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Traffic Engineering, 4th Edition Roess, R.P., Prassas, E.S., and McShane, W.R. Solutions to Problems in Chapter 18 Problem 18‐ 18‐1
The solution involves evaluating the four sight triangles of this intersection. As two of the sight triangles are not obstructed, this problem hinges on the corners occupied by the Wheat Field and Barn. Based upon the relative volumes, the NB and SB approaches will will be be considered to be to be the minor approaches. Beginning with the NB approach (Vehicle A will be on this approach), the position of Vehicle A is assumed to be to be at its safe stopping distance, or: 2
d a = 1.47 S t +
S
30 (0.348 ± 0)
= (1.47 * 35 * 2.5) +
352 30 * 0.348
= 128.6 + 117.4 = 246 ft
Using the geometry of the sight triangle, the actual position of Vehicle B (d b) when the two drivers first see each other can be can be determined: d b (act ) =
a d A d A − b
=
30 * 246 246 − 60
= 39.7 ft
In order for the operation to be deemed safe, one of two conditions for d b must be less than this value. The first value is based upon the safe stopping distance for Vehicle B, while the second allows the two vehicles to pass the collision point without colliding. Then: d b min ( Rule 1) = (1.47 * 40 * 2.5) +
40 2 30 * 0.348
= 147.0 + 153.3 = 200.3 ft
⎛ S B ⎞ 40 ⎞ ⎟⎟ + 12 = (246 + 18) ⎛ ⎜ ⎟ + 12 = 313.7 ft ⎝ 35 ⎠ ⎝ S A ⎠
d b min ( Rule 2) = (d A + 18) ⎜⎜
Neither of these are less than the actual distance of 39.7 ft. Therefore, the intersection cannot be safely operated under basic under basic rules of the road. An analysis of the other obstructed sight triangle could be done, but it is not necessary. As 1
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long as one sight triangle is unsafe, rules of the road cannot be used as the only form of control. Problem 18‐2
In this intersection, there are only two sight triangles, both of which are obstructed. The one that appears to be most restricted is to the left of the vehicle approaching on the one‐way street. It will be analyzed first. The vehicle on the one‐way street is Vehicle A. It will be placed one safe‐ stopping distance from the collision point: d A = (1.47 * 30 * 2.5) +
30 2 30 (0.348 + 0.045)
= 110.3 + 76.3 = 186.6 ft
From the sight triangle, the actual distance of Vehicle B from the collision point when both drivers can see each other is: d b ( act ) =
20 *186.6 186.6 − 20
= 22.4 ft
This must now be compared to the two minimum conditions, as in Problem 18‐1 previously: d b min ( Rule 1) = (1.47 * 45 * 2.5) +
45 2 30 * 0.348
= 165.4 + 194.0 = 359.4 ft
⎛ 45 ⎞ ⎟ + 12 = 318.9 ft 30 ⎝ ⎠
d b min ( Rule 2) = (186.6 + 18) ⎜
Neither rule for safe operation is met. Therefore, operation under basic rules of the road is not safe. In most cases, a STOP‐sign would be recommended. As in Problem 18‐1, the second sight triangle could be analyzed, but it is not necessary, as the intersection has already failed the safety test for one sight triangle.
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Problem 18‐3
In this case, the visibility for SB vehicles is not obstructed. Sight distances for NB vehicles approaching the STOP‐sign, however, should be checked. The distance of Vehicle A from the collision point is found as: d A = 18 + d ci
This assumes that the vehicle is stopped at location where the driver’s eye is 18 ft from the curb line. Distance dci is the distance to the center of the nearest conflicting traffic lane. With 14‐ft lanes, this is 7 ft for the Vehicle B and 21 ft for Vehicle C. Then: d A ( for Veh B) = 18 + 7 = 25 ft d A ( for Veh C ) = 18 + 21 = 39 ft
The minimum required sight distance for Veh A and B is given by: d b (min) = 1.47 S maj t g = 1.47 * 35 * 7.5 = 385.9 ft
This is based upon gap acceptance criteria. The actual visibility distances of both Vehicle A and Vehicle B are computed from the sight triangle. These must be more than 385.9 ft for safety. d b ( act ) = d c ( act ) =
35 * 25 25 − 20 20 * 39 39 − 30
= 175 ft = 86.7 ft
Neither sight distance is safe. There are very few alternatives, however, unless signals are warranted. Sight obstructions might be trimmed back if they are not permanent structures, and/or speed limits reduced on the main street. In practice, drivers will inch forward until they can see approaching vehicles before proceedings.
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Problem 18‐4
Because the approach speeds are in excess of 40 mi/h, the 70% criteria will be applied for appropriate warrants. Note that the volumes shown are minima over a 10‐hour period. Thus, they represent the lowest volume within the 10‐hour period. If volumes meet a particular warrant, they will meet it for 10 hours. If they do not meet a particular warrant, it is possible that within the 10 hours, there are hours that do meet the warrant. The information, however, is insufficient to determine this. Warrant 1 Condition A (at 70%) requires 350 veh/h on the major approach, both directions, and 105 veh/h on the highest‐volume minor approach. Condition B requirements are 525 veh/h and 53 veh/h respectively. Using the highest volume street as the “major” street (N‐S), the actual values are 700 veh/h and 350 veh/h respectively. Both Condition A and B are met. The warrant is met. Warrant 2 The figure below shows the 4‐hour vehicular warrant (at 70%), with [700,350] point plotted.
The warrant is easily met. Warrant 3 Warrant 3 has two criteria – peak hour delay, and peak hour volume. The problem does not give delay data, so this portion of the warrant cannot be evaluated. The volume warrant (at 70%) is evaluated on the figure that follows:
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The volume portion of the warrant is met. The warrant is met. Warrant 4 This warrant (at 70%) evaluates pedestrian crossings. As the N‐S street is the “major” street in this analysis, there are a minimum of 90+70 = 160 peds/h crossing the major street for 10 hours. There are two criteria – one for four hours, one for peak hour only. Both are shown in the figures that follow.
The 4‐hour pedestrian criterion is met.
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The peak‐hour pedestrian criterion is not met. Because the 4‐hour pedestrian criterion was met, the warrant is met. Other Warrants Due to lack of information, no other warrant can be evaluated for this intersection. Recommendation Obviously, a signal should be placed here. The minimum volumes (most hours will have more than this) meet all volume ‐ based warrants. Ped signals should be used, but there is not enough information given to recommend a specific form of signalization. Problem 18‐5
Once again, only vehicular volumes are given. Non‐volume‐ based warrants cannot be evaluated. Only Warrants 1 – 3 may be evaluated with the information given. Note that neither the population nor the approach speeds engage a reduction in criteria, so warrants must be met at 100% in this case. To assist in making this evaluation, the table should be re‐arranged to show total 2‐way volume on the major street (N‐S) and the highest single‐direction volume on the minor street (E‐W). The table that follows shows this.
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Table: Volumes for Warrant Analysis Hour
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Major Street Vol (2‐Way) 50 100 175 300 450 700 850 850 750 400 300 300 300 350 350 450 600 700 800 800 400 200 100 100
Minor Street Vol (High Dir) 30 30 50 50 100 250 400 450 375 300 300 150 100 100 100 250 325 375 400 425 325 150 100 50
Warrant 1 Warrant 1, Condition A requires minimum volumes of 600 veh/h on the major street (2 ways) and 150 veh/h (one way) of the minor street. Condition B requires 900 veh/h and 75 veh/h respectively. Hours 6, 7, 8, 9, 17, 18, 19, 20 meet Condition A (8 hours). No hours meet Condition B. The warrant is met. Warrant 2 While all 24 hourly points could be plotted against the 4‐hour volume criteria, if the top 4 don’t meet the warrant, no other set will meet the
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warrant. Hours 7, 8, 19 and 20 appear to be the worst periods. These eight points are plotted on the figure below: [850,400], [850,450], [800,400], and [800, 425].
As all four points are clearly above the decision line, this warrant is met. Warrant 3 Warrant 3 has two parts: peak hour delay, and peak hour volume. There is no delay information given, so the first part cannot be evaluated. The second can be evaluated. The highest volume point [850,450] is plotted. If this hour does not meet the criteria, no other hourly volume pair will.
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As the intersection has 2 lanes (each direction) on the major street and 1 lane (in each direction) on the minor street, the middle decision line is applicable. The warrant is met. A signal is warranted by all three of the volume criteria. No particular form of signalization is recommended without additional information. Problem 18‐6
Because of the 45‐mi/h speeds on the major street (E‐W), the 70% criteria of the volume warrants apply. Because the minor street is a one‐way street, the “total” volume is the “highest directional volume.” Warrant 1 Condition A requires minimum volumes of [420, 105]. Condition B requires [630, 53]. Condition A is met by the following hours: 3‐4 PM, 4‐5 PM, 5‐6 PM, and 6‐7 PM. This is only 4 hours, while 8 are required. Condition A is not met. Condition B is met by the following hours: all hours between 1 PM and 11 PM. This is 10 hours. Condition B is met. The warrant is met. Warrant 2 The highest four‐hour volume period is between 3 PM and 7 PM. These four hours are plotted against the 4‐hour vehicular volume warrant criteria. As all of these points are off the volume scale on the 70% criteria for Warrant 2, and the minor street volumes are above the minimums required, the warrant is met. Warrant 3 The highest volume hour [1150, 160] or [1200, 135] are plotted against the peak hour vehicular volume warrant criteria (70% level).
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As both points lie above the decision line, the warrant is met. The delay portion of Warrant 3 can also be evaluated for vehicles on the STOP‐ controlled approach. In the peak hour, 160 vehicle experience 72 s/veh of delay for a total of 72*160 = 11,520 veh‐sec, or 3.2 hours of aggregate delay. The warrant requires a minimum of 4.0 hours, so this part of Warrant 3 is not met. The warrant is met, as the volume criterion is met. Warrant 4 The highest four hours of pedestrian activity occur between 1 and 4 PM, and between 8 and 9 PM. During these four hours, the major street vehicular volume and pedestrian volumes (crossing the major street) are [800, 200], [855, 210], [1025, 205] and [975,200]. These are plotted against the four‐hour pedestrian warrant (70% level). The highest period [1025, 205] is plotted against the one‐hour pedestrian warrant (70% level).
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As both criteria are met, this warrant is met. Warrant 5 The School Crossing Warrant is not applicable. Warrant 6 The Coordinated Signal Warrant is not applicable. Warrant 7 The Crash Experience Warrant can be evaluated. All relevant criteria are met: There is STOP‐control in place, there are 8 right turn, 3 left turn, and 4 pedestrian accidents that can be corrected by signalization, and Warrant 1B is met at 100%. The warrant is met. Warrant 8 The Roadway Network Warrant is not applicable. Warrant 9 The RR Grade Crossing Warrant is not applicable.
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A signal is clearly warranted at this location. Given the high pedestrian volumes, use of pedestrian signals is suggested for crossing the major street. If an actuated controller is used, a pedestrian actuator should be provided. Problem 18‐7
The high speeds on Broad Street allow the use of 70% criteria in all vehicular and pedestrian volume warrants. Warrant 1 Condition A requires [420, 105] for 8 hours. Condition B requires [630, 53] for 8 hours. Condition A is met by the following hours: 12‐1 PM through 10‐11 PM. This condition is met. Condition B is met by the following hours: 11 AM through 10 PM. This condition is met. The warrant is met. Warrant 2 The four highest volume hours occur between 1 PM and 5 PM, and are as follows: [875, 150], [930, 165], [930, 170], and [870, 160]. These are plotted on the 4‐hour volume criteria (70%).
This warrant is met. Warrant 3 The highest volume hour occurs between 3 and 4 PM [930, 170]. This is plotted against the peak hour volume criteria (70%).
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As the middle decision line is used, the volume portion of the peak‐hour warrant is met. In the worst hour, 170 veh/hr are delayed for 45 s/veh by the STOP‐sign. This is 170*45 = 7,650 veh‐sec or 2.125 veh‐hrs of delay. The warrant requires 4 veh‐hrs, so this portion of the warrant is not met. The warrant is met. Warrant 4 The worst four hours of pedestrian‐vehicle conflict in crossing the major street occur between 2 and 6 PM, with the following volumes: [930, 122], [930, 135], [870, 140], and [780, 125]. These are plotted vs. the 4‐hour pedestrian warrant (70%). The highest of these, [930, 135], is plotted vs. the one‐ hour pedestrian warrant (70%).
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Both the 4‐hour and peak hour pedestrian criteria are satisfied. This warrant is met. Warrants 5 and 6 These warrants do not apply. Warrant 7 The three criteria of this warrant are met. There is already a STOP‐ sign in place; there are 14 accidents that are susceptible to correction by a signal, and Warrants 1, 2, and 3 are met. This warrant is met. Because of the pedestrian accidents, it is imperative that pedestrian signals be used at both crosswalks crossing the major street. If the signal is pretimed, the timing should accommodate pedestrians in every cycle. If the signal is actuated, a pedestrian actuator must be used. Problem 18‐8
The first part of the solution is to determine the “equivalent” volume crossing the tracks. There are no buses, but there are tractor‐trailers. There is also an adjustment for train frequency. For 20 trains per day, from Table 18.11, an adjustment of 1.33 is applied. For 20% tractor‐trailers, from Table 18.13, an adjustment of 1.35 is applied. Thus, the equivalent volume crossing the tracks is 14
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150*1.33*1.35 = 269 veh/h. This is plotted against 300 veh/h on the major street on the Figure 18.9 criteria curve:
The warrant is clearly met, and a signal should be placed. coordinated with the RR crossing signals and gates.
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It should be
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