Design Friction Factors of Different Countries Versus Actual Pavement Friction Inventories

Transcription

1 TRANSPORTATION RESEARCH RECORD Design Frition Fators of Different Countries Versus Atual Pavement Frition Inventories RUEDIGER LAMM, ELIAS M. CHOUEIRI, PREM B. GOYAL, AND THEODOR MAILAENDER A fundamental sale is presented for evaluating appropriate levels of tangential and side frition fators with respet to design speed for new designs, redesigns, and rehabilitation strategies. The frition data used were obtained from the geometri highway design guidelines of the United States and several Western European ountries, and from atual pavement frition inventories in New York State and in the Federal Republi of Germany (FRG). From the frition data of the ountries in this study, relationships were developed between tangential or side frition fators and speed. The urves resulting from these relationships were then ompared with perentile level distribution urves obtained from the atual pavement frition inventories. Analyses indiated that (a) the frition fators produed by the overall regression urves oinided with those obtained from the 9th-perentile level distribution urve of New York State, and with those derived from the 3th-perentile level distribution urve of the FRG; and (b) the frition fators derived from the 95th-perentile level distribution urve of New York State oinided with the frition fators derived from the 95th-perentile level distribution urve of the FRG. On the basis of these results, reommendations are provided for highway design for minimum stopping sight distanes and minimum radii of urve. It is estimated that in applying the proposed frition fators for design, redesign, and rehabilitation strategies 95 perent of wet pavements will be overed in the United States and Europe. The reommendations provided should not be regarded as a final solution, but perhaps an international disussion of a larger dynami safety supply for driving may be useful in reduing aidents on 2-lane rural highways. Beause there are often inadequate safety fators in tire-road frition, frition demand often exeeds frition supply, ausing more aidents than neessary. An international review of existing design guidelines (1-7) has shown that European ountries diretly or indiretly address three design issues in their guidelines muh more expliitly than United States agenies to gain safety advantages. For example, German, Swedish, and Swiss designers are provided with geometri design riteria that diret them toward l. Ahieving onsisteny in horizontal alignment, 2. Harmonizing design speed and operating speed on wet pavements, and 3. Providing adequate dynami safety of driving. R. Lumm. In titllle ofhighway and R11ilroad Engjnering. nive r~ ily of Karl ruhe, D- 75 Karl ruh I, Kaiserstrn e 12. Federnl Republi of Germany. E. M. houeiri, North (mntry orrnnunity ollge. Sarna Lake, Route I, Box 12, Potsdam. N.Y P. B. oyal. 1 Hunter Lane. Elmsford. N.Y. 1()523. T. Mailaendr. Mailt1ndr Ingenieur Consult, D-75 Karlsruhe 1, Mathystrasse 13, Federal Republi of Germany. Criteria 1 and 2 were the subjet of several reports, publiations, and presentations by the authors. For example, for the National Siene Foundation (8), for the New York State Governor's Traffi Safety Committee (9, 1), for the Transportation Researh Board (11-14), for the Ohio Transportation Engineering Conferene (15-18), for the International Road Federation (1, 19), for the Swedish Road and Traffi Researh Institute (2), for the International Road and Traffi Conferene in Berlin (21), and for the German researh ommunity (22). These investigations inluded (a) proesses for evaluating horizontal design onsisteny and inonsisteny; (b) proesses for evaluating design speed and operating speed differenes; () relationships between geometri design parameters, operating speeds, and aident rates; ( d) reommendations for ahieving good and fair design praties, as well as reommendations for deteting poor designs, provided (9-11, 19) on the basis of hanges in degrees of urve and operating speeds between suessive design elements. For example, Figure 1 shows the relationships between degree of urve and operating speeds and aident rates for individual lane widths, derived from the analysis of data of 322 two-lane rural highway setions in New York State. The researh has demonstrated that (a) the most suessful parameter in explaining muh of the variability in operating speeds and aident rates was degree of urve, and (b) the relationship between degree of urve and operating speed is valid for both dry and wet pavements so long as visibility is not appreiably affeted by heavy rain (23). This paper is primarily onerned with the geometri design Criterion 3, providing adequate dynami safety of driving. Reent skid researh investigations by Mason and Peterson (24) have indiated that suffiient frition supply is to be regarded as an important safety issue. Brinkman (25) found that resurfaing alone did not have a signifiant effet on the mean skid number. He indiated that skid resistane should be regarded as a main safety issue when resurfaing roadways. Glennon et al. (26) indiated that the probability that a highway urve may beome a frequent aident site inreases with dereasing pavement skid resistane. The primary objetive of this study is to develop an objetive sale for relating skid resistane-desribed by oeffiient of frition, skid number, or frition number-to speed. In order to ahieve this goal, a omparative analysis of tangential and side frition fators in the highway design guidelines of the United States and four Western European

2 ft: V8S.. 11 ft: V ft: vas TRANSPORTA T/ON RESEARCH RECORD DC; R DC; R DC; R2.753., 12' 11' II) > «u ( DC ' so '... 12'......, DC Degree of urve (d99ree/1 feet), '1 V85 Estimate of operating speed, expressed by the 8Sth-perentile speed (mph) (ranqe up to 21 >, ACCR Estimate of aident rate (a./16 vehile-miles) range: 1-21). 12 ft: ACCR DC; R ' ft: ACCR DC; R ft: ACCR DC: R 2.3 FIGURE 1 Nomogram for evaluating operating speeds and aident rates as related to degree of urve for individual lane widths (W, 12). ountries was arried out to determine the type of relationships that exist between frition fators and design speed, and onsequently the development of overall relationships between frition and design speed. These overall relationships will then be ompared to atual pavement frition inventories in the United States and in the Federal Republi of Germany (FRG), to determine the perentage of wet pavements that ould be overed by suh relationships. COMPARATIVE ANALYSES OF FRICTION FACTORS IN DIFFERENT COUNTRIES How the issue of frition, and equally important the issue of speed in relation to geometri design, are being applied in the United States and several European ountries will be subjet for disussion later in this setion. Beause of the lower oeffiients of frition on wet pavements as ompared with dry, the wet ondition governs in determining stopping sight distanes and radii of urve, as revealed in the studied design guidelines. Furthermore, the ountries in this study assume that the oeffiients of frition used for design riteria should represent not only wet pavements in good ondition but also surfaes approahing the end of their useful lives. The values should enompass nearly all signifiant pavement surfae types and the likely field onditions, as it is expressed, for example, in AASHTO 1984 (7). Contats with responsible transportation agenies in the ountries under study revealed that frition data measurements are onduted using an apparatus similar to that of ASTM E 274 (27). The apparatus normally onsists of the following: 1. An automotive vehile with one or more test wheels inorporated into it or forming part of a suitable trailer towed by a vehile.

3 Lamm et al. 2. A transduer, instrumentation, water supply, and a proper dispensing system and atuation ontrols for the brake of the test wheel. The test wheel is equipped with a standard test tire, whih is different in different ountries. 3. The test apparatus is brought to a desired test speed. The test speeds are different in different ountries as they are different in different states of the United States. For example, in the FRG a road setion is tested at speeds of 25, 37.5, and 5 mph ( 4, 6, and 8 km/hr). For evaluating skid resistane, the standard proedure is to ompare the measured values with reommended values (28):.42 for V = 25 mph,.33 for V = 37.5 mph, and.26 for V = 5 mph. These reommended values represent the skid resistane values that an be reahed on 9 perent of road surfaes in the FRG. Similar reommendations exist in several other European ountries. 4. Water is delivered ahead of the test tire and the braking system is atuated to lok the test tire. For the test, a waterfilm thikness of 1 mm is widely used (29). 5. The resulting frition fore ating between the test tire and the pavement surfae, and the speed of the test vehile are reorded with the proper instrumentation. The skid resistane of the paved surfae is determined from the resulting fore torque reord and reported as the oeffiient of frition, the skid number, or the frition number. These values are determined from the fore required to slide the loked tire at a stated speed, divided by the effetive wheel load. The wheel load depends on the weight of the test trailers used in the different ountries. Beause of some variations in testing proedures, the frition data used in this study may be biased. But, the fat remains that the basi method used to measure skid resistane is, to a ertain extent, omparable between the ountries. With the exeption of the FRG (2) and Switzerland (3, 3, 31), the rest of the ountries in this study do not learly show how the design frition fators used in their guidelines are obtained from the measured skid resistane values. Despite this lak, the authors still attempted to determine how the frition data used in the guidelines of the subjet ountries would ompare to perentile level distribution urves developed from atual pavement frition inventories in the United States and in the FRG. Suh a omparison should be allowed from a researh standpoint beause in reality there exist differenes in every researh field, e.g., mediine and engineering, in testing, as well as in reporting proedures. In performing omparative analyses of data in different ountries, there always exists the possibility that the data may be biased. TANGENTIAL FRICTION FACTOR The data in Table 1 represent the maximum allowable tangential frition fators for wet pavement with respet to the design peed applied in lhe highway design guidelines of th United tates (USA), Federal Republi of Germany (FRG). Frane (F), Sweden (S), and Switzerland (CH). Figure 2 shows an overview of the maximum allowable tangential frition fators of the studied European guidelines TABLE 1 MAXIMUM ALLOWABLE TANGENTIAL FRICTION FACTORS FOR DIFFERENT DESIGN SPEEDS IN DIFFERENT COUNTRIES (34) Design Tangential Frition Fator (frl - rounded Speed (mph) USA FRG F s CH , , and for highway design in the United States with respet to design speed. Note that, with the exeption of Frane, all relationships in Figure 2 are quadrati. The European ountries in this study were onsidered typial European ountries by Hayward et al. (1). In Figure 2, all speeds have been onverted to miles per hour for omparison purposes. Figure 2 shows that (a) as design speeds inrease, frition fators derease; (b) the frition-speed urves for Switzerland and FRG are nearly parallel, with the frition values of Switzerland higher by about.1; () the tangential frition values of Sweden are limited beause of a maximum design speed of 5 mph on 2-lane rural roads in this ountry; ( d) the Amerian values interset the German urve at a design speed of about 3 mph and the Swiss urve at a design speed of about 6 mph. In omparison to the other ountries, the United States has the lowest differenes in frition values (see Table 1). For example, between design speeds of 3 and 7 mph the differene in the Amerian tangential frition values is.7 (.35 to.28), whereas for Germany and Switzerland the differene is.19. In the higher, more ritial design speed ranges, for example, between 55 and 7 mph, the differene in the Amerian values is only.2, whereas for Germany the differene is.5, and for Switzerland,.4. These small differenes in the Amerian frition values, or these low speed gradients of tangential frition, learly ontradit the worldwide researh experiene that shows that frition values should substantially derease with inreasing speeds (see Figure 2). If this experiene is not met, ritial driving maneuvers may our, speially when operating speed exeeds design speed by onsiderable amounts under wet pavement onditions (9-11, 19). 137

4 138 TRANSPORTATION RESEARCH RECORD t" <.) LL. : l.j... <.) : QI. 2 Ol : ~.\ s Overall Regress ion Curve ~~ -. (equation ( 1)) '-::::... ~ O '--~~~-'-~~~~"--~~~-'-~~~~... ~~~-' [mph] 7 Design Speed FIGURE 2 Relationships between maximum allowable tangential frition fator and design speed for different ountries, along with the overall regression urve. On the basis of the data of the five studied ountries, the fol!o,ving overall regression equation \.Vas developed relating tangential frition fator f T and design speed Vd: ft = l*I- 3 Vd I- 5 (Vd) 2 R 2 =.731 SEE=.44 where ft = tangential frition fator, vd = design speed (mph), R 2 = oeffiient of determination, and SEE = standard error of estimate. The high value of R 2 and low value of SEE of Equation 1 indiate that the relationship between tangential frition and design speed is a strong one. Figure 2 shows the alulated values of the tangential frition fator (Equation 1) as a solid line superimposed on the urves of the ountries in this study. This figure indiates that (a) the Swiss and Swedish tangential frition values are higher (1) than the tangential frition values of the overall regression urve; (b) for design speeds gn;aler than 35 mph, the Frenh values are higher; () the FRG values are lower; and (d) the U.S. tangential frition values interset the overall regression urve at a design speed of about 5 mph. For design speeds greater than 6 mph, the Frenh and U.S. tangential frition values are higher than the tangential frition values of the other ountries. SIDE FRICTION FACTOR The data presented in Table 2 give the maximum allowable side frition fators for wet pavements with respet to the design speed applied in the highway design guidelines of the same five ountries. Figure 3 shows an overview of the maximum allowable side frition fators of the European guidelines and for highway design in the United States with respet to design speed. Note that, with the exeption of the United States, all relationships in Figure 3 are quadrati. In Figure 3, all speeds have been onverted to miles per hour for omparison purposes.

5 Lamm eta/. 139 On the basis of the data of the five ountries in Table 2, the following overall regression equation was developed relating side frition fator fr and design speed Vd: where f R = side frition fator, and vd = design speed (mph). fr = *1-3 Vd + l.5*1-5 (Vd) 2 (2) The high value of R 2 and the low value of SEE for Equation 2 indiate that the relationship b tween side frition and design R 2 =.799 speed is a. trong on. SEE=.18 Figure 3 show the alulated values of the side frition fator fr m Equali.on 2 as a solid line superimposed on the TABLE 2 MAXIMUM ALLOWABLE SIDE FRICTION FACTORS FOR DIFFERENT DESIGN SPEEDS IN DIFFERENT COUNTRIES (34) urves for the ountries in this study. For speeds greater than 4 mph, this figure indiates that the U.. side frition values Design Speed (mph) USA Side Frition Fator FRG F (fr) - rounded s CH are lightly higher than the values of th overall regres ion urve and the frition values of the European untri in lhi study, with the exeption of Switzerland , llO ADDITIONAL INFORMATION FOR DESIGN PURPOSES In the guidelines of the United States and Europe, maximum allowable tangential frition fators are used to alulate minimum stopping sight distanes, whereas side frition fators are used to alulate minimum radii of urve (J-7). For alulating minimum stopping sight distanes, the United States uses a pereption-reation time of 2.5 se, whereas the European ountries use 2. se. Both values were found to be adequate in reent papers presented at the 68th Annual Meeting of the TRB, January Taoka (32), for instane, onluded the following: "It appears that the AASHTO design value of 2.5 seonds may orrespond to the response time of the 95th-perentile driver. The stopping sight distane design driver assumption is satisfatory at the present time." In ontrast, Wilson et al. (33) ame to the following onlusion: "The urrent design standard for pereption and reation time is 2.5 seonds. This value ompares with the study -so lq 8Q, - 95 [km/h] , , ,. ' --; '~--=----Tt-- --lo.18 ~ Overall Regression Curve (equation (2)) =:::~+--~s.;...;?"'~-d l i ~.1 t-----t t---":...c~-t-...;.::::...:~:'!iil en [mph] 7 Design Sp~ed FIGURE 3 Relationships between maximum allowable side frition fator and design speed for different ountries, along with the overall regression urve.

6 14 findings at the 99th-perentile of 1.6 seonds indiating that the urrent design standards are onservative." The maximum superelevation. rates used m the different ountries for alulating minimum radii of urve an be seen in the following table. The applied super levation ra tes ran e fro m 5.5 perent in Sw de n to 8 per nt ii tile Unit1;d Sta le~. Pereption- Reation Superelevation Superelevalion Time Rate Rate Country (se) (%) Qualifia tion United States Maximum under snow and ie onditions Federal 2. 7 Desirable Republi of 8 Exeption Germany Switzerland 2. 7 Unqualified Great Britain NIA 5 Desirable 7 Absolute Frane 2. s Desirable 7 Absolute Sweden Maximum COMPARATIVE ANALYSES OF THE OVERALL REGRESSION CURVE VERSUS ACTUAL PAVEMENT FRICTION INVENTORIES In addition to the data in this paper, other studies (34-38) were used to dete rmine how the overall regressio.n urve (E quation 1) developed from the data of the ountrie in this study ompares to atual pavement frition inventories. The investigations were based on one frition inventory from New York State (NYS), developed by Goyal (34) (see Figure 4), and one inventory from the F'RG developed by Wehner and Shulze (e.g., 37, 38) (see Figure 5). Equations that orrespond to the urves in Figures 4 and 5 are given in Table 3, in whih V is given in units of miles per hour. The frition values produed by the perentile level distribution urves in Figures 4 and 5 are representative of 6 to 95 perent of wet pavements in the investigated state or ountry. The relationships in Pigure 4 indiate that the overaii regression urve (Equation 1) learly oinides with the 9thperentile level distribution urve of NYS. That means that 9 perent of wet pavements ould be overed by using the overall regression urve as a driving dynami basis for design purposes. Figure 5 shows that the overall regression urve ould over about 8 perent or more of wet pavements in the FRG. Figure 6 shows the results more learly. This figure shows that the 95th-perentile level distributi n urve for NYS nearly inides with the 95th-perentile level distribution urve for FRG. Furthermore, this figure suggests that AASHTO maximum allowable tangential frition fators (7) represent (a) up to a design speed of about 5 mph, 9 perent or more of wet pavements in NYS; (b) up to a design speed of about 6 mph, 8 perent of wet pavements in NYS; and () up to a design speed of about 7 mph, only about 65 perent of wet pavements in NYS. For design speeds greater than 5 mph, AASHTO allows higher tangential frition fators, as ompared to the tangen- TRANSPO RTATION RESEARCH RECORD 126 tial frition fators of the overall regression urve of Equation 1 developed from the data of the ountries in this study. Related to the 95th-perentile level distribution urve for NYS and FRG, these statements would already be true for design speeds greater than 3 mph. The tangential frition faiors applied in the German geometri design standards are based on the 95th-perentile level distribution urve for wet pavements, aml haw been in use in the FRG sine 1973 (39). RECOMMENDATIONS FOR HIGHWAY DESIGN In order not to be too onservative, it is reommended that at least the tangential frition fators produed by the overall regression urve (Equation 1) shall be used for highway design. However, in order to seure the ondition that frition supply should most of the time exeed frition demand (2,35,4), it may be more appropriate for new design, redesign, and rehabilitation strategies to apply tangential frition fators that orrespond to the 95th-perentile level distribution urves developed from atual pavement frition inventories in NYS :rnd FRG. TANGENTIAL FRICTION FACTOR AND STOPPING SIGHT DISTANCE The minimum stopping sight distane is defined in most of the geometri design standards studied as follows: The minimum stopping sight distane (SSD) is the sum of two distanes: (a) Lh di ta nee trav r. tl l>y a hile from lbe in tant the driver ight. an ohjot for whih n Lop i n e.~sa r y I<) the in ~ t;ull the brakes ur applied (pereption-reation time). and (u) the distane r equired to stop the vhil 'after the l>rn k appliati n begins (braking distane). TI1 former is primarily a fun tion of speed and pereption-reation time, the latter a funtion of speed and fritional resistane between the pave ment surfae and tires. SSD on level roadway, therefore, may be omputed by the formula where minimum stopping sight distane (ft); design speed (mph); maximum allowable tangential frition fator; and t = pereption-reation time (se). In using a 2.-se pereption-reation time as generally reommended in Europe, or 2.5 se urrently in use in the United States, Equation 3 then beomes or (3) (4a) (4b)

7 Lamm et al [km/h] "--"' t CJ LL.... CJ LL. QI. 2 O'I ~ /o 1 1. so 1. 9 /. 95 /..1 so Speed V FIGURE 4 Perentile distribution urves for the relationship between tangential frition fator and speed for 93 wet pavements in NYS (34). The data in Table 4 present the omputed SSD values from Equations 4a and 4b by using the tangential frition fators produed by the overall regression urve (Equation 1), by the 95th-perentile level distribution urves of NYS and FRG, and by pereption-reation times of 2. and 2.5 se, respetively. For omparative reasons, AASHTO maximum allowable tangential frition fators and ranges of stopping sight distanes (7) are also presented in Table 4. Data in Table 4 indiate that (a) for design speeds greater than 55 mph, AASHTO tangential frition fators are higher than the tangential frition fators produed by the overall regression urve (.3 >.28); (b) for design speeds greater than 35 mph, AASHTO tangential frition fators are higher than the tangential frition fators produed by the 95thperentile level distribution urves (.34 >.32); and () between design speeds of 5 and 7 mph, the differene in the reommended tangential frition fators is between.6 (.3 to.24) and.8 (.25 to.17), whereas the differene in AASHTO tangential frition fators is only.2 (.3 to.28). For the pereption-reation time of 2.5 se urrently in use by AASHTO, note that (a) the omputed stopping sight distanes, based on the overall regression urve (Equation 1), exeed the upper limit ranges of AASHTO at speeds of 55 mph (56 ft > 55 ft); whereas (b) the omputed stopping sight distanes, based on the 95th-perentile level distribution urves, exeed the upper limit ranges of AASHTO values already at speeds of 45 mph (41 ft > 4 ft). Table 4 was developed only to present, in omparison to AASHTO, the signifiant differenes that exist between the omputed stopping sight distanes from Equation 3 by using different pereption-reation times and by inluding different tangential frition fators aording to the overall regression urve and the 95th-perentile level distribution urves of NYS and FRG. The omputed stopping sight distanes in Columns 3, 4, 6, and 7 of Table 4 will have to be modified additionally when taking into onsideration the effet of air resistane, as has been done, for example, in the FRG (2, 35, 4), and in the Swedish Standard Speifiations for Geometri Design ( 4). Consequently, different minimum stopping sight distanes ould result from the appliation of different models, different pereption-reation times, and different tangential frition fators. These findings learly indiate that AASHTO offiials, in ollaboration with the TRB Committee on Geometri Design (A2A2), should onsider the following steps, for example,

8 142 TRANSPORTATION RESEARCH RECORD t- L-... u LL.4... u.3 L- LL Cl.I. 2 Ol I- I Overall Regression Curve..._ (equation(!)}-, _..._ / 95 / Speed V 6 [mph) 7 FIGURE 5 Perentile distribution urves for the relationship between tangential frition fator and speed for 6 wet pavements in FRG. TABLE 3 REGRESSION EQUATIONS FOR TANGENTIAL FRICTION FACTOR VERSUS SPEED FOR PERCENTILE DISTRIBUTION CUR\lES CORRESPOi~Dii~G TO FIGURES 4 AND 5 (34) Perentile Level New York State 6 % fr = o v v 2 7 % fr = J V+2. 1-SV2 8 % fr = J V+2. l-sv2 9 % fr = V+2. l-svz 95 % fr = V+2. lo- Sv 2 Perentile Level Federal Republi of Germany 6 % ft = V VZ 7 % fr = J V v 2 8 % fr = o v+s v 2 9 % fr = V v 2 95 % fr= J V SV2 in any future plans for ahieving well-founded and reliable stopping sight distanes: 1. Seletion of a model inluding or not inluding air resistane. (A model that inludes air resistane is reommended.) 2. Seletion of pereption-reation time. (A pereptionreation time of 2. se is suffiient.) 3. Seletion of reliable maximum allowable tangential frition fators. [At least the values omputed from Equation 1 (see Column 2 of Table 4), but preferably the values produed by the 95th-perentile level distribution urves (see Column 5 of Table 4), are reommended.] SIDE FRICTION FACTOR AND MINIMUM RADIUS OF CURVE In the German Design Guidelines (2), the maximum allowable side frition fators are defined as 46 perent of the maximum allowable tangential frition fators for rural highways. In the Swiss Design Norms (3, 3, 31) and in the Swedish Speifiations ( 4), the maximum allowable side frition fators are defined as 44 perent of the maximum allowable tangential frition vaiues for rurai highways. AH three guideiines indime

9 BO - 95 [km/h] ,, , , New York 9 /. ~.4 ~~-.:--~lloi-1f..:...,...-..::...oe:. ~ :... u Q ~~~~~--:::::ll... id.oo,_.~::-"'"...,, i~~ tt -... : ~ l : ~ j-----r '1 OL.-.. _, [mph] 7 Design Speed FIGURE 6 Relationships between maximum allowable tangential frition fators and design speed for AASHTO 1984, FRG (8th and 95th perentiles) and NYS (6th, 8th, 9th, and 9Sth perentiles) along with the overall regression urve. TABLE 4 RECOMMENDED MAXIMUM ALLOWABLE TANGENTIAL FRICTION FACTORS AND COMPUTED STOPPING SIGHT DISTANCES VERSUS DESIGN SPEEDS Design Speed (mph) vd Stopping Sigl t Distanes based on the Overall Regression Curve (equation (1)) Stopping Sight Distanes based on the Stopping Sight 95th-Perentile Level Distanes Curves of AASHTO 1984 New York State and FRG fr max* SSD (ft) SSD (ft) fr max* SSD (ft) SSD (ft) ftmax SSD (ft) t = 2, s t= 2,5 5 t = 2, s t = 2,5 s t = 2, , *Rounded Values

10 144 that by using these perentages of side frition there is still between 8 and 9 perent available for frition in the tangential diretion when driving through urves (35,4). By this proedure, onsiderable dynami safety reserves are still available in the tangential diretion in spite of using the maximum allowable side frition fators. In this study, the maximum allowable side frition fator is defined as 45 perent of the maximum allowable tangential frition fator. This should guarantee that there will be about 9 perent of frition available in the tangential diretion for aeleration, deeleration, braking, or evasive maneuvers when driving through urves (34,35). Thus, the equation for the maximum allowable side frition fator for rural highways is Consequently, the equation for the maximum allowable side frition fator for NYS at the 9th-perentile level is (see Table 3): and the equation for the maximum allowable side frition fator for NYS at the 95th-perentile level is (see Table 3): Equations 6 and 7 are shematially shown in Figure 7. In addition, this figure inludes the overall regression urve (Equation 2) between side frition and design speed, based on the data of the five ountries in this study, as well as the maximum allowable side frition fators of AASHTO 1984 (7). Figure 7 indiates that (a) the side frition fators produed by the 9th-perentile level distribution urve of NYS learly (5) (6) (7) TRANSPORTATION RESEARCH RECORD 126 oinide with the frition fators produed by the overall regression urve (Equation 2); (b) the side frition fators produed by the 95th-perentile level distribution urve of NYS learly oinide again with the side frition fators produed by the 95th-perentile level distribution urve of the FRG; and () AASHTO side frition fators interset the overall regression urve at a design speed of about 4 mph. A reliable estimate of urve radius may be obtained from the standard entripetal fore equation (7): where D "-"min minimum radius of urve (ft); vd = design speed (mph);!rm,, = maximum allowable side frition fator; and e = maximum superelevation rate (ft/ft). Beause Equation 8 is ommonly applied in the geometri design guidelines of the ountries in this study, reommendations for minimum radii of urve will be easier to make here. The diffiulties enountered with the assumptions used to alulate minimum stopping sight distanes do not apply here. To onform with the findings of the ountries in this study, typial superelevation rates of.5 and.7 were seleted. Maximum allowable side frition fators and omputed minimum radii of urve with respet to design speed are presented in Table 5. The values in this table are again based on the side frition fators produed by the overall regression urve (Equation 2) and by the 95th-perentile level distribution urves of NYS and FRG. For omparative reasons, AASHTO minimum radii of urve are also shown with respet to design speed in the table. Table 5 indiates that, for design speeds between 5 and 7 mph and superelevation rates of.5 and.7, AASHTO (8) so - GS Cweiall Regn:s~ion Cuive (equation (2 )1 BO -9S [km/h] I.. IJ.. QI "CJ (/).14.1 Germany.9S /o (orresponds to German Design Standard [2) 1 - a::: so Design Speed 6 [mph] FIGURE 7 Relationships between maximum allowable side frition fators and design speed for AASHTO 1984, l<'k(; (IJSth perentile), and NYS (9th and 95th perentile), along with the overall regression urve. 7

11 Lamm et al. 145 TABLE 5 RECOMMENDED MAXIMUM ALLOWABLE SIDE FRICTION FACTORS AND RECOMMENDED MINIMUM RADII OF CURVE VERSUS DESIGN SPEEDS The least Reonmended Minimum Design Superelevation Radii of Curve Speed Rate Overall Regression Curve (equation (2)) vd (mph) e frmax* Rmin (ft) Reonmended Minimum Radii of Curve Minimum Radii 95th-Perentile AASHTO 1984 Level Curve of New York State and FRG frmax* Rm1n (ft) frmax Rmin (ft) OB * Rounded Values minimum radii of urve are 2 to 6 perent lower than those orresponding to the side frition fators produed by the overall regression urve (Equation 2), and about 13 perent lower than those orresponding to the side frition values produed by the 95th-perentile level distribution urves. It is reommended that at least the side frition fators produed by the overall regression urve (Equation 2) should be regarded in highway design. However, for safety reasons it may be more appropriate to relate minimum radii of urve to the side frition fators produed by the 95th-perentile level distribution urves of NYS and FRG to over 95 perent of wet pavements, as has been already done in several Western European ountries. CONCLUSIONS It is diffiult to deide where the ritial margins for tangential and side frition fators and, derived from them, for minimum stopping sight distanes and radii of urve shall be assigned. This is a ruial onsideration for engineers onerned with both ost and safety. But using lower maximum allowable frition fators will ertainly lead to a higher driving dynami safety supply, and ould redue the number and severity of aidents. It will also support maintenane personnel by easing the problems of maintaining high tangential and side frition fators for higher design speed lasses. Therefore, it is reommended for new designs, redesigns, and rehabilitation strategies to relate minimum stopping sight distanes and minimum radii of urve to the proposed tangential and side frition fators that over 95 perent of wet pavements in this study. The reommendations provided in this paper should not be regarded as a final solution, but perhaps an international disussion of a larger dynami safety supply for driving may be useful in reduing aidents on two-lane rural highways. Beause there are often inadequate safety fators in tire-road frition, frition demand often exeeds frition supply, ausing more aidents than neessary. One of the most important tasks in modern highway design requires that responsible national and international agenies develop reliable inventories of frition data. If the reommendations about the design riteria mentioned in the introdution are regarded-( a) ahieving onsisteny in horizontal alignment, (b) harmonizing design speed and operating speed on wet pavements, and () providing adequate dynami safety of driving-deisive safety advantages may be expeted in future geometri highway design of two-lane rural roads. REFERENCES 1. J. Hayward, R. Lamm, and A. Lyng. Survey of Current Geometri and Pavement Design Praties in Europe: Geometri Design. International Road Federation, Washington, D.C., July Geometri Design Standards. In Guidelines for the Design of Roads. RAS-L-1, German Road and Transportation Researh Assoiation, Committee 2.3, Swiss Assoiation of Road Speialists (VSS), Swiss Norm SN 648a. Highway Design, Fundamentals, Speed as a Design Element National Swedish Road Administration. Standard Speifiations for Geometri Design of Rural Roads. Borlenge, Sweden, Ministere de l'equipement et du Logement. Instrution sur!es Conditions Tehniques D'Amenagement des Routes Nationales. Paris, 1975.

12 146 TRANSPORTATION RESEARCH RECORD DepaitrneJJ( u[trampurl. Highway Link Design, Geometri Aiignment Standards. Departmental Standard TD9/81, London, A Poliy on Geometri Design of Highways and Stree/s. AASHTO, Washington, D.C., R. Lamm and E. M. Choueiri. A Design Proedure to Determi11e C:ri1iral Di.,similriri1ies in Horizonf!l! Alignment and Enhane Traffi Safety by Appropriate Low-Cost or High-Cost Projets. Final Report for the National Siene Foundation, Washington, D.C., Marh E. M, Choueiri and R. Lamm. Operating Speeds and Aident Rates on Two-Lane Rural Highway Curved Setions-Investigations about Consisteny and Inonsisteny in Horizontal Alignment. Part I of Rural Roads Speed Inonsistenies Design Methods. State University of New York Researh Foundation, Alh8ny, N.Y., July R. Lamm, E. M. Choueiri, and A. Paluri. A Design Method to nptprminp rriti r"~ nnpr-:1tinn ~nr.u::.rl Tnl"'nn"i-h,nri.:.,, r..... _r... ~ _ ,..._..... _....._... f-'...,... _.,,b._,,...,...,......_..,._,.._.~... 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Chou111. New ldeas Lor the Design of Two-Lane Rural Roads in the U.S.A. Jn1ernational Tehnial Journal: Road and Co11s1rutio11, Federal Republi of Germany, Vol. 5, pp , May 1989, and Vol. 6. pp June R. Limm, E. M. Chouiri, ~nd T. Mai!ander. Comparison of Operating Speeds on Dry and Wet Pavements of Two-Lane Rural Highways. In Transportation Researh Reord, TRB, National Researh Counil, Washington, D.C., 199 (forthoming). 24. J. M. Mason and H. C. Peterson. Survey of States' R-R-R Praties and Safety Considerations. In Transportation Researh Reord 96, TRB, National Researh Counil, Washington, D.C., C. P. Brinkman. Safety Studies Related to RRR Projets. T>'a 1sportation Journal of ASCE, Vol. LOS, July J. C. Glennon, T. R. Neuman, and J. R. Leish. Safety and Opiational Considiations fo; Design of Rura: t Iighvvay Curves. Final Report, Aug H. W. Kummer and W.. Meyer. NCH RP Report 37: Tentative Skid-Resistane Requirements for Main Rural Hig!J111ays. HRB. 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