Induced Drag Reduction with the WINGGRID Device Ulrich* and Lucas La Roche, La Roche Consulting Heilighüsli 18, CH-8053 Zürich, email: ularoch@attglobal.net 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). Xell 1.5 1 0.5 Xell for b'/b = 0.6/0.8/1/1.2/1.5/2 0.6 0.8 1 1.2 1.5 b'/b 2 0 0 0.1 0.2 0.3 0.4 0.5 Rk/b Fig. 1: Relative induced drag vs core radius Rk and vortex separation b /b after [3] 1 von 8
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 stagger theorem [1] multiple wakes ([2], [4]) wake streamwise vortices with linear interference of all lifting elements Multiple wake on part span with nonlinear interference airfoil representation Superposition of arbitrary lifting lines fields get represented by circumference Different parts of span only coupled by circulation transfer minimum drag limit is defined by variation calculus in linear interference space constant No limit defined induced drag can be reduced to near zero with the right span loading downwash control of span loading is linked to streamwise vortices elliptic distribution is optimal (planform) 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. 2 von 8
1 Windtunnel tests: elliptic reference vs winggrid and spiroid 0,9 0,8 0,7 0,6 cl^2 0,5 0,4 0,3 0,2 0,1 ellipt ref slope Spiroid Winggrid Winggrid Winggrid 0 0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,1 Fig. 2: Wind tunnel experiments: slope comparison of elliptic wing, SPIROID and WINGGRID show span efficiency of > 1.5 for the latter two cw 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)*cl 2 +cd0 shows a span efficiency e of 2. A curve fit with L/D= 1/(π*e*AR)*cl 2 +B*cl+cd0 does also show e=2 for cl<0.67 in fig. 4. 3 von 8
Alternative explanations that could explain this anomaly as data scatter, laminar drag bucket or fuselage separation were not found to match the required magnitude in cw or location in terms of cl. L/D polars compared The measured points of the L/D polars are fitted with the expected polars for e = 2 (supercritical with WINGGRID) and e = 1 (elliptic with /without parasitic drag of WINGGRID), see fig. 5. Again the result, that in supercritical speeds the full WINGGRID-effect results in e = 2 is plainly visible. Also visible is the influence of the additional drag of the WINGGRID-configuration used: interference drag and profile-drag. If verified on absolute values, cf. [9], this measured additional drag is within 10% of calculated values. Based on [9] and its cited literature it is possible that the interference drag can be eliminated essentially to zero by proper fillets and roundings. 1 cw= 0.0128+cl*cl/(3.14159*28.29) 0,9 cl 0,8 0,7 0,6 0,5 Discontinuity cw= 0.0208+cl*cl/(3.14159*12.63*2) cl 23 m foto cl 23m GPS cl winggrid foto cl winggrid GPS cl 23m theor cl wg theor 0,4 0,01 0,02 0,03 0,04 0,05 cw Fig. 3: Fit polars (L/D= 1/(π*e*AR)*cl 2 +cd0) for Idaflieg measurements show a span efficiency of 2 for the WINGGRID Since no effort on interference drag reduction was spent on this test configuration a properly designed WINGGRID will exhibit almost negligible additional drag, because higher profile drag is mainly compensated by the overlap being less than 0.7 in most practical cases and interference drag can be eliminated by known means. Vortex-sheets visualizations From the independent test with smoke bombs the following experimental evidence can be inferred, cf. [5]: -b /b 0.95, which means we have a near rectangular span load (elliptic has b /b 0.8). -the smoke pattern taken with the WINGGRID endplate mounted camera shows indentations of individual vortex-sheets leaving the two foremost WINGGRID-blades, which is evidence for a multiple wake configuration as shown in fig. 6. Summary of improvement potential and design of WINGGRID As summarized in [6] the information from the early tests 97 and 99 Idaflieg/DLR permits to do reasonable prototype design with pre calculation of performance. It is important to recognize, that the speed of cutoff, which with the testbed is situated at a cl-value below 0.7 is an important design parameter. In the following the main design features of the WINGGRID are summarized: 4 von 8
0,03 cw vs cl 0,028 cw 0,026 0,024 0,022 0,02 0,018 0,016 0,014 0,012 wg: cw = 0,0125*cl 2 + 0,006*cl+ 0,0182 S10: cw= 0,0144*cl 2 + 0,0027*cl + 0,0087 cw S10 cw wg Winggrid Polynomfit S10 Polynomfit 0,01 0,4 0,5 0,6 0,7 0,8 0,9 1 cl Fig. 4: Polar fit with linear element, L/D= 1/(π*e*AR)*cl 2 +B*cl+cd0, for cl <0.67 shows a span efficiency of 2 for the WINGGRID, i.e. 1/(π*e*AR)=0.0125 with AR=12.6 24 24 23 23 22 L/D 22 points are measurements, curves are polar fits Split Wing- Effekt WINGRID- Effekt Legend: b=span e= span efficiency cd0= drag at cl=0 a:b=12, e=1, cd0=0,02181(elliptic, parasitic drag) b: b=12 m, e=2, cd0=0.02181 (supercritical) c: b=12, e=1, cd0=0,01219*18,7/11,4 (elliptic) Promf2po, foto promf3po, foto 21 21 WINGGRID effect promf4po, foto PolK1 20 20 parasitic drag polk2 GPS method 19 35 40 45 50 55 IAS m/s Fig. 5: L/D measurements compared to fit polars There are five conditions to be met for a WINGGRID to operate, which have to be met as a logic AND. the devices span should not exceed a certain part of total span, say L2 < 50% of L. the device has to have a stagger angle of at least the maximum angle of attack (corresponding to lowest speed without stall) considered for the main wing. the devices grid winglets should be parallel. the device should have essentially the same lift per span as the main wing profile in 2-D flow would have at the attachment point. overlap of the grid winglets should be less than 1. polk3 5 von 8
Vortex-Sheets of Winggrid-Flow La Roche Consulting 00 Fig. 6: Multiple vortex sheets of the non planar wake configuration WINGGRID. The vortex sheet of the main wing is split into several vortex sheets at the tip. Fig. 7: WINGGRID design with individual stagger angles Stagger-angle design criteria A design consideration worked on is treatment of the so called stagger angle, the rotation between the WINGGRID and the main profile chord necessary to obtain the nonlinear multiple vortex-sheets of the WINGGRID operation to reduce induced drag. The example in fig. 7 demonstrates the present approach for the design of the WINGGRID stagger angle for the MCR01 project. The condition for stagger angle depending on Cl-value is set for each blade individually. Lift-distribution designs The different designs of a WINGGRID regarding blade load are shown below: a) all blades with the same angle of attack. This will lead to the foremost blade having more than 200% of lift then the last, but will guarantee on the other side correct angle of attack at all speeds b) as a) but with foremost blade corrected for a smaller angle of attack. This will alleviate the problem of very high lift for the first blade. c) As b) but with chord of first blade made bigger. This allows to independently have a smaller local Cl-value. d) For a preferential operational speed adjust all angles of attack in order to arrive at equal lift load for all blades 6 von 8
Potentials of improvements WINGGRID L/D comparison L/D polars can be used to compare different wing designs. The equation giving L/D for a specific flight situation has to combine influence of drag components as a function of indicated airspeed. Of prime interest is the relation of induced drag to total drag as a function of span efficiency e, see also details in [4] and [6]. With the much increased span-efficiency available with the WINGGRID the L/D for aircraft designed to fly near the optimum relation of induced drag to total drag around 30 to 50% an improvement of 30 to 100% of L/D is within realistic expectations. UL-Prototype MCR01 A Project is in progress to bring the WINGGRID to production (in cooperation with DYN AERO and ONERA). The aircraft main parameters are described in box 1. Span: 9.8 m TOW: 450 kg Vmin 55 kmh Vcruise 240 kmh Vglide 90-140 kmh Vmax 300 kmh L/D max 30 Wing Area 9.35 m^2 box 1: Target specification Data of the MCR01 motor glider-version Three different wingtip-arrangements with identical span are tested: No wingtip/classic wingtip/winggrid Wing system with WINGGRID at transsonic speeds The preliminary design shown is for demonstrating the main design challenges. Starting from the profiles, the critical mach numbers of the profiles were evaluated with cl-values used. With three blades and a relative span of 20% of the WINGGRID (relative to total half span) the resultant span efficiency will reach e = 2. It is of course essential to keep compressibility drag small. Shocks on WINGGRID-blades Because of the small overlap-value we do not have effective overlap. Shock wave patterns will develop individually on each blade of the WINGGRID (as in transsonic compressor-bladings) Possible shockwave patterns on the blades of a WINGGGRID Fig. 8: Transonic behavior of the WINGGRID (supercritical profiles preferred) Preliminary design of transonic wing The design shown in fig. 9 is an adaption of a infinite sheared wing with spanwise rectangular lift distribution after [6]. No corrections are added for the critical parts of the wing, where the infinite sheared wing model has to be substantially modified for its ending at the fuselage and WINGGRID junctions. The same applies to the individual blades of a WINGGRID. Sweep angles The necessary sweep angles result from profile and cl-data of the WINGGRID for use in the preliminary design. WINGGRID s would add 10 to 30% lift to drag improvement to transonic transport airplanes with shorter span, prolonging the lifecycle of the classic Cayley type aircraft. 7 von 8
Transonic wing with WINGGRID L L2 M = 0.9 Mcrit wing = 0.7 Mcrit winggrid = 0.65 L2/L = 0.2 overlap = 0.6 nb = 3 e = 2 Fig. 9: Base design of transonic WINGGRID Conclusion With span efficiencies e > 2 possible there are profound consequences to be exploited. In order to get the most benefits of the WINGGRID one usually has to design a completely new wing due to the following conditions: Rectangular span load for maximum effect, which means no taper and no twist Rectangular spanload leads to Cl max being equal to Cl average, resulting in higher wing load for the same Cl max Lift load on the WINGGRID is high, one has to take the structural consequences for this Smaller kinetic energy in the rolled up vortices in the wake Acknowledgements This work would not have been possible without enthusiastic and visionary cooperation of various organizations and people. We acknowledge and thank for: The initiative of Idaflieg to do the tests in 99 coached by Andre Jansen. The ontime cooperation of Dietmar Schmerwitz from DLR with test results [10]. The preparation of the WINGGRID s by Ivo Stengele from ETHZ/ILS. The availability of the testbed from EFF represented by Thomas Bircher. The GPS measurement results provided by Gerko Wende and Stefan Ronig from IFF [11]. References: [1] Munk Max M., The Minimum Induced Drag of Aerofoils, NACA Report 121 [2] Stephen C. Smith, A Computational and Experimental Study of nonlinear Aspects of Induced Drag, NASA Technical Paper 3598, Ames Research Center [3] Spreiter J.R., Sacks A.H., the rolling up of the trailing vortex sheet and its effect on the downwash behind wings, Journal of the Aeronautical Sciences jan.51, p. 21 ff. [4] La Roche U. et al., WING-GRID, Development, Qualification and Flight Testing of a WINGGRID on a jetpowered testbed, Proceedings ICAS 98 Melbourne (Australia), [5] http://www.rhone.ch/winggrid, the website of the WINGGRID [6] Küchemann D., The Aerodynamic Design of Aircraft, Pergamon Press, ISBN 0-08-020515-1 [7] Cone C.D., The theory of induced lift and minimum induced drag of nonplanar lifting systems, NASA technical report R-139 1962 [8] Procter P., Winglet designs to cut fuel burn, Aviation week&space technology, dec, 6 1994, p.3 [9] Hoerner S., Fluid-Dynamic Drag, Library of congress card number 64-19666 [10] Schmerwitz D. et al., Messbericht Idaflieg/DLR 1999, Flugsystemtechnik DLR-Braunschweig/IFF TU-Braunschweig/Idaflieg) [11] http://www.idaflieg.de 8 von 8