So are the statements that Induced Drag decreases as Aspect Ratio increases fundamentally wrong? No, as long as the Planform Area, A, is held constant and the Aspect Ratio is increased by increasing the span and decreasing the chord. Induced Drag = 1 / * * (1 + Sigma)ĪR, Aspect Ratio, vanishes from the equation! For a given Lift and load distribution the Induced Drag is proportional to the Span squared only! Using the definitions of CL, CDI and AR in the equation above and simplifying results in: The amount of lift which a keel or rudder needs to provide is determined by what is required to offset the force of the sails and/or steer the boat. How fast a boat sails depends on the physical lift and drag and the size of the boat, not on non-dimensional coefficients. It’s obvious based on the plots mentioned above or this equation that the higher the AR the lower CDI is for a given CL. Sigma = 0 for an elliptical load distribution, and greater than 0 for other load distribution shapes. Or perhaps from this equation from wing theory agrees with the plots: So where does the common belief that high aspect ratio wings produce less induced drag come from? It probably starts with plots of CL vs CD or CDI for wings of various AR’s which show larger CL and smaller CD/CDI as AR increases. For a keel or rudder it is approximately twice the distance the keel or rudder extends under the hull.ĬL = Lift / : Lift CoefficientĬD = Drag / (0.5 * Density of Water * Speed ^ 2) * A] : Drag CoefficientĬDI = Induced Drag / (0.5 * Density of Water * Speed ^ 2) * A] : Induced Drag CoefficientĪR = S ^ 2 / A : Aspect ratio, the ratio of the span to the average chord. S : Span, for a wing this is the distance from wing tip to wing tip. Induced Drag: Drag increment of a wing due to the longitudinal vorticity shed into the wake as a result of a finite wing producing lift. Now for the longer answer:įor the purposes of this discussion I’ll be talking about wings but remember that a keel or rudder can be considered as a half-wing moving through the water, with the other half of the wing “mirrored” by the hull.
(Added to avoid confusion) Area and therefore aspect ratio are important when total drag including viscous drag, not only induced drag, is considered. The very short answer: Draft of the keel or rudder is critical for induced drag, not the aspect ratio. less drag for the same amount of turning input)”īut is this generally the case for keels and rudders on boats? “the higher aspect ratio rudder is more efficient (i.e. “The aspect ratio is the most important ratio for the lift and drag of a wing.” When the design of keels and rudders is discussed statements are sometimes made which imply that aspect ratio is a critical parameter when consider lift and drag, and that higher aspect ratios are better.
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