Form Factor and Critical Mach Number Estimation for Finite Wings

Abstract

Empirical methods used in conceptual aircraft design for the calculation of form factor drag and critical Mach number typically have been based on two-dimensional profile considerations alone or, at most, limited wing parameters. This paper compares many of these legacy methods. Motivated by the limited wing features modeled in current approaches, surrogate models for form factor and critical Mach number have been built as functions of airfoil thickness and trapezoidal wing parameters. These surrogate models are regressed from the results of a threedimensional potential flow solution coupled to a profile boundary-layer analysis. The surrogates are physics based, yet their simple functional forms make tbem applicable for inclusion in aircraft sizing algorithms for rapid conceptual and preliminary design trade studies. The models capture the increasing influence of tip effects and spanwise flow as the aspect ratio is decreased and sweep is increased. A primary finding is the strongly beneficial effects of reduced aspect ratio on the form drag and critical Mach number of thick wings. AR AR* cNomenclature wing aspect ratio wing aspect ratio transformation for regressions chord length drag coefficient compressibility drag coefficient excrescence drag coefficient skin friction drag coefficient for entire wing total profile drag coefficient for one surface of the wing (upper or lower) skin friction drag coefficient for one surface of a wing section (upper or lower) lift-dependent drag coefficient minimum drag coefficient zero-lift drag coefficient Co = pressure drag increment to the lift-dependent drag coefficient o«»« ~ extemal stores drag coefficient Cf = skin friction drag coefficient for one surface of the wing (upper or lower) Cf = skin friction drag coefficient for one surface of a wing section (upper or lower) CL = lift coefficient i.u,."g" = three-dimensional design lift coefficient Ci^ = two-dimensional design lift coefficient 'Design Ĉ p = pressure coefficient Cp._ = critical pressure coefficient Pmin ~ compressibility corrected minimum pressure coefficient Pmino ~ incompressible minimum pressure coefficient FF = form factor for the wing // = form factor for a wing .section k = Korn equation technology factor (for critical mach number) ¿0 = Kom equation offset from critical Mach number to drag divergence Mach number L = DATCOM fonn factor wing maximum thickness location coefficient M = Mach number M" = critical Mach number MQP = drag divergence Mach nutnber Design = three-dimensional design Mach number ' Wtjesign,,, = two-dimensional design Mach number q = dynatnic pressure Re = Reynolds number RL.S. -Mach number and sweep correction factor for DATCOM foi m factor equation 5ref = wing reference area •Swei = wetted area TR = taper ratio t/c = wing thickness-to-chord ratio 173 174 TAKAHASHIETAL.x,/c Z = ratio of local wing veloeity to freestream veloeity = ehordwise loeation of maximum wing thickness = form faetor Maeh number and sweep correction faetor = gas specific heat ratio = change in drag divergenee Mach ...

Multi-Disciplinary Design of a Rocket Engine Thrust Augmentation Ejector for Endoatmospheric Flight

“…The equivalent flat-plate area is the product of the surface area wetted to the external aerodynamic flow, Swet, and a semi-empirical "form-factor," FF, multiplier which accounts for the blockage induced supervelocities of flow over real wings and bodies. 22,23 Wave drag and base drag comprise two aspects of forces resulting from an integration of the axial projection of surface static pressure fields found over wing and body.…”