CHAPTER 53 



Quantitative Data on Dynamic Lift and Planing 



53.1 



53.3 



53.4 

 53.5 



Relationship to Other Chapters 263 53.6 



Principal Quantitative Factors Involved in 



Planing 263 53.7 



Principal Forces and Moments on a Planing 



Craft 264 53.8 



Determination of Dynamic Lift 264 



Typical Pressure Distribution and Magnitude 53 . 9 



on Planing-Craft Bottoms 266 



Wetted Length, Wetted Surface, and Friction 



Resistance 268 



Variation of Total and Residuary Resistances 



with Speed 209 



Selected Bibliography on Planing Surfaces, 



Dynamic Lift, and Planing Craft .... 269 

 Partial Bibliography on Hydrofoil-Supported 



Craft 271 



53.1 Relationship to Other Chapters. The (1) Length, breadth, and planform shape of the 



basic phenomenon of planing is described in 

 Chap. 13, and the behavior of planing craft in 

 general is discussed in Chap. 30. Rules and pro- 

 cedures for the hydrodynamic design of a full- 

 planing type of motorboat are to be found in 

 Chap. 77, with a preliminary design worked out 

 for one boat. 



The basic data for predicting the behavior of 

 simple planing surfaces are rather voluminous, 

 when the test results on flying-boat and seaplane- 

 float models are included. Several workers in the 

 field, as related in the sections following, have 

 succeeded rather well in their efforts to assemble, 

 analyze, correlate, and systematize the available 

 planing-surface data, so as to make them directly 

 applicable to and useful for new designs. It is not 

 possible, within the scope of this chapter, to do 

 much more than reference a few of the sources 

 which contain quantitative data in a form to be 

 readily usable to the designer of planing craft. 



In addition to the selected bibhography on 

 planing in Sec. 53.8, a partial bibliography on 

 hydrofoil-supported craft is included as Sec. 53.9. 



53.2 Principal Quantitative Factors Involved 

 in Planing. The magnitude of the dynamic pres- 

 sure intensity and the dynamic lift under a 

 planing surface inclined at a small angle of attack 

 a(alpha), or under a V-bottom boat running at 

 a trim ^(theta) by the stern, is a function of a 

 considerable number of factors. Further, the 

 center CP of this pressure system, or the point 

 where the resultant dynamic lift is exerted, and 

 its location with respect to the center of gravity 

 CG, is as important for the proper design of a 

 planing craft as it is for the design of an airplane. 



Among these factors may be mentioned: 



planing surface actually in contact with the 

 water in any given running condition, with respect 

 to an axis parallel or nearly so to the direction of 

 motion. At running attitude and position, the 

 length dimension becomes the mean wetted 

 length Ljrs and the breadth dimension becomes 

 the mean chine beam Be ■ 



(2) Wetted area of the planing surface. This is 

 the actual and not the nominal area. 



(3) Forward speed V with respect to the water 

 underneath the bottom of the planing craft, 

 neglecting the cosine of the angle of trim 



(4) Mass density p(rho) and weight density w of 

 the water 



(5) Trim angle d with reference to the horizontal 



(6) Rise-of -floor angle /3(beta), for a planing sur- 

 face that is V-shaped in transverse section 



(7) Distance of the CP from the after termina- 

 tion, usually a sharp edge of the planing surface, 

 in any given running condition. 



Related to these features are the: 



(8) Dynamic lift L 



(9) Total resistance or drag Rt , in the direction 

 of motion 



(10) Friction resistance Rf , exerted parallel to 

 the wetted bottom surface 



(11) Residuary resistance Rjt , as for any other 

 surface craft 



(12) Total weight W(ot A) of the craft 



(13) Buoyancy B, due to partial immersion of 

 the hull at some speeds 



(14) Acceleration of gravity g. 



There are a number of dimensionless ratios and 

 coefficients utihzed in planing-surface and planing- 

 craft design: 



263 



