CHAPTER 61 



The Prediction of Ship Behavior in 

 Confined Waters 



61.1 General 389 



61 . 2 Typical Shallow-Water Resistance Data . . 389 



61 . 3 The Quantitative Effect of Shallow Water on 



Ship Resistance and Speed in the Sub- 

 critical Range 390 



61.4 The Square-Draft to Water-Depth Ratio . . 393 



61.5 Features Associated with the O. Schlichting 



Procedure 394 



61.6 Practical Cases Involving a Given Depth of 



Water 396 



61.7 Case la: To Find the Shallow- Water Speed 



from the Deep-Water Resistance-Speed 

 Data 397 



61.8 Case lb : To Find the Shallow- Water Resist- 



ance from the Deep-Water Resistance- 

 Speed Data 400 



61 . 9 Case Ic : To Find the Deep-Water Speed and 



Resistance When the Shallow- Water Speed 

 and Resistance are Measured 400 



61 . 10 Limiting Case of 2 Per Cent Speed Reduction 



in Water of a Given Depth 403 



61.11 Cases 2a and 2b : To Find the Limiting Depth 



for a 2 Per Cent Increase in Resistance . . 404 



D. W. Taylor's Criterion for the Limiting 

 Depth of Water for Ship Trials 407 



Predicted Shallow-Water Resistance by 

 Inspection 408 



Calculating and Using the Hydraulic Radius 

 of Channels 409 



Estimating the Effect of Lateral Restrictions 

 in Shallow Water in the Subcritical Range 410 



Lack of Reliable Data on Power and Pro- 

 pulsion-Device Performance 411 



Data on Confined- Water Operation at Super- 

 critical Speeds 412 



Data on Offset Running Positions and 

 Steering in a Channel 413 



Prediction of Ship Resistance in Canal Locks 413 



Unexplained Anomalies in Shallow and Re- 

 stricted Water Performance 414 



Summary of Shallow- and Restricted- Water 

 Effects 414 



Partial Bibliography on the Effects of 

 Confined Waters on Models and Ships . 415 



61.1 General. The elements of the flow 

 around a body or ship moving in shallow and 

 restricted waters are described in Chap. 18. 

 Aspects of the behavior of actual ships under these 

 conditions are covered in Chap. 35. Some data 

 on shallow-water waves are furnished in Sees. 

 48.15 and 48.16. Quantitative information on 

 sinkage and change of trim in confined waters is 

 given in Sec. 58.4. 



The discussion in the present chapter is cen- 

 tered on the behavior, in shallow and restricted 

 waters, of vessels intended primarily for operation 

 in deep water. That in Chap. 72 is centered on the 

 design of vessels intended to give the best possible 

 performance in confined waters; their performance 

 in deep water is usually a secondary consideration. 



For hydrodynamic analysis and practical pur- 

 poses shallow water is defined as an area of un- 

 limited extent in a horizontal plane, of a depth 

 that is generally uniform and equal to or less 

 than that in which the resistance for a given 

 speed is 1 per cent greater than in a deep-water 

 area of the same unlimited extent. 



Restricted water, applying generally to a hori- 



zontal plane, is defined as water of a reasonably 

 uniform depth, deep or shallow, in which the 

 lateral boundaries are sufficiently close to a vessel 

 to increase its resistance for a given speed by 

 1 per cent or more. In this case, the percentage 

 increase is considered to be due solely to the lateral 

 restriction. 



In the limiting case of water that is both shallow 

 and restricted, known by the short term confined 

 water, the combination of depth and width is 

 such as to increase the open-sea deep-water 

 resistance by 2 per cent or more. For this case, 

 the limiting depth of shallow water for any ship 

 is found from the diagram of Fig. 61.J. One way 

 of determining the limiting width of restricted 

 water is by calculating the least width for which 

 the hydraulic radius Rh is diminished to an 

 arbitrary ratio of 0.99 times the shallow-water 

 depth, on the basis that for unlimited water the 

 hydraulic radius R^ equals the depth h. This may, 

 however, be much too severe a limitation for 

 practical use. This requirement is, for example, 

 practically never met in a model testing basin. 



61.2 Typical Shallow- Water Resistance Data. 



389 



