Experimental tests to validate a new slender body theory in steady, incompressible Oseen flow.

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The proposed research is based upon a set of experiments to test a new slender body theory in steady, incompressible Oseen flow.The new theory has been developed over a series of seven publications by the proposer in the leading mathematical science peer-reviewed journals.The theory is useful because it gives us a fundamental understanding into how the lift on a slender body moving in a fluid is generated.These ideas can then be further developed for a wide-range of fluids problems in ship and submarine manoeuvring, missile and rocket guidance, aerodynamics for low aspect-ratio aeroplanes, and hydrodynamics for marine animals.The most significant parameter governing manoeuvring slender bodies is the lift, or side force, on the slender body moving at a steady forward speed due to the fluid flowing around the body. There are also additional contributions due to acceleration and rotation which are included by a linearisation about the steady result. Compressibility of the fluid also affects results, but again the changes in lift force on a slender body are relatively small and this effect can be treated as an additional factor to the incompressible result. The lift force on a slender body moving at steady forward speed is presently evaluated by using the semi-empirical Allen and Perkins viscous cross-flow approach. For example, the US Air Force's (USAF)'s computer code Missile DatCom uses this approach. However, this is geared particularly for bodies of circular cross-section, and the Allen and Perkins approach is difficult to extend for bodies of other general cross-section some of which are known to give improved manoeuvring performance. One exception is slender bodies with elliptical cross-section for which Jorgensen has provided a straightforward extension to the Allen and Perkins approach. A new theory by the proposer has been developed which has two advantages over the Allen and Perkins approach. First, it incorporates the viscous contributory effect within the theory rather than as a semi-empirical add-on. Second, it is easily adaptable to slender bodies with general cross-section.This theory is based upon Oseen flow theory, but as yet no experiments have been specifically performed to test it. Furthermore, existing experiments incorporate variability in the results by presenting them for the lift coefficient which divides over the base area of the slender body. This particularly incorporates unnecessary variability in the results when the base area is very small. Variability in the results has also been created by testing over a range of Mach numbers. Unfortunately, this has meant that existing experiments have proven inconclusive as to whether the new theory is more or less accurate than the Allen and Perkins approach. This proposal presents a definitive experimental test for this new theory. The lift of a series of nine slender bodies with elliptical cross-section placed in a low-speed wind tunnel will be evaluated. All the slender bodies will have the same semi-major axis radius, and so can be compared against the same base line.A graph of the lift curve slope against ellipticity is then plotted (see case for support).The new theory predicts this line to be perfectly straight, whereas the Jorgensen development to Allen and Pekins predicts the line to be curved with a significant bow.The test of the new theory and the comparison of it against the Allen and Perkins method will be measured against how closely experimental results fit the straight line predicted by the new theory as opposed to the bowed line predicted by the Allen and Perkins method.