1 h. Page 1 of 12 FINAL EXAM FORMULAS. Stopping Sight Distance. (2 ) N st U Where N=sample size s=standard deviation t=z value for confidence level

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1 Page 1 of 12 FINAL EXAM FORMULAS Stopping Sight Distance 2 2 V V d 1.47Vt i f a 2 2 Vi Vf d 1.47Vt 30( f 0.01 G) Where d = distance (ft) V = speed (mph) t = time (sec) a=deceleration rate (ft/sec 2 ) f = friction value (note f=a/g) G = grade (percent) Peak Hour Factor V PHF 4V m15 Where V = peak hour volume V m15 =maximum 15 minute volume within the peak hour Speed-Flow-Density relationships q SD D S Sf 1 D j 2 D q Sf D D j 2 S q Dj S S f SfDj qmax capacity 4 Where q=flow, S=speed, D=density q 1 h Where h = average headway Sample Size (2 ) N st U 2 2 Where N=sample size s=standard deviation t=z value for confidence level ε=precision of measurements U=percentile speed factor, see table below U Percentile Speed th th or 85th th or 93rd th or 95th TMS AND SMS TMS Confidence Level (%) z statistic N Si N i 1 N d SMS N t i i1 Units must be adjusted to mph where: Sign Legibility 2 tan H 2 D N = number of vehicles S = speed at a point d = length of road t = time to travel length of road Cosine Correction measured speed actual speed cos( )

2 Page 2 of 12 Webster s Minimum Delay Equation 1.5L 5 Cmin (1 v ) s Interval Times G=C-(Y+AR) v g s G v s 1.47V y t 2a G W L ar 1, 1.0 sec min 147V. Where: C=cycle length y = phase yellow time Y=y ar = phase all-red time AR=ar g= phase green time G=g t = reaction time, sec For through movement: V = 85 th percentile if provided V = speed limit +7 if using speed limit For left turn movement V = (speed limit 5) for yellow calculation V = 20 mph for all red calculation a = deceleration rate, ft/s 2 (use positive value in equation) G = grade, percent W = width of intersection L = average vehicle length Minimum Green Times Major street through: 10 seconds Minor street through: 7 seconds Major street left: 7 seconds Minor street left: 7 seconds Pedestrian Signal Timing Pedestrian Clearance Time = Pedestrian Change Interval + Buffer Interval Pedestrian Change Interval = Flashing Don t Walk Indication Method A: Ped Clearance Time = time to walk from curb to curb at 3.5 fps Method B: Walk + Ped Clearance Time = time to walk from ped detector to far curb at 3.0 fps. If ped detector not provided, use 6 ft for distance to near curb Signal Delay Control delay = d 1 +d 2 +d C [1 g /C)] d1 1 [min (1,X )g /C] 2 8kIX d2 900T X 1 X 1 ct ,600 Q b Qe Q Qe Q Q eo eo b d3 ta vt 2 2cA 2cA dv d i i A vi Where: Terms as before plus X = v/c ratio for lane group T = analysis time period, hr k = adjustment factor for type of controller I = upstream filtering/metering adjustment factor c = capacity of lane group d A = delay for approach LOS Criteria for Signal Delay LOS Control Delay (sec/veh) A 10 B > C > D > E > F > 80

3 Page 3 of 12 Saturation Flow Rate s=s o Nf w f HV f g f p f bb f a f LU f LT f RT f Lpb f Rpb Where: s= adjusted saturation flow rate (veh/h/ln) s 0 = base saturation flow rate (pc/h/ln), f w =adjustment factor for lane width, f HV =adjustment factor for heavy vehicles in traffic stream, f g =adjustment factor for approach grade, f p =adjustment factor for existence of a parking lane and parking activity adjacent to lane group, f bb =adjustment factor for blocking effect of local buses that stop within intersection area, f a =adjustment factor for area type, f LU =adjustment factor for lane utilization, f LT =adjustment factor for left-turn vehicle presence in a lane group, f RT =adjustment factor for right-turn vehicle presence in a lane group, f Lpb =pedestrian adjustment factor for left-turn groups, and f Rpb =pedestrian-bicycle adjustment factor for right-turn groups. where P g is the approach grade for the corresponding movement group (%).

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5 Page 5 of 12 Roundabout Control Delay 3,600 x 3,600 2 c d 900T x 1 x 1 5 min x,1 c 450T Roundabout Capacity Formulas No. of No. of Opposing Formula Entry Lanes Circulating Lanes v c 1,130e c,pe One One e,pce v c 1,130e c,pe One Two e,pce v c c,pe e,pce 1,130e Two One for each lane v c 1,130e c,pe Two (right lane only) Two e,r,pce v c 1,130e c,pe Two (left lane only) Two e,l,pce c e,pce =lane capacity, adjusted for heavy vehicles, pc/h v c,pe =conflicting flow, pc/h LOS Criteria for Roundabout Delay LOS Control Delay (sec/veh) A 10 B > C > D > E > F > 50 or v/c > 1.0

6 Page 6 of 12 Freeway Segment Analysis Steps: 1. Compute free flow speed 2. Select free flow speed curve 3. Adjust demand volume 4. Check capacity limits 5. Estimate speed and density 6. Determine level of service

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8 Maximum Service Flow Rates Page 8 of 12

9 Page 9 of 12 Weaving Analysis Steps 1. Volume adjustment 2. Maximum weaving length 3. Weaving section capacity 4. Lane changing rates 5. Average speed of weaving and non-weaving vehicles 6. Density and level of service

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