5.7 Form (Eddie-Making) Resistance Previously, we made an assumption that the friction resistance coefficient of a ship (or a model) is the same as that of a smooth flat plate with the same length (Re) & wetted surface area; namely, the friction resistance of a ship is the same as that of a flat plate with the same length and wetted surface area. In generally, this assumption is approximately correct. However, a careful investigation has shown that there are differences between the friction resistance of a ship and that of a plate with the same length & wetted surface. Usually, the friction resistance of a curved surface object is greater than that of a flat plate with same length & wetted surface. Their difference is called the form resistance or form drag.

The form drag consists of 3 parts. 1.Eddy-making Resistance; the curvature causes the pressure change along the ship. Due to the viscosity, the pressure change will cause the flow separation from the surface, & generate eddies. Energy is fed into eddies, and the resulting resistance is called eddy-making resistance. Main contribution to the form resistance is made by eddy-making resistance. For a low speed ship, it is important to avoid the abrupt change of the hull in order to minimize the eddy-making resistance.

2. The curvature of a ship (or a model) will change the local velocity along the ship. Since the path along a streamline from bow to stern is longer on a shaped body than on a flat plate, the average velocity along a ship > V. Thus 3 Interaction between viscous & wave-making resistances, which is very complicated. It is a research topic in Marine Hydrodynamic and ship-model test. The increase or decrease of resistance due to the interaction are classified into form drag. Sometimes, some items may be directly classified into wave-making resistance. It is understood now that why the difference between the total resistance coeff. & frictional resistance coeff. is called the residual coefficient,

5.8 Air or Wind Resistance

5.9 Appendage Resistance Usually, the model resistance test gives the resistance of the “naked” hull (without appendages). Appendages, such as bilge keels, rudder and bossings (open shafts and struts), will result in additional resistance, aka appendage resistance. It is usually added to the “naked” hull resistance, about 10 – 15% of the latter as listed in the following table. 1.Appendage resistance of a multiple-screw (propeller) ship is larger that that of a single-screw ship. 2.The upper limit for V/(L 0.5 )= 0.7 seems to be higher. Ship typeSpeed/length ratio Large fast quadruple-screw ships10-16%10-16% Small fast twin-screw ships20-30%17-15%10-15% Small medium V twin-screw ships12-30%10-23% Large medium V twin-screw ships8-14%8-14% All single-screw ships2-5%2-5%

5.10 Computing the naked ‘hull’ resistance according to its model test results The model resistance test follows the Froude # similarity.

Ex. 1 Computation of Resistance & EHP Ship Dimensions 390’ x 54’ x 23’ (L WL x B x T) C B = 0.69, V S = 12 knots, S S = 29,621 ft 2, sail is S.W. Its model L m = 15’, sail in F.W. t = 67.5˚ F, R tm = 4.4 lb at corresponding velocity, find R ts, & EHP.

Ex. 9.1 Computation of Resistance & EHP (see textbook p ) Ship Dimensions 140 x 19 x 8.5 m (L WL x B x T) C B = 0.65, V S = 15 knots, S S = 3,300 m 2, sail is S.W. Its model L m = 4.9 m, measured, sail in F.W. at corresponding velocity of V S. Find R TS and EHP at V S = 15 knots

Problems of predicting the resistance of ships based on model tests (Summary) 1.It is assumed that the frictional resistance coeff. of a ship (or model) is equal to that of a flat plate at the same Re #. However, there is difference between the friction resistance of a ship (curved surface) & the friction resistance of a flat plate is form resistance as described in section 5.7. C R = C T – C F, includes wave-making & form resistances, not only wave resistance. That is why C R is called residue resistance coefficient. 2.It is noted that a model test follows the Froude similarity. The form drag depends on viscosity or Re # and does not obey the Froude Law. Therefore C RS is not exactly equal to C Rm. These problems result in errors in determining ship resistance from its model test.

5.11 Methods of Presenting Model Resistance Results It is desirable that there is a standard method of presenting model resistance data. However, so far it has not been reached. 1.Users want the original data. (speed, resistance, water temperature, method of turbulence stimulation, cross sectional area) The user can convert them to any desired form. 2.The data in the past were not presented in non-dimensional form. Introduced the following are a few methods commonly used in presenting Model Resistance data.

1.C T ~ Re or C T ~ Fr 2. 3.circle K & circle C system, they are non-dimensional.

At a low speed,, is almost independent of. When increase in speed,, increases with Dimensional Form of circle C & circle K

5.12 Relation between Hull Form & Resistance Choice of Ship Dimensions p The owner usually specifies that the new ship shall carry a certain deadweight (How much cargo can be loaded) at a particular speed, and the designer estimates the probable displacement and principle dimensions. Displacement = cargo weight (dead weight) + self weight Length – Cost, scantling, manning, docking, navigations. longer L reduces wave-making resistance at high speed. Draft – increase draft will decrease resistance, reduces scantling, but is restricted by the water depth of harbor or channel & stability. Breadth – important to have adequate stability. Increase in B may decrease L (smaller Fr, smaller wetted surface) thus reduces the cost but results in the increase in wave-making resistance. Also is limited by the width of canals.

Choice of Form Coefficients The most important form coefficient may be the block coeff., or prismatic coeff. A larger C B, results in larger wave-making & form resistance. Block or prismatic coeff. should be reduced as the speed of a ship increases so that in designing a ship there is a limit of fullness to be observed for a given speed. A formula of the type, called the ‘economical’ block coefficient has often been used.

Definition of trial, service, & sustained speed Before an owner receives a newly built or renovated ship, there is a trail sail for the ship. Trial speed is the required speed when the newly built ship takes a trial sail. Service speed is the required speed for the ship is service. Usually a service speed is smaller than the trial speed. Sustained speed lies very close to that at which the resistance coeff. curve begins to rise steeply; i.e., to the speed at which the power begins to increase rapidly than V 3.

5.13 Series Experiments & Model Resistance Data Sheets Series Experiments A series of models is a set of models in which the principal characteristics are changed in a systematic manner. The purposes of having resistance test of a series of models are: 1.A series of tests can be made to ascertain the best form of the ship to give minimum resistance & this would involve tests run with various alterations to some basic form. 2.The data from the tests of series models can be used to estimate the resistance & EHP of a ship

Well-known series models: 1.Taylor’s Standard Series: starting from a single “parent ship” 2.Series 64. For naval ship. 3.Series 60. Began 1948 with ATTC Cooperation and is published in 1963, (TMP Report 1712).

Model Resistance Data Sheet, SNAME. This valuable sheet was issued by SNAME Project 2 of Hydrodynamics Sub-Committee of SNAME. “Model and Expanded Resistance Data Sheets,” available from Society. About 200 ships, their model test results were obtained in various towing tanks and all types of ships were included, which is different from the Series Experiment. The sheet gives: 1.) all principal form coeff., 2.) basic model data 3.) results are presented in

Estimation of EHP from Series Resistance Results The series forms a very suitable basis for making estimate of power (EHP), particularly in the early stage of a design (concept design).

It is important to use the units of variables consistently.