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16 This section presents background information on the con- ceptual models utilized by AASHTO in determining minimum recommended acceleration and deceleration lane lengths for entrance and exit terminals, respectively. The focus of this research is on evaluating the appropriateness of the existing AASHTO models given current driver behavior and vehicle performance characteristics. 3.1 Freeway Mainline Entrance Terminals At least since the 1965 Blue Book, and still in the 2004 Green Book, AASHO/AASHTO policies have, in principle, used a sim- ple kinematic equation (i.e., Equation 1) with constant accelera- tion to calculate minimum acceleration lane lengths for freeway mainline entrance terminals. The minimum acceleration lane length is based on a combination of the following: A. The speeds at which drivers enter the acceleration lane (i.e., the speed at the end of the rampâs controlling feature). B. The manner of acceleration. C. The speeds at which drivers merge with through traffic (i.e., the speed at the end of the acceleration lane). These three components are used in the following equa- tion to determine the recommended length of the acceleration lane: L V V a Acc m r = ( ) â ( )1 47 1 47 2 1 2 2 . . ( ) where: LAcc = Acceleration lane length, ft Vm = Merge speed, mi/h Vr = Initial speed on ramp (or speed after exiting controlling feature), mi/h a = Acceleration rate, ft/s2 The 1965 Blue Book provides the most detailed informa- tion on how the current design values in the 2004 Green Book are determined, but it should be noted that for some combi- nations, the 2004 Green Book acceleration lane lengths differ slightly from the 1965 Blue Book values. From the 1965 Blue Book, the following points are noted concerning the three primary inputs: â¢ For Point A, the 1965 Blue Book assumes that drivers will exit the curve at an âaverage running speedâ that is less than the curveâs design speed. Because a longer acceleration length is needed to bring the vehicleâs speed up to the merging speed, this is a conservative assumption. â¢ For Point B, the 1965 Blue Book provides graphs that show acceleration rates for different conditions. The curve used to generate the 1965 Blue Book acceleration rates was for ânormal accelerationâ for passenger vehicles on level grade as determined in a 1937 Bureau of Public Roads study. Per the 1965 Blue Book, the data were con- verted to show âdistance traveled while accelerating from one to another.â The resulting curves could be used to determine the acceleration distance from initial speed values to speed reached values, although the 1965 Blue Book also included these values. â¢ For Point C, the 1965 Blue Book states that the speed of the entering vehicles should approximate that of the through traffic which would be equal to the average running speed of traffic on the highway. Later, the 1965 Blue Book states âit is satisfactory and does not unduly inconvenience through traffic for vehicles from the acceleration lane to enter the through pavement at a speed approximately 5 mi/h less.â Table 1 presents the minimum acceleration lane lengths for entrance terminals from Green Book Exhibit 10-70, for flat grades of 2 percent or less. Table 1 also presents the accelera- S e c t i o n 3 AASHTO Models for Freeway Entrance and Exit Terminals
17 tion rates used to generate those values, based on Equation 1. Overall, the pattern is a decreasing acceleration rate as the initial speed increases, but there are situations when this overall pat- tern is not followed. Exhibit 10-71 in the 2004 Green Book includes adjustment factors for when the acceleration lane occurs on a grade of 3 to 4 percent or 5 to 6 percent (see Table 2). Similar values were included in the 1954 AASHO Policies on Geometric High- way Design (an earlier version of the AASHO Blue Book). Given the similarities between the values in the 2004 and 1954 editions, it appears that the source of the adjustment factors in the 2004 Green Book could be the values in the 1954 Blue Book. The source of the adjustment factors per the 1954 Blue Book was to apply principles of mechanics to rates of speed change for level grades. The direct quote from the 1954 Blue Book follows: Deceleration distances are longer on downgrades and shorter on upgrades, while acceleration distances are longer on upgrades and shorter on downgrades. Data on driver behavior while decelerating or accelerating on grades are not available, but they may be approximated by applying principles of mechanics to rates of speed change for level grades, recognizing that drivers accelerating on upgrades open throttles more than the equiva- lent for normal acceleration on level grades. Calculations result in lengths of acceleration and deceleration lanes on grades as compared with those on the level . . . The ratio . . . multiplied by the length (on level) . . . gives the length of speed-change lane on grade. 3.2 Freeway Mainline Exit Terminals At least since the 1965 Blue Book, and still in the 2004 Green Book, AASHO/AASHTO policies have used a basic two-step process for establishing design criteria for exit ramps. Deceler- ation is accomplished first as the driver removes his or her foot from the accelerator pedal and the vehicle slows in gear for a period of time (assumed to be 3 s) without the use of brakes, and then as the driver applies the brakes and decelerates at a comfortable rate. Equations 2 and 3 are used to represent this dual process. The minimum deceleration lane length is based on the combination of the following inputs: A. The speed at which drivers maneuver onto the auxiliary lane. B. The speed at which drivers turn after traversing the deceleration lane. C. The manner of deceleration. L V t d t V V Decel h n n n r a = â ( ) + ( ) â1 47 0 5 1 47 1 472 2 . . . .( )2 2 2 dwb ( ) V V d t a h n n = +1 47 1 47 3 . . ( ) where: LDecel = Deceleration lane length, ft Vh = Highway speed, mi/h Design speed (mi/h) Speed reached (mi/h) Acceleration length, L (ft) for entrance curve design speed (mi/h) Stop 15 20 25 30 35 40 45 50 Initial speed (mi/h) 0 14 18 22 26 30 36 40 44 2004 Green Book 30 35 40 45 50 55 60 65 70 75 23 27 31 35 39 43 47 50 53 55 180 280 360 560 720 960 1,200 1,410 1,620 1,790 140 220 300 490 660 900 1,140 1,350 1,560 1,730 â 160 270 440 610 810 1,100 1,310 1,520 1,630 â â 210 380 550 780 1,020 1,220 1,420 1,580 â â 120 280 450 670 910 1,120 1,350 1,510 â â â 160 350 550 800 1000 1230 1,420 â â â â 130 320 550 770 1,000 1,160 â â â â â 150 420 600 820 1,040 â â â â â â 180 370 580 780 Acceleration Rates (ft/s2) Used to Reproduce Acceleration Lengths 30 35 40 45 50 55 60 65 70 75 23 27 31 35 39 43 47 50 53 55 3.18 2.81 2.88 2.36 2.28 2.08 1.99 1.92 1.87 1.83 2.57 2.62 2.76 2.27 2.17 1.98 1.91 1.84 1.81 1.77 â 2.73 2.55 2.21 2.12 2.03 1.85 1.79 1.77 1.79 â â 2.45 2.11 2.04 1.89 1.83 1.79 1.77 1.74 â â 2.57 2.12 2.03 1.89 1.82 1.76 1.71 1.68 â â â 2.19 1.92 1.86 1.77 1.73 1.68 1.62 â â â â 1.87 1.87 1.79 1.69 1.63 1.61 â â â â â 1.79 1.57 1.62 1.59 1.48 â â â â â â 1.64 1.65 1.63 1.51 Table 1. 2004 Green Book minimum acceleration lane length values and corresponding acceleration rates (adapted from AASHTO, 2004).
18 Va = Speed after tn s of deceleration without brakes, mi/h Vr = Entering speed for controlling exit ramp curve, mi/h tn = Deceleration time without brakes (assumed to be 3 s), s dn = Deceleration rate without brakes, ft/s2 dwb = Deceleration rate with brakes, ft/s2 The 1965 Blue Book provides the most detailed information on how the current design values in the 2004 Green Book are determined, but it should be noted that the 2004 Green Book deceleration lane lengths differ slightly from the 1965 Blue Book values. From the 1965 Blue Book, the following points are noted concerning the three primary inputs: â¢ For Point A, the 1965 Blue Book states that âmost drivers travel at a speed not greater than the average running speed of the highway.â For example, on a freeway with a 70 mi/h design speed, the assumption is that a driver will enter the auxiliary lane at 58 mi/h. â¢ For Point B, the 1965 Blue Book provides assumed aver- age running speeds for the ramp, based on the design speed of the limiting curve on the ramp. For example, a ramp with a 40 mi/h curve design speed, the speed reached at the end of the deceleration length is assumed to be 36 mi/h. â¢ The values for points A and B are clearly provided in the 1965 Blue Book. However, for Point Câthe manner of decelerat- ing or the deceleration factorsâthe values are not as clear. The 1965 Blue Book states that deceleration is a two-step process: first, the accelerator pedal is released (assumed for 3 s) and the vehicle slows in gear without the use of brakes and second, the brakes are applied. Two graphs are included in the 1965 Blue Book (Blue Book Figure VII-15) to provide these distances. The graphs were based on data from studies conducted in the 1930s. The 1965 Blue Book also states: âA comfortable overall rate of deceleration while braking from 70 to a complete stop has been found to be about 6.2 mi/h per second (9 ft per second) . . . In applying this rate at approaches to intersections, it is logical to assume that it decreases as the approach speed is lowered in a manner similar to that found in approaching a stop sign. Accordingly, the overall deceleration rate is assumed to vary from 6.2 mi/h per second (f = 0.28) for initial speed of 70 to 4 mi/h per second (f = 0.18) for initial speed of 30 mi/h.â Table 3 provides the deceleration rates for the recommended minimum deceleration lane lengths as provided in Green Book Deceleration Lanes Design speed of highway (mi/h) Ratio of length on grade to length on level for design speed of turning curve (mi/h)* All speeds 3 to 4% Upgrade 0.9 3 to 4% Downgrade 1.2 All speeds 5 to 6% Upgrade 0.8 5 to 6% Downgrade 1.35 Acceleration Lanes Design speed of highway (mi/h) Ratio of length on grade to length on level for design speed of turning curve (mi/h)* 20 30 40 50 All speeds 3 to 4% Upgrade 3 to 4% Downgrade 40 45 50 55 60 65 70 1.3 1.3 1.3 1.35 1.4 1.45 1.5 1.3 1.35 1.4 1.45 1.5 1.55 1.6 â â 1.4 1.45 1.5 1.6 1.7 â â â â 1.6 1.7 1.8 0.7 0.675 0.65 0.625 0.6 0.6 0.6 5 to 6% Upgrade 5 to 6% Downgrade 40 45 50 55 60 65 70 1.5 1.5 1.5 1.6 1.7 1.85 2.0 1.5 1.6 1.7 1.8 1.9 2.05 2.2 â â 1.9 2.05 2.2 2.4 2.6 â â â â 2.5 2.75 3.0 0.6 0.575 0.55 0.525 0.5 0.5 0.5 *Ratio in this table multiplied by length of acceleration/deceleration distances gives length of acceleration/deceleration distance on grade. Table 2. SCL adjustment factors as a function of grade (AASHTO, 2004).
19 Exhibit 10-73, based upon the assumptions described above. The overall pattern shows higher rates of deceleration for higher speeds. (Note: working down several of the columns in Table 3, some of the initial deceleration rates during braking are inconsistent with other rates in the column. The inconsis- tencies are a result of scaling distance and speed information from graphs in the 1965 Blue Book.) Similar to the design of acceleration lanes, the 2004 Green Book includes adjustment factors for when the deceleration lane occurs on a grade of 3 to 4 percent or 5 to 6 percent (see Table 2). The adjustment factors are based upon principles of mechanics to rates of speed change for level grades. For comparison purposes, Table 4 provides deceleration rates for the recommended minimum deceleration lane lengths as provided in Green Book Exhibit 10-73, assuming a constant rate of deceleration from the average running speed on the freeway to the average running speed entering the controlling exit ramp curve. The deceleration rates in Table 4 are less than the deceleration rates while braking provided in Table 3. 3.3 Operational Assumptions of AASHTO Models AASHTO policy for the geometric design guidance of free- way mainline ramp terminals is based on a single set of oper- ational assumptions that can be characterized as representing free or unconstrained merging behavior. Acceleration lane lengths are based on vehicle capabilities, driver comfort, and simplifying assumptions regarding initial speed and freeway operating speed of the merge. One could characterize this operational model as being reflective of rural, high-speed, low-density conditions. Perhaps the greatest apparent need is to explicitly consider design under a range of freeway density, speed, and gap condi- tions. It is now common practice for agencies to reconstruct urban freeways, or construct new interchanges with design- year traffic and conditions no better than LOS E. As such, the designer intends that traffic during the design hour will merge into a traffic stream with limited gaps. Such gaps may occur Highway design speed (mi/h) Speed reached (mi/h) Deceleration length, L (ft) for design speed of exit curve (mi/h) Stop 15 20 25 30 35 40 45 50 For average running speed on exit curve (mi/h) 0 14 18 22 26 30 36 40 44 2004 Green Book 30 35 40 45 50 55 60 65 70 75 28 32 36 40 44 48 52 55 58 61 235 280 320 385 435 480 530 570 615 660 200 250 295 350 405 455 500 540 590 635 170 210 265 325 385 440 480 520 570 620 140 185 235 295 355 410 460 500 550 600 â 150 185 250 315 380 430 470 520 575 â â 155 220 285 350 405 440 490 535 â â â â 225 285 350 390 440 490 â â â â 175 235 300 340 390 440 â â â â â â 240 280 340 390 1st Deceleration Rates (ft/s2) While Coasting in Gear Used to Reproduce Deceleration Lane Lengths 30 35 40 45 50 55 60 65 70 75 28 32 36 40 44 48 52 55 58 61 â1.04 â1.53 â1.52 â2.01 â2.51 â2.01 â2.98 â2.50 â2.50 â2.99 â1.04 â1.53 â1.52 â2.01 â2.51 â2.01 â2.98 â2.50 â2.50 â2.99 â1.04 â1.53 â1.52 â2.01 â2.51 â2.01 â2.98 â2.50 â2.50 â2.99 â1.04 â1.53 â1.52 â2.01 â2.51 â2.01 â2.98 â2.50 â2.50 â2.99 â â1.53 â1.52 â2.01 â2.51 â2.01 â2.98 â2.50 â2.50 â2.99 â â â1.52 â2.01 â2.51 â2.01 â2.98 â2.50 â2.50 â2.99 â - â â2.51 â2.01 â2.98 â2.50 â2.50 â2.99 â â â â â2.51 â2.01 â2.98 â2.50 â2.50 â2.99 â â â â â â â2.98 â2.50 â2.50 â2.99 2nd Deceleration Rates (ft/s2) While Braking Used to Reproduce Deceleration Lane Lengths 30 35 40 45 50 55 60 65 70 75 28 32 36 40 44 48 52 55 58 61 â5.75 â5.83 â5.66 â6.38 â6.74 â7.10 â7.07 â7.55 â7.40 â7.76 â6.42 â5.75 â5.22 â6.05 â6.57 â7.08 â7.19 â7.43 â7.41 â8.02 â5.49 â5.38 â5.11 â5.68 â6.28 â6.86 â6.99 â7.27 â7.27 â7.90 â8.97 â6.68 â5.66 â6.91 â7.20 â7.55 â7.45 â8.03 â7.77 â8.06 â â10.29 â5.95 â6.83 â7.86 â7.86 â7.70 â7.76 â7.53 â7.85 â â â4.42 â6.18 â6.55 â7.46 â7.34 â7.49 â7.60 â7.65 â â â â â6.23 â7.49 â6.98 â7.51 â7.45 â7.70 â â â â N/A â7.86 â7.43 â7.66 â7.54 â7.62 â â â â â â â16.84 â9.60 â8.17 â8.49 Table 3. 2004 Green Book minimum deceleration lane length values and corresponding deceleration rates (adapted From AASHTO, 2004).
20 randomly, and may not occur when the entering driver is pre- pared to merge. As a result, drivers routinely are faced with judg- ing gaps, adjusting their speeds, and often aborting their merge or producing extreme acceleration and/or speed behavior. The current AASHTO model does not provide for such behavior, but it is less clear whether the dimensions the model produces can accommodate extreme acceleration or speeds. There may be circumstances where it does, but also some where it does not. Ideally, a robust ramp merging model will reflect, within reason, the above design expectation. The following condi- tions represent potential traffic operational scenarios, any one of which may control the geometric design of a given entrance ramp: Condition IâFree Merge at LOS A to C. This traffic condition is consistent with current AASHTO design assumptions and approaches. At high LOS, gaps are frequent and well in excess of the minimum acceptable gap. Merging speeds may vary to reflect the range in AASHTO mainline operating speeds (50 to 70 mi/h dependent on the context). Traffic opera- tions entering the freeway are based on vehicle performance capabilities and driver comfort. The âtaskâ of navigation and merge is relatively simple. The driver workload may be so simple as to allow driving tasks to be shared or overlapped as long as the three-dimensional geometry provides sufficient sight lines. In other words, drivers can search for a gap and comfortably accelerate at the same time. Condition IIâConstrained Merge at LOS D to E. This traf- fic condition is common in urban areas with high-volume freeways. Freeway operating speeds may still be relatively high (e.g., 40 to 50 mi/h), but long gaps are non-existent, median gaps are shorter, and acceptable gaps may be less frequent than merging vehicle arrivals. The merging task is thus inherently more complex. Drivers may vary their acceleration behavior, slowing down to wait for a gap or speeding up to catch a gap before upstream traffic reaches the painted nose. Gap acceptance behavior would appear most significant in designing for this condition. Condition IIIâForced Merge at LOS E to F. When mainline traffic is dense in Lane 1 and overall operating speeds are below 40 mi/h, the entire merging maneuver is significantly different from the previous two conditions. Drivers can eas- ily adjust to the mainline speed because mainline traffic is typically moving slowly, but they may need considerable length to find or ânegotiateâ a gap for merging. Consideration of a conceptual merging model in terms of these three operating conditions would acknowledge the need for a ramp to serve a range of conditions varying throughout a day. Correspondingly, it may be desirable to evaluate a con- ceptual diverging model in terms of these three operating con- ditions, although the diverge maneuver should be less critical under constrained and forced conditions, since vehicles will be entering the deceleration lane at reduced speeds. Highway design speed (mi/h) Speed reached (mi/h) Deceleration (ft/s2) for design speed of exit curve (mi/h) Stop 15 20 25 30 35 40 45 50 For average running speed on exit curve (mi/h) 0 14 18 22 26 30 36 40 44 2004 Green Book 30 28 â3.59 â3.16 â2.91 â2.30 â â â â â 35 32 â3.93 â3.56 â3.59 â3.14 â2.50 â â â â 40 36 â4.36 â4.01 â3.95 â3.72 â3.60 â2.75 â â â 45 40 â4.47 â4.31 â4.22 â4.07 â3.98 â3.42 â â â 50 44 â4.79 â4.62 â4.50 â4.40 â4.30 â3.91 â3.06 â2.07 â 55 48 â5.16 â4.98 â4.84 â4.77 â4.61 â4.31 â3.80 â3.22 â 60 52 â5.49 â5.39 â5.33 â5.19 â5.07 â4.79 â4.33 â3.96 â3.44 65 55 â5.71 â5.63 â5.59 â5.47 â5.38 â5.19 â4.77 â4.51 â4.18 70 58 â5.88 â5.78 â5.74 â5.63 â5.56 â5.41 â5.06 â4.86 â4.52 75 61 â6.06 â5.97 â5.89 â5.80 â5.70 â5.67 â5.32 â5.18 â4.92 Table 4. Corresponding deceleration rates for 2004 Green Book minimum deceleration lane length values assuming constant deceleration.