Furthermore, they can be applied to the seafaring problems involved in the design of the unusual new high-speed craft and floating. It is shown that, with knowledge of the wave spectrum and the characteristic response of a ship to the component waves of the irregular sea, a response spectrum can be determined.
STORM
Section 3
Ship Responses to Regular Waves’
Section 4 The Ship in
Much if not most of the theory of the linear response of a marine system to random excitation was developed in the context of electronics and communications (Rice, 1944), (Lee, 1960). While the wave heights in a stationary wave process vary with time and position in the wave field, the probability structure of the process does not.
Section 5
Derived Responses”
Introduction. The aspects of ship response to rough seas that are generally of greatest importance
Also of interest is the relative vertical motion between a point on the ship and the surface of the facing wave. The traditional assumption is that the main component is the incident wave and that the other components tend to cancel each other out; i.e., the incident wave is not distorted by the presence of the ship. Assuming that the wave is not distorted by the presence of the ship and B = 0, the amplitude of the relative vertical motion is generally given by.
For this case the character of the relative motion curves is the same as Fig. The second is the change in freeboard due to the draft and trim caused by the forward speed of the vessel. It is possible that the differences in cover wetness were caused by differences in the detailed design of the arches.
Added resistance. The increase in required power resulting from ship motions in heavy seas arises
This is very significant because it means that the principle of superposition can be applied to additional resistance in irregular waves, as well as to ship motions. The superposition principle for the mean additional resistance (or thrust or moment) was first noted without elaboration by Maruo (1957). Later, Hasselmann (1966) and Vassilopoulos (1966) pointed out that the basic result can be explained in terms of the theory of quadratic, non-linear systems.
HEAD SEAS
Section 6
Control of Ship Motiond2
Section 7
Assessing Ship Seaway Perforrnan~e’~
Section 8 Design
1974), “A Numerical Investigation of the Ogilvie Tuck Formulas for Added Mass and Damping Coefficients,” Journal of Ship Research, Vol. 1974), “Motions of Large Structures in Waves a t Zero Froude Number,” Proceedings, International Symposium on Dynamics of Marine Vehicles in Waves, University College, London. State of the art,” University of Michigan Report no. 1967), "On predicting the seakeeping characteristics of hydrofoil ships", SNAME /. AIAA Symposium on Advanced Marine Vehicles. Pitching and heaving of a ship in regular waves,” SNAME Transactions, Vol. 1898), “A New Theory of the Pitching Motion of Ships on Waves and the Stresses Caused by That Motion,” Trans., INA, London.
1959), "Increasing the Sea Speed of Merchant Ships," SNAME Transactions, Vol. 1960), "Semi-submerged Ships for High-speed Operation in Rough Seas," 3rd ONR Symposium on Naval Hydrodynamics, Washington, D.C. 1929), "The Inertia of the Water Surrounding a Vibrating Ship," SNAME Transactions, VOl. 1957), "On the Generation of Waves by Turbulent Wind," Journal of Fluid Mechanics, Vol. 1966), The Dynamics of the Upper Ocean, Cambridge University Press, England. 1980), "Nogle kommentarer til visse idealiserede variansspektre af søvejen, der i øjeblikket er på mode," Journal of Ship Research, december.
Section 1 Introduction
The study of the complex subject of manageability is usually divided into three separate areas or functions: The main interest is in the ease with which the ship can be kept on course. Because controllability is so important, it is an essential consideration in the design of any floating structure.
The purpose of this chapter is to introduce the basic principles of controllability analysis and its many facets in a manner that will lead to the use of rational design procedures to ensure adequate ship controllability. The chapter is organized to provide an understanding of controllability and to influence it as it interacts with the design of the vessel's hull, machinery and other features. The final sections (16 and 17) provide an introduction to the application of maneuverability analysis tools and methods to the design of the ship and its appendages for satisfactory control by the helmsman and autopilot.
Section 2
The Control loop and Basic Equations of Motion
ANGLE
4 SHIPS PATH POSITION
Equations (5) were developed for the case where the origin of the axis, 0, is at the center of gravity of the ship. Moving the rudder produces a moment that causes the ship to change course by taking an angle of incidence (solid angle) with respect to the direction of motion of the center of gravity. As a result, hydrodynamic forces are created on the hull, which after some time cause a change in the lateral movement of the center of gravity.
These forces are generally proportional to the above-water surface of the ship and the square of the relative velocity between the ship and the wind. Forces and moments also vary with the direction of the wind velocity relative to the ship's axes. Pitching motion changes the shape of the submerged hull and can therefore have a significant effect on the coefficients in the equations of motion, especially in quartering and following seas.
Motion Stability and linear Equations
Section 4
Analysis of Coursekeeping and Controls-Fixed Stability
It is the slope of the Y force with respect to an acceleration d, and appears in the definition of both A and B of (14). Therefore, the inertial reaction pressure of the water accelerated by the hull produces forces in the negative y direction on both the bow and stern. For ship-shaped bodies with large length to beam ratios (L/B), the magnitude of Y5 approximates the magnitude of the ship's displacement, A.
As noted in the Y derivative analysis, both bow and stern add to contribute a large negative Yi. It is seen that as a result of the angle of attack, /3 z -v/V on the body, both the bow and the tail section experience a lift force directed opposite to v. However, the contribution of the bow to the total Y Force v is usually greater than that of the stern, so that the center of action of the total force in the y direction due to v is well forward of the ship's mid-length.
The slope of the yaw rate curve at zero rudder angle is a measure of the degree of stability or instability. 14, which is stable in heeling, the slope of the righting moment relative to the heeling angle curve is a t + = 0. When the rudder deflection is continued to port, the ship still continues to turn to starboard in the direction of the rudder deflection, until point (a) on curve B is reached.
Any increase in rudder angle to port beyond point (a) will cause the ship to suddenly assume the large angular velocity to port indicated by point (a) and may even temporarily exceed (al). The degree of instability is important depending on the type, size and speed of the ship. The results still provide a loop shape to estimate the degree of instability.
Stability and Control
The naval architect is primarily concerned with elements (b), (4), and (e) of the course-keeping and course-changing problems. The results of this maneuver are an indication of the ability of a ship's rudder to control the ship. , just as the results of the spiral maneuver give an indication of control efficiency (rate of yaw versus rudder angle), so the results of the zigzag test depend somewhat on the stability characteristics of the ship as well as on the efficiency of the rudder.
It has been shown that the amount of oversteer angle decreases with increased stability but increases with increased rudder efficiency. This expression for the coefficients in terms of the time constants TI', Tz', T3' and T,' as well as the system gain K' is consistent with control engineering practice. One of the advantages of these indices is that they can be derived from the results of standard experiments or free-running model maneuvers for comparison with the calculation.
Analysis of Turning Ability
On the other hand, if the magnitude of (N',) is greater than N' 6 , then an increase in the magnitude of Y , will typically increase the radius of the bend. While steering is intended to produce motion only in the yaw (xy) plane, motions are also induced by transverse coupling in the pitch (xx) and roll (yx) planes. If moments are taken about the center of gravity of the ship, it is seen that the heel angle.
It is seen that the amplitude of the initial heeling to starboard in the first phase of the turn is small compared to the amplitude of the second heeling to port. This is also part of the reason why the first roll to port of the surface ship in fig. This partly explains that the ratio between the value of the first large roll and the stable pitch shown in fig.
Free-Running Model Tests and Hydraulic Models
Hydraulic Models. Models of harbor and ves- sel waterway systems accurately modeling hydraulic
In this particular case, after investigation, it was determined that the channel bend would be the most critical problem in maneuvering container ships. Although the existing fairway was wide enough for a large container ship, the combined effects of the turning maneuver and wind and currents limited sailing time to a window of only two hours per day. A hydraulic model of the Eemhaven waterway configuration has been drawn up at MARIN and many different large proposed container ship models have been run through the turning maneuver.
As a result of the project, the Port of Rotterdam Authority approved the expensive easing of the canal bend entering Eemhaven. While hydraulic modeling of a waterway can be made quite accurate to correctly reflect water flows, there are still scaling issues and the issues mentioned in the previous sections apply. Scales are usually small (1 to 100 is common) due to the cost of constructing waterway models.
Section 8
And even with this restraint, entry was still judged risky by the Rotterdam pilots. When the proposed dredging to facilitate the turn was tried in the hydraulic model, grounding was reduced to zero with the appropriate assistance of the tug (the operation of the tug was simulated using small fans mounted on the model mounted).
Nonlinear Equations of Motion and Captive Model Tests
Section 9 Theoretical
Prediction of Hydrodynamic
Coefficients and Systems
Identification
However, it is assumed by Martin (1961) and confirmed by Porter (1966) that if the scale of the abscissa of Fig. Prediction of the second term on the right side of Equation (71) depends on knowledge of x, for ship-like bodies, since ( Y J h can be easily calculated from (64a). Jacobs (1964) suggests that x be measured from G to the center of the hull profile.
As noted in (ll), the derivative Y , is only one of the terms in the coefficient of r'; the other is A'. Jacobs (1964) has shown that the hydrodynamic derivatives of the bare husk-deadwood combinations shown in Figs. Jacobs assumes that the derivatives (YJf, (N'Jf, Due to the high aspect ratio of the small dead wood shown in Fig.
