## 4 Discussion  
We obtained the maximum allowable inlet spacings for roadways of various purposes under different slope orientations and found that increasing longitudinal slopes increase maximum allowable spacing as a general trend, as shown in Figures 3-8. For the cross-slope variations, however, the relationship is not as clear at first sight and varies depending on the flow-depth criteria. While one sees increasing spacing in Figure 3 with increasing cross slope, the trend changes in Figure 4 as the slope increases, and Figure 5 shows the opposite of Figure 3. Figures 6 and 8 also produce results similar to Figure 4 in that maximum  
Figure 9: Maximum allowable inlet spacing (blue) and over-lane flow depths (red) for a 3-lane road with 3% along-road slope (\(S_{L}=3\%\)) and a 3 m shoulder. spacing increases first and then starts decreasing with increase in cross slope, and Figure 9 shows (in blue) neither extremum results nor maximum spacing, in line with the former figures. When one examines Equation (5), an inverse correlation is captured between the spacing and cross slope, but this is not reflected in the figures except in Figure 5. To clarify what first seems as a contradiction, Equation (6) should be considered. When Equation (6) is placed in Equation (5), spacing changes with \(S_{x}^{5/3}\) instead of \(S_{x}^{-1}\). However, this still does not explain why the trend changes direction with increasing cross slopes. It is clear from Equation (6) that cross slope multiplied by the maximum allowable spread produces the depth value, and in this study we set the general criterion to be 10 cm for the maximum flow depth, and when \(S_{x}>z_{\text{max}}/T_{\text{max}}\), flow depth is replaced by \(z_{\text{max}}\) per the criterion. In such a case (i.e., when \(S_{x}>z_{\text{max}}/T_{\text{max}}\)), spacing changes with \(S_{x}^{-1}\) in Equation (6), as the depth is constant and is not a function of cross slope. Figure 5, in which flow depth is limited to 3 cm (as opposed to 10 cm otherwise), clearly depicts the decreasing spacing trend (with increasing cross slope). Flow depth is limited to 3 cm with a half-lane maximum spread (180 cm); that limit is reached for an \(S_{x}\) value below 2%. Thus, the depth is kept constant for \(S_{x}\) values 2% and above (to 7% in Figure 5). Figure 6 shows that as 10 cm is reached at 3.33% for a highway setting with a 3 m shoulder, the increasing spacing trend plateaus around 3 and 4% cross slope and starts decreasing from there on. For the half-lane spread criteria (and 10 cm flow depth), 5.55% cross slope is the turning point beyond which the inverse relationship begins. Thus, to address cross-slope impact on spacing, one needs to be aware of the constraints for design; if designing for a fixed spread with no regard to flow depth, then spacing increases with increasing cross slopes (as it does up to 3% in Figure 6), but if flow depth becomes a limitation, then an inverse correlation governs the case (as it does beyond 3% in Figure 6). The results also show that while higher longitudinal slopes enable wider spacing of inlets, depending on the roadway width and cross-slope values, the design may collapse altogether due to hydroplaning risks, leaving no reason to analyze the spacing. [PERSON] [38] mentions inlet capacity controlling the inlet spacing along with gutter capacity; while this study looks into the impact slope orientation has on inlet spacing, it does not consider the impact of inlet capacity. This is because different regions have different practices for inlet designs, and considering a specific inlet type and design prevents obtaining a larger view of the other controls on inlet spacing and its maximum allowable values. While, for example, most regions in the United States practice curb-opening inlets, grate inlets are practiced in Turkey--the authors are yet to see any application of curb-opening inlets in Turkey despite producing some of the earliest studies on curb-opening inlet capacity [39].