Relation of Hull Form to Resistance
Choice of Ship Dimensions
In merchant ships speed is seldom the dominant consideration, and the proportions and shape of the hull, as a rule, cannot be chosen solely to attain minimum resistance. Nevertheless,lower power and lower fuel costs have an important effect on the profits a ship can earn.
Click here for Online resistance and power calculations
Some containerships are capable of speeds as high as 30 knots. Such ships have stimulated renewed interest in the design of hull forms which can achieve such speeds economically in smooth water and still have good seakeeping qualities and small loss of speed in rough weather. At the other end of the scale are the bulk carriers,such as oil tankers and ore ships. Speed is not so important in such ships, because the minimum cost of transport per ton-mile is achieved by carrying as great
a deadweight as possible in one ship at moderate speeds. Ships have been built with dead weights in excess of 500,000 t, with lengths such that even for a speed of 15 knots the Froude number is as low as 0.15.
Restrictions on the drafts of such ships have increased the beam-draft ratios, and the block coefficients are in the 0.85 region. The efficient design of such ships poses many problems.
The prospective owner usually specifies that the new ship shall carry a certain deadweight at a particular speed, and the designer estimates the probable displacement and principal dimensions. The latter are usually subject to restrictions not associated with resistance and propulsion. Length is expensive in first cost, is limited by docking and navigation restrictions,
while added length increases scantlings, equipment and manning scales. From a resistance point of view, greater length for a given displacement will reduce the wave-making resistance but increase the frictional resistance, so that longer lengths will be beneficial in ships running at high speeds and vice-versa. Longer lengths are also generally beneficial for behavior in
rough seas.
An increase in draft, T, is generally beneficial for resistance, and is a cheap dimension in terms of cost. However, it may be limited by depths of harbors, canals,rivers, and dock sills.
The beam, B, is one of the governing factors in ensuring adequate stability, and a minimum value of B/T is generally necessary on this account. An increase in B will increase the resistance unless it is accompanied by a corresponding reduction in fineness coefficient. In cases of low-speed ships, however, a small reduction in length and a compensating increase in beam, because of the resulting decrease in wetted surface, may result in little or no increase in resistance.
This results in a cheaper ship and also meets the need for increased stability in ships with large superstructures.This idea has been exploited in a number of large tankers.
The minimum wetted surface for a given displacement is also sensitive to the B/T ratio, the optimum value of which is about 2.25 for a block coefficient of 0.80 and about 3.0 at 0.50. However, the penalty for normal departures from these values is not very great. The effects of changes in B/T on wave-making resistance can be studied from model-experiment results.
Generally, stability considerations and limiting drafts usually preclude values below 2.25 for full ships and 2.5 or even more for fine, higher speed ones. While such considerations may be of guidance to naval architects in the choice of dimensions, they must meet many other demands, and will be influenced to a large extent by their knowledge of the particulars of existing successful ships. The process of design is essentially an iterative one, in which the various elements are changed until a proper balance is attained.
Choice of Form Coefficients
power at the trial speed is about 25 percent greater than that at the sustained sea speed under trial conditions. This is in keeping with the general design practice that the service speed should be attained under trial conditions at 80 percent
of the maximum continuous power.
The above relationships are intended as rough guides to the designer and do not take the place of a careful analysis and comparison of alternative designs.
For passenger liners, cross-channel ships and other craft in which high speed is important ,Comparative economic evaluations are essential in these cases.
Economic criterion used is the Required Freight Rate. Impact of variations of fuel costs, interest rates, insurance costs
and construction costs on the Required Freight Rate shall be considered.These procedures are valid and useful when costs (capital and operational) are known as general functions of the primary design parameters.These are, however, most often not known with enough accuracy.
The final decision on length and fullness should not be taken without considering the sea-going qualities of the ship. A short, full ship may well suffer such loss of speed in bad weather as to justify the extra cost of a longer, finer ship. The choice depends on many things, including the ocean conditions on the trade routes in question, particularly the length of the predominant waves and the frequency of their occurrence.
Thus to maintain a weekly service on the North Atlantic in winter, requiring speeds of 28 or 29 knots,the length of express liners cannot well be less than 950 ft .
Excessive fullness also promotes a tendency to bottom damage due to slamming. Flat areas on the bottom forward should be avoided. The floor lines should begin to lift immediately the parallel body ends, so as to give a V-shape which will allow the hull to enter the water smoothly when the ship is pitching .
The wave-making resistance humps occur approximately at values of Fn equal to 0.24, 0.30 and 0.48, and their importance
depends upon the speed and fullness of the ship. The coaster, with a prismatic coefficient CP = 0.83 cannot be driven above Fn = 0.158 without an excessive increase in resistance.
In the trawler, with a finer hull form of =0.57, the lower humps are not very marked, and a Fn value of 0.24 can be reached before the rise in the curve begins. However, speed has great significance in these ships, to get to the fishing grounds quickly and to get home to market afterwards, and they are usually overdriven up to values of Fn = 0.30.
The cross-channel ship, of = 0.58, can be driven to Fn = 0.33 without excessive resistance,for although the is the same as in the trawler, the length is perhaps twice as great, showing the advantage of length in delaying the onset of heavy wave-making.
The destroyer, in which economy in the commercial sense is not paramount, normally has a top speed of Fn = 0.6 or more, well beyond the last hump at about Fn = 0.48.
When the principal dimensions and fullness coefficients have been chosen, the resistance then depends chiefly upon the following elements of ship form:
(a) Distribution of displacement along the length,as typified by the curve of cross-sectional areas and the LCB.
(b) Shape of the LWL, particularly in the fore body.
(c) Shape of the transverse sections, especially near the ends.
(d) Midship-section area coefficient.
(e) Type of stern; i.e., raised counter, cruiser, transom, and so on.
The midship-section coefficient varies with fullness. In merchant ships with block coefficients around 0.80, it may be as high as 0.995. As the fullness decreases and the length of parallel body becomes shorter, it is necessary to ease the Midship section area somewhat to avoid too pronounced shoulders in the lower waterlines.
The choice of the shape of section area and LWL curves depends upon the values of Fn and and will also be influenced by the need to provide adequate stability.
The load waterplane coefficient decreases with decreasing fullness, its value depending also to a considerable extent upon the type of transverse sections.In full ships considerable parallel body can be worked in with advantage, and the entrance can be short, the run being long and fine to minimize separation and form resistance. As decreases, so does parallel body, and the entrance is made longer to reduce the increase in wave-making resistance, the LCB moving aft in consequence.
Most of the reduction is thus accomplished by fining the entrance, the change in the coefficient of the run being much less.
The sectional area curve and load waterline follow a similar pattern. At low Fn values and high prismatic coefficients, both are slightly convex forward and aft. As Fn increases, they become straight and eventually S-shaped with a hollow near the stern. At Fn values of 0.45 and above, the hollow should disappear in the LWL, which should be straight or even slightly convex in destroyers and other high-speed types. In such ships, too, the onset of high wave-making resistance calls for
as long a length as is compatible with the other design requirements.the shape of the midship section was not an important factor in determining residuary resistance.
The principal advantages claimed for such ships are the elimination of wave-making resistance and independence of weather conditions. Volume for volume, the submarine has a greater wetted surface than the ordinary ship, and so
starts off with the handicap of greater frictional resistance.The absence of wave-making resistance therefore does not make itself felt until relatively high Froude numbers are reached, perhaps in excess of Fn = 0.25. Because of cargo-handling problems, most proposals have been for oil or ore-carrying submarines,and these cargoes do not call for high speeds of transport.
Effect of Bulbous Bows on Resistance
At low speeds Wigley found the total resistance to be increased owing to the additional frictional and form drag of the bulb. At high speeds, the reduction in wave resistance due to the interference between the wave systems of hull and bulb, if properly located, is more than sufficient to overcome the frictional and form drag of the bulb, and the net result is a reduction in total resistance.
Wigley's principal conclusions were:
(a) The useful speed range of a bulb is generally from about Fn = 0.24 to 0.57.
(b) Unless the lines are extremely hollow, the best position for the bulb is with its center at the bow; that is, with its nose projecting forward of the hull.
(c) The bulb should extend as low as possible, and should be as short longitudinally and as wide laterally as possible, consonant with fairness in the lines of the hull.
(d) The top of the bulb should not approach too near to the water surface.
two of the principal features of ship form which control the resistance are the shapes of the area and load-waterline curves, especially at the forward end. Both of these can be altered materially by the use of a bulb. The area curve can be filled out at the extreme fore end by adding displacement near the forefoot in the shape of a bulb without altering the LWL, although there will be a forward movement of the LCB. Alternatively, without changing the total displacement, the LWL can be made
finer to balance the volume added by the bulb.
To achieve improvements, the bulb must not be treated merely as an addition or appendage, but the whole forebody should be redesigned, a fine load waterline being used with half-angles of entrance 5 to 10 deg less than those of a normal trawler, and with the LCB as far aft as possible. The bulb area should not exceed 5 percent in order to avoid risk of slamming damage.
while some ships are built with sharp stems, often heavily raked, others, designed for similar operating conditions,are built with pronounced bulbous bows and vertical stems. One of the reasons commonly given against the adoption of bulbs is the fear of rough-water effects,
At low speeds the smaller bulb showed the better performance, at high speeds the larger, the changeover occurring between Fn = 0.21 and 0.24.
The wide variation in bulb size was found to have only a small effect on power or speed and on pitching motion in head seas. The wave length LW and the period of encounter had a much greater effect on these characteristics than did bulb size.
No evidence was found that large bulbs should not be used if found desirable for smooth-water performance.
Bulbs have little effect on pitching and if anything are beneficial in reducing such motions. Slamming and resultant hull damage are also feared, though in general there is little evidence that ships with bulbs have suffered any worse in this respect. Out-size bulbs do introduce problems in berthing and anchoring. A problem that has arisen in high-speed ships with bulbs is the occurrence of cavitation on the bulb surface, resulting in erosion and noise. The nose of the bulb should be elliptical rather than circular, and calculations should be made to ensure that the curvature is nowhere sharp enough to cause cavitation. Special attention should be paid to smoothing off weld beads and other roughnesses in this area.
Large bulbs are now commonly fitted to big tankers and bulk carriers running at low Fn values, at which the wave-making resistance is relatively small. Reductions in resistance of approximately 5 percent in full load and 15 percent in the ballast condition have been obtained in model tests. These results are confirmed in full-scale trials. In general about 1 knot increase
in speed in the ballast condition is realized. Such gains are apparently possible on ships with block coefficients around 0.80 and at Froude number values of about 0.18. It is significant that the most substantial improvements are found in the ballast condition when the bulb is near the surface. The draft forward appears to be critical and care should be taken in choosing the ballast operating condition.
For ballast as well as full load condition the optimum bow size increases with increasing Fn. The higher the block coefficient the larger the cylindrical bow should be. The optimum bow size for ballast condition is considerably smaller than for full load condition.
Using these results one often finds that a cylindrical bow has a slight negative effect in ballast especially at lower speeds. The improvements in the required power at the propeller are even a little more pronounced than the improvements in bare hull resistance.
Elliptical bow forms turned out to have remarkably better resistance characteristics. The knuckled elliptical bow form has a
slightly lower resistance values compared to the smooth elliptical bow, the latter having higher building costs.
In merchant ships speed is seldom the dominant consideration, and the proportions and shape of the hull, as a rule, cannot be chosen solely to attain minimum resistance. Nevertheless,lower power and lower fuel costs have an important effect on the profits a ship can earn.
Click here for Online resistance and power calculations
Some containerships are capable of speeds as high as 30 knots. Such ships have stimulated renewed interest in the design of hull forms which can achieve such speeds economically in smooth water and still have good seakeeping qualities and small loss of speed in rough weather. At the other end of the scale are the bulk carriers,such as oil tankers and ore ships. Speed is not so important in such ships, because the minimum cost of transport per ton-mile is achieved by carrying as great
a deadweight as possible in one ship at moderate speeds. Ships have been built with dead weights in excess of 500,000 t, with lengths such that even for a speed of 15 knots the Froude number is as low as 0.15.
Restrictions on the drafts of such ships have increased the beam-draft ratios, and the block coefficients are in the 0.85 region. The efficient design of such ships poses many problems.
The prospective owner usually specifies that the new ship shall carry a certain deadweight at a particular speed, and the designer estimates the probable displacement and principal dimensions. The latter are usually subject to restrictions not associated with resistance and propulsion. Length is expensive in first cost, is limited by docking and navigation restrictions,
while added length increases scantlings, equipment and manning scales. From a resistance point of view, greater length for a given displacement will reduce the wave-making resistance but increase the frictional resistance, so that longer lengths will be beneficial in ships running at high speeds and vice-versa. Longer lengths are also generally beneficial for behavior in
rough seas.
An increase in draft, T, is generally beneficial for resistance, and is a cheap dimension in terms of cost. However, it may be limited by depths of harbors, canals,rivers, and dock sills.
The beam, B, is one of the governing factors in ensuring adequate stability, and a minimum value of B/T is generally necessary on this account. An increase in B will increase the resistance unless it is accompanied by a corresponding reduction in fineness coefficient. In cases of low-speed ships, however, a small reduction in length and a compensating increase in beam, because of the resulting decrease in wetted surface, may result in little or no increase in resistance.
This results in a cheaper ship and also meets the need for increased stability in ships with large superstructures.This idea has been exploited in a number of large tankers.
The minimum wetted surface for a given displacement is also sensitive to the B/T ratio, the optimum value of which is about 2.25 for a block coefficient of 0.80 and about 3.0 at 0.50. However, the penalty for normal departures from these values is not very great. The effects of changes in B/T on wave-making resistance can be studied from model-experiment results.
Generally, stability considerations and limiting drafts usually preclude values below 2.25 for full ships and 2.5 or even more for fine, higher speed ones. While such considerations may be of guidance to naval architects in the choice of dimensions, they must meet many other demands, and will be influenced to a large extent by their knowledge of the particulars of existing successful ships. The process of design is essentially an iterative one, in which the various elements are changed until a proper balance is attained.
Choice of Form Coefficients
power at the trial speed is about 25 percent greater than that at the sustained sea speed under trial conditions. This is in keeping with the general design practice that the service speed should be attained under trial conditions at 80 percent
of the maximum continuous power.
The above relationships are intended as rough guides to the designer and do not take the place of a careful analysis and comparison of alternative designs.
For passenger liners, cross-channel ships and other craft in which high speed is important ,Comparative economic evaluations are essential in these cases.
Economic criterion used is the Required Freight Rate. Impact of variations of fuel costs, interest rates, insurance costs
and construction costs on the Required Freight Rate shall be considered.These procedures are valid and useful when costs (capital and operational) are known as general functions of the primary design parameters.These are, however, most often not known with enough accuracy.
The final decision on length and fullness should not be taken without considering the sea-going qualities of the ship. A short, full ship may well suffer such loss of speed in bad weather as to justify the extra cost of a longer, finer ship. The choice depends on many things, including the ocean conditions on the trade routes in question, particularly the length of the predominant waves and the frequency of their occurrence.
Thus to maintain a weekly service on the North Atlantic in winter, requiring speeds of 28 or 29 knots,the length of express liners cannot well be less than 950 ft .
Excessive fullness also promotes a tendency to bottom damage due to slamming. Flat areas on the bottom forward should be avoided. The floor lines should begin to lift immediately the parallel body ends, so as to give a V-shape which will allow the hull to enter the water smoothly when the ship is pitching .
The wave-making resistance humps occur approximately at values of Fn equal to 0.24, 0.30 and 0.48, and their importance
depends upon the speed and fullness of the ship. The coaster, with a prismatic coefficient CP = 0.83 cannot be driven above Fn = 0.158 without an excessive increase in resistance.
In the trawler, with a finer hull form of =0.57, the lower humps are not very marked, and a Fn value of 0.24 can be reached before the rise in the curve begins. However, speed has great significance in these ships, to get to the fishing grounds quickly and to get home to market afterwards, and they are usually overdriven up to values of Fn = 0.30.
The cross-channel ship, of = 0.58, can be driven to Fn = 0.33 without excessive resistance,for although the is the same as in the trawler, the length is perhaps twice as great, showing the advantage of length in delaying the onset of heavy wave-making.
The destroyer, in which economy in the commercial sense is not paramount, normally has a top speed of Fn = 0.6 or more, well beyond the last hump at about Fn = 0.48.
When the principal dimensions and fullness coefficients have been chosen, the resistance then depends chiefly upon the following elements of ship form:
(a) Distribution of displacement along the length,as typified by the curve of cross-sectional areas and the LCB.
(b) Shape of the LWL, particularly in the fore body.
(c) Shape of the transverse sections, especially near the ends.
(d) Midship-section area coefficient.
(e) Type of stern; i.e., raised counter, cruiser, transom, and so on.
The midship-section coefficient varies with fullness. In merchant ships with block coefficients around 0.80, it may be as high as 0.995. As the fullness decreases and the length of parallel body becomes shorter, it is necessary to ease the Midship section area somewhat to avoid too pronounced shoulders in the lower waterlines.
The choice of the shape of section area and LWL curves depends upon the values of Fn and and will also be influenced by the need to provide adequate stability.
The load waterplane coefficient decreases with decreasing fullness, its value depending also to a considerable extent upon the type of transverse sections.In full ships considerable parallel body can be worked in with advantage, and the entrance can be short, the run being long and fine to minimize separation and form resistance. As decreases, so does parallel body, and the entrance is made longer to reduce the increase in wave-making resistance, the LCB moving aft in consequence.
Most of the reduction is thus accomplished by fining the entrance, the change in the coefficient of the run being much less.
The sectional area curve and load waterline follow a similar pattern. At low Fn values and high prismatic coefficients, both are slightly convex forward and aft. As Fn increases, they become straight and eventually S-shaped with a hollow near the stern. At Fn values of 0.45 and above, the hollow should disappear in the LWL, which should be straight or even slightly convex in destroyers and other high-speed types. In such ships, too, the onset of high wave-making resistance calls for
as long a length as is compatible with the other design requirements.the shape of the midship section was not an important factor in determining residuary resistance.
The principal advantages claimed for such ships are the elimination of wave-making resistance and independence of weather conditions. Volume for volume, the submarine has a greater wetted surface than the ordinary ship, and so
starts off with the handicap of greater frictional resistance.The absence of wave-making resistance therefore does not make itself felt until relatively high Froude numbers are reached, perhaps in excess of Fn = 0.25. Because of cargo-handling problems, most proposals have been for oil or ore-carrying submarines,and these cargoes do not call for high speeds of transport.
Effect of Bulbous Bows on Resistance
At low speeds Wigley found the total resistance to be increased owing to the additional frictional and form drag of the bulb. At high speeds, the reduction in wave resistance due to the interference between the wave systems of hull and bulb, if properly located, is more than sufficient to overcome the frictional and form drag of the bulb, and the net result is a reduction in total resistance.
Wigley's principal conclusions were:
(a) The useful speed range of a bulb is generally from about Fn = 0.24 to 0.57.
(b) Unless the lines are extremely hollow, the best position for the bulb is with its center at the bow; that is, with its nose projecting forward of the hull.
(c) The bulb should extend as low as possible, and should be as short longitudinally and as wide laterally as possible, consonant with fairness in the lines of the hull.
(d) The top of the bulb should not approach too near to the water surface.
two of the principal features of ship form which control the resistance are the shapes of the area and load-waterline curves, especially at the forward end. Both of these can be altered materially by the use of a bulb. The area curve can be filled out at the extreme fore end by adding displacement near the forefoot in the shape of a bulb without altering the LWL, although there will be a forward movement of the LCB. Alternatively, without changing the total displacement, the LWL can be made
finer to balance the volume added by the bulb.
To achieve improvements, the bulb must not be treated merely as an addition or appendage, but the whole forebody should be redesigned, a fine load waterline being used with half-angles of entrance 5 to 10 deg less than those of a normal trawler, and with the LCB as far aft as possible. The bulb area should not exceed 5 percent in order to avoid risk of slamming damage.
while some ships are built with sharp stems, often heavily raked, others, designed for similar operating conditions,are built with pronounced bulbous bows and vertical stems. One of the reasons commonly given against the adoption of bulbs is the fear of rough-water effects,
At low speeds the smaller bulb showed the better performance, at high speeds the larger, the changeover occurring between Fn = 0.21 and 0.24.
The wide variation in bulb size was found to have only a small effect on power or speed and on pitching motion in head seas. The wave length LW and the period of encounter had a much greater effect on these characteristics than did bulb size.
No evidence was found that large bulbs should not be used if found desirable for smooth-water performance.
Bulbs have little effect on pitching and if anything are beneficial in reducing such motions. Slamming and resultant hull damage are also feared, though in general there is little evidence that ships with bulbs have suffered any worse in this respect. Out-size bulbs do introduce problems in berthing and anchoring. A problem that has arisen in high-speed ships with bulbs is the occurrence of cavitation on the bulb surface, resulting in erosion and noise. The nose of the bulb should be elliptical rather than circular, and calculations should be made to ensure that the curvature is nowhere sharp enough to cause cavitation. Special attention should be paid to smoothing off weld beads and other roughnesses in this area.
Large bulbs are now commonly fitted to big tankers and bulk carriers running at low Fn values, at which the wave-making resistance is relatively small. Reductions in resistance of approximately 5 percent in full load and 15 percent in the ballast condition have been obtained in model tests. These results are confirmed in full-scale trials. In general about 1 knot increase
in speed in the ballast condition is realized. Such gains are apparently possible on ships with block coefficients around 0.80 and at Froude number values of about 0.18. It is significant that the most substantial improvements are found in the ballast condition when the bulb is near the surface. The draft forward appears to be critical and care should be taken in choosing the ballast operating condition.
For ballast as well as full load condition the optimum bow size increases with increasing Fn. The higher the block coefficient the larger the cylindrical bow should be. The optimum bow size for ballast condition is considerably smaller than for full load condition.
Using these results one often finds that a cylindrical bow has a slight negative effect in ballast especially at lower speeds. The improvements in the required power at the propeller are even a little more pronounced than the improvements in bare hull resistance.
Elliptical bow forms turned out to have remarkably better resistance characteristics. The knuckled elliptical bow form has a
slightly lower resistance values compared to the smooth elliptical bow, the latter having higher building costs.
