Ship Resistance CalculationsChapter – 05 (Harvald) Most of the material is from R and P – Harvald Telfer's Method: Consider a family of geometrically similar models Situation 1 1. Keep Froude Number Constant 2. Determine the specific resistance by varying Re Situation 2 1. Keep Re constant 2. Determine the specific resistance by varying Fr (Speed‐ Length ratio) 3. Since Re is constant, Specific Frictional resistance is constant. So change occurs only due to wave making or Most of the material is from R and P ‐ Harvald g y g more generally inertia resistance. 3. All contours of constant speed‐length ratio will be mutually parallel to a base of Re 4. To a base of speed‐length ratio, all contours of Re will be parallel. 5. This principle of parallelismwas brought out by Telfer 6. To make use of this principle as a practical means of extrapolating model specific resistance, it was essential to determine the law of variation of the constant speed length contours with Re. 7. Telfer Proposed the function Most of the material is from R and P ‐ Harvald Most of the material is from R and P – Harvald and Molland et al 8. Here 'a' for total specific resistance depends on the speed‐ length ratio and is constant for constant speed‐length ratio and 'b' depends on the amount of total resistance subject to scale effect. 9. The value of 'b' was found for very fine forms to be the same as that derived fromplank tests. 10. The ship extrapolators will have a slightly greater slope than that of the plank and in general every form of model will have a different extrapolator. 11. The extrapolator for any form can be determined when a number of geometrically similar models are tested and Most of the material is from R and P ‐ Harvald g y analyzed by the methods described. 12. The Figure shows Telfer's Method for a fine form. By using as abscissa the extrapolator will be a straight line Most of the material is from R and P ‐ Harvald 13. The first condition that an extrapolation method has to fulfill i h i h ld bl h i l l b i d i h is that it should enable the experimental results obtained with models of the same ship to various scales to be derived from one another. 14. Therefore by using the results obtained from experiments with a number of geometrically similar models a so called model family, this condition is automatically satisfied. 15. The slope of the extrapolator is well determined in the region covered by the experiments carried out with the model family. However even with reliable results from experiments with a large model family at one's disposal, extrapolation outside the Most of the material is from R and P ‐ Harvald experimental region of the Re remains a risky affair. Results from experiments with a model family Most of the material is from R and P ‐ Harvald 16. The total resistance coefficient is given as function of Re for different models of the ship 17. The above equation gives the total resistance coefficient for the underwater part of the hull of the smooth ship. 18. If the coefficient C TS for the rough ship is wanted, a roughness allowance C A ( in general called the incremental resistance coefficient for model‐ship correlation) has to be added. 19. An air resistance coefficient can also be added if this correction is not included in the C A . Most of the material is from R and P ‐ Harvald 20. The curves for constant Froude numbers are nearly parallel to the line described by which is the the line described by which is the Shoenherr's flat plate friction drag formula. 21 This line can therefore be used as an extrapolator 21. This line can therefore be used as an extrapolator. 22. The resistance of the ship is then determined by where C is the total resistance coefficient for ship where C TS is the total resistance coefficient for ship Most of the material is from R and P ‐ Harvald Problems With Telfer's Method: 1. Even when using a large model family the distance from the model region to the ship region is very large. Minor inaccuracy on the extrapolator can imply a large inaccuracy on the resistance forecast. 2. One of the conditions to be met for obtaining satisfactory results from experiments with model family is complete similarity. This means that the ships model as well as the surroundings have to be similar. 3. When performing experiments with big models in the family, the towing tank boundary will often be at a distance Most of the material is from R and P ‐ Harvald y g y that it can give rise to interfering influence. 4. Usually the wall results in increased model resistance. 5. When testing the small models in the family the flow over a large party of the models can be laminar. If laminar flow occurs along part of the model, the result with be that a resistance is measured which is low compared with those in turbulent flow. 6. To perform experiments with a model family is expensive and time consuming. 7. Some of the largest families have been that of Simon Bolivar model family (Lammeren 1938) and the series in the so‐called Victor ship research program (Lammeren et 1l 1955). In this Most of the material is from R and P ‐ Harvald last family a 21 mmodel model was also includede ITTC Method: 1. The main question discussed in nearly all ITTC has been 1. The main question discussed in nearly all ITTC has been "how to transform the model test result from model to full scale” scale . 2. This method (ITTC Method), is based on Froude's principle and on the ITTC 1957 Model ship correlation line and on the ITTC 1957 Model ship correlation line 3. In 1957, ITTC decided that the line given by the formula be adopted as correlation line adopted as correlation line. 4 Figure below illustrates the method The total resistance 4. Figure below illustrates the method. The total resistance coefficient for the model is determined by the towing test d f th f l Most of the material is from R and P ‐ Harvald and fromthe formula Most of the material is from R and P ‐ Harvald 5. The residuary resistance coefficient for the model is then calculated by C RM = C TM ‐C FM where the frictional coefficient resistance is calculated from 6. Now it is supposed that the residuary resistance coefficient for the ship at the same Froude number as for the model and at the corresponding Re number is C RS = C RM 7. Using ITTC 1957 model‐ship coefficient for a smooth ship can be determined by C TSS = C FS + C RM and C TS = C FS +C RM + C A 8. C A can be taken same for all ships or A Most of the material is from R and P ‐ Harvald Hughes's Method: 1. In Hughe's Method we use g 2. There was a good agreement of this formula with the experiment curve. p 3. Hughes Proposed that the hull resistance as being sumof three parts – See Next Slide being sumof three parts See Next Slide Most of the material is from R and P ‐ Harvald a The friction resistance in two dimensional flow (i e without a. The friction resistance in two‐dimensional flow (i.e. without edge effect) of a plane surface area and the same mean length th h ll as the hull. b. The form resistance, being the excess above (1) that would be i d b h h ll if d l b d f experienced by the hull if deeply submerged as part of a double model. c. The free surface resistance, being the excess of the total resistance of the surface model above that of a deeply submerged hull when part of a double hull Most of the material is from R and P ‐ Harvald Most of the material is from R and P ‐ Harvald 4. This division is only for analytical purposes only; these three resistances cannot be measured separately resistances cannot be measured separately. 5. On the other hand it is a logical one since (1), The sumof (1) + (2) and the total of (1)+(2)+(3) can all exist independently and the total of (1)+(2)+(3) can all exist independently. 6. Hughes meant that there must be a universal law governing the resistance in turbulent flow of all smooth streamlined bodies of resistance in turbulent flow of all smooth streamlined bodies of symmetrical form when towed at zero incidence submerged in a fluid without boundary interference. fluid without boundary interference. 7. Streamlining implies that there is no separation of flow at any point. p 8. Symmetry about two planes at right angles is essential to ensure no lift in any direction when the body is towed in the direction of Most of the material is from R and P ‐ Harvald y y its axis. 9. The law proposed by Hughes was “For a given body, the mean specific resistance is a constant ratio of the specific resistance of a plane surface of infinite aspect ratio at the same Re. The ratio is independent of Re and depends only on the formof the body”. 10. The resistance equation could be written as Total resistance = Base friction resistance + form resistance + free surface resistance. Using the law, this nowbecomes Total Resistance = (Basic friction resistance)* r + free surface resistance where ‘r’ is the resistance ratio and is constant factor for a given hull form or “r = 1+k” where k is the form Most of the material is from R and P ‐ Harvald factor Most of the material is from R and P ‐ Harvald 8. For basic friction resistance coefficient, one can use the formula formula 9. The curve of C F together with the curves of C F *(1+k) for different values of k can be drawn as a function of Re different values of k can be drawn as a function of Re Most of the material is from R and P ‐ Harvald 10. The value of r or k can be determined from the low speed test. The specific resistance from this test is plotted in the diagram, The specific resistance from this test is plotted in the diagram, a resistance curve C T is drawn, and the curve C F (1+k) having tangent common with the C T curve is found (run‐in‐point) tangent common with the C T curve is found (run in point). 11. Thereby k is determined and the C F (1+k) curve can be used as an extrapolator an extrapolator. 12. The free surface resistance can be found from the model tests as the excess of the total resistance above the friction plus form as the excess of the total resistance above the friction plus form resistance. It will be assumed that this scales up according to Froude's Law Froude's Law. 13. A correction C A taking into account the roughness of the hull f b d t k d th t t l i t f th hi Most of the material is from R and P ‐ Harvald surface can be undertaken and the total resistance for the ship can be calculated by 14. With regard to the decisions made at ITTC ( after discussing Hughes Method), most delegates were in favour of adopting a Hughes Method), most delegates were in favour of adopting a single line (the ITTC Model Ship correlation line) owing to the difficulty in estimating the value of the formfactor 'k' difficulty in estimating the value of the formfactor k . 15. Many towing tanks have used Hughes method with good results results,. 16. Often this method is combined with Prohaska’s method. 17 An investigation of the 1+k variation with some of the form 17. An investigation of the 1+k variation with some of the form parameters has been carried out at NPL. 18 Fig shows according to this investigation 1+k may vary with 18. Fig shows, according to this investigation, 1+k may vary with the block coefficient and with the length displacement ratio L/∆ 1/3 Most of the material is from R and P ‐ Harvald L/∆ 1/3 Most of the material is from R and P ‐ Harvald 19. For ships below100m, k is very difficult to determine. p , y 20. Many of these small ships have sharp shoulders and shapes leading to separation and high pressure drag. leading to separation and high pressure drag. 21. Owing to the procedure normally used, the high resistance measured at the model tests will result in high values of the measured at the model tests will result in high values of the formfactor k. 22 Minsaas (1979) gives values for 1+k between 1 2 and 2 1 22. Minsaas (1979) gives values for 1+k between 1.2 and 2.1, the highest being for full forms. It is unrealistic to assume that the highest of these form factors are the real form that the highest of these form factors are the real form factors. Most of the material is from R and P ‐ Harvald 23. In cases where strong vortices are created owing to sharp shoulders and where the model tests have been given a form factor that is much higher than that of a conventional ship of similar dimensions, then some towing tanks discard the form factor assumption and instead treat formdrag in the same way as wave drag. 24. This means that the form drag coefficient is assumed to the same in model and full scale. Most of the material is from R and P ‐ Harvald