16-05-2012, 11:42 AM
Wave making resistance
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1 Definition of wave making resistance
Wave making resistance of ship is the net fore and aft force upon the ship due to fluid
pressures acting normally on all parts of hull
The variation in pressure due to the motion of body in the fluid (sea water) is creating the
waves (wave making)
Energy expended in moving the body against the flow is equal to energy necessary to
maintain the wave system
Wave making resistance depends on sectional area curve, water lines geometry and
sectional areas of hull form
Wave making resistance REAL FLOW = Wave making resistance POTENTIAL FLOW +
Viscous effects
2 Ship wave system
Kevin wave pattern - concept of pressure point moving and creating a set of transverse
waves and divergent waves system
Transverse wave diminish along after portion. Transverse waves are turned back some
distance from center line to meet diverging waves at cusps. The height of the cusps also
decrease , but less rapidly than transverse waves away from the center line.
Divergent waves
Cusps Transverse waves
Rt V6
Rt V2
Rt
V
At stern and bow divergent waves become more predominant. At parallel middle body
transverse waves are dominant and also if the ship has high velocity then transverse
waves at stern are also dominant at stern
Since the wave pattern moves along with the ship it is good to assume that velocity of
transverse waves is equal to ship velocity
Initially the transverse waves are of shorter wave length , then to about ship length after
bow portion and then to about 2 ship’s lengths far after stern portion
3 Wave making resistance of surface ships
At low speeds wave making resistance is very small , so viscous resistance is dominant.
If we observe the Ct curve it decreases along the Cf curve in a small speed range i.e.
Fn < 0.25 and as speed increases Rt varies as V 6 or more i.e. Fn >0.45
Ct curve - Humps and Hollows
For Transverse waves
For Divergent waves
As the ship speed increases the length of the wave , both transverse and longitudinal
waves will increase and the relative positions of crests and troughs will alter
Hump – Crest coinciding with crest
Hollow crest and trough tend to cancel one another
4 Experimental Studies on ship wave making resistance
Eggert (1939) proved the concept of Froude hypothesis of Cr being same for model as
well as fro full scale ship at corresponding speeds by his pressure measurements on the
hull model and finally calculating the Cr
The important outcome of his experiments was that large portion of wave making
resistance was from the upper portion with respect to still water
5 Theoretical studies on ship wave making resistance
Michell (1898) theoretically calculated the wave making resistance on slender bodies in
non viscous fluid ( by formulating a velocity potential ), it was Havelock who projected
importance of his work Assumptions are slender body , inviscid fluid , no free surface
waves etc.
Havelock (1951) theoretically calculated the wave making resistance by the concept of
energy to maintain the wave system. His method is of source – sink method and finding
the wave pattern far astern
Both these theoretical methods lead to same final mathematical expression. The beauty of
Havelock’s theoretical model was well put up by Prof.Inui by applying the calculation of
theoretical wave making resistance in the optimum hull form design ( i.e. a vessel with
minimum wave making resistance at desired speed)
Source and sink concept
6 Developments in Theoretical Wave making resistance calculation
A) Linearised potential flow theory
B) Improvements to linearised potential flow theory by inclusions of non linear effects
C) Application in hull form improvements through iterative schemes
D) Numerical methods and computation to predict wave making resistance (panel
methods)
Applications : Choice of shapes of waterline and sections
Choice of size and location of bulbous bow