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Figure 1 shows the upright drag, plotted against boat speed, for the model test and the four CFD codes. The canoe body results show close agreement at low speeds and a significant under-prediction by CFD of drag at high speeds. The CFD results are consistent among themselves. The trending of drag vs speed is very similar to that from the tow tank test. At higher speeds the boat is transitioning into planing, where the weight of the boat is supported more by dynamic lift and less by buoyancy. The water flow characteristics are entirely different from those at lower speeds. This places a greater challenge on the computa- tional methods.


The appended results show significant disagreement. Star-CCM+ and FINE/Marine results compare favourably with tank tests, while FlowLogic under-predicts and Open- FOAM greatly over-predicts. (OpenFOAM was used with a simplified mesh on the foils to meet computational time constraints.) In general, there is a consistent pattern when comparing the upright resistance for tank test and CFD. A correlation can be established between the two. This should lend some confidence to those using these tools. Also it should be noted that the apparent discrepancy occurs at very high speeds. Although some high-performance contemporary boats will attain those speeds in certain conditions, handicappers are more interested in performance at lower speeds where most racing occurs. It is useful to express the heeled results as the ratio of heeled to upright drag plot- ted against boat speed. Figure 2 shows this ratio for the 25° heel tests at zero leeway. For a boat with a conventional keel this does not represent a realistic sailing condi- tion. Leeway is required to generate a hydrodynamic side force to balance the aerodynamic side force that is heeling the boat. Nevertheless, this condition is quite valid for analysing the effects on drag of hull shape. (And for those boats that have rotating appendages or other ways of gen- erating lift, leeway is not necessarily required.) Star-CCM+ is very close to the tank data in both value and trending. In general, FINE/Marine is close in value and FlowLogic close in trending. All four data sources show an increase in heeled drag ratio with speed. OpenFOAM displays the opposite trend.


Creating lift, and doing so efficiently, are critical to sailing yacht performance. Figure 3 shows the curves of lift vs leeway at two representative conditions: 15° heel at a Froude Number (Fn) of 0.35 and 25° at a Fn of 0.5. (The Froude Number is a non-dimensional representation of speed for a given size of boat. It permits compar- isons between boats of different sizes. A Fn of 0.35 and a heel angle of 15° can repre- sent an upwind sailing condition in a medium to strong wind. Few boats, if any, can sail upwind at a Fn of 0.5. However, that Fn with a heel angle of 25° can repre- sent high-speed reaching.)


At 15° there is close agreement between 48 SEAHORSE


1


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  


  


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CFD and tank. The agreement breaks down at negative leeway angles, but that situation is unlikely ever to occur in real life. The lift slope, how much lift is gener- ated per degree of leeway, is important. The tank test data curve for 15° has the greatest lift slope. FlowLogic is quite close at positive leeway angles while the other CFD methods develop less lift with leeway. At 25° of heel the lift slopes are all more similar but there is vertical separation between the curves indicating that the CFD predicts less lift. The exception is FlowLogic which has a higher lift slope which results in closer results with the tank test at the higher leeway angles where a conventionally keeled boat would sail. Induced drag is the ‘cost’ of generating lift. Great effort goes into designing lifting surfaces, whether wings with tip winglets on commercial aircraft or keel/rudder combinations on sailboats, with a goal of minimising induced drag. The less the induced drag for a given lift, the more effi- cient the system. For the purposes of com- parison and analysis, it is convenient to express induced drag as an effective draft (span for an aeroplane wing.) The greater the effective draft, for a fixed physical draft, the less the induced drag. Figure 4 shows effective draft vs boat speed for both 15 and 25° of heel. The tank data illustrates familiar trends: the reduction in effective draft for both speed and heel. A moving boat generates its own


             


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 


  


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wave system. At higher speeds that system will have a trough amidships, in the vicinity of the keel. This is particularly true for heavy boats. That trough, or depression of the free surface, results in less physical draft for the keel, therefore more induced drag, and consequently less effective draft. Figure 4 shows the drop for the tank data from 0.87 to 0.69 at 15° heel, and from 0.70 to 0.54 at 25°.


As the boat heels a conventional keel rotates towards the water surface, and the lift on the keel starts to have a vertical component that does nothing to balance the rig’s side force. In other words, the side force generated by the keel is less while induced drag is essentially unchanged. The same drag for less side force translates into a smaller effective draft. Figure 4 shows a drop at a speed of 2.4m/s from about 0.87 at 15° heel to 0.70 at 25°. At the higher speed the drop is from 0.69 to 0.54. Looking again at Figure 4 it is apparent that at the lower speed for both heel angles the CFD results are under-predicting the effective span (over-predicting the induced drag for a given amount of lift.) The predictions are much closer at the higher boat speed. This discrepancy is both troubling and interesting and worthy of further investigation. Among the codes, OpenFOAM is the furthest from the tank data, likely the result of the coarser appendage meshing mentioned earlier. Star-CCM+ and FINE/Marine are closer


     


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