TRANSPORTATION RESEARCH RECORD 1500 31 Sight Distance on Horizontal Alignments with Continuous Lateral Obstructions YASSER HASSAN, SAID M. EASA, AND A. 0. ABD EL HALIM For safe and efficient highway operation, sight distance has been of great interest to researchers in the field of highway geometric design. Several formulas have been developed to relate the available sight distance to the horizontal and vertical alignment of the highway and the existing obstruc- tions. Among these formulas is the one presented by (AASHTO) to deter- mine the available sight distance on a simple horizontal curve with a length greater than the sight distance. For shorter curves in which the sight dis- tance is greater than the curve length, other methods have been developed. However, none of these methods considered the case of continuous lateral obstructions or complicated horizontal alignments. Consequently, it has been recommended that the available sight distance be checked graphically or in the field. For this study, general analytical procedures were developed to check the available sight distance on horizontal alignments with single and continuous obstructions. A horizontal alignment may consist of any combination of horizontal components, such as straight segments, circular curves, and spiral curves. Based on the analytical procedure, a computer software program was developed to establish the no-passing zones on two- lane highways, according to the specifications used by the Ministry of Transportation of Ontario, Canada. The developed procedures and com- puter software proved to be very accurate. Using them would save time and effort and would avoid possible human errors when the sight distance is checked using current graphical or field techniques. The computer soft- ware can also be used to develop design tables and charts for the available sight distance on different horizontal alignments. Sight distance is vital for safe and efficient highway operation. The driver must be able to see ahead a distance sufficient for stopping to avoid hitting an unexpected object on the roadway. Moreover, it is recommended that the design of two-lane rural highways should provide drivers with a sight distance sufficient to pass slower vehi- cles. In many cases, however, the sight distance is restricted to acer- tain length. On horizontal curves, the driver's sight line may be lim- ited by lateral objects such as trees, buildings, and cut slopes. On crest vertical curves, the sight line may be limited by the vertical curve itself. Also, sight distance on sag vertical curves may be lim- ited to the farthest point covered by the vehicle's headlight beam. Therefore, the designer must check the available sight distance against the required stopping site distance (SSD) or decision site distance (DSD) on any highway, and the passing site distance (PSD) on two-lane rural highways. For horizontal curves, many models have been developed to relate the available sight distance to the lateral clearance. Among these models is the one presented by the AASHTO for the case of S :::; L, where Sis the sight distance on the curve and L is the curve length (1). Although this formula is easy and direct, it is "of limited practical value except on long curves" (1). Therefore, AASHTO recommends that "the designer must use graphical methods to check sight distance on horizontal curves" (1). Y. Hassan and A. 0. Abd El Halim, Department of Civil Engineering, Carle- ton University, Ottawa, Ontario KIS 5B6, Canada. S. M. Easa, Department of Civil Engineering, Lakehead University, Thunder Bay, Ontario PTB SEI, Canada. The other case in which the sight distance is greater than the curve length has been studied by many researchers. Neuman and Glennon (2), Waissi and Cleveland (3), Berg et al. (4), and Easa (5) developed different methods to check the required lateral clearance on simple horizontal curves. Easa (6, 7) also studied the case of a single lateral obstruction on compound and reverse curves and developed other formulas to relate the lateral clearance to the avail- able sight distance. None of these methods has considered the case of continuous obstructions. According to the standards of the Man- ual of Uniform Traffic Control Devices (MUTCD), which is used by the Ministry of Transportation of Ontario (MTO), Canada, for establishing the no-passing zones (8), the available sight distance for drivers in the inside lane is limited by a continuous obstruction represented by a theoretical 3 m wide shoulder. Continuous obstruc- tions also may be encountered because of cut slopes. For this study, general analytical methods were developed to evaluate sight distance on horizontal alignments for both cases of continuous and single obstructions. The terms "horizontal align- ment" and "horizontal curve" refer to any combination of horizon- tal highway components, such as straight segments, circular curves, or clothoid spiral curves. A computer software program was devel- oped to determine the available sight distance and, in turn, the no- passing zones on two-lane rural highways according to the stan- dards of MUTCD used by MTO. THEORETICAL DEVELOPMENT This study examines available sight distance (which may be SSD, DSD, or PSD) on general horizontal curves consisting of any com- bination of straight segments, circular curves, and spiral curves. Figure 1 shows some of the cases of horizontal alignments that are covered in this report. More complicated alignments that can be encountered on actual highways are also covered in this paper. Continuous Obstruction: General Procedures Assuming a constant lane width and lateral clearance, the continu- ous obstruction will be parallel to and have the same geometry of the highway centerline; the sight distance will be restricted by hav- ing the sight line tangent to the obstruction. The point of tangency may be located on a circular curve, spiral curve, or the point of inter- section of two successive straight segments without curves. The fol- lowing sections present general procedures that can be used to determine the available sight distance, regardless of the components of the horizontal curve. Relationships are then presented for the spe- cial alignments of intersecting long tangents without a curve and for the simple circular curve.