Ship Theory

Hull Stresses

A vessels hull may be comparable to a simple beam ( in fact a box section) under even loading (weight of structure plus contents) and supported evenly (buoyancy in water). Simple beam theory may be applied in calculating the compound bending and shear stresses caused by loading and wave action. In addition torsional stresses may be significant especially during grounding.

The total stress in the hull is a combination of all three

Causes of Primary Structural stresses

Weight Distribution

With the vessel at a constant draft forces, both bending and shear, may be altered by movement of loads within a vessel. Were weights are locted such as to cause deflection downwards of the ends this is termed Hogging.

Were the weights are more centrally located such that the midships section deflects downwards then this is termed Sagging

Uneven point loading caused by tank, cargo and stores distribution as well as hull design cause stresses within the hull structure

Hydrostatic pressure

All weights contained within the vessel are bourne by buoyancy resulting from water pressure. The effects of this pressure is to distort the structure inwards an is resisted by the hull plating and associated stiffening arrangements


Uneven water pressure caused by wave action leads to distortion of the structure as shown and is resisted by the Shear Stresses in the structure including most significantly the Transverse bulkheads and framing. Racking stresses are highest at the corners of the box section and thus the corner brackets are specially inspected.


When a vessel is docked on keel blocks only there is a tendency to sag transversely. This is reduced by including additional rows of blocks outbd of this


This leads to special case loading on the hull dependent on how the vessel has landed. Uneven loading on the hull structure will occur when the vessel is landed at one end due to uneven bouyancy distribution. Where the landing is narrow transerse sagging can also occur

Causes of Secondary and Tertiary Structural stresses


. Caused by oscillatory motion on the shell plating at the Bow and Stern caused by the uneven water pressure as the vessel passes through waves. It is resisted by a system of Panting Beams, Panting Stringers, Breast Hook and a deep floor

Pounding or slamming

. Caused by bow pitching clear of the water then coming dow heavily on the sea. This is resisted by a reduction in framing pitch and possibly increased plate thickness

Local Loads

. These are due to such as deck Machinery, hull design etc


. Localised stresses resisted by adjacent stresses are caused by vibrations from main engine, propellers etc

Hull resistance

For a vessel to move through the water certain resistance have to be overcome.

These can be classed into three groups;

Container Ship  Oil Tanker  

Frictional resistance      FR      45%      90%  

Wavemaking resistance RW     40%       5%  

Eddy Making resistance              5%       3%  

Air Resistance                         10%       2%  

When a vessel moves the water contact the hull exerts a pressure dependent on the vessels speed, the density of the water and the wetted surface area of the hull

K =1/2. V 2.AS
K is Force if the vessels was being stopped completely by force of water
V is the speed of hull through water
AS is the wetted surface area of the Hull including rudder

(From Bernoulis)

The total resistance R = C x K
C is a dimensionless coeeficient

C can be calculated using known factors such as the wetted surface area, block coefficients etc and can be confirmed using towing tests in tanks.

Frictional Resistance RF

This is related to the wetted surface area. It can make up the main part of the total resistance reaching 70 to 90% for large slow moving vessels such as tankers reducing to 40% for high speed craft.

Hull resistance increases as the hull fouls due to marine growth the effect of which is to reduce vessel speed and increase fuel consumption. The use of antifoulant paints attempts to restrict this. A heavily fouled hull can have increased frictional resistance by 25 to 40%.

Residual Resistance RR

This consists of two main factors

Wave resistance- At low speeds the wave resistance is proportional to the square of the velocity but increases much faster as the speed increases. This effect means that there is an effective maximum sped of the vessel were increasing power does not result in effective increases in speed instead the excess energy simply goes into creating large waves.

Residual resistance can greatly increase in shallower water as the displaced underhull water has more difficulty moving aft

Air resistance RA

Is proportional to transverse sectional area above the waterline and the square of the vessels speed It normally adds up to 2% of the total resistance however for large high seed craft such as Container ships it can be as much as 10%.

Effects of sea and weather state

The vessels trading pattern can be seriously effected by the prevailing weather and sea conditions. For a medium sized tanker of bulk carrier the effective resistance can increase by 100 to 200% due to weather and sea effects only.

Towing resistance RT

This the summation of all the resistances. The power required to move vessel is said to be the vessels speed multiplied by the total resistance.

PE = RT x V
T= RF + RR + RA
This power is somewhat less than the propulsion power due to propeller losses due to flow around the propeller and the propeller efficiency it self

Ship Nomenclature

Load Line Length(m)- taken as 96 per cent of the total length on a waterline at 85 per cent of the least moulded depth measured from the top of the keel, or as the length from the fore side of the stern to the axis of the rudder stock on that waterline, if that is greater. In ships designed with a rake of keel, the waterline on which this length is measured is to be parallel to the designed waterline. The length is to be measured in metres.

LR Scantling Length-Rule length, is the distance, in metres, on the summer load waterline from the forward side of the stern to the after side of the rudder post or the centre of the rudder stock if there is no rudder post. L is to be not less than 96 per cent, and need not be greater than 97 per cent, of the extreme length on the summer load waterline.

The ship’s Draught D is the vertical distance from the waterline to that point of the hull which is deepest in the water The foremost draught DF and aft most draught DA are normally the same when the ship is in the loaded condition.

The Scantling Draught is the ships design draught and is equal to the Summer Load Line draught.

Breadth on waterline BWL-the largest breadth on the waterline BWL


This is the equivalent mass of sea water (sg = 1.025) displaced by the hull. It is therefore equal to the Total weight of the vessel


Deadweight is the difference in tonnes (1000Kg) between the displacement of a ship in water of specific gravity 1.025 at the load waterline corresponding to the assigned summer freeboard and the lightweight of the ship.
It includes bunkers and other supplies necessary for the vessel to proceed on passage as well as cargo.
The Deadweight may be quoted at the design draught although this would be specially denoted


Lightweight is the displacement of a ship in tonnes without cargo, fuel, lubricating oil, ballast water, fresh water and feedwater in tanks, consumable stores, and passengers and crew and their effects.


Gross Register Tonnage, Net Register Tons

This is a volume measurement where one Register Ton is equivalent to 2.83 m3 and express the total moulded internal size of the vessel and are used for the calculation of harbour and canal dues. It can be found on the International Tonnage Certificate each vessel must hold

Hull Form description

Parallel midbody In many modern ships, the form of the hull’s transverse section in the midships region extends without change for some distance fore and aft. This is called parallel midbody and may be described as extensive or short, or expressed as a fraction of the ship’s length.

Forebody The portion of the hull forward of the midship section.

After body The portion of the hull abaft the midship section.

Entrance The immersed portion of the hull forward of the section of greatest immersed area (not necessarily amidships) or forward of the parallel midbody.

Run The immersed portion of the hull aft of the section of greatest immersed area or aft of the parallel midbody.

Deadrise The departure of the bottom from a transverse horizontal line measured from the baseline at the molded breadth line. Deadrise is also called rise of floor or rise of bottom. Deadrise is an indicator of the ship’s form; fullbodied ships, such as cargo ships and tankers, have little or no deadrise, while fine-lined ships have much greater deadrise along with a large bilge radius. Where there is rise of floor, the line of the bottom commonly intersects the baseline some distance from the centerline, producing a small horizontal portion of the bottom on each side of the keel. The horizontal region of the bottom is called flat of keel, or flat of bottom. While any section of the ship can have deadrise, tabulated deadrise is normally taken at the midships section.

Knuckle An abrupt change in the direction of plating or other structure.

Chine The line or knuckle formed by the intersection of two relatively flat hull surfaces, continuous over a significant length of the hull. In hard chines, the intersection forms a sharp angle; in soft chines, the connection is rounded.

Bilge radius The outline of the midships section of very full ships is very nearly a rectangle with its lower corners rounded. The lower corners are called the bilges and the shape is often circular. The radius of the circular arc is called the bilge radius or turn of the bilge. The turn of the bilge may be described as hard or easy depending on the radius of curvature. If the shape of the bilge follows some curve other than a circle, the radius of curvature of the bilge will increase as it approaches the straight plating of the side and bottom. Small, high-speed or planing hulls often do not have a rounded bilge. In these craft, the side and bottom are joined in a chine.

Loadline (Plimsoll) Marking

Each vessel is required to hold a Loadline Certificate. Part of the requirements for this is the permanent marking of loadlines on either side of the hull arounf about midhsips. Permanent marking means that they have to be impressed or welded so that they cannot be removed by normal wear and tear. They should be white or yellow on a dark contrasting back ground. Regulations govern the number and size of these, the main ones are described below.

Danish Load mark

The Load Line Mark shall consist of a ring 300 millimeters (12 inches) in outside diameter and 25 millimeters (1 inch) wide which is intersected by a horizontal line 450 millimeters (18 inches) in length and 25 millimeters (1 inch) in breadth, the upper edge of which passes through the centre of the ring. The centre of the ring shall be placed amidships and at a distance equal to the assigned summer freeboard measured vertically below the upper edge of the deck line

Deck Mark

The deck line is a horizontal line 300 millimeters (12 inches) in length and 25 millimeters (1 inch) in breadth. It shall be marked amidships on each side of the ship, and its upper edge shall normally pass through the point where the continuation outwards of the upper surface of the freeboard deck intersects the outer surface of the shell. The location of the reference point and the identification of the freeboard deck is indicated on the International Load Line Certificate (1966). Lines to be used with the Load Line Mark

Loadline Mark

The lines which indicate the load line shall be horizontal lines 230 millimeters (9 inches) in length and 25 millimeters (1 inch) in breadth which extend forward of, unless expressly provided otherwise, and at right angles to, a vertical line 25 millimeters (1 inch) in breadth marked at a distance 540 millimeters (21 inches) forward of the centre of the ring . Aft of theoretical mark refers to loading in freshwater only. For'd refers to loading in sea water only


Freeboard is the distance between the waterline and the freeboard deck at mid length. The freeboard deck is the uppermost continuous deck which has means of closing all openings. Rules allow different freeboards for different ships in relation to their construction and cargo they carry. There are two types of ship;

Type A -which covers vessels designed to carry only liquid cargoes.

Type B-Which covers all other types of ship,

For type A ships cargo tanks must only have small openings which can be effectively sealed

Type B ships must have sufficient bulkheads and sealing arrangements for openings, but such openings e.g. hatches can be large

The freeboard allowed will be smaller for the type A ship compared to the type B ship of similar length because of the type of cargo carried and means of access for water. Type B ships classed as B-60 may have their freeboard reduced by 60% of that required for a normal B-100 ship provided that its method of construction approaches that of the type A ship. This type exists with OBO's.