The actual loss of land to the south of Holland (attributed to the naviga- 
tion structure) is relatively small, at the most 22 percent. This figure has 
been derived as a 23-year average, but with current high lake levels the pres- 
ent natural erosion rate is certainly higher than the average. 
The evolution of the shoreline at Holland was studied using the present 
model. The relevant physical data and the estimates of offshore sediment losses 
were used in the analysis. Interpolation of values shown in Table 1 gives the 
shoreline every 100 feet along the base line. The channel at the harbor en- 
trance was collapsed to zero so that the south reach ended at O- and the north 
at 0+. These shorelines indicate that the shore is stable at the breakwater; 
therefore, when the direction of transport is toward the breakwater it is as- 
sumed that the sand transported to the breakwater is entirely lost offshore. 
Monthly lake levels were taken from Figure 21. The results of these computa- 
tions are not given since they are essentially previously described results. 
The average beach slope at the waterline was determined to be 1:10; the beach 
profiles in Figure 17 near the breakwater show that this is a reasonable esti- 
mate although the slopes are not constant from profile to profile. The height 
of the berm is assumed to be 10 feet. The depth to no sediment motion was esti- 
mated at 30 feet, based on visual consideration of the offshore bathymetry and 
the use of Weggel's method (J.R. Weggel, personal communication). An offshore 
loss of 3.2 cubic yards per year per foot of beach is also included (see Fig. 26). 
The transport equation for this situation can be written (see eq. 53) 
A een 3 2 eh 
Be Os (KpQ) m dt dt 
where 
Q | COS G, Sin hy and 2 — (K5Q) 
m = beach slope at waterline 
D = dimensionless lake level 
ea = dimensionless offshore line loss 
This equation will be applied on each side of the breakwater. When the in- 
coming wave direction gives drift toward the breakwater, the boundary condi- 
tions expressed in Q are 
Q | b 
= COS a sin ap 
xX = wo 
Conversely, when the incoming wave direction gives drift away from the break- 
water, the conditions become 
Le) 
i] 
[e) 
and 
cos a sin On, 
57 
