fifiO 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 72.2 



(c) Baker, G. S., "Ship Design, Resistance and Screw 



Propulsion," 1933, Vol. I, pp. 209-212; Vol. II, 

 Chap. XXVI, pp. 136-142 



(d) MitcheU, A. R., "Shallow Draught Ships," INA, Jul 



1952, pp. 145-153 



(e) Mitchell, A. R., "Tunnel Tj-pe Vessels," lESS, 1952- 



1953, Vol. 96, pp. 125-188. 



72.2 Reference Data on River, Canal, and 

 Channel Slopes and Currents. The free surfaces 

 of all flowing ri\'ers, tidal estuaries, open channels, 

 and canals in which horizontal currents flow, 

 have some slope with reference to the horizontal. 

 Data on the surface slopes of all the principal 

 rivers in the United States, subdivided into river 

 regions where the slopes change rapidly or where 

 there are reliable data, are given in both tabular 

 and graphic form in a paper by H. Gannett 

 entitled "Water-Supply and Irrigation Papers of 

 the U. S. Geological Survey, No. 44, Profiles of 

 Rivers in the United States," U. S. Geological 

 Survey, Washington, 1901. 



Nothing in this paper indicates the slopes 

 which might occur during flood conditions, or 

 those which might obtain in short reaches of the 

 order of 1 mile in length. The construction of 

 dams in many of the rivers since 1901 has of 

 course changed the situation materially. The 

 slopes cover a rather wide range, as indicated 

 hereunder: 



Location Drop in ft per geographical mile of 



6,280 ft 

 Sacramento River 3.0, maximum 

 Missouri River 1.0 average; varies from 0.7 to 1.3 



Platte River Averages 5.0 or 6.0 



Colorado River Two steepest slopes are 22.0 and 



31.2, corresponding to natural 



tangents of 0.00417 and 0.00591; 



remainder are 6.0 to S.O. 



G. Nowka gives the surface slopes of some 

 European rivers as about 1 in 1000 ["New Knowl- 

 edge on Ship Propulsion," 1944, BuShips Transl. 

 411]. Here the slope thrust is sufficient to produce 

 a speed which gives steerageway to a non-self- 

 propelled barge when drifting downstream. This 

 is equivalent to a 5.28-ft drop per geographical 

 mile or a 6.08-ft drop per nautical mile. 



The steepest reaches in any large navigable 

 river of the world are in the Yangtze in China, 

 where the river rises some 600 ft in the 1000 miles 

 between its mouth and the city of Chungking. 

 Certain sections when in flood have free surfaces 

 so steep that the currents in the navigable chan- 

 nels reach velocities of 12 to 14 kt. 



The method of calculating the drag and thrust 



due to the declivity of the surface upon which a 

 ship or body is floating is described in Sec. 57.10. 



72.3 Economical and Practical Speeds in 

 Shallow and Restricted Waters. Decisions as to 

 the designed speeds for shallow-water vessels are 

 properly made b)y the prospective owners and 

 operators, on a basis of many factors other than 

 hydrodynamics. However, the designer may be 

 called upon to give information and advice on 

 this matter. He is therefore required to have 

 some knowledge of the factors involved and some 

 quantitative data for reference. 



The first things to know about the shallow- 

 water and restricted-water regions in which the 

 ship is to run are the depth, bottom contours, 

 channel dimensions, water-section outlines, cur- 

 rent directions, current velocities, and local 

 current irregularities. This may be greatly com- 

 plicated by variations in these factors due to 

 flood and tidal conditions. These in turn depend 

 upon the weather as well as the seasons and the 

 rotation of the earth. 



It is not adequate to depend upon average 

 values of the water factors previously hsted, 

 either as averages of distance or of time. It is 

 necessary to assume extremes as well, if ship 

 operation is to be maintained on schedule. Further, 

 disaster may, and usually does lurk around the 

 corner of the one operating situation that has 

 not been investigated properly and for which 

 preparations have not been made. 



First, a reasonably uniform depth h is deter- 

 mined for a certain section of the route, under 

 given conditions. The next step is to find the 

 speed of the solitary wave in that depth, so 

 that the ratio of a given shallow- water ship 

 speed Fj to the critical wave speed Cc may be 

 known. As an aid in relating contemplated ship 

 speeds to the solitary-wave speed for any depth. 

 Table 72. a gives the latter speed for a consider- 

 able range of depths to be encountered in practice. 

 The values given in this table are for still- 

 water conditions, with no current. When the 

 water in an estuary, river, or channel is flowing 

 in one direction or the other, the solitary wave 

 speed of Table 72. a is still valid when reckoned 

 with reference to a point fixed in the water. When 

 a ship is overtaking a solitary wave, therefore, 

 it makes no essential difference whether the ship 

 is moving with the current or against it. The 

 important factors are the wave speed and the 

 ship speed, both reckoned through the water. 

 It is emphasized, however, that the critical 



