However, to apply the result to typical engineering problems, the same 

 assumptions must be made about Yg and a' to get back to a value of 

 Q, since Q is the quantity needed in design. The steps involved for 

 the present immersed weight procedure are shown in Figure 2. 



Although immersed weight rates are not presently practical in field- 

 work, immersed weight rates of longshore transport are routinely measured 

 in some laboratory experiments (Savage, 1959). 



IV. RESULTS 



The results of this analysis are summarized as follows: 



In practical application, the immersed weight formulation does not 

 presently improve the engineering prediction. The required engineering 

 quantity is a volume rate of sand in place, Q, and all the existing 

 data were originally measured in terms of Q, or in Q equivalents. 

 Therefore, to develop the immersed weight formulation from existing 

 data, it is necessary to estimate values of a' and y s and convert 

 Q values to 1^ by equation (3) . Then, to use the immersed weight 

 formulation to solve a problem, the procedure must be reversed and con- 

 verted back to the required Q. 



Available data have led the investigators who have worked with 1^ 

 to assume that both a' and y~ are constants. To the extent that 

 this is a fact, 1^ is directly proportional to Q, independent of any 

 other variables, and the use of I- is equivalent to Q, after two 

 added calculations. However, in the three sets of data on which the SPM 

 design curve is based, it is probable that neither a' or y s were 

 constant. 



The available soil mechanics information indicates the need for more 

 data on void ratio and sand grain specific gravity. The Table and re- 

 lated information suggest that a' may vary significantly, although the 

 upper limit of variation is probably less than the theoretical 42-percent 

 increase in a' possible in going from loosest to most dense packing of 

 spherical sand grains. Most sand beaches are quartz, but calcium carbo- 

 nate sands of the tropics could have a y s (for pure aragonite) as much 

 as 18 percent higher than quartz sands, or even less than quartz sands 

 when the carbonate grains are derived from porous shell material. 



V. CONCLUSIONS 



1. Volume rate, Q, is the longshore transport parameter needed 

 for design. 



2. As presently used, the immersed weight rate equation is equal to 

 the volume rate equation recommended by SPM, multiplied by a constant (eq. 

 3). Thus, the volume rate prediction (eq. 2) arrives more directly at Q. 



