Induced Drag Reduction with the WINGGRID Device Ulrich* and Lucas La Roche, La Roche Consulting Heilighüsli 18, CH-8053 Zürich, email: [email protected]

Summary The WINGGRID is a nonplanar, multiple wake producing wingtip, which allows span loading control independent from wake interaction. Experimental verification and new design proposals of wing systems at subsonic speed are reported. Recent theoretical and experimental work has cleared the way to understand more radical reductions of induced drag than possible with wing systems describable by the Munk stagger theorem, cf. [1]. These are wingtip configurations, that allow for span load control independent from wake interaction of the lifting wing system. Experiments and theoretical insights are treated in parallel to other configurations belonging to the same class of devices, i.e. the split-wing [2] and the SPIROID [8]. Paradigmata on limits of induced drag for lifting systems In classic wing systems with linear interference of streamwise vortices, deviation from elliptic lift distributions towards rectangular distribution are limited, because of the interdependency between vortex-sheet linear interference and span load. Recent work (cf. [2], [4]) on non planar multiple wake systems show experimentally and theoretically, that the Munk stagger theorem (cf. [1]) is limited to wing systems with linear interference of the streamwise vortex-sheet. Munk’s theorem and it’s connected variation calculus for the determination of the minimum induced drag limit does not explain nonplanar multiple wakes with wake independent span load. Smith's work [2] is especially enlightening due to its detailed theoretical and experimental investigation. It identifies the split wing-tip configuration with non-linear interference and clearly bigger span-efficiencies than the Munk theorem would allow for experimentally and by calculation using force-free wake calculus in the Trefftz plane. It also compares the split wing to conventional wings with an nonplanar wake obeying Munk’s stagger theorem, such as investigated by C.D.Cone [7]. For assessment of possible reductions of induced drag the result of Spreiter & Sacks [3] is used, that only two basic parameters are necessary to characterize the induced drag of any wing-system (Munk or non-planar multiple wake).

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These two parameters are the separation distance of the rolled up vortices b‘ and the radius Rk of the Rankine vortex-core. Independent choice of these two parameters allows for any reduction of induced drag. Figure 1 shows Xell, the relative induced drag compared to an elliptic planform wing of the same aspect ratio vs the core radius Rk of the rolled up vortex. As parameter the separation distance of the vortices b‘ relative to the span b of the wing is used. Table 1 summarizes the two positions of stagger theorem and the multiple wake configurations category wake

stagger theorem [1] streamwise vortices with linear interference of all lifting elements airfoil Superposition of arbitrary lifting lines – representation fields get represented by circumference minimum drag is defined by variation calculus in linear limit interference space – “constant downwash” span loading control of span loading is linked to streamwise vortices – elliptic distribution is optimal (planform)

multiple wakes ([2], [4]) Multiple wake on part span with nonlinear interference Different parts of span only coupled by circulation transfer No limit defined – induced drag can be reduced to near zero with the right configuration Span loading control independent from wake interaction – e.g. true rectangular lift distribution possible

Flight-Model- and wind tunnel studies on WINGGRID and SPIROID Asymmetric free flying model planes were used for configuration screening and wind tunnel tests for quantitative and configuration analysis with the most successful screening selections, cf. [5]. Two potential competitors in the new class „multiple wake“ are the SPIROID and the WINGGRID, which resulted both in flyable asymmetric models, indicating the two conditions for stable flight, namely near rectangular span load and massive reduction of induced drag to be present. The wind tunnel-tests verified the reduction of induced drag (apparent aspect ratio) and the rectangular lift distribution by force-moment measurements and independent smoke trail measurements, cf. [4]. Comparison of the slope representing the apparent aspect ratio of WINGGRID and SPIROID models to an elliptic reference wing show aspect ratio * e, where e is the span efficiency. The wind tunnel tests based on force measurement and smoke trail verifications, show that the SPIROID and the WINGGRID are equivalent in effect and operate on the same principles. Progrid 97 full scale tests WINGGRID Based on the wind tunnel tests, the first fullscale WINGGRID was designed to fly on the testbed PROMETHEUS, a jet powered motor glider. The tests comprised glide path measurements of absolute L/D with GPS 8 channel and piezo-barograph. Span load measurements of the WINGGRID blades using strain-gauges did provide independent check on the WINGGRID in flight behavior. • L/D polars results Below a certain critical speed or above the equivalent Cl-value the WINGGRID starts to behave like an ordinary slit-wing, loosing the effect of induced drag reduction. As was learned in the wind tunnel experiments this critical speed of the „cutoff“ is a function of the stagger angle used. It is a design parameter, [4]. For speeds above „cutoff“ polar fitting consistently confirmed a span efficiency of around e = 2.

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Windtunnel tests: elliptic reference vs winggrid and spiroid 1 0,9 0,8 0,7 cl^2

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Fig. 2: Wind tunnel experiments: slope comparison of elliptic wing, SPIROID and WINGGRID show span efficiency of > 1.5 for the latter two

Lift-Loads of WINGGRID blades measured on the testbed Above the critical speed of > 45 m/s a loading of 200 N per winglet is reached, equivalent to a rectangular span load, below the load of lift typically is about 70% of this former value. The critical speed as measured turned out to be higher than expected from the extrapolation from the preliminary wind tunnel tests, this will be an ongoing concern in further developement. Load calculations of WINGGRID blades Since above cutoff in supercritical speeds the blades produce lift individually, a basic vortexsuperposition-calculation is sufficient to reproduce the resulting lift distribution, including mutual interference. Calculation and actual load measurement are found to be within 10% difference, cf. [4]. Idaflieg 99 full scale tests WINGGRID L/D polar and smoke visualisation for control of downwash-geometry and span load and comparison of the testbed’s two wing-configurations for direct evaluation of the dragcomponents were performed by Idaflieg/DLR. Idaflieg & DLR method The identical testbed with WINGGRID has been measured with the well known Idaflieg/DLR method of comparison to a calibrated sailplane by the classic photographic measurement and also by a new differential GPS-method, cf. [11] and [12]. The low mean error of 2% for the photographic measurements allowed for direct comparison of two configurations of the testbed. One is the testbed with its 23m span Stemme S10-wing, the other with the base S10-wing and WINGGRID added with total span of 12m. The comparison allows to eliminate directly fuselage drag and to obtain the WINGGRID drag figures on an absolute basis. Important results of this full scale tests is confirmation of the findings of the 97 PROGRID tests for the span efficiency. A new result is the assessment of the additional drag the WINGGRID exhibits. It is firstly interference drag of the blades at base and tip and secondly profile drag due to lower Re-numbers on the smaller chords of the blades and drag of the interconnection body and endplates. cl-cw polars If we analyze the cl-cw polars obtained, the cutoff already identified in the 97 tests is plainly visible as a discontinuity at Cl = 0.67 in fig. 3. A curve fit L/D= 1/(π*e*AR)*cl2+cd0 shows a span efficiency e of 2. A curve fit with L/D= 1/(π*e*AR)*cl2+B*cl+cd0 does also show e=2 for cl