More on keel and rudder hydrodynamic forces
Regarding Eric Sponberg's article on rig replacement in a recent issue ("Replacing an older rig is a question of balance," Issue No. 77), I would like to suggest a qualification to the stated desirability of holding 3° to 5° of weather helm, assuming the spade rudder underwater configuration shown in figures 2 and 3 and maximizing velocity made good to weather/speed upwind.
With the vessel sailing hard on the wind, and assuming leeway of 4° to 8°, then 3° to 5° of weather helm could put the spade rudder at an angle of 7° to 13° to the flow of water past the hull. It would seem to me that 0° of rudder would still be providing enough lift while allowing the vessel to round up into the wind should the tiller be released.
In comparing figures 2 and 3 it appears as though the total aerodynamic line has been moved forward somewhat from figure 2 to figure 3 to show a balance of forces, whereas it would seem that rudder force would only move the total hydrodynamic force line, in this case aft, to line up with the total aerodynamic force line, which has no reason to be moved.
Referring to the article that follows by Chuck Husick on keels ("Winged keels," Issue No. 77) the illustration at the top of page 74 compares the cross-sectional views of an airplane wing and a sailboat keel, showing that airplane wings are asymmetrical and sailboat keels are symmetrical. A boat with keel-attached rudder, carrying a small amount of weather helm, say 3° to 5°, does, in effect, cause the keel and rudder in combination to become asymmetrical on either tack, providing beneficial lift at the expense of slight detrimental drag.
Robert Griffiths lives in Orinda, Calif.
Eric Sponberg responds:
In response to Mr. Griffiths, one must remember that force diagrams such as figures 2 and 3 in the article are merely tools to visualize certain circumstances. The force vectors are not meant to be exact but are only approximations of the basic forces on a sailboat. It is impossible to detail all of the forces on a sailing vessel because there are too many unknowns with an infinite variety of combinations for any given circumstance and sailing attitude. Therefore, one cannot expect to derive discrete values from an approximate diagram.
As to the comments regarding figures 2 and 3, we have no way of knowing exactly what angle of attack the spade rudder sees because rudders are situated within the boundary layer of the hull and behind the downwash of the keel. Generally, the true angle of attack nearer the hull is slightly increased from the free stream flow (hull boundary layer effect) while the angle of attack nearer the tip is slightly decreased from the free stream flow (keel downwash effect). The point of figures 2 and 3 is to show that some rudder action causes the overall hydrodynamic forces to balance with the overall aerodynamic forces.
When the boat in figure 2 applies tiller action to become the boat in figure 3, increased rudder force is not the only thing that happens. Many things that influence the motion of the boat and the balance of forces change their values and directions of movement: heel angle, leeway angle, boat speed, apparent wind speed and direction, keel angle of attack, lift and drag, etc. The result is that both the resultant aerodynamic and hydrodynamic forces come into line.
Mr. Griffiths' observation about a rudder attached to the trailing edge of a keel being an approximation of an asymmetric airfoil is valid. One must also observe, however, that such a rudder/keel combination does not necessarily have an ideal asymmetric shape because of the knuckle that is formed at the rudder/keel joint. The airfoil on page 74 has a fair upper surface (lifting side) which is critical to the creation of lift and the prevention of excess drag. The knuckle of a rudder/keel combination generally causes flow to separate prematurely from the rudder/keel airfoil, particularly at larger rudder angles.
On my new open class 60 design, now under construction in South Africa, we solved the problem of this knuckle in the keel/trim tab joint by designing the trim tab to be fair to the keel in the deflected position (see diagram). This eliminates knuckle flow separation and, therefore, a large drag component in typical trim tab configurations. Any drag that results from the section shape being indented when the trim tab is positioned on centerline is negligible because flow eddies are captured in the indentations, the boundary layer remains attached over the eddies and onto the trim tab, and so the keel/trim tab combination remains hydrodynamically smooth.