SHIP RESISTANCE AND PROPULSIONResistance to Ship Motion:Whenever a body moves through a fluid (eg: water or air), there is a force which opposes the motion of the body. This force is known as resistance. This is quite a common definition but do you know what is meant by the term resistance in context of ship motion? Let us see what all is happening when a ship is moving through water.We know that the ship is moving through water as well as through air (some part of ship). So it experiences both the forces due to water as well as air. The water may itself be in motion due to the water currents and air in motion due to the winds. Their magnitudes and directions will be of course different, only the resistance due to water will be considered unless the winds are strong enough.Types of Resistance:The total resistance may have a number of components namely: 1. Wave making resistance, 2. Frictional resistance, 3. Form resistance, 4. Air resistance 5. Appendage resistance. Let us see them briefly first.Wave Making Resistance: Consider a body moving on an undisturbed water surface. The effect of it on water is it will produce a wave system. Generally three different waves are produced namely, stem divergent, transverse divergent, and bow divergent. This wave system arises from the pressure field that is around the ship. The energy possessed by the pressure field is derived from the ship. This energy transfer itself is a force opposing the forward motion is termed as wave making resistance.Frictional Resistance: Whenever a body is moving through a fluid, a thin layer of fluid will stick to the surface of the body and moves along the ship. The change in velocity of the fluid is close to body but it reduces with increase in distance from the body. This region which is subjected to change in velocity is called as boundary layer. The thickness of boundary layer increases from forward to aft. The body experiences a resistance called frictional resistance.Form Resistance:The water particle in the streamline which passes the ship cannot always follow the ships form. Because of this, some water particles in the streamline breaks away and hence eddies are formed. This eddies will absorb energy and hence it causes a resistance to the motion. This resistance is called as form resistance.Air Resistance:Air being a fluid, it will resist the passage of the exposed part of the ship. For example consider the following situation at full speed of:a. No Wind: When there is no wind, the air resistance is considered as 2-4% of the total water resistance.b. Severe Weather Condition: Consider a situation where the weather condition is severe. This may even slow down the ships speed.Appendage Resistance:Appendages are rudder, propeller, shaft brackets, bilge keel, bossing, stabilizers, and so on. The resistance due to these appendages is termed as appendage resistance. The resistance is mostly in the order of say 10% of that of hull.Major Classification:In actual practice the resistance is classified into two: a. Frictional resistance, and b. Residuary resistance. The resistance such as wave making resistance, appendage resistance and form resistance are collectively termed as residuary resistance.The value of frictional resistance Rf depends upon the following factors: Wetted surface area of the ship, Speed of the ship, Degree of roughness of the hull, Length of the ship. The idea of dividing the total resistance into two (ie frictional and residuary) was put forward by Froude. He found that when he observed geometrically similar forms of ships at different speeds, the wave patterns appeared to be similar.

Froude's Law of Comparison There are three important observations given by Froude. They are: 1. For geometrically similar ships, the speed of the ships is found to be directly related with the square root of their lengths (ie) v/l = V/L where, v and l are the speed and length of the ship model, V and L are the speed and length of the ship respectively. This speed is called as corresponding speed.2. For any two geometrically similar ships or between a ship and its model which runs at corresponding speed, their residuary resistance is directly related with the displacement (ie) Rr1 / l3 = Rr2 / L3 where, Rr1 and Rr2 are the residuary resistance of the model and the ship, l, L are the length of the model and the ship respectively.3. Froude gave the formula for frictional resistance as Rf = f S v n Where, f - coefficient depending upon the length of the surface, S - wetted surface area of the ship in m2, v - speed of the ship in m/s, and n = 1.825.The wetted surface area can be given by S = c(l), where c- coefficient mostly = 0.28, - Displacement in tonnes, and l- length of the ship in m.Froude's Tank for Measurement of Resistance The Froude's tank was constructed in 1871. It is used for measuring the total resistance of a geometrically similar model to that of a ship. The tank will be filled with freshwater and the model will be towed with the help of carriages and the resistance records are made by the dynamometer which is connected with the model and will be placed remote from the model. Procedure for Measuring the Resistance of a Model and Calculation of the Ship's Resistance Measure the total resistance of the model by towing the model in the Froude's tank. Now the total resistance will be recorded in the dynamometer. The frictional resistance for the model is calculated by using the formula : Rf model = f S1 v n. This value to be corrected with the density as the model runs at fresh water but practically the ship runs mostly at sea water. If 'x' is the resistance in fresh water then its resistance in seawater having a density (1025kg/m3 ) will be product of the 'x' and 1.025 (t/m3 ). We have earlier discussed that the total resistance can be given by the sum of frictional resistance and the residuary resistance. Hence Residuary resistance of the model is given by: Rr1 = Rt1 - Rf model . From the froude's law Rr1 / l3 = Rr2 / L3. The value of the Residuary resistance of the ship can be calculated (Rr2). Now calculate the frictional resistance of the ship by using the formula: Rf2 = f S2 V n. Now we can calculate the value of the total resistance by using the expression: Rt2 = Rf2 + Rr2.Use of Calculating the Total Resistance The propelling device for the ship must be able to do effective work in order to overcome this resistance. This is taken as effective power as the appendages are not considered. Effective power = Rt x v x 0.5144 in kNm/s. The value 0.5144 is used to convert the speed of the ship from knots to m/s. The use of calculating the Rt is to know how much power is required to overcome the resistance so that the engine power can be chosen accordingly.

Components of Total Resistance:Total resistance RT

Residual resistance RRSkin friction resistance RFO

Form effect on skin friction

Pressure resistance RPFriction resistance RF

Wave resistance RWViscous pressure resistance RPV

Wavemaking resistance RWMWavebreaking resistance RWBViscous resistance RV

Total resistance RT

Hull speedHull speed, sometimes referred to as displacement speed, is a rule of thumb used to provide an approximate maximum efficient speed for a hull. It is only ever an approximation and only applies where the hull is a fairly traditional displacement design. It is usually described as a speed corresponding to a speed-length ratio of between 1.34 and 1.51 depending on which of the limited sources one refers to. In English units, this may be expressed as: v 1.34 x (LWL) where: "LWL" is the length of the waterline in feet, and "v" is the speed of the vessel in knots. The constant may be given as 1.34 to 1.51 knotft, or in metric units, 4.50 to 5.07 kmh1m- (where LWL is measured in metres and v is the speed in km/h).The concept of hull speed is not used in modern naval architecture, where considerations of speed-length ratio and Froude number are considered more helpful. It is still used by amateurs in relation to traditional displacement hulls.Wave Making Resistance begins to increase dramatically in full-formed hulls at a Froude number of about 0.35, which corresponds to a speed-length ratio of slightly less than 1.20. This is due to a rapid increase of wave-making resistance due to the transverse wave train. At a Froude Number of 0.40 (speed-length ratio about 1.35) the wave-making resistance increases further due to the increase of the resistance caused by the divergent wave train which is added to the transverse wave train resistance. This rapid increase in wave-making resistance continues up to a Froude Number of about 0.45 (speed-length ratio about 1.50) and does not reach its maximum until a Froude number of about 0.50 (speed-length ratio about 1.70).This very sharp rise in resistance at around a speed-length ratio of 1.3 to 1.5 probably seemed insurmountable in early sailing ships and so became an apparent barrier. On the other hand, these values change dramatically as the general proportions and shape of the hull are changed. Modern displacement designs that can easily exceed their 'hull speed' without planing include hulls with very fine ends, long hulls with relatively narrow beam and wave piercing designs. These benefits are commonly realised by some canoes, competitive rowing boats, catamarans, fast ferries and other commercial, fishing and military vessels based on such concepts.Since the wave amplitude increases the energy transferred to the wave for a given hull length the wave drag can be very sensitive to the vessel's weight.Froude numberThe Froude number is a dimensionless number defined as the ratio of a characteristic velocity to a gravitational wave velocity. It may equivalently be defined as the ratio of a body's inertia to gravitational forces. In fluid mechanics, the Froude number is used to determine the resistance of an object moving through water, and permits the comparison of objects of different sizes. Named after William Froude, the Froude number is based on the speed/length ratio as defined by him.The Froude number is defined as: Fr = V / c where V is a characteristic velocity , and c is a characteristic water wave propagation velocity. The Froude number is thus analogous to the Mach number. The greater the Froude number, the greater the resistance.Quantifying resistance of floating objects is generally credited to William Froude, who used a series of scale models to measure the resistance each model offered when towed at a given speed. Froude's observations led him to derive the Wave-Line Theory which first described the resistance of a shape as being a function of the waves caused by varying pressures around the hull as it moves through the water. The naval constructor Ferdinand Reech had put forward the concept in 1832 but had not demonstrated how it could be applied to practical problems in ship resistance. Speed/length ratio was originally defined by Froude in his Law of Comparison in 1868 in dimensional terms as:Speed Length Ratio = V / (LWL) where: V = speed in knots and LWL = length of waterline in feet. The term was converted into non-dimensional terms and was given Froude's name in recognition of the work he did. In France, it is sometimes called ReechFroude number after Ferdinand Reech.

Definitions of the Froude number in different applicationsShip hydrodynamicsFor a ship, the Froude number is defined as: Fr = V / (gL) where V is the velocity of the ship (in m/s), g is the acceleration due to gravity (9.81 m/s^2), and L is the length of the ship at the water line level (in m), or L in some notations. It is an important parameter with respect to the ship's drag, or resistance, including the wave making resistance.Shallow water wavesFor shallow water waves, like for instance tidal waves and the hydraulic jump, the characteristic velocity V is the average flow velocity, averaged over the cross-section perpendicular to the flow direction. The wave velocity, c, is equal to the square root of gravitational acceleration g, times cross-sectional area A, divided by free-surface width B:so the Froude number in shallow water is: Fr = V / (g (A/B)) where c = (g (A/B)) For rectangular cross-sections with uniform depth d, the Froude number can be simplified to:Fr = V / (gd)For Fr < 1 the flow is called a subcritical flow, further for Fr > 1 the flow is characterised as supercritical flow. When Fr1 the flow is denoted as critical flow.An alternate definition used in fluid mechanics is where each of the terms on the right have been squared. This form is the reciprocal of the Richardson number.Densimetric Froude numberWhen used in the context of the Boussinesq approximation the densimetric Froude number is defined as where g' is the reduced gravity: The densimetric Froude number is usually preferred by modellers who wish to non-dimensionalize a speed preference to the Richardson number which is more commonly encountered when considering stratified shear layers. For example, the leading edge of a gravity current moves with a front Froude number of about unity.The Froude number is used to compare the wave making resistance between bodies of various sizes and shapes. In free-surface flow, the nature of the flow (supercritical or subcritical) depends upon whether the Froude number is greater than or less than unity.

Heavy Boats, Light Boats, and Hull SpeedA boat displaces its own weight in water. When the boat is moving, it must push that much water out of the way as it goes forward. Since a heavy boat has to push more water out of the way, it makes bigger waves. (As a boat moves faster it has to push aside more water in less time, so that makes the waves bigger too.) Each boat creates a bow wave and a stern wave. When a boat reaches "hull speed" the bow and stern waves coincide to make one huge wave system. A heavy boat gets trapped in its own wave system. (For a 20 foot boat, hull speed is about 6 knots. For a 30 foot boat, hull speed is about 7.3 knots.) The best example of this is a tugboat. Tugboats are very heavy, since they have huge engines for shoving ships around; and when they are not shoving a ship, they are racing as fast as they can to the next job. That's why you see them with a huge bow wave, a huge stern wave, and a deep wave trough in between. In spite of their enormous horsepower, they can't break loose from the trap of their own wave system. They dig a big hole in the water, and can't climb out of it. A light displacement boat such as a dinghy, a ULDB (Ultra-light displacement boat), or a multihull doesn't have so much water to move out of the way - so they make smaller waves. When they reach the speed that would be hull speed for a heavy boat the wave system is not big enough to trap them. They are able to exceed the "speed limit" where bow and stern waves coincide. A planing hull actually climbs up its own bow wave and is lifted partially out of the water. Obviously ocean waves affect a light boat more strongly, since the weight of the wave is bigger compared to the weight of the boat. Consequently light boats surf more readily; but are often slowed down more when going against the waves. The upwind loss is diminished though, because light boats tend to be narrower and more maneuverable. Wave making resistanceWave making resistance is a form of drag that affects surface watercraft, such as boats and ships, and reflects the energy required to push the water out of the way of the hull. This energy goes into creating the wake.For small displacement hulls, such as sailboats or rowboats, wave making resistance is the major source of drag. The unique properties of deepwater waves (where the water depth is deeper than half the wavelength) mean that the wave making resistance is very dependent upon the hulls interaction with the wake.The propagation speed of deepwater waves is proportional to the square root of the wave length of the generated waves, and the wavelength of a boat's wake is based on its waterline length so: there is a direct relationship between the waterline length (and thus wave propagation speed) and the rate at which drag increases.A simple way of considering wave-making resistance is to look at the hull in relation to its wake. At speeds lower than the wave propagation speed, the wave rapidly dissipates. As the hull approaches the wave propagation speed, however, the wave at the bow begins to build up faster than it can dissipate, and so it grows in amplitude. Since the water is not able to "get out of the way of the hull fast enough", the hull, in essence, has to climb over or push through the bow wave. This results in an exponential increase in resistance with increasing speed. To calculate the speed of wave propagation, the following formula is used: Plugging in the appropriate value for gravity and solving yields the equation: Or, in metric units: These values, 1.34 and 2.5, are often used in the hull speed rule of thumb used to compare potential speeds of displacement hulls, and this relationship is also fundamental to the Froude number, used in the comparison of different scales of watercraft.

When the vessel exceeds a speed/length ratio of 0.94, it starts to outrun most of its bow wave, the hull actually settles slightly in the water as it is now only supported by two wave peaks. As the vessel exceeds a speed/length ratio of 1.34, the hull speed, the wavelength is now longer than the hull, and the stern is no longer supported by the wake, causing the stern to squat, and the bow rise. The hull is now starting to climb its own bow wave, and resistance begins to increase at a very high rate. While it is possible to drive a displacement hull faster than a speed/length ratio of 1.34, it is prohibitively expensive to do so. Most large vessels operate at speed/length ratios well below that level, at speed/length ratios of under 1.0.Ways of reducing wave making resistanceSince wave making resistance is based on the energy required to push the water out of the way of the hull, there are a number of ways that this can be minimized.a. Reduced displacementReducing the displacement of the craft, by eliminating excess weight, is the most straightforward way to reduce the wave making drag. Another way is to shape the hull so as to generate lift as it moves through the water. Semi-displacement hulls and planing hulls do this, and they are able to break through the hull speed barrier and transition into a realm where drag increases at a much lower rate. The downside of this is that planing is only practical on smaller vessels, with high power to weight ratios, such as motor boats. It is not a practical solution for a large vessel such as a supertanker.b. Fine entryA hull with a blunt bow has to push the water away very quickly to pass through, and this high acceleration requires large amounts of energy. By using a fine bow, with a sharper angle that pushes the water out of the way more gradually, the amount of energy required to displace the water will be less, even though the same total amount of water will be displaced. A modern variation is the wave piercing design.c. Bulbous bowA special type of bow, called a bulbous bow, is often used on large motor vessels to reduce wave making drag. The bulb alters the waves generated by the hull, but due to its very limited range of effect, is only useful on large motor vessels operating at constant speeds.d. Semi-displacement and planing hullsSince semi-displacement and planing hulls generate a significant amount of lift in operation, they are capable of breaking the barrier of the wave propagation speed and operating in realms of much lower drag, but to do this they must be capable of first pushing past that speed, which requires significant power. Once the hull gets over the hump of the bow wave, the rate of increase of the wave drag will start to reduce significantly.

A graph showing resistance/weight ratio as a function of speed/length ratio for displacement, semi-displacement, and planing hullsA qualitative interpretation of the wave resistance plot is that a displacement hull resonates with a wave that has a crest near its bow and a trough near its stern, because the water is pushed away at the bow and pulled back at the stern. A planing hull simply pushed down on the water under it, so it resonates with a wave that has a trough under it, which has about twice the length and therefore four times the speed.Ship resistance and propulsionShip resistance is defined as the force required to tow the ship in calm water at a constant velocity. Resistance is measured so as to calculate the power of the engine. The resistance determines the thrust required to be produced by the propulsion device. In other words, it is the force required to pull the ship in calm water.A ship must be designed to move efficiently through the water with a minimum of external force. For thousands of years ship designers and builders of sailing vessels used rules of thumb based on the midship-section area to size the sails for a given vessel. The hull form and sail plan for the clipper ships, for, example evolved from experience, not from theory. It was not until the advent of steam power and the construction of large iron ships in the mid-19th century that it became clear to ship owners and builders that a more rigorous approach was needed.A body in water which is stationary with respect to water, experiences only hydrostatic pressure. Hydrostatic pressure always acts to oppose the weight of the body. If the body is in motion, then there are also hydrodynamic pressures that act on the body. If the body is in non-viscous fluid, fully submerged and far from the water surface, then the body experiences no resistance. This is the dAlemberts paradox. This happens because the pressure forces at the fore end of the ship opposing the motion are equal in magnitude, opposite in direction as the pressure forces at the aft end of the ship.In a viscous fluid, a boundary layer is formed. This causes a net drag due to skin friction. Further, because the ideal pressure now acts on the boundary layer, as opposed to the ship, and the boundary layer grows along the length of the ship, the net opposing forces are greater than the net supporting forces. This further adds to the resistance.A ship moving over the surface of undisturbed water sets up waves emanating from the bow and stern of the ship. The waves created by the ship consist of divergent and transverse waves. The divergent wave are observed as the wake of a ship with a series of diagonal or oblique crests moving outwardly from the point of disturbance. These waves were first studies by Lord Kelvin, who found that regardless to the speed of the ship always make a 19 degree angle to the ship. These waves produce little in the way of resistance against the ships forward motion. Transverse waves appear as troughs and crests along the length of a ship and constitute the majority of the wave-making resistance of a ship. The energy associated with the transverse wave system travels at one half the phase velocity or velocity of propagation of the waves. The prime mover of the vessel must put additional energy into the system in order to make up for this difference. The relationship between the ships velocity and that of the transverse waves can be found by equating the wave celerity and the ships velocity.

Calculation of Resistance:

To move a ship, it is first necessary to overcome resistance, i.e. the force working against its propulsion. The calculation of this resistance R plays a significant role in the selection of the correct propeller and in the subsequent choice of main engine.

A ships resistance is particularly influenced by its speed, displacement, and hull form. The total resistance RT, consists of many source- resistances R which can be divided into three main groups, viz.:

1) Frictional resistance2) Residual resistance3) Air resistance

The influence of frictional and residual resistances depends on how much of the hull is below the waterline, while the influence of air resistance depends on how much of the ship is above the waterline. In view of this, air resistance will have a certain effect on container ships which carry a large number of containers on the deck.

Water with a speed of V and a density of has a dynamic pressure of: V 2 (Bernoullis law)

Thus, if water is being completely stopped by a body, the water will react on the surface of the body with the dynamic pressure, resulting in a dynamic force on the body. This relationship is used as a basis when calculating or measuring the source-resistances R of a ships hull, by means of dimensionless resistance coefficients C. Thus, C is related to the reference force K, defined as the force which the dynamic pressure of water with the ships speed V exerts on a surface which is equal to the hulls wetted area AS. The rudders surface is also included in the wetted area. The general data for resistance calculations is thus:

Reference force: K = V 2 AS and source resistances: R = C K

On the basis of many experimental tank tests, and with the help of pertaining dimensionless hull parameters, methods have been established for calculating all the necessary resistance coefficients C and, thus, the pertaining source-resistances R. In practice, the calculation of a particular ships resistance can be verified by testing a model of the relevant ship in a towing tank.

Frictional resistance RF

The frictional resistance RF of the hull depends on the size of the hulls wetted area AS, and on the specific frictional resistance coefficient CF. The friction increases with fouling of the hull, i.e. by the growth of, algae, sea grass and barnacles. An attempt to avoid fouling is made by the use of antifouling hull paints to prevent the hull from becoming longhaired, i.e. these paints reduce the possibility of the hull becoming fouled by living organisms. The paints containing TBT (tributyltin) as their principal biocide, which is very toxic, have dominated the market for decades, but the IMO ban of TBT for new applications from 1 January, 2003, and a full ban from 1 January, 2008, may involve the use of new (and maybe not as effective) alternatives, probably copper based antifouling paints.

When the ship is propelled through the water, the frictional resistance increases at the rate that is virtually equal to the square of the vessels speed. Frictional resistance represents a considerable part of the ships resistance, often some 70-90% of the ships total resistance for low-speed ships (bulk carriers and tankers), and sometimes less than 40% for high-speed ships (cruise liners and passenger ships). The frictional resistance is found as follows: RF = CF K

Residual resistance RR

Residual resistance RR comprises wave resistance and eddy resistance.

Wave resistance refers to the energy loss caused by waves created by the vessel during its propulsion through the water, while eddy resistance refers to the loss caused by flow separation which creates eddies, particularly at the aft end of the ship. Wave resistance at low speeds is proportional to the square of the speed, but increases much faster at higher speeds. In principle, this means that a speed barrier is imposed, so that a further increase of the ships propulsion power will not result in a higher speed as all the power will be converted into wave energy. The residual resistance normally represents 8-25% of the total resistance for low-speed ships, and up to 40-60% for high-speed ships. Incidentally, shallow waters can also have great influence on the residual resistance, as the displaced water under the ship will have greater difficulty in moving aftwards.

The residual resistance is found as follows: RR = CR K where, CR is specific residual resistance coefficient.

Air resistance RA

In calm weather, air resistance is, in principle, proportional to the square of the ships speed, and proportional to the cross-sectional area of the ship above the waterline. Air resistance normally represents about 2% of the total resistance. For container ships in head wind, the air resistance can be as much as 10%.

The air resistance can, similar to the foregoing resistances, be expressed as RA = CA K, but is sometimes based on 90% of the dynamic pressure of air with a speed of V, ie.:RA = 0.90 air V 2 Aair where, air is the density of the air, and Aair is the cross-sectional area of the vessel above the water.

Towing resistance RT and effective (towing) power PE

The ships total towing resistance RT is thus found as: RT = RF + RR + RAThe corresponding effective (towing) power, PE, necessary to move the ship through the water, i.e. to tow the ship at the speed V, is then: PE = V RTThe power delivered to the propeller, in order to move the ship at speed V is, however, some what larger. This is due to the flow conditions around the propeller and the propeller efficiency itself.

Total ship resistance in general

When dividing the residual resistance into wave and eddy resistance, as earlier described, the distribution of the total ship towing resistance RT could also be stated as:Total ship towing resistance RT = RF + RW + RE + RA.During the operation of the ship, the paint film on the hull will break down. Erosion will start, and marine plants and barnacles, etc. will grow on the surface of the hull. Bad weather, perhaps in connection with an inappropriate distribution of the cargo, can be a reason for buckled bottom plates. The hull has been fouled and will no longer have a technically smooth surface, which means that the frictional resistance will be greater. It must also be considered that the propeller surface can become rough and fouled. The total resistance, caused by fouling, may increase by 25-50% throughout the lifetime of a ship. Experience shows that hull fouling with barnacles and tube worms may cause an increase in drag (ship resistance) of up to 40%, with a drastic reduction of the ship speed as the consequence. Furthermore, in general for every 25 m (25/1000 mm) increase of the average hull roughness, the result will be a power increase of 2-3%, or a ship speed reduction of about 1%.

Resistance will also increase because of sea, wind and current. The resistance when navigating in head on sea could, in general, increase by as much as 50-100% of the total ship resistance in calm weather. The larger the ship, the less the relative increase of resistance due to the sea. On the other hand, the frictional resistance of the large, full bodied ships will very easily be changed in the course of time because of fouling. In practice, the increase of resistance caused by heavy weather depends on the current, the wind, as well as the wave size, where the latter factor may have great influence. Thus, if the wave size is relatively high, the ship speed will be somewhat reduced even when sailing in fair seas. In principle, the increased resistance caused by heavy weather could be related to:a) wind and current against, andb) heavy waves, but in practice it will be difficult to distinguish between these factors.

How to Calculate Total Resistance to the Motion of a Ship:Some new coefficients of resistance are: Ct for total resistance Cf for frictional resistance Cr for the residuary resistanceThe Reynold's NumberConsider a flat smooth surface such as a plate moving through a viscous fluid. Because of the motion some fluid near the plate travels with it. After some distance from the plate, the fluid has no motion, only the plate along with the layer travels. This layer which is moving along with the plate is called as boundary layer or frictional wake. The movement of the fluid in the wake takes two forms. One assumption is made here: "The fluid next to the surface has no motion relative to it, but is carried with it". The two forms being either laminar or turbulent.Laminar means the fluid travels in a series of layer in-between the wake without mixing. For example: the movement of oil is laminar.Next is turbulent which means there will be intermixing of fluid in between the wake because of the eddies. For example: the movement of water is turbulent.The type of flow depends upon the inertia forces and the viscous forces. The ratio between these two forces is known as the Reynolds number.Reynolds number Rn = vl/, wherev - is the speed in m/s,l - is the length of the surface in m, - is the co efficient of kinematic viscosity of the fluid in m2/ sec.Here the value of the depends upon the temperature ( deg Celsius ) . The values of the are expressed in terms of cst, (ie) centistokes. for seawater = 1.190 cst = 1.190 x 10-6 m2 /sec, for fresh water = 1.140 cst = 1.140 x 10-6 m2 /sec.The co-efficient of frictional resistanceThe coefficient of frictional resistance can be given by the formula:Cf= (0.075)/(logRn- 2)2where, Rnis the Reynold's number.Also Cf = Rf / (0.5 S v2 )This method has been given by the ITTC (INTERNATIONAL TANK TOWING CONFERENCE).The procedurea. Calculate the value of the Reynold's number Rn by using the formula for the model and take this as Rn ship.b. Calculate the value of the co efficient of frictional resistance using the formula Cf model = (0.075)/(logRn model - 2)2 .c. Now find the value of the total resistance from the tank towing experiment for the model as Rt modeld. Now calculate the co efficient of the total resistance Ct model = Rt model /( 0.5 Smodel vmodel2 ) where Smodel is the wetted surface area of the model and v is the speed of the model in m/s.e. Now we can calculate the coefficient of the residuary resistance by using the formula Cr = Ct model - Cf model (since we have discussed that total resistance is equal to the sum of the two resistances)f. The value of the coefficient of the residuary resistance is the same for the ship and its model. (ie) Cr model = Cr ship.g. Now we have calculated all the co-effecients related to the ship and one value related to ship.h. Now calculate the value of the Reynolds number for the ship and take it as Rn ship .i. Calculate the value of the co-efficient of frictional resistance using the formula Cf ship = (0.075)/(logRn ship - 2)2 .j. Now calculate the value of the co efficient of the total resistance using the formula Ct ship = Cf ship + Cr shipk. The formula for the co efficient of the total resistance is given by: Ct ship = Rt ship /(0.5 Sship vship2 )l. With the above formula the value of the total resistance can be calculated.m. After calculating the total resistance the value of the effective power can be given by the formula: Effective power = Rt ship x Vship where Rtship is the total resistance offered by the ship in N, and Vship is the speed of the ship in m/s.In this way we shall determine the resistance of the ship and hence the effective power.Resistance and Propulsion Calculation in Ship Design

Brake Horse Power (BHP)- Power output at the shaft coming out of the engine before the reduction gears

Shaft Horse Power (SHP)- Power output after the reduction gears- SHP = BHP - losses in reduction gear

Delivered Horse Power (DHP)- Power delivered to the propeller- DHP = SHP losses in shafting, shaft bearings and seals

Thrust Horse Power (THP)- Power created by the screw/propeller- THP = DHP Propeller losses

Effective Horse Power (EHP) -The power required to move the ship hull at a given speed in the absence of propeller actionEHPcan be determined from thetowing tank experiments at the various speeds of the model ship.EHP of the model shipis converted into EHP of the full scale ship by Froudes Law.

Naval architect when designing a ship has to perform resistance and propulsion calculation. This is done using statistical methods which are available from various data released by a number of ship model basins around the world. There are various power prediction methods available but naval architects have to determine or choose one of them based on the similarities in hull forms of the designed ship and the model data.

For large ships, the power prediction method may not be enough. To better predict the resistance and propulsion characteristics of the designed ship, model has to be carried out.

After performing the resistance calculation, the next step is adding the losses from the effective horse power obtained to predict the delivered horse power, the shaft horsepower and the brake horse power of the main engine of the designed ship. This is also known as forward calculation. The bhp obtained in this calculation might slightly be different from the available engine on the market. Therefore, after selecting the main engine, usually based on the brochure data from the marine diesel engine manufacturer, the propulsion calculation will be continued at afterward direction to the propelling device or themarine propeller.

Here, the brake horse power of the real engine will be reduced with the frictional losses along the shaft bearings and hull forms to obtain what is called effective horse power curve of the resistance calculation and the reduction of losses from the real main engine. When naval architects delineate these curves they will be able to check the resistance and power of the designed ship.

If you are designing a propeller, the power of the main propulsion machinery must not be 100% MCR (Maximum Continuous Rating). The rate that naval architects or propeller designers must choose is the normal continuous rating which is around 80% of the MCR. The easiest way to find is by reading the engine's performance graph which is the work of the engine at the most efficient fuel consumption. This is chosen to prevent the engine from broken down. Naval architects must do propeller design based on the engine brochure supplied by the manufacturer, on the most efficient rating of the curve on power - speed and specific fuel oil consumption of the marine diesel engine.

After determining the main engine and the propulsive efficiency of the designed ship, the next calculation is determining the QPC or Quasi Propulsive Coefficient which can be obtained by using Emerson formula. The design of the propeller can then be done if speed of advance of the ship VAand the value of Bphas been obtained.

The propeller designer must also perform cavitation calculation usually using Burril Cavitation Chart, and propeller blade strength calculation usually using D.W. Taylor method to ensure that the propeller is safe and reliable in performing its duties during the operation of the ship.

The last step in the design of propeller is drawing.

Resistance and propulsion calculation of a ship is now easier to be performed due to the availability of various software on the market. But it is advisable fornaval architectsand propeller designers to understand the whole process of manual design procedures which is the concept or philosophy of ship design that has supported the art and science of naval architecture for hundreds of years.

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