Feature 1 | CAD/CAM Trimming the stern flap equation


Trim tabs and stern wedges are well-known devices used to reduce planing hull drag by providing liſt and altering the running trim. Te full hydrodynamics of these devices are complex, but relatively simple techniques are available to include the effect of these devices in planing hull resistance prediction.


rectangular flaps [Brown 1971]. This test series and corresponding prediction method


T has been cited in many


subsequent technical papers [Savitsky 1976], and is utilised in many planing hull resistance prediction tools (e.g., NavCad ). Te scope of the flap models in the test series are for rectangular plan form flaps with (span-chord) aspect ratios from 1.25 to 5.0 and deflection angles less than 15degs (although the bulk of the data was for deflection angles less than 5degs). In the original source, the prediction


coefficients for flap liſt and drag were based on a linear fit through the data points. The plot (Figure 1) shows the nature of the original fit (“EQN BROWN”), which offered a single line for all flaps regardless of aspect ratio.


he principal prediction method for the effect of stern flaps is based on a model test series of


form of the multiplier, which is based on rectangular plan forms, is:


Multiplier = 2 AR AR+3


As shown in the figure above, the


multiplier greatly improves the precision of the prediction of flap liſt, and thus reasonably allows extrapolation to higher and lower aspect ratios. Since flap drag is directly related to liſt, no change was made to the form of the drag equation [Savitsky 1976]. Te prediction of the longitudinal centre


of flap liſt was also re-evaluated as part of the HydroComp study. Te original prediction algorithm [Brown 1971] recommended that the centre of the flap liſt was 60% of the vessel’s beam forward of the flap. It was deemed that ship beam was not entirely suitable as an independent variable, so the test data was rearranged to determine the center of effort of flap liſt forward of the trailing edge of the flap (XCE) as a function of the flap span. Tis, too, displayed a correlation to aspect


Figure 1: Lift coefficient versus deflection angle (new & original).


ratio, whereby the position of XCE was substantially further forward with low AR flaps (suggesting that low AR flaps would be less effective in producing a trimming moment). Te position of XCE approached one flap span as aspect ratio increased. Flaps with reducing aspect ratio approaching unity, however, displayed an XCE position of many flap spans ahead. Te following plot (Figure 2) demonstrates the new estimation of XCE: Of course, prudent constraints should be


HydroComp has conducted a


re-analysis of this original data to develop an aspect ratio (AR) multiplier to the original equation for liſt coefficient. Tis multiplier is based on a well-known aspect ratio correction for the lift coefficient of ideal foils [Jones 1941]. Te


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applied to the application of the estimation of XCE (e.g., limit to positions aſt of the vessel LCG).


Figure 2: Longitudinal centre of effort (XCE) of flap lift forward of trailing edge of flap (new).


The Naval Architect January 2012 Tis re-analysis of the stern flap test data


• Aspect ratio does affect stern flap performance.


• Flaps of higher aspect ratio (i.e., wider span and shorter chord)


where stern flaps are used.


• Tese same higher aspect ratio flaps also have a center of effort farther aſt, thus


providing a more effective trimming moment.


References Brown, P.W., “An Experimental and Teoretical Study of Planing Surfaces with Trim Flaps”, Davidson Laboratory Report 1463, Stevens Institute of Technology, April 1971. Jones, R.T., “Correction of the Liſting Line


Teory for the Effect of the Chord”, NACA Report 817, July 1941. Savitsky, D. and Brown, P.W., “Procedures


for the Hydrodynamic Evaluation of Planing Hulls in Smooth and Rough Waters”, Marine Technology, Vol. 13, No. 4, October 1976. NA


provide greater lift for the same plan form area.


can be applied to all planing hull resistance prediction that is based on an equilibrium- trim analysis (i.e., the Savitsky “general case”). From this re-analysis, we can clearly conclude that:


• Consideration of aspect ratio should be part of any planing hull drag prediction


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