74 TRANSP()RTATl()N RF.SF.ARl.H RECORD 133 Safety Considerations for Truk Climbing Lanes on Rural Highways ANDREW D. ST. JOHN AND DOUGLAS w. HARWOOD Data on the speed profiles of truks on sustained upgrades an b.e ombined with safety estimates to quantify the inreased aident rates aused by slow-moving truks and the hanges in aident rate with distane up the grade. Truk performane and speed data were taken from reent field measurements and were evaluated using the truk performane equations presented in NCHRP Report 185. The effet of speed differenes on aident rate is based on the relationships developed by Solomon. The results show that there is a pronouned inrease in aident rates of passenger ars and truks in the traffi stream only when a sizeable portion of the truk population falls to speeds of 22.5 mph or less. The results indiate that, from a safety standpoint, there 1s little apparent need for truk limbing lanes on moderate upgrades (2 perent) or in the first portion of steeper upgrades. i:owever, t.he results must be interpreted autiously in light of hm1tat1ns 1 the Solomon data that were found during the analysis. In partiular, the Solomon data do not show how aident involvement rates hange within the very important speed range fr?m zero to 22.5 mph, and these data may represent setions with more intersetion- and driveway-related aidents than would typially be found on a sustained grade. Further researh is needed to quantify relationships between speed differenes and aident involvement rates that are speifially appliable to sustained grades. It has long been reognized that truks an ause traffi servie and safety problems on steep, sustained grades. Current AASHTO riteria for truk limbing lanes address these onsiderations through the onept of a ritial grade (1) (one in whih the alignment, truk population, and flow rate may ause an unaeptable redution in the level of traffi servie). Current AASHTO riteria (1) define a ritial grade as one that is long and steep enough to slow a 3-lb/hp truk by at least 1 mph. The AASHTO Green Book reognizes the potential for ollisions between slow-moving truks and faster vehiles overtaking them, but this effet has not been quantified to provide guidane on where truk limbing Janes may be needed. The relationship of speed differenes in the traffi stream to aidents is well known from the work of Solomon (2), who demonstrated that the aident involvement rates of vehiles inrease as the deviation of the vehile speed from the mean speed of traffi inreases. Figure 1 illustrates the form of the relationships developed by Solomon. Although the Solomon data were not olleted speifially for upgrades, Solomon's results suggest that slow-moving truks on a steep upgrade should have higher aident involvement rates than A. D. St. John, 847 E. Amethyst Plae, Tuson, Ariz. 85715. D. W. Harwood, Midwest Researh Institute, 425 Volker Blvd., Kansas City, Mo. 6411. faster-moving vehiles. Data on the speed profiles of truks on grade an be ombined with the safety estimates developed by Solomon to quantify the inreased aident rates of passenger ars and truks in the traffi stream aused by slowmoving truks and the hanges in aident rate with distane up the grade. The results obtained from this analysis have some obvious limitations but illustrate an approah that ould be used to develop safety warrants for truk limbing lanes. This approah ould be used to obtain results more diretly appliable to truk limbing lanes if future researh ould identify relationships between aident rates and speed differentials similar to those of Solomon, but speifially for steep grades. TRUCK PERFORMANCE ON GRADES Truk performane on grades is influened by truk aeleration and speed-maintenane apabilities (typially represented by the truk weight-to-power ratio), by aerodynami drag (represented by the truk weight-to-frontal area), and by the aeleration and speed preferenes of drivers. The truk population used is that doumented in a 1979 paper by St. John (3), whih was the basis for the passenger ar equivaleny fators for truks in Chapters 3 and 7 of the 1985 Highway Capaity Manual (4). The tive-axle truk omponent of the 1979 truk population was updated with speeds measured by the California Department of Transportation in 1983 and 1984 on sustained 4 and 6 perent grades (5). Table 1 summarizes the relative proportions of eight typial ranges of truk harateristis that olletively represent the truk population. The table inludes the relative proportion of eah truk type determined from the ited soures. The horsepower values used in Table 1 represent the installed net horsepower, whih is usually about 94 perent of the engine manufaturer's maximum rated net horsepower. The omputations assume that no truks are present in the traffi stream with weightto-power ratios outside the range of 5 to 4 lb/hp, as represented by the truk population in Table 1. The performane apabilities of truks were omputed using the performane equations in Appendix C of NCHRP Report 185 (6) together with an improved version of the orretion for gear shift delays in Appendix D. The aerodynami drag oeffiients were also redued to values appropriate for modern truk onfigurations. The truk performane equations in the NCHRP report allow the determination of the maximum speed of a truk at any point on a speified grade, as a funtion of truk engine, transmission, aerodynami drag, and driver harateristis.
St. John and Harwood 75 E 1=., i., E 1< -., (I) 1ii a: (I)., E (I),, g <( 1,,.------.-----.-----.----.------,.------, 5, 1, 5, speeds of truk drivers were represented in this investigation by a trunated normal distribution that orresponds well with measurements of free speeds on highways with 55-mph speed limits obtained in NCHRP Projet 3-33 (7). A range of 43 to 67 mph was used for desired speeds of truk drivers, based on a desired speed distribution with a mean value of 55 mph and a standard deviation of 5 mph suggested by field data (7). Table 2 presents eight speifi desired speed levels drawn from that distribution, ranging from 2.4 standard deviations below the mean ( 43 mph) to 2.4 standard deviations above the mean (67 mph), whih were used to represent the range of speed preferenes of drivers. Sine driver speed preferenes were assumed to be normally distributed, the perentages of truk drivers in eah desired speed stratum shown in Table 2 were determined from tables of the standard normal distribution. ESTIMATION OF TRUCK SPEED DISTRIBUTIONS ON SPECIFIC GRADES Variation from Average Speed, mph FIGURE 1 Example of U-shaped urves for aident involvement rate versus speed from Solomon (2). DESIRED SPEEDS OF TRUCK DRIVERS Driver speed preferenes (also referred to as desired speeds) will determine truk speeds at any loation where the desired speed is Jess than the truk speed apability. The desired The truk performane apabilities and truk driver desired speeds an be used together to estimate atual speeds on upgrades. The entrane speed of a truk at the foot of the grade is the lesser of the driver's desired speed and the speed apability of the truk on the approah grade. Truks with exess performane apabilities are assumed not to exeed the driver's desired speed. Table 3 shows the joint distribution of truk harateristis and driver speed preferenes that results from ombining the distributions shown in Tables 1 and 2. Eah of the 64 entries in Table 3 represents the relative likelihood of a partiular TABLE 1 CHARACTERISTICS OF TYPICAL TRUCKS Range of weight/power ratio (lb/hp) Range of weight/frontal area ratio ( 1 b/ft2) Proportion of truk population Lowest performane truks Highest performane truks 318-4 258-318 227-258 195-227 161-195 134-161 15-134 5-15 1161-146 942-1161 829-942 712-829 588-712 489-588 383-489 183-383.122.47.721.15.1392. 1742. 21. 2466 TABLE 2 DESIRED SPEEDS OF DRIVERS Driver desired speed (mph) Standard deviations above or below mean speed Proportion of driver population Slowest drivers Fastest drivers 43-46 46-49 49-52 52-55 55-58 58-61 61-64 64-67 -2.4 to -1.8-1.8 to -1.2-1.2 to -. 6 -.6 to.. to.6.6 to 1. 2 1.2 to 1.8 1.8 to 2.4.282.85.1618 o. 2295.2295.1618.85.282
76 TRANSPORTATION RESEARCH RECORD 133 TABLE 3 PROPORTIONS FOR COMBINATIONS OF SPECIFIC TRUCK TYPE AND DESIRED SPEED Truk Desi red seeed!meh l weight /power Proportion 43-46 46-49 49-52 52-55 55-58 58-61 61-64 64-67 ratio in truk Proe:ortion in driver e:oe:ulation (lb/hp) popu I at ion.282.85.1618.2295.2295.1618.85.282 318-4.122.344.982.1974 258-318.47.1148.3276.6585 227-258.721.233.584.11666 195-227.15.2961.8453.16989 161-195.1392.3925.1126.22523 134-161 o. 1742.4912.1423.28186 15-134.21.5922.1695.33978 5-15.2466.6954.19851.399.28.28.1974.982.344.9341.9341.6585.3276.1148.16547.16547.11666.584.233.2498.2498.16989.8453.2961.31946.31946.22523.1126.3925.39979.39979.28186.1423.4912.48195.48195.33978.1695.5922.56595.56595.399.19851.6954 ombination of the eight truk performane strata and eight desired speed strata. Beause these 64 ombinations are assumed to represent all possible truk performane-desired speed ombinations, the sum of all entries in Table 3 is 1.. Several typial grades were seleted for analysis, inluding sustained 2, 4, and 6 perent upgrades with level ( perent) approah grades. Truk speeds were alulated on eah grade at 2-ft stations until a point on the grade was found where the truks for all ombinations of truk type and desired speed had reahed steady speeds. The weight fators in Table 3 were used to assemble a truk speed distribution at eah station on eah grade using speed strata with a width of 5/3 mph (i.e., 1.67 mph), whih was a onvenient stratum width for orrespondene with the aident data. If no ombinations of truk type and desired speed produed speeds in a partiular 5/3-mph speed stratum, but speeds were produed in strata on either side, the proportion of truk speeds in the empty strata was determined by linear interpolation. This smoothing of the umulative speed distribution urves is logially onsistent beause eah type speed ombination alulated (exept the lowest one-the 4-lb/hp truk with a desired speed of 43 mph) defines the upper speed bound for some portion of the truk population. PASSENGER CAR SPEEDS The passenger ar speed distribution at all stations on eah grade was assumed to be represented by the desired speed distribution shown in Table 2. This approah neglets the moderate dereases in passenger ar speeds that are known to our on steep grades. This ommon assumption is also made in the Highway Capaity Manual proedures (4); that is, passenger ar equivalents are not alulated for passenger ars on grades. SPEED DISTRIBUTIONS FOR MIXED FLOWS The speed distributions in the mixed passenger ar and truk flows at eah 2-ft station on eah grade were obtained by ombining the passenger ar and truk speed distributions for four different proportions of truks in the traffi stream: 5, 1, 15, and 2 perent. These speed distributions are all expressed in terms of the proportion of vehile speeds in eah 5/3-mph speed stratum. The use of expliit speed strata in this way is appropriate beause Solomon's results (2) an then be used to determine the safety impliations of the speed distribution expressed in this form. ACCIDENT RATES AS A FUNCTION OF SPEED DIFFERENCES In evaluating the need for truk limbing lanes on rural highways, the primary safety onern is the risk of rear-end or same-diretion sideswipe aidents involving slow-moving truks. Steep, sustained grades generally have less than average roadside development and few intersetions and driveways, so there is less onern about the potential for angle or turning aidents than at other loations. Climbing lanes may have the potential to eliminate some head-on or oppositediretion sideswipe aidents, but these aident types have no diret relationship to the internal dynamis of the speed distribution in the uphill traffi. Therefore, the aident rate evaluation has been limited to rear-end and same-diretion sideswipe aidents whih, for onveniene, are referred to as rear-end aidents. Two methods for estimating the aident rate orresponding to a partiular speed distribution an be used with Solomon's data (2). These methods are as follows: Method 1: Use data from Table 5, Table 41, and Figure 18 of Solomon's report to estimate rear-end aident rates for all possible ombinations of slower and faster speed strata. For example, the Solomon data an be used to estimate the rear-end aident rate per 1 8 veh-mi for a slower vehile traveling 25 mph and a faster vehile traveling 6 mph. Method 2: Use the data in Tables 5 and 41 of the Solomon report to estimate rear-end involvement aident rates (ounting eah two-vehile aident as two separate aident in-
St. John and Harwood volvements) for speifi speed strata. In other words, the Solomon data an be used to estimate the rear-end aident involvement rate for vehiles traveling in a speifi speed stratum, assuming that the speed distribution of other vehiles on the road is similar to that observed by Solomon. It was found that by smoothing Solomon's data, Method 2 ould be diretly used to determine aident involvement rates. However, the assumption (desribed above) that the speed distribution on the roadway must be similar to that observed by Solomon seems unrealisti for steep grades, so Method 2 appears to be too simplisti for the proposed appliation. Method 1 requires the assumption that the distribution of flow rates on the steep grades being analyzed is the same as the distribution of flow rates at Solomon's field sites; otherwise, the aident rates would need to be adjusted for the differenes in flow rates. This assumption appears more aeptable than the assumption involving speed distributions that must be made to use Method 2. The derivation of Method 1 suggests that, with other fators held onstant, aident rate is proportional to flow rate. It would be desirable to have data from steep grades to onfirm or refute this relationship. Method 1 has the advantage that it expliitly aounts for the effets of hanges in vehile mix and grade geometris. Method 1 an be used to determine aident involvement rates only after reasting Solomon's aident data into slower-vehile-fastervehile ells. The available data and the required iterative proedures annot provide unique results, but do provide very narrow onstraints, whih ensure results that follow logially from Solomon's data. Figures 2 and 3 present overviews of the aident rates derived with Methods 1 and 2. For illustrative purposes, Figure 2 assumes that for eah pair of slower and faster vehile speeds, vehiles with those speeds are present in the traffi stream in equal proportions. (This assumption is neessary to illustrate the aident rates in Figure 2; it is not needed for the analyses that were performed.) The most prominent feature in Figure 2 is the onsequene of low vehile speed, partiularly below 4 mph. A vehile traveling less than 4 mph has a muh inreased likelihood of involvement as either the faster or slower vehile in a two-vehile aident. This ompounded effet from slow vehile speeds leads to nonlinearities in aident-speed relationships and illustrates why it is important to use the Method 1 approah, whih avoids assumptions about similarities in the speed distributions between the field data (Solomon's) and the alulated speed distribution on grades. Figure 3 presents the rear-end aident involvement rates based on speed strata alone. The foregoing 77 1,, 1,, Note: Based on Solomon's data, assuming that equal proportions of vehiles at eah pair of slower and faster speeds are present in the traffi stream. In the reported analyses, these proportions were based on the atual speed distributions. 1,., :;; a: 1 1 With slower vehiles at 55 mph and above the rates inrease slightly above 5 mph values. 2 3 4 5 6 Speed of Faster Vehiles (mph) 7 FIGURE 2 Example of rear-end aident rates for speifi ombinations of slower and faster vehile speed determined using Method 1.
78 TRANSPORTATION RESEARCH RECORD 133 1,,.E J::. 1, Note: Based on Solomon's data, m but adjusted to eliminate aident involvements with zero speed vehiles. 'iii E.!: 1, 1J :; Jii <I) 1, n; er: E "' E 1 1J :; < " 1J :.,.!. "' 1 er: 1 1-----,-.-...---,-.-...----. 1 2 3 4 5 6 7 Vehile Speed (mph) FIGURE 3 Rear-end aident involvement rates as a funtion of vehile speed determined from Solomon's data using Method 2. disussion of Figures 2 and 3 illustrates why Method 1 was found to be more realisti than Method 2, beause Method 1 expliitly onsiders the speed differenes in the traffi stream and was used as desribed below. For simpliity, Solomon's data were ombined over roadway types and over day and night. In Method 1, aident rates were omputed for an array in whih eah ell represented aidents between vehiles in a slower speed stratum (v;) and a faster speed stratum (v;). The aident rate array elements for Method 1 were determined as Ae = 2: 2: [1; 1 P,P/l 4 ] (1) I where Ae = rear-end and same-diretion sideswipe aidents per 1 8 veh-mi, Iii = l 1 [a; 1 N]l[T(p;p;)] (2) a; 1 = perent of observed rear-end and same-diretion sideswipe, aidents involving the ombination of the ith and jth speed strata (Solomon), N = total number of rear-end and same-diretion aidents observed by Solomon = 4,39/2, P; = perent of vehile-miles in ith speed stratum, P 1 = perent of vehile-miles in jth speed stratum, T = total vehile-miles of travel observed by Solomon = 3.671 x 1 9, p; = perent of observed vehile-miles m the ith speed stratum (from Solomon), and p 1 perent of observed vehile-miles in the jth speed stratum (from Solomon). Method 1 uses the onept that aidents between vehiles in the ith and jth speed strata are proportional to the frequeny with whih their speed differene brings them into potential onflit. There are 43 vehile speed strata, eah 5/3 mph in width, to whih Equation 1 is applied. Thus, there are 93 unique ombinations of faster and slower vehile speeds (i.e., [(43)(43) - 43]/2), and Equation 1 involves the summation of 93 separate terms. Aident involvements as a funtion of speed were taken from Table 41 of the Solomon report, with night and day values ombined. Aident frequenies were set equal to half of the aident involvement frequenies, assuming that eah rear-end aident involved only two vehiles. Speed differene data were obtained from Figure 8 of the Solomon report. Although these data are for passenger ars only, most of the vehiles in the mixed flow onsidered here are passenger ars as well. The important point is that these data properly inorporate the role of speed differenes in aident situations. Thus, Table 41 and Figure 8 from the Solomon report provide the raw data for determining the a; 1 in Equation 2. The a; 1 are not uniquely defined by the available data. However, numerial experiene with iterations and adjustments indiates that the overall pattern is strongly onstrained. In the derivation of the a; 1 for 5-mph speed inrements, it is lear
St. John and Harwood that the vehiles in the highest speed stratum must be the faster vehile in any rear-end aident in whih they are involved, and the vehiles in the lowest speed stratum must always be the slower vehile. Vehiles in other speed strata may be the faster vehile in some aidents and the slower vehile in others. However, beause all rear-end aidents were assumed to involve only two vehiles, there must be an equal number of faster vehile and slower vehile involvements. In addition, the perentage of involvements by speed stratum are known from the data in Solomon's Table 41. Solomon's Figure 8 provides the perentage of aidents within eah speed differene. These assumptions and onstraints were used to alulate the a 1 i, within the added onstraint that the a 1 i must vary smoothly between ells. After the l 1 i were alulated for the 5-mph speed strata, interpolation was used to obtain values at 5/3-mph intervals that mathed the speed distribution data derived earlier. CALCULATED RESULTS Upgrade of 2 Perent Figure 4 shows the alulated truk speed distributions at six loations on the sustained 2 perent upgrade with a level approah. The loations seleted for illustrative purposes in this figure are the start of the grade, and stations loated 8, 1,6, 3,2, 6,4, and 9,6 ft up the grade. As explained earlier, similar speed distributions were determined at 2-ft intervals on eah grade. The minimum truk speed on this grade was about 29 mph, but only about 3.6 perent of the truk speeds would fall below 4 mph. In the mixed flow with 2 perent truks and 8 perent passenger ars, the estimated speed distributions for truks and passenger ars orrespond to a rear-end aident rate of 26 aidents per 1 8 veh-mi for the final steady-speed on- 65 ditions on the upper portion of the grade. Thus, although some truks deelerate to speeds of 29 mph and some passenger ars travel as fast as 67 mph on the upper portion of the grade, aident rates would be expeted to inrease by only 1 perent above the aident rate in level terrain. The 2 perent upgrade is simply not steep enough to have a major effet on aident rates. Upgrade of 4 Perent Figure 5 shows the estimated truk speed distribution urves at various points on the 4 perent upgrade. The figure shows that on the upper portion of the 4 perent upgrade, 4 perent of the truks travel at speeds of 4 mph or less, and 5 perent of truks fall to speeds less than 25 mph. The minimum truk speed on this grade is 18 mph. Figure 6 shows the safety impliations of these speed redutions based on Solomon's aident and exposure estimates for strata of slower and faster vehiles. The figure shows that aident rates do not hange appreiably until the truks are about 2,5 ft up the grade; this is where truk speeds start to drop below 22.5 mph. With 5 perent truks in the flow, aident rates inrease only about 4 perent over the length of the grade, but aident rates more than double with 2 perent truks in the traffi stream. Finally, the figure shows that at about 7,5 ft up the grade, where truks reah their steady speeds, the aident rates stop inreasing. Upgrade of 6 Perent Figures 7 and 8 show omparable data for truks on a sustained 6 perent upgrade. Figure 8 shows that rapid inreases in the estimated aident rate begin at about 1,8 ft up the grade and that, as in the 4 perent ase, aident rates inrease ------- 79 6 55 5 45 :2 4 a..s 'O 35 "' a. If) 3 () 2 t- 25 Approah Grade = % Grade= +2% Desired Speeds Mean= 55 mph CT= 5 mph 2 15 1 5 a.1.1 1 2 3 4 5 6 7 8 9 95 98 99 99.9 99.99 Perent of Truk Population At and Below Indiated Speed FIGURE 4 Perent of truk population at or below indiated speed on 2 perent upgrade.
65 -- - --- 6 55 5 45 4 :2 a... 35 "' a. 3 Cf) -" 2 f- 25 2 Approah Grade= % Grade= +4% Desired Speeds Mean= 55 mph a-= 5 mph 15 1 5.1.1 1 2 3 4 5 6 7 6 9 95 96 99 99.9 99.99 Perent of Truk Population At and Below Indiated Speed FIGURE 5 Perent of truk population at or below indiated speed on 4 perent upgrade. 9 8 7 % Approah Grade +4% Grade.E i::. "' m 6 "' 5 1ii "' a: 4 'E "' 8 5% <( : w "- a: "' "' 3 2 1 1-- 5 1 15 2 25 3 35 4 45 5 55 6 65 7 75 6 65 Distane Up Grade (1 fl) FIGURE 6 Calulated rear-end aident rates on 4 perent upgrade.
St. John and Harwood 81 65 6 55 5 45 4. a. 35.s 3 a. Cf) -" 25 u 2 2 Approah Grade= % Grade= +6% Desired Speeds Mean= 55 mph -= 5 mph 15 1 5.1.1 1 2 3 4 5 6 7 8 9 95 98 99 99.9 99.99 Perent of Truk Population At and Below Indiated Speed FIGURE 7 Perent of truk population at or below indiated speed on 6 perent upgrade. 2 18 % Approah Grade 6% Grade 2. nonlinearly with inreasing perent truks. The figure implies that the inrease in aident rate with 2 perent truks will be more than 1 times greater than with 5 perent truks. 16 DISCUSSION OF RESULTS 'iii "E 14 12 1 1'ii a: "E 8 w g <( -g UJ "- "' w a: 6 4 2 FIGURE 8 upgrade. 8 12 16 2 24 28 32 36 4 44 48 Distane Up Grade (1 tt) 52 54 Calulated rear-end aident rates on 6 perent 15. u 2 "E <' w.. 1. 5. 2.5 The inreases in aident rate on upgrades presented in Figures 4 and 6, relative to the aident rates shown for level terrain, are undoubtedly larger than those observed in the real world. Nevertheless, the results reported here ertainly indiate the manner in whih onflits between slow and fast vehiles inrease with inreasing perent grade and inreasing perent truks. These results should help guide future researh. The results imply that there is a pronouned rise in rearend aident rates whenever a sizeable portion of the truk population,.5 perent or more, falls to speeds below 22.5 mph. However, these results must be interpreted in light of the limitations of the Solomon data. The Solomon data ontain a single ategory for speeds of aident-involved vehiles greater than zero and less than or equal to 22.5 mph. This broad speed range, oupled with the extremely high aident involvement rate for these lower-speed vehiles, makes it very diffiult to determine the exat harater of the lower-speed aident rates. This is in ontrast to the higher-speed strata, whih are only 5-mph wide with muh better defined aident rates. Other aspets of the data set raise additional questions. Solomon's data indiate that 12. 7 perent of the rear-end aident involvements were vehiles at zero speed (stopped
82 and presumably waiting for the opportunity to make a turning maneuver). Beause the seond vehile in eah aident involving a stopped vehile must be moving, Solomon's data imply that about 25 perent of all rear-end aidents involved a stopped vehile. This high proportion of zero-speed aidents has not affeted the results reported here beause all aidents involving a zero-speed vehile were omitted from the analysis. However, the presene of these zero-speed aidents in Solomon's data implies that the presene of intersetions or driveways may be overrepresented in omparison to typial sustained grades. This possibility is reinfored by the aident rates in Figure 2, where two vehiles at generally low speeds are muh more likely to be involved with eah other than with a higher-speed vehile. The onerns disussed about the Solomon data and their appliability to sustained grades our in the speed range that is most responsible for the large aident rate inreases that were alulated for truks. Thus, the large aident rate inreases shown for truks in Figure 6 and 8 should not be taken too literally. It is likely that they show aident rate inreases larger than those that would be observed in the field. Nevertheless, the results have impliations that may be useful in deiding where truk limbing lanes are not needed from a safety standpoint. First, the analysis results show (not surprisingly) that there would be almost no safety benefit to installing a truk limbing lane on a 2 perent grade and that there is little apparent need for truk limbing lanes in the first portion of steeper grades. There are unlikely to be safety benefits from limbing lane installations in the first 2,5 ft of a 4 perent grade or the first 1,8 ft of a 6 perent grade. Thus, it is reasonable to onsider introduing the limbing lane on the grade itself, rather than at the foot of the grade. Seond, the potential safety benefits of truk limbing lanes learly appear to inrease with perent grade, length of grade, and perent truks. Although these findings are not surprising, the nonlinear effet of inreasing perent truks may have important impliations. Installation of truk limbing lanes on grades with high truk perentages and high proportions of very low performane truks may be muh more important than is suggested merely by the inreased number of truks. However, these nonlinear effets need to be investigated further to determine whether they are an artifat of the apparent predominane of aess-point-related aidents in the Solomon data. Third, if one aepts the Solomon data as aurate for vehile speeds above 22.5 mph but potentially misleading for speeds below 22.5 mph, this implies that the urrent AASHTO truk limbing lane riteria may be overly onservative from a safety standpoint. The truk speed redution required under AASHTO riteria to warrant a limbing lane was hanged in 1984 from 15 to 1 mph on the rationale that the 1-mph riterion was needed for inreased safety. However, the data on whih Figures 6 and 8 are based learly imply that there is little, if any, inrease in aident rate for vehiles traveling at speeds above 22.5 mph (whih is 32.5 mph below the speed TRANSPORTATION RESEARCH RECORD 133 limit of most rural highways and the mean speed of truks on those highways). Thus, it appears that redutions in truk speeds muh larger than 1 or 15 mph are needed to produe inreases in aident rate large enough to warrant onstrution of a limbing lane. With better data on the aident rates atually assoiated with speifi speed differenes on grades, it might be possible to develop a formal aident warrant for truk limbing lanes. Thus, there is a need for further researh patterned on the Solomon study but fousing on steep grades and with better stratifiation of the speed range below 22.5 mph. SUMMARY In summary, the analyses imply that the Solomon data are not adequate to predit aident rates on steep upgrades, primarily beause of the poor definition of aident rates for vehiles traveling at speeds less than 22.5 mph. However, the Solomon data for vehiles traveling faster than 22.5 mph imply that there is little safety justifiation for truk limbing lanes at loations where essentially all truk speeds remain above 22.5 mph. Of ourse, traffi servie onsiderations should also enter into the deision to install a truk limbing lane. Furthermore, the truk performane data show that very few truks would be slowed to speeds of 22.5 mph or below on any 2 perent upgrade, in the first 2,5 ft of a 4 perent upgrade, or in the first 1,8 ft of a 6 perent upgrade. Further researh is needed to better quantify the safety effets of vehile speeds below 22.5 mph, but the Solomon data for this speed range, although flawed, imply that aident rates on steep grades may be more strongly influened by perent grade, length of grade, and perent truks than previously thought. REFERENCES 1. A Poliy on Geometri Design of Highways and Streets. AASHTO, Washington, D.C., 199. 2. D. Solomon. Aidents on Main Rural Highways Related to Speed, Driver, and Vehile. FHWA, U.S. Department of Transportation, 1964 (reprinted April 1974). 3. A. D. St. John. The Truk Population on High-Type Rural Highways. Midwest Researh Institute, Kansas City, Mo., 1979. 4. Speial Report 29: Highway Capaity Manual. TRB, National Researh Counil, Washington, D.C., 1985. 5. Speed Trends of Five-Axle Truks on Grades in California. California Department of Transportation, Saramento, Jan. 1985. 6. A. D. St. John and D. R. Kobett. NCHRP Report 185: Grade Effets on Traffi Flow Stability and Capaity. TRB, National Researh Counil, Washington, D.C., 1978. 7. W. R. Reilly et al. Capaity and Level of Servie Proedures for Multilane Rural and Suburban Highways. Final Report, NCHRP Projet 3-33. TRB, National Researh Counil, Washington, D.C., May 1989. Publiation of this paper sponsored by Committee on Operational Effets of Geometris.