VIEWS: 47 PAGES: 7 POSTED ON: 8/22/2012
Drag calculation short write-up. To be tied in with performance…? Once the configuration, geometry and sizing were set in place, it was necessary to calculate the total drag over the airplane to aid the propulsion team in selecting an engine with an appropriate amount of thrust. A useful measure of the drag of an airplane is the zero-lift drag coefficient, Cd,0. Accurately estimating the value of Cd,0 is vital in the design of any aircraft. The main component of Cd,0 for most aircraft is the skin friction drag. Appendix A shows the calculation of skin friction drag for the current design, arriving at a value of skin friction drag coefficient of 0.0064. The other components of Cd,0 include pressure drag, interference drag and drag due to the interactions between the wing and fuselage and the tail and fuselage. Without wind tunnel testing, it is extremely difficult to accurately gauge the effect of these parameters. Thus, reflecting upon the value of skin friction drag obtained and on comparison of similar aircraft the conservative value of Cd,0 = 0.02 has been used throughout the design of this UAV. Output from MATLAB program Tornado has largely agreed with this approximation. To go in Appendices: SKIN FRICTION DRAG Wings ASSUME: wing can be treated as a flat plate (assumption should hold for a wing of 10% thickness flying at relatively low angles of attack). Need to determine what portion of the airfoil has a laminar boundary layer, and conversely what portion is turbulent. ASSUME: transition to turbulence occurs at Re=5x105 for a flat plate. Thus . Given: Mean chord length = 0.72m, wing span = 5m. At a cruising height of 500ft, For air at STP, ASSUME: air is an ideal gas. Using the temperature-viscosity relationship for air as an ideal gas: We obtain for air at 500ft: From definition of Reynolds number: Therefore from the leading edge to 0.1820m from the leading edge the boundary layer is laminar, and from 0.1820m to the trailing edge at 0.72m from the leading edge the boundary layer is turbulent. Firstly, assuming that the boundary layer is turbulent over the entire airfoil: The skin friction drag coefficient for a turbulent boundary layer is given by: Therefore the total drag due to skin friction over an entire turbulent airfoil is given by: Where: Thus: Secondly, assuming that the boundary layer is turbulent from the leading edge to x = 0.1820m: Therefore the total drag over the turbulent section is given by: Finally, considering the laminar boundary layer section of airfoil: The skin friction drag coefficient for a laminar boundary layer is given by: Therefore the total skin friction drag over the surface of a wing becomes: Over both surfaces of both wings, the total skin friction drag over the wing is given as: Tail The skin friction drag over the tail surfaces can be calculated using the same techniques and assumptions as for the wings, with: Mean chord = 0.5m, tail span = 1.7m. Firstly, assuming that the boundary layer is turbulent over the entire airfoil: Secondly, assuming that the boundary layer is turbulent from the leading edge to x = 0.1820m: Therefore the total drag over the turbulent section is given by: Finally, considering the laminar boundary layer section of airfoil: Therefore the total skin friction drag over the surface of a wing becomes: Across the four tail surfaces: Fuselage The fuselage is treated basically the same way as wings and tail, assuming that the fuselage is a perfect cylinder, and that the skin friction over the cylinder is the same as the skin friction over the cylinder opened out to a flat plate. This assumption is reasonable as the flow is parallel to the surface at all points, and hence the orientation of the surface in this z direction has little effect. With this simplification: Fuselage length = 2.6m, fuselage diameter = 0.4m. Thus, the fuselage span = 2π(0.2) = 1.2566m Firstly, assuming that the boundary layer is turbulent over the entire fuselage: Secondly, assuming that the boundary layer is turbulent from the leading edge to x = 0.1820m: Therefore the total drag over the turbulent section is given by: Finally, considering the laminar boundary layer section of the fuselage: Therefore the total skin friction drag over the surface of the fuselage becomes: Since only the outer surface of the fuselage is wetted by the flow, there is no need to multiply this further. Whole aircraft Thus, the skin friction drag over the whole aircraft is given as: Corrected Value Using the skin friction drag correction factor plots from the lecture series, we can calculate a value of whole aircraft skin friction drag corrected for errors incurred when approximating the surfaces as flat plates: Where Kw = Kt =1.21 for a 10% thick lifting surface, and Kf = 1.21 also for a body surface with length/diameter ratio of 6.5. Thus, the corrected whole aircraft skin friction drag value becomes: The whole aircraft skin friction drag coefficient can be determined from this value using the whole aircraft wetted surface area as a reference: Since cd,0 is a parameter based upon wing area, it is this area of reference for which cd,sf will be most useful. Thus, References Fundamentals of Aerodynamics, Anderson Loftin, LK, Jr.. "Quest for performance: The evolution of modern aircraft” NASA SP- 468 Lecture notes.