## 2 Imposed Loads
### Maximum Operating Heads  
The head at the start of generation marks the end of the hold period where the impoundment water surface level is equal to or close to the peak sea levels (high and low tide). Depending on the number of turbines and shuices, at spring tides, the volume of water flowing through the turbines may not match the natural sea flows. When this occurs, the head continues to increase for a period after the start of generation (see Figures 2 and 3 for NW and MB, respectively). For the operational case, it is the maximum difference in surface levels (head) between the sea and impoundment that provides the greatest horizontal force on the barrage. The mean spring tidal ranges for NW and MB are 7.20 m and 8.49 m, respectively [4]. For the design, the highest spring tide in the year should be selected rather than the mean. The maximum operating head can be read from the 0D model. Figures 2 and 3 show examples of daily spring tide cycles. The blue lines represent the sea surface levels, the red lines indicate the impoundment surface levels, and the green lines are the head differences available to generate electricity. As shown in Figure 2, for NW, the highest starting head of 4.05 m occurs on the spring tide. The highest generating head of 4.98 m also occurs on the ebb of the same spring tide. The head initially increases during generation because the volume of water flowing through the turbines is less than that needed to match the natural sea flows, i.e., the gradient of the red line (impoundment level) is lower than the blue line (sea level). At the time of the  
Figure 2: Plots of sea and impoundment water levels and head at a typical spring tide for North Wales Lagoon. highest operating head, the sea level is 3.95 m below OD, and the impoundment level is 1.03 m above OD. The highest starting head for MB of 4.47 m occurs on day 6 of the modelled 32-day period (see Figure 3), but the highest generating head is 6.28 m and occurs on the ebb tide later in the day. At the time of the highest operating head, the sea level is 3.89 m below OD, and the barrage level is 2.42 m above OD. Figures 4 and 5 show the same situation as in Figures 2 and 3 with a modelled 1 m sea level rise (SLR) and constraints to maintain the pre-SLR levels inside the impoundment. According to the Institution of Mechanical Engineers (IMechE), a 1 m rise in average sea levels is likely to occur by the end of this century [5], although they recommend planning for a 3 m rise over the same period. The Lancaster zero-dimensional (0D) model is set to maintain the current tide limits where possible. Figure 4: Plots of sea and impoundment water levels at a typical spring tide for North Wales with 1 m SLR. Figure 3: Plots of sea and impoundment water levels and head at a typical current spring tide for Morceambe Bay. As shown in Figure 4, for NW, the highest starting head increases to 4.47 m on the spring tide. The highest generating head rises to 5.47 m around 2 h later, which is the highest value for a spring tide. At the time of the highest operating head, the sea level is 3.95 m below OD. Around the spring tides, some pumping is still needed to reach the existing high tide level because the equalisation of water levels occurs 2 h after high tide, when the sea level has dropped by 2.1 m from the high tide level. However, for most of the lower tidal ranges, no pumping is required at high tide as the impoundment curve more closely matches that of the sea levels. The highest starting head for MB with 1 m SLR is 4.61 m on day 5 of a 32-day period, as shown in Figure 5. The highest generating head of 5.05 m also occurs on the same day near the end of the flood tide. At the time of the highest operating head, the sea level is 2.60 m below OD when the impounded level is 2.45 m above OD. The fall in the maximum operating head appears due to the shorter generating on the ebb to allow shuicing to reach the lower tide level.