Wave making resistance is the force acting on a ship moving through water that is caused by the waves generated by the ship's hull. As the hull moves through the water, pressure points create diverging and transverse wave systems. The interaction and interference of these four wave systems, generated at the bow, stern, and shoulders, determine the overall wave making resistance, which requires energy to maintain the wave patterns. Methods like thin strip theory and source-sink modeling are used to calculate wave making resistance. Reducing the hull's entrance angle can decrease the size of the forward waves and thus lower resistance.

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Wave Making Resistance
From MarineWiki
Contents
1 Introduction
2 Description
3 References
4 Other Lessons
Introduction
Whenever a body moves in a fluid there is pressure force acting developed that is acting normal to the surface of the body.
Earlier we have seen that if the fluid is non­viscous and completely immersed, then the forward component of the pressure force would
cancel with the aft component of the pressure (Ideal fluid in ideal scenario). But as the body comes up to the surface, the pressure developed
around the body generates waves. This wave generation is dependent on the air­water free surface and gravity.
The net fore­and­aft forces upon the ship due to fluid pressure acting normal to all parts of the hull is the wave making resistance.
Description
If a body is just below the surface of water waves would be generated although a small one. In case of submarine, the resistance would be
maximum just below the surface, where in addition to the frictional resistance of the entire surface there is wave making resistance (middle
figure). In case of floating submarine, the frictional resistance would only be due to the immersed area apart from the wave making
resistance (left figure). In the third case of deeply submerged case, frictional resistance is same as the middle figure case, however, the
wave­making resistance will not be there.
In 1887, Lord Kelvin showed theoretically that if a pressure point has a relative motion with water then it creates a set of waves. These
include a set of divergent waves generated that moves aft. There would also be a set of transverse waves following behind the point whose
width increases with distance from point. He showed that the entire wave system is included in a straight line with a half­angle of 190 28’.
Far away from the pressure point the divergent waves would be dominate and only they would be seen.

2.
In case of a ship flowing in water the bow produces a set of waves as shown below. One can see the first crest of transverse wave close to
the bow, and further waves aft of the ship are too small.

3. This can be clearly seen in the profile view of a ship.
The above set considers only the bow set of waves. As there is a high pressure point in aft just like the forward end, a set of waves would
also be generated in the stern as shown below.
Recollecting from above, the pressure point is created when there is a abrupt change in the flow lines of water. In case of the ship, at the
bow, there is a change in the flow along the water line (angle of entrance). An additional pressure point, this time negative is generated at
the forward shoulder due to the change in shape. Similarly there are two pressure points on the aft shoulder and stern as shown below.

4. Wigley conducted a lot of experiments based on wedge shaped body and came out with very interesting results.
File:Res­WR­img8.jpg
There are four wave systems developed in the body as shown in the figure. Apart from this there is the stationary system formed as a result
of the pressure at points of discontinuities as described above.
The next four are waves generated from the four points of discontinuities. In the order the forward wave is generated just aft of the forward
point and creates a generation of a crest of the wave with reducing wave height as one moves aft. There is another crest on the aft point of
the body because of the discontinuity as shown.
Since the pressure in forward and aft shoulder is negative, these points generate trough as shown in the next two waves system. In case of
ships with less prominent shoulder (curved) these waves are much less in size.
The forward wave and the stern wave are prominent systems with crest being generated at those points.
The result of these waves system is what we see on the sides. The result is the addition of waves by linear superposition. The forward crest
is unaffected and the stern side is a combination of the four waves.
On a ship we see the dominant waves are the forward wave system. The aft and shoulder waves are minor because of the smooth shoulders.
To maintain this waves system it requires lot of energy and this energy is the wave making resistance.
The interference of the waves (from the four systems) can either increase or decrease the resistance depending on whether the stern waves
add up or decrease. If there are two crest in the stern part of the ship, then this increased wave crest means that there would be more force
supporting motion and thereby decrease resistance. However if the trough is present which reduce the stern crest then the forward
component of the force is reduced and the resistance increases.
The transverse waves move at the same speed as the ship. For the divergent waves, the axial component of the wave will be equal to the
speed of the ship.
File:Res­WR­img9.jpg Fig. showing wave and component
for transverse wave for divergent wave
Depending on the interference of the wave systems, the resistance curve form humps at locations
Cw maximum at Fn = 0.173 0.205 0.269 0.47
Minimum at Fn = 0.187 0.231 0.345
(constant + 4 oscillating terms)
File:Res­WR­eq4.png (constant + 4 oscillating terms)
File:Res­WR­img10.jpg
File:Res­WR­img11.jpg
In 1898 Mitchell proposed a theoretical method to estimate wave making resistance called “Thin Strip theory” and the modified one called
“Slender Strip Theory”. The method involves in determining the normal pressure distribution on a flow and then integrating the fore­and­aft
components of these pressures over the hull surface.
Assumptions of the theory:
• Fluid is non­viscous
• Fluid is irrotational
• Hull assumption is thin (breadth is low compared to length)
• Slender (breadth and depth is low compared to length)

5. • Wave height is small compared to length
• No sinkage or trim
• Radiation condition (wave only in aft side and no wave in forward section)
A second method is to calculate the wave pattern generated by the ship at a great distance, and to determine the energy necessary to
maintain this system.
An alternate method is to use the theory of source and sinks to model the thin ship in a flow developed by Havelock.
Source­sink
Observation: • Strength of the source is dependent on the slope of the waterline
To reduce the wave height of the forward wave, the half angle of entrance needs to be reduced. As L/B ratio is increasing (for same
displacement) the wave making resistance will come down.
References
Principles of Naval Architecture. Publisher SNAME (http://www.sname.org)
Ship Resistance Video Lectures. Publisher NPTEL ­ A Joint Venture by Indian Institute of Technology & Indian Institute of Science
(http://nptel.iitm.ac.in/video.php?courseId=1045)
Other Lessons
Previous ­ Resistance Types, Resistance ­ Dimensional Analysis, Frictional_Resistance
Next ­ Other_Components_of_Resistance
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