37 percent) . The 48-percent value is then applied to the average values 

 (25 and 15.5 percent) given above for the 1 on 3 and 1 on 6 smooth slopes. 

 The resulting percentage increases applied to small-scale smooth-slope 

 runup values to estimate runup on large-scale smooth slopes (prototype 

 roughness) are 12 and 7.4 percent for the 1 on 3 and 1 on 6 slopes, re- 

 spectively (i.e., k = 1.12 and k = 1.074). The value of 1.074 for the 

 1 on 6 slope was determined by assuming that the roughness reduction is 

 the same for the 1 on 3 slope. 



Saville (1960) notes that earlier tests showed no scale effect for 

 a 1 on 15 sand slope; thus, k = 1.0 for the 1 on 15 slope. The three 

 k values derived for the three slopes are plotted in Figure 49 and 

 connected by a curve. Although no data are available for steeper slopes, 

 the curve is extended to reach a maximum k value of 1.14 at cot 6 = 1.25. 

 A maximum value of k is reasonable and, in fact, a decrease is likely 

 for very steep slopes because, for a given incident wave, the length of 

 structure slope covered by the uprushing water becomes relatively small; 

 also, the wave would likely be a surging wave rather than a breaking 

 wave. 



The scale-effect corrections in the SPM have one curve labeled 

 "H = 1.5' to 4.5'," which is similar to the curve in Figure 49. The 

 second curve is not based on data, but was suggested for larger wave 

 heights. After a review of Figure 48, it is recommended that the curve 

 in Figure 49 be applied to all wave heights until further testing 

 warrants a change, based on the following reasoning. Wave heights 

 larger than those tested would require larger Reynolds numbers if the 

 same wave conditions were tested as in Figure 48. However, any in- 

 crease in R/H^ with increasing Reynolds numbers beyond what has been 

 tested appears unlikely. Because of the relatively constant values of 

 R/Uq for the 1 on 6 slope for R g > 2.1 * 10 5 and because the large 

 variation in 1 on 3 slope runup values at low Rg numbers includes 

 values as high as those at large R e numbers, a "critical" Reynolds 

 number appears to be in the range 2 x 10 5 < (Re) a < 4 x 10 5 for low 

 dg/H^ values such as dg/H^ = 1.5. The critical Reynolds number is a 

 value beyond which relative runup would not increase for increasing 

 Reynolds numbers. 



The values for the lowest wave steepness (H^/gT 2 < 0.003) in Table 

 21 suggest that no scale-effect correction is necessary for waves of low 

 steepness if the slope roughness is properly modeled. For low wave 

 steepnesses in Table 20 (1 on 3 slope), not all of the k values are 

 small and some scale effect may remain after the slope roughness is 

 properly modeled. The 1 on 6 slope (Table 20) has even larger k 

 values for the low wave steepnesses tested, and, again, proper modeling 

 of slope roughness may not account for all of the scale effect. There- 

 fore, Figure 49, derived principally for waves of higher steepnesses, 

 is also recommended for use in the low wave steepness range as an esti- 

 mate. The values in Figure 49 are replotted in Figure 50, and the 

 curve is extended over steeper slopes up to and including a vertical 

 wall. 



