Abstract
N order to estimate the static stability derivatives of streamlined bodies of revolution with attached stern planes, ' it is useful to have a way of calculating the lift-curve slope of low-aspect-ratio control surfaces taking into account fin-body interaction factors. Dempsey measured the lift and deduced the lift-curve slopes of a body of revolution with stern planes. These measurements were taken for a family of symmetrical stern planes intersecting the axis of the body of revolution. Dempsey found that the stern plane effectiveness can be correlated on the basis of a partial span factor K in the following manner. Let C,, be the lift-curve stope coefficient of a stern plane without the body present and C,, be the effective lift-curve slope coefficient of the stern plane mounted on the body. Let A be the total projected area of the stern plane, extended to the body centerline. Let p be the density of the fluid, U the freestream velocity, and a the angIe of attack of the plane. Then for any force F acting on the plane, the force coefficient slope is defined by Cm =F/ ( ?+AU2a) at a =O. Now suppose that the span of the stern plane is 2b and that d is the maximum diameter of the body. Dempsey computed CLu based on integrating an elliptic lift distribution over the entire span of the stern plane and C, based on integrating the elliptic lift distribution from the stern plane tips inward to the point a distance of Kb from the centerfine of the body. The value of the ratio C,/C,, is then only a function of K. Dempsey finds experimentally that the value of (2b/d)K for each stern plane deviates less than 2% from the average value of 0.4 for the entire family of stern planes. This indicates that the body interference effects on the stern planes causes a defect in the stern plane span of about 2Kb =50.4d. It would be useful to have a method for computing estimates of the interference factor K in order to avoid relying on experimental data to estimate the value of C, /C,, . This Note presents a very simple method for relating the value of K to the bare body axisymmetric momentum boundary-layer thickness.
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