Homework 6 (HW 6) Solutions / Due: Fri. 26 October 2007
CE361 HW7 - 2 -
GEOMETRIC DESIGN AND UNSIGNALIZED INTERSECTIONS
1. (15 points) Speed Limit in School Zone (Vertical Curves). FTE Problem 7.7.
Because speed is an unknown, it would take a large number of trial calculations to determine the speed at which the SSD standard is met. FTE Table 7.6 summarizes such calculations for standard values of h1 and h2. With A = |-5.4 - 7.6| = 13% and L = 190 feet, K = L/A = 190/13 = 14.6. Interpolate K=14.6 in the “Crest Curves” column of Table 7.6 between K=12 at 25 mph and K=19 at 30 mph to get 26.85 mph à27 mph.
2. (15 points) Horizontal Curve (freeway ramp). FTE Problem 7.14.
The “centerline” of a single lane is also the middle of the innermost lane, so that R = Rv. Ms = 19.4 ft. To use FTE (7.20), we need to find Rv from the information provided.
(7.9)’ D = ; (7.8)’ R = = 399.80 ft. = Rv
(7.20) SSD = = 13.955*17.92 = = 250.12 ft.
From interpolation in Table 7.4, speed = 35 mph.
3. (15 points) Superelevation on offramp. An offramp for part of a proposed cloverleaf freeway interchange must fit in a space that allows only Rv = 440 feet. Offramps of this type usually have a posted speed limit of 40 mph. To the nearest 0.001, what value of e should be considered for the design of this offramp?
In FTE Figure 7.22, V = 40 mph corresponds to f = 0.15. After rearranging (7.23), e = - fside = - 0.15 = 0.244 – 0.15 = 0.094.
4. (20 points) Gap acceptance analysis.
Sort the accepted and rejected gaps in ascending order. Convert these columns into “%aRT<t” and “%rRT>t”. Find the value of t (by interpolation between 5 and 6 seconds) at which “%aRT<t” = “%rRT>t”. See the data and cumulative plot below. Tcrit = 5.73 seconds.
t sec / %aRT<t / %rRT>t0 / 0 / 100.0
1 / 0.0 / 89.1
2 / 0.0 / 47.7
3 / 0.0 / 27.3
4 / 1.1 / 17.2
5 / 6.8 / 9.4
6 / 8.0 / 7.0
7 / 18.2 / 2.3
8 / 23.9 / 1.6
9 / 29.5 / 1.6
10 / 36.4 / 0.8
11 / 40.9 / 0.0
/
5. Critical approach speeds. An intersection is laid out as shown in FTE Figure 8.5. North is to the top of the figure. Major Street is 44 feet wide and Minor Street is 26 feet wide. Parking is allowed on both sides of Major Street, but not on Minor Street. The building on the NW corner is 25 feet from Major Street and 14 feet from Minor Street. The building on the SW corner is 45 feet from Major Street and 19 feet from Minor Street. The typical speed on Major Street is 38 mph.
A. (10 points) Parking permitted on Major Street.
a’ = 12ft, b’ = min{26/2 + 3; 26 – 12} = min{16;14} = 14ft; c’ = 6ft, d’ = 44/2 + 3 = 25ft. a = a’ + a” = 12 + 25 = 37ft; b = b’ + b” = 14 + 14 = 28ft; c = c’ + c” = 6 + 19 = 25ft; d = d’ + d” = 25 + 45 = 70ft. Therefore, (b,a) = (28,37) and (c,d) = 25,70). Draw a line from 38 mph on the A scale in FTE Figure 8.6 (see next page) through point (28,37) to the B scale. The value on the B scale is 13 mph. Because this peed is between 10 and 15 mph, this indicates that a Yield sign is appropriate, subject to other considerations.
B. (5 points) Parking prohibited.
a’=6ft now, making a = a’ + a” = 6 + 25 = 31ft. Nothing else changes. Draw a line from 38 mph on the A scale in FTE Figure 8.6 through point (28,31) to the B scale. The value on the B scale is 11 mph. This speed is still in the 10-15 mph Yield sign range, subject to other considerations.