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Paper Number 02 Feb 2016 draft status Aerodynamic and Artistic Study of the German Jets J. Philip Barnes Pelican Aero Group For more information, visit www.HowFliesTheAlbatross.com INTRODUCTION In April 1937, the world’s first turbojets independently made their first runs in Britain and Germany (1). Just four days before the outbreak of WWII, the world’s first jet aircraft took flight (2). By the last year of the war, the Germans were perhaps five years ahead of the allies in aerodynamic technology. At the time of this article, some 65-years on, the conceptual and real designs of the early “German Jets” continue capturing our imagination, as evidenced by widespread literature and artwork thereof. Our presentation, after reviewing some fundamental aerodynamic principles, introduces a computationally- efficient method for aerodynamic forces and moments. We then apply the method to study the top-level Messerschmitt 262 and Jumo 004 aerodynamics of seven German jets, each noted for its unique configuration. Also, renowned computer-graphic The rocket-powered Me 163 was test flown beyond its artists Mario Merino and Gery Gueville share some of critical speed by pilot Heini Dittmar, to Mach 0.84 where their work herein copyright-free. Thus our title: it exhibited instability about all three axes, in part “Aerodynamic and Artistic Study of the German Jets.” because the forebody, in effect a low-aspect-ratio wing, develops lift and side force coefficients which are unaffected by Mach number (per Robert T. Jones), whereas a fin with a relatively “thick” airfoil suffers a reduction of lift coefficient (or side force coefficient) above its critical transonic Mach number. In addition, just as the wing is immersed in downwash due to forebody lift, the fin is immersed in sidewash due to forebody side forces. For both surfaces, such “downwash” degrades aerodynamic effectiveness. Although the fin has higher aspect ratio than the forebody and enjoys an “end-plate” benefit in its attachment to the afterbody, the forebody and fin of the Me 163 are in close competition with nearly equal and opposite effects on yaw stability. Although an isolated planar wing is marginally stable in yaw, Albert Betz showed that such depends on lift. For twisted wings, we interpret this to mean “tip-local” lift. But Blohm und Voss P.209 at high speed, both lift coefficient and isolated-wing yaw stability vanish. Thus misbehaved the Me 163. THE FIRST JETS Although the Allied aircraft Gloster Meteor entered operational service just days before the Me 262, the Me 262 was the world’s first jet aircraft to be used in aerial combat (3). Fortunately for the Allies, the contribution of the Me 262 to the German war effort was delayed by Hitler’s insistence on its conversion into a fighter-bomber to hold off the coming Allied invasion. Nevertheless, the Me 262 took its toll on Allied bombers in the last months of the war. Its wing was swept to manage the center of gravity (c.g.). Not taking advantage of available German high-speed aerodynamic research, the Me 262 owed its Lloyd S. Jones maximum speed of 870 km/hr to the Jumo 004 engine. Messerschmitt 163B German Jets J. Philip Barnes www.HowFliesTheAlbatross.com 1 SOME OF THE FOUNDING FATHERS THE VERSATILE HORSESHOE VORTEX Our aerodynamic study takes strong advantage of the Our “Wing-body Linear Longitudinal-Lateral Lifting Line” pioneering work of many of the “Founding Fathers” of (WBL5) method gives the lift (normal force) distribution, aerodynamics. With the horseshoe vortex as modeling as well as profile drag and induced drag over all clay, we’ll apply Ludwig Prandtl’s lifting line and induced significant aerodynamic surfaces including the forebody drag concepts and shift the companion downwash line planform, forebody profile, wing, and empennage. The with the compressibility rule independently developed by analysis, limited to subsonic, linear aerodynamics below Ludwig Prandtl and Hermann Glauert, including the critical Mach, aligns “horseshoe vortices” along lifting effects of wing sweep. Although supersonic sweep was lines, nominally at ¼-chord, with empirical modifications. first theorized by Adolf Busemann, and later independently by Robert T. Jones, Albert Betz was first A corresponding downwash line, nominally at ¾-chord, to suggest and test the benefits of subsonic sweep to but shifted aft via the Prandtl-Glauert compressibility delay transonic effects (4,5). Finally, to include forebody “rule,” connects the points where the equivalent flat-plate effects, we integrate Max Munk’s theory of airships with (EFP) airfoil flow-tangency boundary condition is Robert T. Jones’ theory of low-aspect-ratio wings. applied. The local EFP incidence is determined from the cross products of three vectors representing the chord, flight velocity, and local dihedral. Cambered airfoil Chord line, Zero-lift line ζ α Ludwig Prandtl Max Munk Albert Betz Aero equivalent Thin, flat airfoil α+ζ Adolf Busemann Hermann Glauert Robert T. Jones MaryEvans.com Rather than adjust aircraft and vortex geometry for angle CONFIGURATION AERODYNAMICS of attack and sideslip, instead the flight velocity vector is With the advent of the jet engine, the aircraft forebody tilted by these angles, with only selected adjustments of stretched forward as the wings swept aft. These wing coordinates applied to account for differential geometric changes decreased both the pitch and yaw sweep and downwash-node position in sideslip. stability of the aircraft. Accordingly, our method of Simultaneous equations, typically less than 100 per aerodynamic analysis includes the forebody as a aircraft, are then solved to yield the distribution of significant longitudinal and lateral “lifting surface.” In horsehoe-vortex strength, from which local normal forces keeping with the basic method, it will be modeled as a can be computed. The “apparent downwash” method “cruciform” consisting of two low-aspect-ratio wings. The then determines the local induced drag by comparing the forebody planform, wing and empennage together set observed local lift to that expected based on local the “aerodynamic center” (a.c.) of the aircraft, where the incidence and local sweep, together with Mach number. total lift is concentrated for the purposes of analysis. The German Jets would have been statically stable, with the We postulate that the well-known “Lifting-line” methods center of gravity (c.g.) residing forward of the a.c. and cannot obtain aerodynamic loads in sideslip without with a nose-up pitching moment balancing the offset of empirical modeling thereof. Thus, in the appendix we the lift and weight vectors. Such pitch-up moment can be characterize NACA-measured yaw and roll moments for provided by any combination of airfoil reflex, wing sweep planar wings of various sweep, aspect ratio, and taper with twist, and “decalage” of a canard or horizontal ratio. We then add or subtract “bumps” to or from the stabilizer, the latter designated herein as a “tail,” with lifting-line-computed lift and drag distributions to yield the vertical stabilizing surfaces designated herein as “fins.” overall yaw or roll moment. Such modeling is founded on Albert Betz’ observation that both yaw and roll moments Lift @ vehicle ac of an isolated wing arise from differences in local induced drag, whereby such moments vanish as planar (untwisted) wing lift coefficient (cL) becomes small, or in our interpretation for twisted wings, as “tip-local” lift Weight cMac vanishes. Thus, an aircraft configured largely as an isolated wing will go either marginally stable, or unstable, Vehicle Aerodynamic Center in yaw at “high” speeds approached by the German jets. German Jets J. Philip Barnes www.HowFliesTheAlbatross.com 2 TOP-LEVEL VALIDATION OF METHOD of attack, the lift distribution remains largely positive and A thorough validation of the WBL5 method would involve “half-sinusoidal,” with only a small region of negative lift a wide range of configurations and conditions far at the tips. exceeding the scope of this article. Also, at this time the Chord-weighted Normal-force Coef. method is still in development with validation on-going. 0.40 0.30 cN C/Cav Nevertheless, in this section we validate the method for 0.20 selected cases applicable to the German jets to be 0.10 studied subsequently. 0.00 p/h -0.10 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 First and foremost is the distribution lift for a wing and body combination. NASA TN D-712 represents a rare, Plan View but immensely useful, characterization of wing-body aerodynamic loads by adding pressure taps to the portion of the body coinciding with the “submerged” Looking Fwd portion of the wing. As seen in the figure below, where h only the forebody has been retained for modeling purposes, the wing lift distribution exhibits a pronounced p “dip” which is essentially replaced by forebody lift, Looking Starboard whereby the total wing-body lift is nearly elliptical. Here, the forebody wake has induced downwash on the wing to an extent somewhat greater than that calculated by Flat-plate Incidence, deg Chord-weighted Drag Coefficient 10 0.030 the method. Nevertheless, computed loads reasonably cD C/Cav match the measurements, even though 0.9 flight Mach 5 0.020 number is outside the applicability of the Prandtl-Glauert 0 0.010 p/h p/h -5 0.000 correction for compressibility used by the method. -1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 Method Validation ~ Wing-body lift with body pressure taps Chord-weighted Normal-force Coef. 0.40 cN C/Cav Our third and final top-level validation of the method 0.30 Data applies to a swept wing with dihedral in sideslip.
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