

4. The number of vehicles (n) passing a designated roadway point in a given time interval (t) The unit of flow usually is vehicle per hour. 4 Flow Rate (q) measurement point

5. Headway is the time (in seconds) between vehicles passing a specific location, h Relationship between flow and headway 5 Headway (h) h (ave) = 1 / q

6. Key equations 6 Flow headway (h) - (s/veh) Flow rate (q) - (veh/h) q=1/(h) (1) T=3sec T=0 sec h 1-2 =3sec

7. Example 1 If the total time for all the vehicles to cross the measurement points is 5 minutes, what is the flow per hour if 15 vehicle pass the counter point? 15 vehicles cross in 5 minutes n=15, t= 1/12 hour Flow, q = 15/(1/12)= 180 vehicles per hour What is the average headway? h = 1/q = 1/180 = 0.0055 hour or 20 sec 7

8. The number of vehicles (n) occupying a given length (l) of a lane roadway at a particular length. The unit of density usually is vehicle per mile. 8 Density (k) D

9. Spacing is the distance (ft) between successive vehicles in a traffic stream (measured from front bumper to front bumper). Relationship between density and spacing 9 Spacing (S) s1s1 s2s2 s3s3 s4s4 D k = 1 / s

10. Key equations 10 Density Spacing (s)-(ft/veh) density-concentration(k) - (veh/mi) k=1/(s) (2) S 1-2 S 2-3

11. Example 2 If there are 8 vehicles in a 1/5 mile of a road, calculate the density and spacing. n=8, l= 1/5 mile density: k = 8/(1/5)= 40 vehicles per mile Spacing s = 1/k = 1/40 = 0.025 mile or 132 ft 11

12. Time  flow Distance  density Time and Distance  Speed 12 Speed (u)

13. Key equations 13 Speed U(TMS)= 1/n ∑ vi (3) U(SMS)=

14. Example 3 In a study, the spot speeds of eight vehicles were observed to be 35, 25, 30, 25, 40, 40, 25 and 20 miles/hour, respectively. Calculate the time mean speed (TMS) and space mean speed (SMS). 14

15. time mean speed (TMS) u tms = 1/n ∑ v i u tms=( 35+25+30+25+40+40+25+20)/8= 240/8=30 (miles/hour) 15

16. space mean speed (SMS) 16

17. Key equation; Speed, Flow, Density 17 q=u.k(4) flow=u(SMS) * density q = k  u (veh/hr) = (veh/mi)  (mi/hr) h = 1 / q (sec/veh) = 1 / (veh/hr)  (3600) s = 1 / k (ft/veh) = 1 / (veh/mi)  (5280)

18. Example 4 Data obtained from aerial photography showed six vehicles on a 600 ft-long section of road. Traffic data collected at the same time indicated an average time headway of 4 sec. Determine (a) the density on the highway, (b) the flow on the road, (c) the space mean speed. 18

19. Solution Given: h=4 sec, l=600 ft, n=6 19 Part (a): – Density (k): K= (n)/(l)= 6/600= 0.01 veh/ft k=0.01*5280= 52.8 veh/mile Part (b): – flow (q): q= 1/h= ¼= 0.25 veh/sec q = 0.25*3600= 900 veh/hour

20. 20 Solution Part (c): – Space Mean Speed (U(sms)): U(sms)= q/k =900/52.8 U(sms)= 17 miles/hour

21. Traffic Flow Curves Maximum Flow, Jam Concentration, Freeflow Speed 21 u k u q k q q max kjkj ufuf k j - jam concentration u = 0, k = k j q max - maximum flow u f - free flow speed k = 0, u = u f

22. Example 5 Assume that : u=57.5*(1-0.008 k) Find: a) u f free flow speed b) k j jam concentration c) relationships q-u, d) relationships q-k, e) q max capacity 22

23. 23 Solution Part a):free flow speed? i)when k=0 u f ii)u=57.5*(1-0.008 k) i+ii)u=57.5*(1-0.008 k)= 57.5*(1-0.008*0) u f =57.5 miles/hour kjkj ufuf

24. 24 Solution Part b): k j jam concentration? i)when u=0 k j ii)u=57.5*(1-0.008 k) i+ii)0=57.5*(1-0.008 k)---- 0.008k=1 k j = 125 veh/miles kjkj ufuf

25. 25 Solution Part c): relationships q-u? i)q=u.k ii)u=57.5*(1-0.008 k)  u/57.5=1-0.008k 1-u/57.5=0.008K  K=125-2.17u (iii) i+iii)q= u.k= u.(125-2.17u) q= 125u-2.17u^2 u q

26. 26 Solution Part d): relationships q-k? i)q=u.k u=q/k ii)u=57.5*(1-0.008 k) i+ii)q/k=57.5*(1-0.008k) q=57.5k -0.46k^2 k q

27. 27 Solution Part e): q max capacity ? i) ii)q=57.5k -0.46k^2 d(q)/d(k)=0 57.5-0.92k=0 k m =62.5 q max =1796 veh/hour k q q max

28. Example 6 The data shown below were obtained on a highway. Use linear regression analysis to fit these data and determine – (a ) the free speed, – (b) the jam density, – (c) the capacity, – d) the speed at maximum flow. 28 Speed (mi/h)Density (veh/mile) 14.285 24.170 30.355 36.847 40.141 50.620 55.015

29. Plot data 29

30. from plot: u = -0.57k + 62.92 Part a) u f =62.92 miles/hour Part b)k j = 110.8 veh/mi Part c) q max = 1736 veh/hr @ q max, u = 31.5 mphandk = 55.2 veh/mi 30 Solution