View source for Systematic studies for recording squat and trim together with ship-induced pressure and wave systems when passing through channels in confined shallow water

[[de:Systematische Untersuchungen zur Erfassung von Squat und Trimm sowie schiffserzeugter Druck- und Wellensysteme bei Fahrt im Revier mit seitlich begrenzter Fahrrinne im Flachwasser]]

Author: [mailto:klemens.uliczka@baw.de K. Uliczka]

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===Boundary conditions===

The studies into the dynamic behaviour of very large Post-Panamax container ships when passing through waterways of confined width and depth were conducted in BAW-DH’s [[shallow water]] basin (length approx. 100 m, width approx. 35 m, max. [[water depth]] 0.7 m) at 1:40 scale in accordance with Froude’s [[model]] laws.<br>
The dimensions and investigated parameters for the [[model]] ships used were as follows:
{| align="center" border="1"
|Designation
|Length
|Beam
|[[Draught]]
|UKCR*
|cB-value** 
|SR+ 
|Weight [[trim]]
|KG++
|-
|align="center"|-
|align="center"|m
|align="center"|m
|align="center"|m
|align="center"|m
|align="center"|- 
|align="center"|- 
|align="center"|-
|align="center"|m 
|-
|align="center"|JUMBO
|align="center"|320
|align="center"|40
|align="center"|14,5
|align="center"|1-2
|align="center"|0,740
|align="center"|6,29
|align="center"|Hard
|align="center"|11,8
|-
|align="center"|MEGA-JUMBO
|align="center"|360
|align="center"|55
|align="center"|15,5
|align="center"|1-1,5-2
|align="center"|0,677
|align="center"|6,10
|align="center"|Hard
|align="center"|10,2
|-
|}
''*UKCR: under-keel-clearance, **cB: block coefficient , +SR: slenderness ratio, ++KG: centre of gravity above keel''

The Froude numbers amounted to 0,27 < Fr<sub>h</sub> < 0,68. The Reynolds numbers were determined to be 3,1 · 10<sup>6</sup> < Re < 6,2 · 10<sup>7</sup> (factor 10 > Re<sub>KRIT,erf</sub>). Fulfilling the geometric and dynamic similarity conditions ensured that the studies would deliver valid forecasts.

The waterway cross-sections and (partial-)cross-sectional ratios are presented in Figure 1 taking the MEGA-JUMBO as an example:
* Trapezoidal profile, central course, cross-sectional ratios n = 25, 20, 15, 10 ([http://www.baw.de/EN/wasserbau/methoden/mathemat_verfahren/cfd_berechnungen/cfd_berechnungen.html Results of CFD-Simulations]).
* Trapezoidal profile, off-centre [[course]], partial cross-sectional ratios nT = 10/5, 20/10, 25/10.
* Combined profile, off-centre course, partial-cross-sectional ratios nT = 25/10, 20/10, 10/5.

[[File:Revierfahrt_Bild01_horiz20170913en.jpg|thumb|Figure 1: Waterway cross-sections studied including (partial) cross-sectional ratios for the MEGA-JUMBO, amongst others (60k)]]


''Comments:''<br> 
''Cross-sectional ratio'' n = A / A<sub>S</sub> <br> 
''where:'' A ''wetted area of waterway '' <br>
A<sub>S</sub>	''submerged midship cross-section'' <br>
''Partial-cross-sectional ratio'' n<sub>T</sub> = A<sub>T</sub> / 0,5 A<sub>S</sub> <br>
''where:'' A<sub>T</sub>	''area of wetted partial-[[cross-section]] (from [[course]] to [[bank]])''
 	
As well as measuring [[Ship Dynamics|ship dynamics]] (squat, [[trim]]), the speed-dependent changes in the [[water level]] in a transverse profile were also assessed and analysed. Selected results are presented and evaluated below.

===Selected results – squat and trim===

The following relationships have been identified, taking the MEGA-JUMBO measurement results as an example:
* Smaller cross-sectional ratios between the submerged midship [[cross-section]] and the wetted [[cross-section]] mean higher speed-dependent squat values (Figure 2).
* Various [[waterway]] ratios relating to shape and width, from infinite to narrow [[waterway]] widths and down to fairways in shallow open water lead to a marked increase in squat (Figure 3).

[[File:Revierfahrt_S_Bild02_horiz20170913en.jpg|thumb|Figure 2: Impact of cross-sectional ratios on speed-dependent squat behaviour when passing approach channels (MEGA-JUMBO) (60k)]]

[[File:Revierfahrt_S_Bild03_horiz20170914en.jpg|thumb|Figure 3: Impact of waterway cross-sections on speed-dependent squat behaviour when passing approach channels (MEGA-JUMBO) (160k)]]

The results of the extensive studies demonstrate that both [[fairway]] depth and [[waterway]] width (i.e. the [[cross-section]] of the [[waterway]] construction) must be factored into the preliminary calculation of maximum speed- and vessel-dependent squat, particularly in longer approach channels to major seaports such as the [[tidal Elbe]], the tidal Weser or the Schelde flowing into the port of Antwerp, in order for the WSV to guarantee ease and safe shipping to seaports.

===Selected results – ship-generated load===
The changes in [[water level]] measured at the same time as [[Ship Dynamics|ship dynamics]] ([[drawdown]] z<sub>A</sub>, [[primary wave]] H<sub>P</sub> and secondary wave H<sub>S</sub>) as well as their [[cross-section]]-dependent distribution within the [[waterway]] are shown in Figures 4 and 5, taking the [[drawdown]] z<sub>A</sub> as an example:
* A central [[course]] generates a symmetrical distribution and decrease in speed-dependent [[drawdown]] in the [[waterway]] [[cross-section]] (Figure 4, central [[course]], left-hand side).
* At low UKC values, the partial-cross-sectional ratio determines the decrease in [[drawdown]] towards the [[bank]] (Figure 4, off-centre [[course]], right-hand side).
* Comparing the two charts in Figure 4 highlights the decrease in [[drawdown]] in the [[waterway]] [[cross-section]] that depends on the passing clearance between ship and [[bank]]: on the right-hand [[bank]], the [[drawdown]] load is virtually the same as the partial-cross-sectional ratios are similar. On the left-hand [[bank]], however, the larger passing clearance of the moving ship means a much lower load at the foot of the embankment.

[[File:Revierfahrt_zAJU_Bild04_horiz20170914en.jpg|thumb|Figure 4: Illustration of the distribution of speed-dependent drawdown within the waterway cross-section for the cross-sectional ratios n = 21 and nT = 36 / 23 (JUMBO) (90k)]]

* If the cross-sectional ratios are very narrow, even much lower ship speeds (in this case v<sub>S,MAX</sub> = 13,1 kn) can generate high loads on the bank (Figure 5, central course within a fairway in an asymmetrical waterway).

[[File:Revierfahrt_zAMJ_oT_Bild05_horiz20170914en.jpg|thumb|Figure 5: Illustration of the distribution of speed-dependent drawdown in the combined channel cross-section (with underwater dunes within the fairway) for the partial-cross-sectional ratio nT = 10/5 (MEGA-JUMBO) (75k)]]

A more detailed analysis of the long-period ship-generated loads that apply at the toe of slope and that depend on the partial-cross-sections (in this case the [[drawdown]] z<sub>A</sub>) summarises the results from the BAW’s extensive system tests for the JUMBO container ship (PPM40) in Figure 6. The chart illustrates the decrease functions for the [[drawdown]] z<sub>A</sub> depending on the partial cross-sectional ratio n<sub>T</sub> for a PPM40 container ship travelling at various speeds.

[[File:Revierfahrt_zAnT_Bild06_nT_20170914en.jpg|thumb|Figure 6: Decrease functions for the drawdown zA depending on the partial-cross-sectional ratio nT for a PPM40 container ship travelling at various speeds (90k)]]

For example, the decrease function for a PPM40 ship travelling at around v<sub>S</sub> ≈ 13,5 kn (Figure 6, red curve) can be used to predict that partial-cross-sectional ratios of between 10 < n<sub>T</sub> < 23 23 will give rise to a load decrease with a factor of about F ≈ 5.

The speed-dependent trend lines also highlight the lack of any linear relationship between long-period ship-generated load and partial-cross-sectional ratio.

===Conclusions===
* In terms of squat size, both under-keel clearance UKC<sub>R</sub> as well as the cross-sectional ratio n between the submerged midship [[cross-section]] A<sub>S</sub> zand the wetted [[cross-section]] A (S = f (n, UKC<sub>R</sub>, v<sub>S</sub>, ...) with n = A<sub>S</sub> / A) should be taken into account when design [[fairway]] depth.
* An off-centre [[course]] only results in low to minimal increases in squat compared to a central [[course]] (S ≠ f (L, ...) ).
* Neither the shape of the embankment nor the [[foreshore]] area had a significant observable impact on squat assuming the same [[waterway]] [[cross-section]] (S ≠ f (1:m, …) ).
* If the UKC<sub>R</sub> is low, the partial-cross-sectional ratio n<sub>T</sub> of ship A<sub>S</sub>/2 2 and wetted partial-area A<sub>T</sub> will determine the speed-dependent element of the long-period ship-generated wave and flow load (e.g.: [[drawdown]] z<sub>A</sub> = f (n<sub>T</sub>, v<sub>S</sub>, …) with n<sub>T</sub> = 0,5 A<sub>T</sub> / A<sub>S</sub> at A<sub>T</sub> = f (L, ...) ).

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