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39 CHAPTER 5 TRUCK CHARACTERISTICS RELATED TO GEOMETRIC DESIGN This chapter reviews the available data on truck character- istics that should be considered in the development of high- way design and operational criteria. The review of truck char- acteristics is based primarily on data from existing sources in published and unpublished literature. The review focuses primarily on the characteristics of the current truck population. The effects of recent trends in truck- ing and recent legislative changes are accounted for when- ever possible. This review of truck characteristics provides the basic data used in Chapter 6 to consider the highway design and opera- tional criteria that would be suitable to accommodate trucks. Thus, the review is selective, rather than exhaustive; it focuses on the data needed for the analyses in Chapter 6. For example, some frequently discussed truck safety issues, such as rear- ward amplification in emergency steering maneuvers by multi- trailer combinations, are addressed only briefly because they have no clear implications for highway design and operational criteria. Many such truck safety issues are more in the realm of truck policy and vehicle design than geometric design. More complete reviews of many specific truck character- istics can be found in the references cited. In particular, the National Highway Traffic Safety Administration (NHTSA) report, Heavy Truck Safety Study (17), provides an excellent overview of many truck design issues, and another NHTSA report, A Factbook of the Mechanical Properties of the Com- ponents for Single-Unit and Articulated Heavy Trucks (18), provides the most detailed available data on the ranges of specific truck characteristics. Some of the material in these sources is updated in NCHRP Synthesis 241, Truck Operat- ing Characteristics (19). This section is similar in form to comparable material presented in the FHWA Truck Charac- teristics study (2,3), but has been updated, as appropriate, to describe the current truck fleet. The truck characteristics reviewed in this chapter include the following: â¢ Turning radius, â¢ Offtracking and swept path width, â¢ Trailer swingout, â¢ Braking distance, â¢ Driver eye height, â¢ Acceleration characteristics, â¢ Speed-maintenance capabilities on grades, â¢ Vehicle length, â¢ Vehicle height, â¢ Rearward amplification, â¢ Suspension characteristics, â¢ Load transfer ratio, and â¢ Rollover threshold. The lengths of trucks, their configurations, their weights, and recommended design vehicle configurations have been addressed in preceding chapters. TURNING RADIUS The minimum turning radius of a truck is defined as the path of the outer front wheel, following a circular arc at a very low speed, and is limited by the vehicle steering mechanism. Parameters such as weight, weight distribution, and suspen- sion characteristics have a negligible role in turns at very low speeds (e.g., less than 16 km/h [10 mph]). The dimensions and turning radii of the current and recommended Green Book design vehicles are presented in Chapter 4 of this report. OFFTRACKING AND SWEPT PATH WIDTH There are two types of offtracking, referred to as low- speed and high-speed offtracking. Low-speed offtracking occurs as vehicles traveling at very low speed make a turn; in low-speed offtracking, the weight, weight distribution, suspension characteristics, and other vehicle-dynamic pa- rameters are negligible factors in the amount of offtracking that occurs. High-speed offtracking, as its name implies, incorporates dynamic effects and is more pronounced the higher the speed. Each type of offtracking is discussed below. Low-Speed Offtracking A train travels on tracks and, thus, its rear wheels precisely follow the paths of the front wheels. With vehicles that are not on tracks, such as bicycles, automobiles, and trucks, the rear wheels do not follow the front ones. During turning at low speeds, the front wheels try to drag the rear ones toward them and across the inside of the curve. The magnitude of
this phenomenon is small for bicycles and automobiles and is usually ignored. For trucks, however, it can be substantial and is an important factor in the design of intersections, ramps, and other highway elements. There are two commonly used descriptors of offtracking: one is the offtracking amount, defined as the radial offset between the path of the centerline of the front axle and the path of the centerline of a following axle shown in Figure 20; the other, and more important descriptor for use in highway design, is the swept path width, shown for a tractor-semitrailer in Figure 21 as the difference in paths between the outside front tractor tire and the inside rear trailer tire. Offtracking increases gradually as a vehicle proceeds through a turning maneuver. This developing offtracking is termed partially-developed offtracking (sometimes referred to in the literature as nonsteady-state offtracking or transient offtracking). As the vehicle continues to move in a constant radius curve, the offtracking eventually reaches what is termed its fully-developed offtracking value (sometimes referred to in the literature as steady-state offtracking or, misleadingly, as maximum offtracking). Each is discussed more fully in the following paragraphs. Fully-Developed Offtracking On longer radius turns, such as typical horizontal curves on highways or ramps, fully-developed offtracking is usually reached; once this value is attained, offtracking does not increase further as the vehicle continues around the curve. Fully-developed offtracking is considered in the geometric 40 design of horizontal curves, especially on two-lane roads, in determining whether the roadway needs to be wider on the curve than on the normal tangent cross section. Similarly, it is considered in the design of freeway ramps. Even though such facilities are designed primarily for highway speeds (or near- highway speeds), where low-speed offtracking should not be a factor, consideration is also given to situations such as con- gestion, where vehicles are forced to travel at low speeds. In performing offtracking calculations, certain equations are applied consecutively to the distances between adjacent pairs of axles or hinge points. The contribution to offtrack- ing of each inter-axle distance is roughly proportional to the square of that distance. Thus, the dominant term for the off- tracking of most tractor-semitrailers is the so-called kingpin- to-rear-axle dimension, the largest distance. The offtracking of a vehicle with two axles, for example, may be approximated, using the Pythagorean Theorem (see Woodroofe et al. (20), for example) as (1) where is the distance between the two axles, R is the radius of the curve, and negative offtracking implies tracking inward toward the center of the arc. If << R, then this may be reduced to the simpler form â0.5( 2/R), which is the often used Western Highway Institute formula (21). Equation 1 is sufficiently accurate for most purposes, but additional effects of multiple axles (e.g., tandems and tridems), roadway super- elevation, and body roll may also be included (see Glauz and Harwood (22)). (This formulation also assumes << R.) As noted above, Equation 1, or its equivalent, is applied consecutively to each pair of axles or hinge points of the truck; each application gives the offtracking of the center of OT R R= â + â( )2 2 Figure 20. Illustration of truck offtracking. Figure 21. Illustration of swept path width.
the following axle or hinge point relative to the center of its leader. These computed offtracking amounts are additive, except that the sign of the contribution from the center of the drive axles to the kingpin is reversed if the kingpin is moved forward (the usual case), as is the contribution from the drive axles to the pintle hook of the first trailer in a doubles com- bination (which swings outward rather than tracking inward). Partially-Developed Offtracking Partially-developed offtracking is of concern where trucks traverse shorter curves or, more importantly, curves of smaller radius. Partially-developed offtracking is of particular inter- est as it affects the design of intersections or other locations where vehicles are required to turn rather sharply. In contrast to fully-developed offtracking, partially- developed offtracking cannot be determined from solving a simple equation, even for the case where the tractor travels on a simple circular path. Early attempts to estimate this type of offtracking were made using a mechanical device called a Tractrix integrator, basically a simple scale model of the truck in question. In the early 1980s, computer programs to compute offtracking and swept path width for any specified truck configuration began to be developed (23,24,25). A commercially available software package, known as AutoTURN, is now commonly used by highway agencies to determine partially-developed offtracking. All such computer programs operate by moving the front axle of a specified vehicle forward in small steps or increments along a specified 41 path and then computing the resulting location of the rear axle(s). Table 23 presents the maximum low-speed offtracking and swept path width in 90-deg turns of varying radii for selected design vehicles, including design vehicles from the 2001 Green Book and the proposed new or revised design vehicles presented in Chapter 4. The derivation of these offtracking and swept path width values is described in Appendix C. The FHWA Truck Characteristics study (2,3) found, and the data in Table 23 developed in this research confirm, that the swept path widths for trucks the size of the WB-19 [WB-62] or larger are so great that the truck cannot make a 90-deg right turn from one two-lane road to another while remaining within a 3.6-m [12-ft] lane for turning radii of 23 m [75 ft] or less. Trucks making such turns at locations with curb return radii less than 23 m [75 ft] must either encroach on the roadway shoulder (or curbline) or on an opposing lane. This observation is borne out by the truck turning observa- tions presented in the next section. On a turn between multi- lane roads, trucks with sizes up to the WB-23BD [WB-77BD] can make a 90-deg right turn while encroaching on an adja- cent same-direction lane, but without encroaching on an opposing lane. Trucks with sizes greater than or equal to the WB-30D [WB-92D] are not physically capable of making a 90-deg right turn with a radius of 23 m [75 ft] or less. Observed Low-Speed Offtracking The above discussion of offtracking makes use of math- ematical models. Although drivers may approximate those TABLE 23 Maximum low-speed offtracking and swept path width for selected design vehicles in 90-degree turns Maximum offtracking (ft) for specified turn radius Maximum swept path width (ft) for specified turn radius Design vehicle type Symbol 50 ft 75 ft 100 ft 150 ft 50 ft 75 ft 100 ft 150 ft Single-unit truck SU 3.8 2.7 1.8 1.1 11.8 10.7 9.8 9.1 Single-unit truck (three-axle) SU25 6.1 4.3 3.2 2.1 14.1 12.3 11.2 10.1 Interstate semitrailer WB-62 16.8 12.8 10.1 6.9 25.0 21.1 18.4 15.1 Interstate semitrailer (revised)a WB-62 17.0 13.1 10.3 7.0 25.3 21.3 18.6 15.3 Interstate semitrailer WB-67 19.4 15. 12.1 8.3 27.6 23.4 20.3 16.6 Interstate semitrailerb WB-67 (41-ft KCRT) 17.0 13.1 10.3 7.0 25.3 21.3 18.6 15.3 Long interstate semitrailer WB-71 21.5 17.0 13.8 9.6 29.8 25.3 22.0 17.9 Long interstate semitrailerc WB-71 (41-ft KCRT) 17.0 13.1 10.3 7.0 25.3 21.3 18.6 15.3 âDouble-bottomâ- semitrailer/trailer WB-67D 11.5 8.3 6.3 4.2 19.7 16.6 14.6 12.5 Longer âdouble-bottomâ- semitrailer/trailer WB-77D 14.2 10.6 8.2 5.5 22.4 18.8 16.4 13.7 B-train double- semitrailer/semitrailer WB-77BD 15.6 11.7 9.1 6.1 23.9 20.0 17.4 14.4 Rocky mountain double- semitrailer/trailer WB-92D â â 12.7 8.7 â â 21.0 17.0 Turnpike double- semitrailer/trailer WB-109D â â 17.1 12.0 â â 25.3 19.2 Long turnpike double- semitrailer/trailer WB-120D â â 17.9 12.6 â â 26.1 20.8 a Proposed revision to WB-62 design vehicle; KCRT distance increased from 40.5 to 41.0 ft. b WB-67 design vehicle with axles pulled forward to obtain 41.0-ft KCRT distance. c WB-71 design vehicle with axles pulled forward to obtain 41.0-ft KCRT distance.
findings, in reality there is a fair amount of dispersion in the actual paths used. DeCabooter and Solberg obtained actual offtracking paths for a number of intersections in Wiscon- sin (26). The data were obtained using several synchronized cameras, whose photos were later analyzed and the actual paths determined by phototriangulation. Figure 22 illustrates the results found. Although most drivers approached the intersection with the left front tire on the centerline, some were in the opposing lane. The position where they began their turns varied somewhat. And, at this particular intersection, most intruded into the opposing lane of the target intersection, and a few mounted the curb. High-Speed Offtracking When a vehicle moves through a curve at higher speed, the rear axles of the vehicle tend to move outward. This tendency to move outward is called high-speed offtracking. It acts in the opposite direction to low-speed offtracking, so the two phenomena tend to counteract each other. At lower speeds, low-speed offtracking predominates; as the speed increases, 42 the net offtracking is reduced. At sufficiently high speeds, the two phenomena exactly cancel, resulting in no net offtrack- ing, and at still higher speeds the net result is that the rear of the vehicle tracks outside of the front. The quantification of fully-developed high-speed offtrack- ing was initially modeled by Bernard and Vanderploeg (27), and their model was later expanded by Glauz and Harwood (22). The model includes the fully-developed low-speed off- tracking terms discussed above, plus a speed-dependent por- tion, which is the high-speed contribution. It is proportional to the axle spacing, P, not to its square as is the case with low- speed offtracking. It is, however, proportional to the square of the truck speed and increases with decreasing path radius. In practice, net outward offtracking, due to the high-speed term becoming dominant, does not occur until speeds reach the neighborhood of 89 km/h [55 mph], for example, on highway entrance or exit ramps. Net outward offtracking rarely exceeds 0.6 m [2.0 ft]. Because net high-speed offtracking is usually not a signif- icant factor in roadway design, compared with low-speed offtracking, its transient or partially-developed form has not been studied. Figure 22. Observed wheelpaths for combination trucks turning right at an intersection in Montello, Wisconsin (26).
TRAILER SWINGOUT The front of a trailer is generally ahead of the front axles that support the trailer. Similarly, the rear of a trailer gener- ally overhangs the rear axles. As a result, during a turn the front of the trailer swings to the outside of the front trailer axles (front swingout) and the rear of the trailer swings to the outside of the rear axles (rear swingout). Front and rear swingout are illustrated in Figure 23. Swingout is (1) a function of the trailer wheelbases and other dimensions and the radius of the turn and (2) can be quantified using a modification of the low-speed offtracking programs discussed above. On some trailers, the consequences of front swingout are reduced by beveling or rounding the front of the trailer. Never- theless, in practical trailer configurations, the front overhang of a trailer is only of the order of 1 m [3 ft], and front swingout persists for only a few seconds during a turn. Moreover, it is clearly visible to, and thus under the control of, the driver. For these reasons, drafters of NAFTA IAN standards have sug- gested a fairly liberal limitation of no more than 0.45-m [18-in] front swingout in a 90-deg turn of 14.0 m [45.9 ft]. On the other hand, rear overhang can be substantial. For example, with a 16.2-m [53-ft] semitrailer with the rear axles moved forward to satisfy a 12.5-m [41-ft] king-pin- to-rear-axle limitation, the rear overhang is typically 2.7 m [9 ft]. Although rear swingout is not as pronounced as front swingout due to the geometrics involved, it can persist for much longer periods of time during a turn and is out of view of the driver. For these reasons, the drafters of the NAFTA IAN criteria have suggested a limitation of no more than 0.2 m [8 in] of rear swingout in a 90-deg turn of 14.0-m [45.9-ft] radius. Table 24 shows the maximum rear swingout in 90-deg turns for varying radii for selected design vehicles, includ- ing design vehicles from the 2001 Green Book and the pro- posed new or revised design vehicles presented in Chapter 4. 43 The derivation of these maximum rear swingout values is described in Appendix C. The results for 15.3-m [50-ft] turns in Table 24 indicate that most of the current and proposed Green Book design vehicles are well within the proposed NAFTA IAN criteria, with two exceptions. First, the WB-20 [WB-67] design vehi- cle very slightly exceeds the IAN criteria if the axles are pulled forward to obtain a 12.5-m [41-ft] KCRT distance; the mod- eled value is so close to the IAN criterion that it may be within the margin of error. The WB-22 [WB-71] design vehicle is in Front Swingout Rear Swingout Figure 23. Illustration of front and rear swingout for a tractor-trailer combination making a turn (8). TABLE 24 Maximum rear swingout for selected design vehicles in 90 degree turns Maximum rear swingout (ft) for specified turn radius Design vehicle type Symbol 50 ft 75 ft 100 ft 150 ft Single-unit truck SU 0.35 0.24 0.18 0.12 Single-unit truck (three-axle) SU25 1.07 0.73 0.53 0.35 Interstate semitrailer WB-62 0.18 0.14 0.09 0.06 Interstate semitrailer (revised)a WB-62 0.17 0.13 0.09 0.06 Interstate semitrailer WB-67 0.17 0.14 0.10 0.07 Interstate semitrailerb WB-67 (41-ft KCRT) 0.69 0.51 0.41 0.27 Long interstate semitrailer WB-71 0.17 0.13 0.10 0.07 Long interstate semitrailerc WB-71 (41-ft KCRT) 1.45 1.08 0.84 0.61 âDouble-bottomâ-semitrailer/trailer WB-67D 0.08 0.05 0.05 0.03 Longer âdouble-bottomâ-semitrailer/trailer WB-77D 0.13 0.11 0.08 0.06 B-train double-semitrailer/semitrailer WB-77BD 0.17 0.12 0.10 0.07 Rocky mountain double-semitrailer/trailer WB-92D â â 0.05 0.04 Turnpike double-semitrailer/trailer WB-109D â â 0.09 0.06 Long turnpike double-semitrailer/trailer WB-120D â â 0.37 0.27 a Proposed revision to WB-62 design vehicle; KCRT distance increased from 40.5 to 41.0 ft. b WB-67 design vehicle with axles pulled forward to obtain 41.0-ft KCRT distance. c WB-71 design vehicle with axles pulled forward to obtain 41.0-ft KCRT distance.
compliance with the IAN criterion if the rear axles are pushed back close to the rear of the trailer, but this design vehicle is substantially out of compliance if the rear axles are pulled forward to obtain a 12.5-m [41-ft] KCRT distance. Thus, it is not possible for the possible future WB-22 [WB-71] to simultaneously satisfy the IAN rear swingout criterion and the KCRT limitations of many states. It is important to recognize that rear swingout, like low- speed offtracking, grows as the truck proceeds through a turn. Although the outside rear corner of the trailer follows a path outside of the rear trailer wheels, it is inside of the swept path. The outside of the swept path is determined by the outside front wheel of the tractor and not by the trailer wheels. This phenomenon is illustrated by Figure C-23 in Appendix C. This finding suggests that rear swingout is rarely a concern to other vehicles, unless they are making a parallel turn. BRAKING DISTANCE Braking distance is defined in the Green Book as âthe dis- tance needed to stop the vehicle from the instant brake appli- cation begins.â Braking distance is used in the determination of many highway design and operational criteria, including stopping sight distance, vehicle change intervals for traffic signals, and advance warning sign placement distances. Cur- rently, all of these design and operational criteria are based on passenger car braking distances and do not consider the longer braking distances required for trucks. The process of bringing a truck to a stop requires a complex interaction between the driver, the brake system, the truck tires, the dimensions and loading characteristics of the truck, and the pavement surface characteristics. Because truck braking is much more complex than passenger car braking, it is neces- sary to discuss how each of these characteristics affects truck braking distances. Tire-Pavement Friction in Braking Maneuvers Vehicles are brought to a stop by brakes that retard the rotation of the wheels and allow tire-pavement friction forces to decelerate the vehicle. An understanding of the forces involved in tire-pavement friction is, therefore, critical to the understanding of braking distances. For a horizontal pavement, the coefficient of braking fric- tion (fy) is defined as the ratio of the horizontal braking force (Fy) generated at the tire-pavement interface to the vertical load (Fz) carried by the tire. In other words (2) Side forces, or âcornering forces,â can interact with the braking force and affect the ability to stop a vehicle in a con- trolled manner. If a vehicle is being steered to follow a f F Fy y z = 44 curved path, tire-pavement friction supplies a cornering force, tending to keep the vehicle from departing its intended path. The coefficient of cornering friction (fx) is the ratio of the cornering force (Fx) generated at the tire-pavement inter- face to the vertical load (Fz) carried by the tire. In other words (3) Figure 24 illustrates that both braking and cornering fric- tion vary as a function of percent slip, which is the percent decrease in the angular velocity of a wheel relative to the pavement surface as a vehicle undergoes braking. A freely rolling wheel is operating at zero percent slip. A locked wheel is operating at 100 percent slip with the tire sliding across the pavement. Figure 24 shows that the coefficient of braking friction increases rapidly with percent slip to a peak f FFx x z = Figure 24. Variation of braking and cornering friction coefficients with percent slip.
value that typically occurs between 10 and 15 percent slip. The coefficient of braking friction then decreases as percent slip increases, reaching a level known as the coefficient of sliding friction at 100 percent slip. The coefficient of cornering friction has its maximum value at zero percent slip and decreases to a minimum at 100 percent slip. Thus, when a braking vehicle locks its wheels, it may lose its steering capability due to a lack of cornering friction. Locked-Wheel Braking Versus Controlled Braking The discussion of Figure 24 implies that braking maneu- vers can be performed in two general modes: locked-wheel braking and controlled braking. Locked-wheel braking occurs when the brakes grip the wheels tightly enough to cause them to stop rotating, or âlock,â before the vehicle has come to a stop. Braking in this mode causes the vehicle to slide or skid over the pavement surface on its tires. Locked-wheel braking uses sliding friction (100 percent slip) represented by the right end of the graph in Figure 24, rather than rolling or peak friction. The sliding coefficient of friction takes advantage of most of the friction available from the pavement surface, but is generally less than the peak available friction. On dry pavements, the peak coefficient of friction is relatively high with very little decrease in friction at 100 percent slip. On wet pavements, the peak friction is lower, and the decrease in friction at 100 percent slip is generally larger. The braking distance required for a vehicle to make a locked-wheel stop can be determined from the following relationship: (4) where BD = braking distance (ft) V = initial speed (mph) fs = coefficient of sliding friction The coefficient of sliding friction in Equation 4 is mathe- matically equivalent to the deceleration rate used by the vehi- cle expressed as a fraction of the acceleration of gravity (g), equal to 9.8 m/s2 [32.2 ft/s2]. The coefficient of friction and, thus, the deceleration rate may vary as a function of speed during the stop, so fs in Equation 4 should be understood as the average coefficient of friction or deceleration rate during the stop. Controlled braking is the application of the brakes in such a way that the wheels continue to roll without locking up while the vehicle is decelerating. Drivers of vehicles with conventional brakes generally achieve controlled braking by âmodulatingâ the brake pedal to vary the braking force and BD V30f 2 s = 45 to avoid locking the wheels. Controlled braking distances are governed by the rolling coefficient of friction, which, for a typical vehicle, occurs at a value of percent slip to the left of the peak available friction shown in Figure 24. Due to the steep slope of the braking friction curve to the left of the peak and due to braking techniques used by drivers to avoid wheel lock up, the average rolling friction utilized by vehicles is generally less than the sliding friction coefficient. Therefore, controlled braking distances are usually longer than locked- wheel braking distances, although theoretically they would be less if the driver could use peak braking friction. Locked-wheel braking is commonly used by passenger car drivers during emergency situations. Passenger cars can often stop in a stable manner, even with the front wheels locked. In this situation, the driver loses steering control, and the vehicle generally slides straight ahead. On a tangent sec- tion of road this is perhaps acceptable behavior, although on a horizontal curve the vehicle may leave its lane and possi- bly the roadway. Combination trucks, by contrast, have much more diffi- culty stopping in the locked-wheel mode. Figure 25 illus- trates the dynamics of a tractor-trailer truck if its wheels are locked during emergency braking (17). The behavior depends on which axle locks firstâthey usually do not all lock up simultaneously. When the steering wheels (front axle) are locked, steering control is eliminated, but the truck maintains rotational stability and it will skid straight ahead. However, if the rear wheels of the tractor are locked, that axle slides and the tractor rotates or spins, resulting in a âjackknifeâ loss of control. If the trailer wheels are locked, those axles will slide, and the trailer will rotate out from behind the tractor, which also leads to loss of control. Although a skilled driver can recover from the trailer swing through quick reaction, the jackknife situation is not correctable. None of these locked- wheel stopping scenarios for trucks is considered safe. There- fore, it is essential that trucks stop in a controlled braking mode and that highway geometric design criteria recognize the dis- tances required for trucks to make a controlled stop. The braking distance for a vehicle to make a controlled stop can be determined from the following relationship: Figure 25. Tractor-trailer dynamics with locked wheels (17).
(5) where BD = braking distance (ft) fr = coefficient of rolling friction V = initial speed (mph) As in the case of sliding friction, the coefficient of rolling friction (fr) in Equation 5 represents the average coefficient of friction or average deceleration rate during the entire con- trolled stop. Pavement and Truck Characteristics Affecting Braking Distance In order to stop without the risk of loss of control, trucks must use controlled braking, rather than locked-wheel brak- ing. The deceleration rates used by trucks in making a con- trolled stop are represented by fr in Equation 5. The follow- ing discussion reviews the principal individual pavement and tire characteristics that affect the value of fr and, thus, the braking distance of a truck. Additional factors that can affect braking distance include road roughness, brake adjustment, and brake lining temperature (2,3). Pavement Properties The shape of the braking friction curve in Figure 24 is a function of both pavement and tire properties. Highway agen- cies generally measure pavement friction by means of locked- wheel skid tests with a âstandardâ tire. These tests determine a value equivalent to fs in Equation 4. The results of these tests are often multiplied by 100 and referred to as skid numbers rather than coefficients of friction. Although skid numbers are usually determined at 64 km/h [40 mph], a procedure is avail- able to determine the skid number at any speed from the skid number at 64 km/h [40 mph] (28,29,30). The peak coefficient of friction (fp) can be estimated from the sliding coefficient of friction by the following relationship (28): fp = 1.45fs (6) Equation 6 represents the average relationship for truck tires between peak and sliding friction; this relationship can vary markedly between pavements and for the same pave- ment under wet and dry conditions. Pavements generally have much lower coefficients of friction under wet condi- tions than under dry conditions, so highway design criteria are generally based on wet conditions. Estimates of braking distance by Olson et al. used an assumed pavement skid number at 64 km/h [40 mph] (SN40) equal to 28 (28). The Green Book criteria for stopping sight BD V30f 2 r = 46 distance prior to the 2001 edition were based on a pavement with SN40 equal to 32. Pavement surface condition (wet versus dry) has an impor- tant bearing on braking distances. Locked-wheel braking is directly related to the tire-pavement friction coefficient, but controlled braking is less so. Trucks require greater braking distances than passenger cars on dry pavements, but NCHRP Synthesis 241 reports that the braking distances of passenger cars and trucks on wet pavements are nearly equal. Tire Properties Truck tires are designed primarily for wear resistance. For this reason, they tend to have somewhat lower wet friction coefficients than passenger car tires. It is generally estimated that truck tires have coefficients of friction that are about 70% of those of passenger car tires (28). However, passenger car tires generally have coefficients of friction that are about 120% of the friction coefficients of the standard tires used in skid testing. Thus, the peak coefficient of friction can be esti- mated from skid test results with the following relationship: fp = (1.20)(0.70)(1.45)fs = 0.0122SN40 (7) The coefficient of friction for truck tires decreases as the tires wear and their tread depth decreases. New truck tires have tread depths of 12 mm [15/32 in] for ribbed tires and 25 mm [31/32 in] for lug type tires. Olson et al. assumed, based on the literature, that the tread wear of truck tires has very lit- tle effect on their frictional properties until the tread depth falls below 10 mm [12/32 in] (28,31). Tire tread depth has lit- tle effect on the coefficient of friction on pavements with high macrotexture, but the coefficient of friction does decrease substantially with tread depth for smooth, poorly textured pavements (32). The following relationship was used by Olson et al. to estimate the reduction in friction coef- ficient of tires as their tread depth decreases (28): (8) where TF = adjustment factor for tire tread depth âfp = difference in coefficient of friction between new and bald (completely worn) tires x = remaining tread depth (in) (use 12/32 if x â¥ 12/32) n = minimum tread depth with coefficient of friction equivalent to a new tire (assumed: 12/32 in) Equation 8 is probably based on studies of passenger car tires, but no equivalent relationship for truck tires is currently available. Data on the coefficients of friction for various types of truck tires are available in References 18, 32, 33, and 34. TF f x/n f p p = â â( )1 1â
Both References 32 and 33 indicate that the friction coeffi- cients of truck tires decrease slightly with increasing axle load. Tire inflation pressure has very little effect on peak friction coefficient (fp), but increasing the inflation pressure from 47 to 70 kPa [68 to 102 psi] results in a very small loss (less than 10%) in the sliding friction coefficient (fS) (34). Braking Efficiency Conventional Braking Systems. Conventional truck brak- ing systems are limited in their ability to take full advantage of all of the friction available at the tire-pavement interface. Fancher has estimated that the braking efficiency for single- unit trucks is between 55 and 59% of the peak available fric- tion (35). Both Fancher and Olson et al. assume that this same level of braking efficiency is applicable to tractor-trailer trucks (28,35). A primary reason for this relatively low level of brak- ing efficiency is that most controlled braking takes place at a value of percent slip less than the level which produces the peak braking friction coefficient. Several other vehicle-related factors that contribute to low braking efficiencies are reviewed in this section. Antilock brake systems, which enable increases in braking efficiency, are also discussed. By way of introduction, the operation of air brakesâthe usual braking system for combination trucksâis reviewed. Air brake systems use compressed air to transmit and amplify the driverâs input from the brake pedal to the brakes on individual wheels. The use of air as an amplifying medium results in a slight delay in the system response due to the compressibility of air. (In contrast, hydraulic braking sys- tems provide an almost immediate response, but are not oper- ationally feasible for truck combinations that must be fre- quently disassembled and reassembled.) Once the brake pedal is released, the air in the system is expelled to the atmosphere and is replaced by air from a compressor on board the trac- tor. Therefore, air brakes are not âpumped,â as might be done in making a controlled stop with hydraulic brakes. Pumping of air brakes will result in the rapid depletion of the com- pressed air supply, which in turn results in a total loss of braking ability. Rather, for an air brake system, the pressure within the system is adjusted by slightly depressing or slightly releasing the brake pedal to apply more or less braking force. This braking practice is called âmodulatingâ the brakes. As discussed earlier in this section, âmodulatingâ the brakes requires some experience on the part of the driver to obtain the maximum braking effect from the system without caus- ing the wheels to lock. Antilock Brake Systems. The purpose of antilock brakes is to take full advantage of the available tire-pavement fric- tion capabilities without locking the wheels and losing vehi- cle control. Antilock brake systems try to achieve and main- tain the peak coefficient of tire-pavement friction shown in Figure 24, thereby maximizing the braking effort. 47 Antilock brake systems operate by monitoring each wheel for impending lock up. When wheel lock up is anticipated, the system reduces brake pressure on the wheel. When the wheel begins to roll freely again, the system reapplies brak- ing pressure. The system constantly monitors each wheel and readjusts the brake pressure until the wheel torque is no longer sufficient to lock the wheel. The antilock brake system is con- trolled by an onboard microprocessor. Antilock brake systems are now required for new trucks, tractors, and trailers in accordance with Federal Motor Vehicle Safety Standard (FMVSS) 121 (36). Antilock brake systems have been required for air-brake-equipped tractors manufac- tured on or after March 1, 1997; and air-brake-equipped trail- ers and single-unit trucks manufactured on or after March 1, 1998. Antilock brake systems were also available as an option for some of these vehicles before those dates. Truck tractors have a useful life of approximately 7 years. Therefore, nearly all truck tractors in the current fleet have antilock brakes or will soon be replaced by a tractor that does. Thus, the use of antilock brakes in the tractor fleet can be regarded as nearly 100%. Truck trailers have a useful life of approximately 20 years. Thus, only about 5% of the trailer fleet is replaced each year. There has not been sufficient time since March 1, 1998, for antilock brake systems to come into use for trail- ers as completely as they have for tractors. A field survey at truck weigh stations conducted in three states during 2002 as part of this research, and presented in Appendix B of this report, found that approximately 43% of trailers are equipped with antilock brake systems. Based on the service life of trail- ers, it can be expected that within 10 years nearly all trailers will be equipped with antilock brake systems. FMVSS 121 specifies a performance standard for truck braking distance. The required braking distances are sum- marized in Table 25. These criteria apply to tests of the truck service brakes on a dry pavement with a peak friction coef- ficient of 0.9. Driver Control Efficiency Most drivers, including truck drivers, have little or no prac- tice in emergency braking situations. This lack of expertise in modulating the brakes in critical situations results in braking distances that are longer than the vehicle capability. Olson et al. evaluated the effect of driver efficiency on braking distance using both experienced test drivers and professional truck drivers without test track experience (28). Their study found that the driver efficiencies ranged from 62 to 100% of the vehi- cle capability. The braking performance of the drivers tended to improve during the testing period as the drivers gained expe- rience in emergency stopping. Because so many drivers on the road lack experience in emergency braking, the study recom- mended the use of a driver efficiency of 62% in stopping sight distance design criteria. However, it should be recognized that
this is a very conservative choice. The best-performance drivers can operate at efficiencies approaching 100%. Further- more, because antilock brake systems are becoming ever more common, and will soon be the norm, the concern over driver efficiency is eliminated by providing computer-controlled modulation of the brakes to achieve minimum braking distance, equivalent to a driver efficiency of 100%. Estimation of Braking Distances Olson et al. have suggested a model to predict braking dis- tance as a function of pavement surface characteristics, tire characteristics, vehicle braking performance, and driver con- trol efficiency (28). Parametrically, the model expresses the coefficient of rolling friction, fr, as fr = fp Ã TF Ã BE Ã CE (9) where fp = peak braking friction coefficient available given the pavement surface characteristics TF = adjustment factor for tire tread depth (see Equation (8)) BE = adjustment factor for braking efficiency (the effi- ciency of the braking system in using the available 48 friction, typically 0.55 to 0.59 for conventional brak- ing systems) CE = adjustment factor for driver control efficiency (the efficiency of the driver in modulating the brakes to obtain optimum braking performance, typically 0.62 to 1.00 for conventional braking systems) The factors that influence each term of Equation 9 have been addressed in the preceding discussion. Based on Equation 9, the FHWA Truck Characteristics study (2,3) estimated truck braking distances for a truck with a conventional braking system and the worst-performance driver, a truck with a conventional braking system and the best-performance driver, and a truck with an antilock brake system. Table 26 presents these braking distances along with the updated assumptions about controlled braking distance presented in the 2001 Green Book. DRIVER EYE HEIGHT Driver eye height is a combined driver and vehicle char- acteristic that is essential to the evaluation of sight distance issues. Truck drivers generally have substantially higher eye heights than passenger car drivers, which means that a truck TABLE 25 Truck braking distances specified as performance criteria for antilock brake systems in FMVSS 121 (36) Truck braking distance (ft)a Vehicle speed (mph) Loaded single-unit truck Unloaded truck tractors and single-unit trucks Loaded truck tractors with an unbraked control trailer 20 35 38 40 25 54 59 62 30 78 84 89 35 106 114 121 40 138 149 158 45 175 189 200 50 216 233 247 55 261 281 299 60 310 335 355 a Braking distance for truck service brakes; separate criteria apply to truck emergency brakes. TABLE 26 Truck deceleration rates and braking distances Deceleration rate (g)a Braking distance (ft)a Vehicle speed (mph) Previous AASHTO policyb Current AASHTO policyc Worst- performance driverd Best- performance drivere Antilock brake system Previous AASHTO policyb Current AASHTO policyc Worst- performance driverd Best- performance drivere Antilock brake system 20 0.40 0.35 0.17 0.28 0.36 33 38 77 48 37 30 0.35 0.35 0.16 0.26 0.34 86 86 186 115 88 40 0.32 0.35 0.16 0.25 0.31 186 152 344 213 172 50 0.30 0.35 0.16 0.25 0.31 278 238 538 333 269 60 0.29 0.35 0.16 0.26 0.32 414 343 744 462 375 70 0.28 0.35 0.16 0.26 0.32 583 467 1,013 628 510 a Based on an empty tractor-trailer truck on a wet pavement with SN40 = 32. b Based on 1994 Green Book c Based on 2001 Green Book d Based on driver control efficiency of 0.62. e Based on driver control efficiency of 1.00.
driver can see farther than a passenger car driver on the approach to vertical sight restrictions. The AASHTO Green Book specifies a value of 1,080 mm [3.5 ft] for driver eye height, based on consideration of a passenger car as the design vehicle. By contrast, a value of 2,400 mm [8.0 ft] is recommended by the Green Book for truck driver eye height. This value is based on relatively recent field studies by Fambro et al. (37) and does not appear to be in need of updating. TRUCK ACCELERATION CHARACTERISTICS Two aspects of truck acceleration performance are con- sidered in this section. The first aspect is the ability of a truck to accelerate from a full stop to clear a specified hazard zone such as an intersection or railroad-highway grade crossing. Typically, a hazard zone of this type is less than 66 m [200 ft] long; as a result, the speed attained by the truck is low. This first aspect of truck acceleration performance is, therefore, referred to as low-speed acceleration. The second aspect of truck acceleration is the ability of a truck to accelerate to a high speed, either from a stop or from a lower speed. This type of acceleration, referred to here as high-speed acceler- ation, is needed by trucks in passing maneuvers and in enter- ing a high-speed facility. Low-Speed Acceleration The low-speed (or start-up) acceleration ability of a truck determines the time required for it to clear a relatively short hazard zone such as an intersection or railroad-highway grade crossing. The primary factors that affect the clearance times of trucks are â¢ Length of hazard zone, â¢ Length of truck, â¢ Truck weight-to-power ratio, â¢ Truck gear ratio, and â¢ Roadway geometry (i.e., percent grade and curvature). State and Federal regulations require vehicles transporting passengers and hazardous materials to accelerate at railroad- highway grade crossings without shifting gears. The assump- tion that the truck does not shift gears is probably less realis- tic at intersections than at railroad-highway grade crossings. When shifting gears is allowed, a truck can reach a higher speed but, simultaneously, it loses speed during the delay when the driver is shifting gears. Therefore, the overall effect on clearance time, assuming that there is no gear shift, may be negligible unless the hazard zone is quite long. A simplified analytical model of the low-speed accelera- tion of trucks has been developed by Gillespie (38). The Gillespie model estimates the time required for a truck to clear a hazard zone, starting from a full stop, as 49 (10) where tc = time required to clear zone (s) LHZ = length of hazard zone (ft) LT = length of truck (ft) Vmg = maximum speed in the gear selected by the driver (mph) Equation 10 is based on the assumption that the distance traveled by the truck during the clearance time is the length of the hazard zone plus the length of the truck, LHZ + LT. Nei- ther the weight nor the weight-to-power ratio of the truck is considered explicitly in Equation 10, although it is implicitly assumed that the weight-to-power ratio would affect the driverâs choice of gears. The model assumes that, when start- ing from a full stop, a truck rather quickly reaches the maxi- mum speed in the gear selected by the driver and then trav- els at that constant speed until it clears the hazard zone. Thus, Equation 10 is essentially a constant speed model, and accel- eration rates, as such, are not meaningful. On a level road, Vmg can be calculated as (11) where gr = gear ratio selected by the driver This model of low-speed acceleration is based on the assumption that the gear design, engine speed, and tire size of the truck are such that its maximum speed in high gear without overdrive (gear ratio 11) is 97 km/h [60 mph]. The estimated clearance times for a 19.8-m [65-ft] tractor- trailer truck, obtained from Equation 10, are given in Table 27. The values of clearance times on grades are greater than those on no grade because the truck speed, Vmg, is lower, as illustrated in Table 27. The Gillespie model was compared with the results of field observations of time versus distance for 77 tractor-trailer trucks crossing zero-grade intersections from a full stop (38). These data are shown in Figure 26. There is no information on the weights or weight-to-power ratios of these trucks, although they probably vary widely. A line representing the clearance time predicted by Equation 10 for a level grade is also presented in the figure. Equation 10 provides a relatively conservative estimate of clearance times, given that most of the experimental points fall below the prediction. The experimental data in Figure 26 can be bounded by two parallel lines representing the maximum and minimum observed clearance times. Hutton collected data on the acceleration performance of 31 tractor-trailer combinations (39). Most of the trucks eval- uated by Hutton were cab-over-engine tractors pulling twin V grmg = 60 t 0.682(L L )Vc HZ T mg = + + 3 0.
8.2-m [27-ft] trailers. The engine horsepower of the trucks ranged from 170 to 283 kW [228 to 375 hp], while their gross vehicle weights ranged from 15,100 to 40,900 kg [33,250 to 89,900 lb]. Figure 27 illustrates the resulting time versus dis- tance curves determined by Hutton for initial acceleration by trucks with weight-to-power ratios of 60, 120, 180, and 240 kg/kW [100, 200, 300, and 400 lb/hp]. The Hutton data can be used to calculate clearance times and then compared with the clearance times from the Gil- lespie data from Figure 26. This comparison shows that the Hutton data fall within the boundaries shown in Figure 26. Moreover, all the Hutton data fall below the predictions of Equation 10. Based on these findings, the FHWA Truck Characteristics study recommended that the range for clearance times for trucks be revised as follows (2): (12) tmax = 10.8 + 0.075(LHZ + LT) (13) Table 28 presents the estimated minimum and maximum clearance times for a 19.8-m [65-ft] truck to cross hazard zones of varying length. Fancher compared the results of two studies to the time versus distance for low-speed acceleration from a stop spec- ified in the Green Book and found that the average tested t L Lmin HZ t= â + + +4 2 0 70 36 1 25. . . ( ) 50 heavy vehicles performed with more acceleration than the 1984 Green Book criteria for a WB-15 [WB-50] truck (40). High-Speed Acceleration There is a substantial amount of performance data in the lit- erature for acceleration from a stop to a high-speed. Figure 28 presents speed-versus-distance curves for acceleration to high-speeds developed in References 41, 42, 43, 44, and 45. (The values for Reference 45 are shown in Figure 28 as a range.) All of these sources are dated prior to 1990 and reflect the performance of past truck populations. Hutton also developed acceleration data for trucks classified by weight-to-power ratio (39). Although these data were col- lected in 1970, the fundamental relationships between weight- to-power ratio and truck performance have not changed substantially. Figure 29 shows distance-versus-time curves for accel- eration from a full-stop to higher speeds for 60, 120, 180, and 240 kg/kW [100, 200, 300, and 400 lb/hp] trucks (38). These curves can be approximated by the following analyt- ical relationships: Weight-to-power ratio (lb/hp) Distance-time relationship 100 (14) 200 (15) 300 (16) 400 (17) Figure 30 shows corresponding speed-versus-time curves for the same trucks. The average acceleration rates for accel- eration to 64 km/h [40 mph] from speeds of 0, 16, 32, and 48 km/h [0, 10, 20, and 30 mph] are given in Table 29, based on the data in Figure 30. Acceleration rates of trucks at higher speeds are less than those given in Table 29. For example, the acceleration rate for a 60 kg/kW [100-lb/hp] truck to increase t x= â + +26 6 708 3 57. . t x= â + +22 0 480 2 94. . t x= â + +22 8 523 2 56. . t x= â + +15 1 229 1 64. . TABLE 27 Clearance time (s) for low-speed acceleration by a 19.8-m [65-ft] tractor-semitrailer Length of hazard zone (ft) Percent grade Vmg (mph) 30 40 50 60 70 80 90 100 110 120 0-2 8 11.1 1.9 2.8 3.7 4.5 5.4 16.2 17.1 17.9 18.8 3-5 6 13.8 14.9 16.1 17.2 18.3 19.5 20.6 21.8 22.9 24.0 6-10 5 16.0 17.3 18.7 20.0 21.4 22.8 24.1 25.5 26.9 28.2 11-13 4 19.2 20.9 22.6 24.3 26.0 27.7 29.4 31.1 32.8 34.5 Figure 26. Field observations of times for 19.8-m [65-ft] tractor-trailer trucks to clear intersection distances after starting from a stop (2, 38).
its speed from 56 to 88 km/h [35 to 55 mph] is 0.16 m/s2 [0.53 ft/s2], based on the curve in Figure 30. The corre- sponding rate for a 120-kg/kW [200-lb/hp] truck is 0.11 m/s2 [0.36 ft/s2]. Figure 30 illustrates that 180- and 240-kg/kW [300- and 400-lb/hp] trucks cannot accelerate to 88 km/h [55 mph] within the time scale shown on the figure. SPEED-MAINTENANCE CAPABILITIES ON GRADES The primary factors that determine the ability of a truck to maintain speed on an upgrade are â¢ Weight-to-power ratio, â¢ Percent grade of roadway, â¢ Aerodynamic drag, â¢ Rolling resistance, â¢ Drive line efficiency, â¢ Length of grade, â¢ Tire size, and â¢ Transmission characteristics. The speed of a truck on an upgrade can be approximated by the following equation: 51 mVË = P/V â Fr â Fa â mg sinÎ± (18) where m = mass of truck P = net engine power available at the drive wheels (hp) V = speed (ft/s) Fr = rolling resistance force (lb) Fa = aerodynamic drag force (lb) â = angle of the grade (degrees) g = acceleration of gravity (9.8 m/s2 [32.2 ft/s2]) The steepness of grade (Î±) can be expressed in the more con- ventional percent grade form as 100 tan â. The variable, VË, represents the time derivative of truck speed (dV/dt). Equation 18 can also be written as (19) where W/P is weight-to-power ratio in units of lb/hp. Another way to view truck performance on a grade is pro- vided by Gillespie (46). Figure 31 shows the factors of Equa- tions 18 and 19, expressed as forces propelling a truck forward mV mg(W/P)V F F mgr a= â â â sinÎ± Figure 27. Observed time versus distance curves for initial acceleration from a stop by tractor-trailer trucks (2, 39). TABLE 28 Minimum and maximum clearance times (s) for a 19.8-m [65-ft] tractor-trailer truck Length of hazard zone (ft) Range of clearance times 30 40 50 60 70 80 90 100 110 120 tmin 4.5 4.9 5.2 5.5 5.8 6.1 6.4 6.7 7.0 7.2 tmax 17.9 18.7 19.4 20.2 20.9 21.7 22.4 23.2 23.9 24.7
or resisting its forward motion. This figure is for a very low performance truck, by todayâs standards, that is barely able to achieve 105 km/h [65 mph] on a level road. At that speed, the engine power limit is about 15% of the vehicle weight, but that is reduced to 13% of the vehicle weight by drive train losses. Major losses are about 5% of the vehicle weight due to rolling resistance and 8% of the vehicle weight due to aerodynamic losses. Thus, losses require all the available engine power, and no engine power is left for further acceleration. At speeds above about 80 to 89 km/h [50 to 55 mph], the aerodynamic losses dominate; at lower speeds, rolling resistance is greater. If the truck is on a grade, overcoming the grade becomes extremely important. For this truck, even a small 1% grade requires a force equal to about 8% of the vehicle weight to overcome, so the maximum speed for this very low perfor- mance truck is reduced to about 64 km/h [40 mph]. Several of the key factors in Equations 18 and 19 are dis- cussed below. Literature Review Weight-to-Power Ratio The ability of a truck to maintain speed on an upgrade is very sensitive to its weight-to-power ratio. The weight-to- power ratios of trucks have been decreasing steadily for many 52 years, as tractor engines have become more and more power- ful. Figure 32 illustrates the long-term trends in the weight-to- power ratios of trucks. The figure shows the several lines illus- trating trends in average weight-to-power ratios of trucks as a function of gross weight from 1949 to 1975. Added to the fig- ure is a line based on the 1977 Truck Inventory and Use Sur- vey (TIUS), predecessor of the current VIUS survey, and points representing the Gillespie data (46,47). A comparison of the TIUS and Gillespie data demonstrates that the major reason for the reduced weight-to-power ratios of trucks dur- ing this period is a substantial increase in average engine horsepower. The average tractor power in the 1977 TIUS data was 170 kg/kW [282 hp], in comparison with 210 kg/kW [350 hp] in the Gillespie data of 1984. The trend toward more powerful engines for tractor-trailer combinations has contin- ued through the 1980s and 1990s. Table 30 presents average values of weight-to-power ratios of trucks obtained from field observations at sites located in the Eastern and Western parts of the United States in a 1985 report by Gillespie (46). The table shows the average weight, power, and weight-to-power ratios of trucks by truck type and road class. The number of trucks observed for each road class is given in parentheses following the road class. Data on truck performance on grades collected by Gillespie in 1984 are shown as triangles in Figure 32. Since the reported results did not include the explicit distribution of weight- Figure 28. Speed-versus-distance curves for truck acceleration from a stop (2, 39).
to-power ratios, the database developed in that study was obtained and reanalyzed in the FHWA Truck Characteristics study (2,3). That study presents a detailed discussion of the procedures used to derive weight-to-power ratios for over 3,000 individual trucks theoretically from their final climb- ing speeds and directly from the weights and rated horse- powers of a sample of approximately 500 trucks. This analy- sis addressed only combination trucks (tractor-trailers) and addressed several factors including aerodynamic losses that 53 were not addressed by Gillespie. The distributions of truck weight-to-power ratio were derived indirectly from the final climbing speeds and directly from measured gross weights and rated horsepowers. These distributions showed that the median weight-to-power ratio for trucks was about 100 kg/kW [175 lb/hp], while the 87.5 percentile weight-to-power ratio was about 150 kg/kW [250 lb/hp]. There have been no data reported in the literature to indi- cate how truck weight-to-power ratios have changed since the Figure 29. Observed time versus distance curves for acceleration to high speed from a stop by a tractor-trailer truck (2, 39). Figure 30. Observed speed-versus-time curves for acceleration by truck with various weight-to-power ratios (39).
mid-1980s other than the results of a field study by Harwood et al. (49) performed at one site on a two-lane highway in California in 1997. Furthermore, the choice of a design weight-to-power ratio should be based not on an average or median value like those reported in Table 30, but on a value representative of trucks that perform more poorly, such as the 85th percentile weight-to-power ratio. To obtain up-to-date data on the performance abilities on upgrades of the current truck fleet, field studies were conducted as part of the current research at nine sites on freeways and two-lane highways in three states: California, Colorado, and Pennsylvania. In addi- tion, the data from the 1997 study mentioned above for one 54 two-lane highway site in California were also included in the analysis. Tables 31 and 32 summarize the results for truck weight-to-power ratios in these three states. Comparison of Table 30 with Tables 31 and 32 suggests that, since 1984, average truck weight-to-power ratios on freeways have improved substantially in the western states but have stayed about the same in the eastern states. No com- parative data are available for two-lane highways. Rolling Resistance The rolling resistance of tires, Fr, is defined as the ratio of power lost due to rolling resistance to speed. Fr can be esti- mated using the following SAE equations: Fr = 0.001(4.1 + 0.041 V) for radial tires (20) Fr = 0.001(5.3 + 0.044 V) for mixed tires (21) Fr = 0.001(6.6 + 0.046 V) for bias-ply tires (22) where V is speed in mph. Experimental rolling resistance data for selected truck tires can be found in the literature (50). TABLE 29 Average acceleration capabilities of trucks from specified speed to 64 km/h [40 mph] (39) Acceleration rate (ft/s2) Weight-to- power ratio (lb/hp) 0 mph 10 mph 20 mph 30 mph 100 1.87 1.70 1.47 1.29 200 1.22 1.08 0.96 0.79 300 0.91 0.81 0.72 0.58 400 0.71 0.61 0.50 0.36 NOTE: Based on speed-distance curves shown in Figure 30. Figure 31. Forces acting on a vehicle as a function of speed (46).
Aerodynamic Drag The aerodynamic drag force is estimated by the following relationship (43): Fa = 1.1DCD AV2 (23) where Fa = aerodynamic drag (lb) D = air density (lb/fat) CD = drag coefficient (0.6 with aerodynamic aids, 0.7 without) A = truck frontal area (102 fat for van bodies, 75 fat for cab only) (fat) V = truck speed (mph) VEHICLE LENGTH Vehicle length is addressed primarily in other sections of this report. Chapter 2 of this report addresses vehicle length limits in truck size and weight policies. Chapter 3 addresses the distribution of vehicle lengths in the current truck popula- tion. Chapter 4 addresses the lengths of the Green Book design 55 vehicles (and their individual tractors and trailers) and their suitability for use to characterize the current truck population. VEHICLE HEIGHT Chapter 4 of this report addresses the heights of the Green Book design vehicles. The maximum height of any of the current design vehicles is 4.1 m [13.5 ft]. Most trucks have heights less than this. Chapter 6 addresses the relationship of vehicle height to design criteria for vertical clearance. REARWARD AMPLIFICATION When a combination vehicle makes a sudden lateral move- ment, such as to avoid an obstacle in the road, its various units undergo different lateral accelerations. The front axles and the cab exhibit a certain acceleration, but the following trailer(s) have greater accelerations. This has been experimentally ver- ified and quantified (51). The lateral acceleration of the first trailer may be twice that of the tractor, and the lateral accel- eration of a second trailer may be four times as much. The factors that contribute to increased lateral accelerations of the trailing units, the phenomenon known as rearward amplification (also called transient high-speed offtracking), include the following: â¢ Number of trailing units; â¢ Shortness of trailers (longer ones experience less ampli- fication); â¢ Loose dolly connections; â¢ Greater loads in rearmost trailers; and â¢ Increased vehicle speeds. Quantifying rearward amplification in terms of multiples of lateral acceleration may be appropriate for vehicle regulation, but is not generally relevant to highway geometric design. It has been recommended that a reasonable performance crite- rion would be that the physical overshoot that a following trailer exhibits during such a maneuver, relative to its final displaced lateral position, be limited to 0.8 m [2.7 ft] (51). Figure 32. Trends in weight-to-power ratios of trucks from 1949 to 1984 (46, 47, 48). TABLE 30 Average weights and power values for trucks (46) Weight (lb) Power (hp) Weight/Power Straight trucks InterstateâEast (14) 15,233 219 70 InterstateâWest (6) 35,050 267 131 PrimaryâEast (6) 16,575 273 75 Tractor-trailer InterstateâEast (157) 54,452 328 166 InterstateâWest (233) 64,775 370 175 PrimaryâEast (134) 57,487 330 174 65-ft doubles InterstateâWest (19) 64,920 331 196
SUSPENSION CHARACTERISTICS This section of the report reviews the characteristics of truck suspensions. The review is based primarily on a summary of suspension characteristics from the NHTSA factbook of truck characteristics (18). Other references are cited in the text as appropriate. The suspension of a heavy vehicle affects its dynamic responses in three major ways: â¢ Determining dynamic loads on tires, â¢ Orienting the tires under dynamic loads, and â¢ Controlling vehicle body motions with respect to the axles. Suspension characteristics can be categorized by eight basic mechanical properties: â¢ Vertical stiffness, â¢ Damping, â¢ Static load equalization, â¢ Dynamic inter-axle load transfer, â¢ Height of roll center, â¢ Roll stiffness, â¢ Roll steer coefficient, and â¢ Compliance steer coefficient. These suspension characteristics are important in deter- mining the stability of trucks on horizontal curves. Vertical Stiffness: Dependent on Spring Stiffness The vertical stiffness of a truck suspension is mainly deter- mined by the spring elements. Generally these elements are 56 either leaf springs or air springs. The vertical loads on the tandem axle of the trailer of a loaded truck can be up to four times greater than when the trailer is unloaded (51). Given that the load on the suspension can vary greatly, the springs must be very stiff for a fully loaded truck and much less stiff for an unloaded truck. Air springs are particularly well suited for such a range of loadings, because the spring rate can change significantly with loading. With leaf springs, the stiff- ness can also change under different loadings, but not quite as much as with the air suspension. This creates a poor ride quality for unloaded conditions. The friction of leaf springs also affects its force-displacement relationship. The range of vertical stiffness for the various types of sus- pensions has been measured for a load of 4,500 kg [10,000 lb] on the front axles and 7,300 kg [16,000 lb] on the rear axles. The range of vertical stiffness per axle is given in Table 33. Damping: Dependent on Shock Absorbers and Coulomb Friction of Leaf Springs Suspensions that have leaf springs rely on coulomb fric- tion for damping. Coulomb friction comes from the rubbing at the interfaces of the various leaves of the spring. There- fore, the damping is a function of mean load and displace- ment. Air spring suspensions need shock absorbers to pro- vide damping. Damping has a moderate effect on rearward amplification and the transient dynamic behavior of the vehicle. A lack of damping can create a system that is likely to oscillate and pro- duce large dynamic loads on the axles. Damping is set so that a maximum ride quality can be achieved. Increased damping usually reduces rearward amplification of steering inputs in multitrailer combination trucks and can, thus, increase stabil- ity in emergency maneuvers. A typical range of values for damping is given in Table 34. Static Load Equalization: Dependent on Coulomb Friction and Mechanisms Intended to Distribute Loads Evenly on Both Axles of a Tandem Set Static load equalization results because the design of tandem-axle suspensions tends to distribute the load equally between the two axles of the tandem. This type of load equal- TABLE 31 Summary of truck weight-to-power ratios by percentiles for freeway sites Weight-to-power (lb/hp) ratio Percentile California Colorado Pennsylvania 5th 83 69 111 25th 112 87 142 50th 141 115 168 75th 164 152 194 85th 183 169 207 90th 198 179 220 95th 224 199 251 TABLE 32 Summary of truck weight-to-power ratios by percentiles for two-lane highway sites Weight-to-Power (lb/hp) Ratio Percentile California Colorado Pennsylvania 5th 79 68 79 25th 144 85.5 110 50th 186 107 180 75th 226 149 242 85th 246 180 280 90th 262 193 303 95th 281 214 331 TABLE 33 Typical range of vertical stiffness per axle for truck suspensions (18) Type of suspension Range of vertical stiffness (lb/in) Front suspension 2,000 - 2,750 Air suspension 1,000 - 7,000 Four-spring 8,000 - 21,000 Walking beam 10,000 - 21,000 Single-axle leaf spring 8,500 - 13,750
ization is a static quantity; dynamic inter-axle load transfers are discussed in the next section. Typically, most tandem axles are very good at distributing the load evenly between the axles. Static measurements on tandem axles have shown that the largest variation is on the order of about 5% more weight on one axle than on the other. Dynamic Inter-Axle Load Transfer: Dependent on Coulomb Friction and Mechanisms Intended to Distribute Loads Evenly on Both Axles of a Tandem Set Inter-axle load transfer can occur in dynamic situations, such as during braking or acceleration. Unfortunately, the mechanisms that are used to create good static load equal- ization have just the opposite effect on dynamic load trans- fers. When a braking (or accelerating) force is applied on a tandem axle, there is often a load transfer between the axles of a tandem set. Inter-axle load transfers can be a problem during braking, because the more lightly loaded axle will tend to lock up before the other. If the lockup occurs on the lead axle, then the directional stability is reduced; directional stability can be completely lost if lockup occurs on the trail- ing axle. Another unwanted result of poor load transfer is that the system can produce an under-damped mode. Occasion- ally, this can result in âtandem hop,â which can cause a par- tial degradation of braking and handling performance. Dynamic inter-axle load transfer is measured in pounds of load transferred per pound of brake force. The transfer is pos- itive if it is toward the leading axle. A typical range of val- ues is given in Table 35. Roll Center Height: Dependent on the Line of Action of the Lateral Suspension Forces When the chassis of a truck rolls (tilts sideways as when rounding a horizontal curve), it tends to roll about a theoreti- cal point, called the roll center. With a four-spring suspension, the leaf springs will determine the roll center location. Spe- cial links can be added to provide lateral forces on walking- beam suspensions and air suspensions; these links affect the roll center height. Roll center heights are measured from the ground. Typical values are given in Table 36. 57 Roll Stiffness: Dependent on Spring Stiffness, Lateral Spacing, Roll Center Height, and Auxiliary Mechanisms Such as Anti-Sway Bars Roll stiffness is a measure of a suspension systemâs resis- tance to rolling. As a truck body rolls, the vertical springs deform to cause a resisting moment. This moment is depen- dent on the vertical spring constants and lateral spacing of the springs. The height of the roll center plays an important part in the rolling tendency of a vehicle, as illustrated in Figure 33. As a truck goes around a horizontal curve, the centrifugal force causes the truck body to roll about its roll center. This will also cause the center of gravity to produce a moment about the roll center, due to its shift in position. The higher the roll center (i.e., the closer it is to the center of gravity), the shorter the moment arm and the smaller the moment that is produced. Ideally, the roll stiffness at each axle should be propor- tional to the weight on that axle, which means that the roll stiffness of the trailer axles should be about the same as that of the tractorâs rear axles. However, this is not usually the case. More typically, the trailer has a harder suspension than the tractor. The range of roll stiffnesses for the various suspensions has been measured with a load of 5,500 kg [12,000 lb] on the front axles and 7,300 kg [16,000 lb] on the rear axles. A typ- ical range of roll stiffnesses on a per axle basis is given in Table 37. Roll Steer Coefficient: Dependent on the Layout of Links That Restrain the Axles Nonsteering axles can deflect slightly to create a steering effect as a result of vehicle roll. As the truck body rolls, one side of the axle moves forward while the other side moves TABLE 34 Typical range of damping for truck suspension (18) Type of suspension Range of damping (lb) Front suspension 800 - 1,250 Air suspension 550 - 1,200 Four-spring 1,200 - 2,700 Walking beam 700 - 2,000 Single-axle leaf spring 1,800 - 2,400 TABLE 35 Typical range of inter-axle load transfer for truck suspension (18) Type of suspension Range of inter-axle load transfer (lb/lb) Air suspension 0.035 - (â0.018) Four-spring (â0.10) - (â0.185) Walking beam 0.010 - (â0.030) TABLE 36 Typical range of roll center heights for truck suspension (18) Type of suspension Range of roll center height (in) Front suspension 8.5 - 20 Air suspension 24 - 29.5 Four-spring 23 - 31 Walking beam 21.5 - 23 Single-axle leaf spring 25 - 28
aft. This unintentional steering is created by the suspension and tire forces. The tendency to steer in a roll is measured with respect to the amount of vehicle roll present. This steer- ing can greatly affect truck handling, particularly in a turn. The units used in measuring the roll steer coefficient are degrees of steer per degree of roll. A positive roll steer coef- ficient means that the axle will steer toward the outside of the turn; a negative coefficient means that the axle will steer toward the inside of the turn. A typical range of values is given in Table 38 on a per-axle basis. LOAD TRANSFER RATIO The extent to which vertical load is transferred from the tires on one side of a vehicle to those on the other side is called the load transfer ratio. Load is transferred when a vehicle is stationary on a lateral incline, when rounding a curve, and when making a steering maneuver such as to avoid an obsta- cle. It is calculated as follows: Load Transfer Ratio = Sum(FL â FR)/Sum(FL + FR) (24) where FL and FR are the tire loads on the left and right sides, respectively. 58 The load transfer ratio has a value of 0.0 when the loads on the two sides are equal and Â±1.0 when all the load is trans- ferred to one side or the other. When the latter situation is just reached, the unloaded side is about to lift off from the pave- ment, and rollover is imminent. The load transfer ratio for an automobile or a single-unit truck is, for most practical pur- poses, a single number. For a combination vehicle, it can be computed separately for each unit; the unit with the greatest ratio is usually the most likely to come on the verge of rolling over. The truck properties affected by the load transfer ratio, other than impending rollover, include handling response time, roll steer, and rearward amplification. ROLLOVER THRESHOLD A vehicleâs resistance to rollover is measured by the max- imum lateral acceleration that can be achieved without caus- ing rollover. This maximum acceleration, measured in units of the acceleration of gravity (g), is known as the rollover threshold. Gillespie (52) reports the following typical values of rollover threshold: Low-slung sports car 1.7 g Normal passenger car 1.1-1.5 g Pickup trucks and vans 0.8-1.1 g Heavy trucks 0.4-0.6 g A typical passenger car tracking a horizontal curve or making a turn at too high a speed will likely skid off the road because of inadequate tire-pavement friction long before its rollover threshold is reached. Trucks, on the other hand, gen- erally have rollover thresholds that are less than the available tire-pavement friction on dry pavements. Indeed, Navin (53) states that âdata conclusively show that fully laden heavy trucks, if involved in an accident on a curve, will most likely have rolled over.â Truck rollovers are caused by high lateral accelerations in a turning maneuver. As lateral acceleration increases, the load transfer ratio approaches Â±1.0, and the wheels on the inside of the turn begin to lift off the pavement. Generally, because of uneven load distribution and uneven suspension, tire, and structural stiffness, all of the wheels will not begin to lift off the pavement at the same time. Typically, the rear trailer wheels will be the first to lift off. It is possible for some wheels of a truck to lift off the pavement without producing TABLE 37 Typical range of roll stiffness for truck suspension (18) Type of suspension Range of roll stiffness (in-lb/deg) Front suspension 0.017 - 0.025 Air suspension 0.025 - 0.090 Four-spring 0.065 - 0.140 Walking beam 0.070 - 0.160 Single-axle leaf spring 0.052 - 0.089 TABLE 38 Typical range of roll steer coefficients for truck suspension (18) Type of suspension Range of roll steer (deg steer)/ (deg roll) Air suspension 0.01 - 0.23 Four-spring â0.04 - 0.23 Walking beam 0.16 - 0.21 Single-axle leaf spring 0.0 - 0.07 Figure 33. Diagram of roll by trailer body illustrating location of roll center (18).
a rollover; however, this is a very unstable situation and could ultimately lead to a rollover. Earlier research, largely based on modeling, indicated that an extreme rollover threshold as low as 0.24 was pos- sible (50, 54). However, that work was based on older trucks that had widths of 2.4 m [8 ft] and incorporated a very unusual loading condition. But, beginning with the passage of the Sur- face Transportation Assistance Act (STAA) of 1982, truck widths increased to 2.6 m [8.5 ft]. This has a net effect of increasing the rollover threshold by 15 to 18%, as will be indicated shortly. Also, experimental data (51, 55) show that actual rollover thresholds tend to be 0.03 to 0.04 g higher than modeled values. Thus, a worst-case rollover threshold is now about 0.31 g. The rollover threshold of a truck is largely a function of its loading configuration. The following parameters of a truckâs loading configuration affect its rollover threshold: â¢ Center of gravity (CG) height, â¢ Overall weight, â¢ Longitudinal weight distribution, and â¢ Lateral weight distribution. The sensitivity of truck rollover threshold to these pa- rameters is reviewed below, based largely on results reported in a 1986 FHWA study (55), which have been confirmed by computer simulation analyses reported in the FHWA Truck Characteristics study (2, 3). These findings include â¢ For the baseline case of a 36,400-kg [80,000-lb] semi- trailer truck, with medium density (34 lb/ft3) cargo, loaded evenly left to right and fore and aft on a 2.4-m [8-ft] wide trailer (a pre-STAA trailer), the computed rollover threshold is 0.35 g. â¢ If the trailer and tractor are widened to 2.6 m [8.5 ft], and the tire spacing and spring spacing are widened accord- ingly, the rollover threshold is increased by 15 to 18%. â¢ If the cargo is less dense, it will fill more of the trailer and its CG height will be increased. The rollover thresh- old is reduced by about 0.005 g for every inch the CG is raised. Typical less-than-truckload (LTL) cargo is less dense, but is not of uniform density. Such cargo is nor- mally loaded with the denser cargo on the bottom, and the lighter cargo on top. A âtypicalâ fully loaded LTL trailer will have a CG height of 2.4 m [7.9 ft]. The worst-case scenario is a truck with maximum gross weight with the trailer filled to the roof (âcubed outâ) with uniform den- sity cargo. The cargo density would be about 18.7 lb/ft3, and its CG height would be about 2.7 m [8.8 ft]. Recent research found a rollover threshold of 0.34 g for a truck loaded with LTL freight (56). â¢ Adding weight to the truck by adding more of the same cargo on top of the existing load raises the CG and low- ers the rollover threshold. The effect is a reduction of about 0.01 g per added ton. â¢ If the load is not centered left to right in the truck, its rollover threshold is raised on turns in the direction to 59 which the load is offset and reduced in turns in the opposite direction. The effect can be quite largeâabout 10% for each 76 mm [3 in] of offset. This amount would be realized, for example, if pallets designed for 2.4-m [8.0-ft] wide trailers were loaded along one side of a 2.6-m [8.5-ft] wide trailer. â¢ For the same width, weight, and CG height, double- trailer trucks consistently have rollover thresholds 0.03 to 0.05 g higher than semitrailers. Thus, semitrailers are the vehicles of most concern relative to rollover threshold. â¢ Rearward amplification in doubles caused by sudden maneuvers, such as obstacle avoidance, can lead to rollover of the rear trailer. However, this is more of a concern in emergency maneuvers than in normal track- ing of a curve or turn, which is the basis of geometric design. â¢ Trailer length, per se, has no appreciable effect on rollover threshold, provided that the axle loads are the same for longer and shorter trailers. Conversely, if the load on a shorter trailer is placed in a longer trailer, the CG would be lowered and the rollover threshold would be increased. â¢ The 1986 FHWA study analyzed accident data repre- senting 9,000 single-vehicle accidents involving 5-axle semis (51). Of these, 2,000 resulted in a rollover. Using the reported gross vehicle weight, the authors of said study assumed medium-density freight (and a 2.4-m [8.0-ft] width, the standard at that time). With these assumptions, the CG height was calculated, along with the resulting rollover threshold. The distribution shown in Figure 34 was obtained. The lowest rollover thresh- old obtained was about 0.39 g. Of course, this represents an average of the actual minimum rollover thresholds because the actual cargo densities would have varied Figure 34. Percent of single-truck accidents in which rollover occurs as a function of rollover threshold (51).
about the assumed medium density. No data on cargo density were available, however. â¢ Most researchers suggest that a reasonable value for a minimum rollover threshold for loaded trucks is in the range from 0.35 to 0.40. In an appendix to the U. S. Com- prehensive Truck Size and Weight Study (57), it is stated that fatal accident data show so few cases with rollover 60 thresholds less than 0.35 that rates cannot be calculated. The authors of the study suggest this is because there are so few such vehicles on the road. Indeed, they go on to state that requiring a threshold of 0.38 g would make future fleets comparable with the current fleet with the exception of the very few trucks currently under the threshold.