Dynmic Sorin in Sher Wind Reions Associted with Jet Strems Gotfried Schs nd Orlndo d Cost 1 Technische Universität München Boltzmnnstr. 15, 85747 Grchin, Germny schs@lfm.mw.tum.de Presented t the XXVIII OSTIV Conress, Eskilstun, Sweden, 85 June 006 Abstrct Dynmic sorin enbles n enery in by trnsferrin enery from the movin ir in horizontl sher wind reion to the siplne. There re sher wind reions ssocited with jet strems, extendin from the jet strem core with its hih wind speed to the ltitude where the ir is t rest. The possibility of utilizin this enery in is considered for the dynmic sorin of silplnes. An efficient optimiztion procedure is used to determine the minimum sher wind strenth which is required for the dynmic sorin fliht mnoeuvre, pplyin relistic mthemticl model for describin the dynmics of silplne. It turns out tht the minimum sher wind strenth is smller thn the vlues which cn be encountered in existin sher wind reions ssocited with jet strems. As result, the performnce cpbility of modern silplnes offers the possibility for dynmic sorin in these jet strem reions. 1 Now with IABG mbh, Einsteinstrße 0, D-8551 Ottobrunn, Germny. ki D Nomenclture coefficient C dr coefficient C D h m n lift coefficient dr ccelertion due to rvity ltitude lift mss lod fctor q dynmic pressure, q ( / ) V S reference re t time u, v, w speed components V irspeed V inertil speed K V wind speed W x, y, z eodetic coordinte system fliht zimuth nle fliht pth wind nle fliht bnk wind nle density Introduction Dynmic sorin is fliht technique by which flyin object (bird, silplne) cn extrct enery from the movin ir in horizontl wind field which chnes its strenth with ltitude. This type of ir flow is clled sher wind. Dynmic sorin consists of series of cycles which re continully repeted, s shown in Fi. 1 for sebird. A cycle which forms the bsic constituent of dynmic sorin comprises complex sequence of climbin, turnin nd descendin fliht phses (denoted by Nos. 1 to 4 in Fi. 1). Dynmic sorin erlier hs ttrcted ttention s fliht technique for chievin n enery in from sher wind 1-3. Since then, it is subject of continuous interest 4. Dynmic sorin is prcticed by sebirds, in prticulr by lbtrosses, enblin them to sty loft without flppin. With this fliht technique, the birds cn trvel lre distnces. With respect to the possibility of n enery in from the sher wind, dynmic sorin is lso n issue for silplnes 4-. Usin enery estimtions nd numericl simultions, sinificnt knowlede bout the sher wind strenth necessry for dynmic sorin hs been ined. With the vilbility of modern optimiztion techniques, it ws possible to chieve precise results on dynmic sorin trjectories nd on the mximum enery in which cn be obtined from the sher wind 18-. The results show tht the performnce chrcteristics of modern silplnes offer the possibility of dynmic sorin in sher wind fields. Recent developments in the sorin techniques of model liders re of interest for the problem under considertion 3-7. This is becuse model lider pilots hve prcticed dynmic sorin for some time. They use wind conditions t rides where sinificnt sher flows cn exist. The purpose of this pper is concerned with the possibility of dynmic sorin in the sher wind reions of jet strems for hih-performnce silplnes. Focus is on dynmic sorin trjectories requirin the minimum sher wind strenth. Thus, it is possible to jude whether the performnce cpbility of TECHNICA SOARING 13 VOUME 31, NO. 1 - Jnury 007
modern silplnes is sufficient for dynmic sorin in these sher wind conditions. Sher wind reions ssocited with jet strems There re vrious cuses for the occurrence of horizontl sher winds 8. One concerns the ir flow over the surfce of se or lnd. This type of sher flow t se holds for the dynmic sorin of sebirds. There is sher wind due to boundry lyer effects of the movin ir close to the surfce of the wter. The wind speed rpidly increses from zero or very smll vlues immeditely bove the se surfce until pprochin the vlue of the free ir flow. Another cuse for sher wind is due to rides. A wind comin over the top of ride produces sher wind condition behind the ride where seprtion boundry between the wind re nd zone of still ir exists. Such sher winds re used by model liders for dynmic sorin. There is lso sher wind ssocited with jet strems. The sher wind extends in rne between the core of the jet strem with its extremely hih wind speed nd the ltitude where the ir is t rest or movin slowly. Results re presented in Fi. which shows mesured dt of the sher wind reion ssocited with jet strem. The dt presented in Fi. suest for lre prt of the ltitude rne tht liner dependence of the wind speed with the ltitude cn be used s relistic mthemticl model for describin the sher wind chrcteristics. In this reion, the sher wind rdient mounts to vlue of bout dv W / dh 0.019 s. The sher wind reions ssocited with jet strems cover wide res nd extend over hue distnces. An exmple is presented in Fi. 3. Since the jet strems re continully monitored, it is well known where such sher wind reions occur. The sher wind reions ssocited with jet strems re t hiher ltitudes (Fi. ). For flyin t hih ltitudes, it necessry to hve n pproprite equipment for copin with the tmospheric conditions (oxyen, pressure, temperture) 31. Mthemticl model for silplne dynmics in sher wind The mthemticl model for describin the motion of the silplne in the horizontlly movin ir of sher wind field cn be bsed on point mss dynmics. Reference is mde to n erth-fixed coordinte system nd n pproprite inclusion of the movin ir (Fi. 4). With respect to this coordinte system, the equtions of motion cn be formulted s du D / m / m dv dw dx dy u v dh w u1 v1 D / m w1 u v D / m / m w / m where the coefficients ij re iven by (1) u1 u v1 v w1 w cos cos cos sin sin cos sin cos sin sin cos sin sin sin cos cos cos The lift nd dr forces, nd D, re dependent on the irspeed vector V, concernin their mnitude nd direction of ction, while the motion of the ircrft with respect to the erth is described by the inertil speed vector () V K (Fi. 4). Usin the wind speed vector V W, the followin reltion holds V V K V W (3) Since the x xis is selected such tht is prllel to the horizontl wind (Fi 4), the wind speed vector is iven by T V W ( V W,0,0) (4) With the inertil speed vector T V u, v, w ) (5) K ( the followin expressions cn be obtined T V ( u V v w ) V ( u W,, V W ) v u The nles, nd describe the orienttion of the erodynmic forces with respect to the inertil reference system. The followin reltions hold for nd : w sin V (7) tn u V W The nle which describes the bnkin of the lift vector is control. Thus, it is determined by optimlity conditions. The mthemticl model for describin the dynmics of the silplne lso concerns constrints which re iven by nmin n nmx (8) q qmx The density properties of the tmosphere re described usin model bsed on dt iven in Ref. 3. Usin the bove equtions of motion, dynmic sorin trjectories in sher wind reion cn be determined such tht the enery stte fter completin cycle s shown in Fi. 1 is the sme s t the beinnin. These trjectories cn be desinted s enery-neutrl. This implies tht the speed vectors (by mount nd direction) t the beinnin nd end of dynmic sorin cycle re equl s well s the correspondin ltitudes. There is ret vriety of enery-neutrl trjectories, requirin different vlues of the wind rdient d V W / dh. One is of concern for the issue in mind: It is the one which requires the minimum sher wind strenth in terms of the min- (6) VOUME 31, NO. 1 - Jnury 007 14 TECHNICA SOARING
imum rdient (dv W /dh) min. Knowin this enery-neutrl trjectory, it is possible to jude whether or not the strenth of the sher wind ssocited with jet strem is sufficient for dynmic sorin. The enery-neutrl trjectory requirin the minimum sher wind rdient cn be determined usin techniques for fliht pth optimiztion. Fliht pth optimiztion is systemtic, purposeful serch strtey such tht the best dynmic sorin trjectory cn be computed which yields the mximum enery in from the sher wind. Thus, the dynmic sorin trjectory cn be determined which requires the minimum sher wind strenth. Efficient numericl optimiztion methods nd computtionl techniques re necessry to solve the described trjectory optimiztion problem. The numericl investition ws performed usin prmeteriztion optimiztion technique 33 with rphicl environment 34. Mthemticl model of silplne Dt of hih-performnce silplne re used in the numericl investition for determinin the optiml dynmic sorin trjectory requirin the minimum sher wind rdient (dv W /dh) min. It is similr to the Et silplne in its erodynmics nd size chrcteristics 35. The followin dt re pplied for the reference win re nd the mss: S 18.6 m m 975 k The erodynmic model concerns the lift nd dr chrcteristics of the silplne. The lift nd dr cn be expressed s C ( / ) V S (9) D CD ( / ) V S The lift-dr chrcteristics of the silplne re presented in Fi. 5 which shows the C / CD rtio with rerd to the speed rne. The depicted dt lso include the effect of cmber flps the control of which cn be used to improve the performnce. The utiliztion of the cmber flps ws lso included in the optimiztion of dynmic sorin such tht the best settin of the cmber flps for ech fliht phse ws selected by the computtionl procedure. Further on the erodynmics model, limits in the lift coefficient were ccounted for. For this purpose, the followin reltionship ws pplied C C C (10) min mx Results For determinin the enery-neutrl dynmic sorin trjectory requirin the minimum sher wind strenth in terms of the minimum wind rdient, sher wind model with liner dependence of the wind speed with the ltitude ws pplied, s suested by the dt presented in Fi.. In the computtionl process, the rdient of the wind speed with respect to the ltitude ( dv W /dh) ws not held fixed t iven vlue, but it ws treted s dptble such tht the lowest possible vlue in terms of the minimum rdient ( dv W / dh) min ws determined usin the optimiztion technique described in previous section. Results on the relted optiml eneryneutrl dynmic sorin trjectory requirin the minimum sher wind rdient ( dv W / dh) min re presented in the followin. As min result, the minimum sher wind rdient required for dynmic sorin with the silplne the mthemticl model of which ws presented in the previous section mounts to ( dv W /dh) min 0.01 s Comprison to the mesured sher wind dt with dv W /dh 0.019 s (Fi. ) shows tht required minimum sher wind rdient is sinificntly smller. Properties of the optiml dynmic sorin trjectory with which requires the minimum sher wind rdient ( dv W /dh) min 0.01 s re rphiclly illustrted in the followin fiures. A cycle of the optiml enery-neutrl dynmic sorin trjectory is shown in Fi. 6. This fiure provides perspective view of the dynmic sorin cycle nd ives its extension in the lonitudinl, lterl nd verticl directions. The dotted rrows denote the beinnin nd endin of cycle which is periodiclly repeted. The time required for the optiml enery-neutrl dynmic sorin cycle mounts to t 37.1s. cyc The time history of the ltitude is presented in Fi. 7. The ltitude covers rne of less thn 700 m, in the upper prt of the sher wind reion. The climb is performed in windwrd direction while the descent is fliht with the wind. The turns re conducted t the top nd the bottom of the ltitude rne. The fct tht the ltitude rne is less thn 700 m is importnt with rerd to the possibility of utilizin the sher wind reion ssocited with jet strems for dynmic sorin. This is becuse there my be only smll prt needed out of the entire ltitude reion showin sher wind rdient. For exmple, the sher wind ltitude reion of the jet strem cse presented in Fi. mounts to nerly 4 km. The time histories of the speed with respect to the erth, V K, nd the irspeed, V, re presented in Fi. 8. Durin the climb, V is lrer thn V K becuse of the windwrd fliht direction. The opposite holds for the descent which shows leewrd fliht direction. The chne in the reltion between V K nd V is n indiction for the increse of V K in the upper turn. The increse of V K cn be seen in Fi. 8 when comprin two V vlues t the sme ltitude, one before nd the K other fter the mximum ltitude (Fi. 7). The increse of V K leds to n enlrement of the kinetic enery. The overll enery of the silplne is ccordinly incresed becuse the TECHNICA SOARING 15 VOUME 31, NO. 1 - Jnury 007
two ltitude vlues correspond to the sme potentil enery. Since the increse of the enery stte is due to the upper turn, this fliht phse cn be qulified s most importnt for the enery in of dynmic sorin. In Fi. 9, the time histories of the lift coefficient the bnk nle lift coefficient the lower turn, C nd which re the controls re presented. The C tkes on lre vlues in the upper turn. In C shows smller vlues. The bnk nle shows its lrest vlues in the turns. Here, the vlues of re round ±50 de, with some more bnkin in the upper turn. The time history of the lod fctor n is depicted in Fi. 10. For lre prt of the dynmic sorin cycle, the lod fctor is close to n 1. There is n increse in the lower turn where the silplne chnes its direction from lee- to windwrd nd the inertil speed tkes on its hihest vlues. Here, the increse of n reches the limit n mx 4. 5 so tht the constrint iven by Eq. (8) becomes ctive. Conclusions There re sher wind reions ssocited with jet strems, coverin wide res nd extendin over hue distnces. The possibility of utilizin these reions for dynmic sorin is investited. For this purpose, enery-neutrl dynmic sorin trjectories re determined which require the smllest sher wind strenth in terms of the minimum wind rdient with respect to the ltitude. It turns out tht modern silplnes with hih erodynmic efficiency need sher wind rdients which re smller thn those of existin sher winds. As result, hih-performnce silplnes offer the possibility to conduct dynmic sorin in sher wind reions ssocited with jet strems. References 1 Ryleih, J.W.S., The Sorin of Birds, Nture 7, pp. 534-535, 1883. Idrc, P., Étude théorique des mnœuvres des lbtros pr vent croissnt vec l'ltitude", C.r. hebd. Sénc. Acd. Sci., Pris 179: 1136139, 194. 3 Prndtl,., Beobchtunen über den dynmischen Seelflu, Zeitschrift für Flutechnik und Motorluftschifffhrt, 1. Jhr., p. 116, 1930. 4 Klemperer, W., A Review on the Theory of Dynmic Sorin, OSTIV-Bericht, pp. 498-501, 1958. 5 Contensou, P., "Optimiztion du Vol Plne dns un Vent Horizontl Vrible", Conress of Appl. Mechnics, Stnford University, 1968. 6 Fritsch, E., Zum dynmischen Seelflu, Aero-Revue, Heft 1, pp. 669-67, 1971, Heft 1, p. 40, 197. 7 Hendriks, F., Dynmic Sorin, Disserttion, University of Cliforni, os Aneles, 197. 8 Hendriks, F., Dynmic Sorin in Sher Flow, AIAA Pper 74-1003, 1974. Trommsdorff, W., Flumechnische und technische Vorussetzunen für den Dynmischen Seelflu mit bemnntem Fluerät, OSTIV-Bericht, 1974. 10 Trommsdorff, W., Vorussetzunen für die Durchführun des dynmischen Seelflus, Aerokurier, Heft 1, pp. 1106107, 1976. 11 Renner, I., Dynmischer Seelflu, Aerokurier, Heft 1, pp. 1104105, 1976. 1 Gorisch, W., Enery Exchne between Silplne nd Movin Air Msses under Insttionry Fliht Conditions with Respect to Dolphin Fliht nd Dynmic Sorin, Aero-Revue, Heft 11, pp. 691-69 (Teil 1), Heft 1, pp. 751-75 (Teil ), 1976, Errtum, Heft 3, p. 18, 1977. 13 Gorisch, W., Zum Problem des dynmischen Seelflus in der horizontlen Grenzschicht zwischen ruhender und beweter uftmsse, Aerokurier, Heft 9, pp. 855-858, 1977. 14 Nottebum, T., Ein Rechenprormm zur Simultion des Dynmischen Seelflu, DGR-Jhrbuch, pp. 39-338, 1987. 15 Goebel, O., Scherwindmessunen n Bord einer Piper PA 18 und Ausleun eines Modellseelfluzeus für den Dynmischen Seelflu, DGR-Jhrbuch, pp. 3-38, 1987. 16 Nottebum, T., Goebel, O., Simultion optimler Flubhnen des dynmischen Seelflus und Ausleun eines Modellfluzeus, Zeitschrift für Fluwissenschften und Weltrumforschun, Vol. 13, pp. 48-56, 1989. 17 issmn P, Wind Enery Extrction by Birds nd Fliht Vehicles, AIAA Pper, AIAA 005-041, Americn Institute of Aeronutics nd Astronutics, 005. 18 Schs, G., Minimlbedinunen für den dynmischen Seelflu, Zeitschrift für Fluwissenschften und Weltrumforschun, Vol. 13, pp.18898, 1989. 19 Schs, G., Knoll, A., esch, K., Optiml Control for Mximum Enery Extrction from Wind Sher, AIAA Guidnce, Nvition nd Control Conference, AIAA Pper 89-3490, 1989. 0 Schs, G., Knoll, A., esch, K., Optiml utiliztion of wind enery for dynmic sorin, Technicl Sorin, Vol. 15, No., pp. 48-55, 1991. 1 Schs, G., Optiml Wind Enery Extrction for Dynmic Sorin, Applied Mthemtics in Aerospce Science nd Enineerin, Plenum Press, New York nd ondon, Vol. 44, pp. 1-37, 1994. Schs, G., Myrhofer, M., Sher Wind Strenth Required for Dynmic Sorin t Rides, Technicl Sorin, ISSN 0744-8996, Bnd 5, Nr. 4, October 001, pp. 095, 001. 3 Wurts, J., Dynmic Sorin, S&E Modeler Mzine, Vol. 5, Auust/ September, pp. -3, 1998. 4 Foel,., Dynmic Sorin?, S&E Modeler Mzine, Vol. 9, December/Jnury, pp. 4-7, 1999. 5 Schlösser, W.M.J., A Contribution to the Study of Dynmic Sorin, S&E Modeler Mzine, Vol. 5, Mrch 000, pp. 4-7, 000. 6 Schs, G., Myrhofer, M., Dynmic Sorin Bsics: Prt 1 Model Gliders t Rides, Quiet Flyer, ISSN 153-3803, December 00, pp. 3-37, 00. 7 Schs, G., Myrhofer, M., Dynmic Sorin Bsics: Prt Minimum Wind Strenth, Quiet Flyer, ISSN 153-3803, Jnury 003, pp. 8-85, 003. 8 Swolinsky, M., Beiträe zur Modellierun von Scherwind für Gefährdunsuntersuchunen, Disserttion, TU Brunschwei, 1986. 9 Weber, F., Jet Strem nd Cler-Air-Turbulence, Aerokurier 1/1968, pp. 0, 1968. http://squll.sfsu.edu/crws/jetstrem.html. 31 Köhler, H., Köhler, I., Fly Hih Seelflieen in den USA, Verl Dr. Neufn KG, Gelsenkirchen-Buer, 1984. 3 U.S. Stndrd Atmosphere 1976, Wshinton D.C., Ntionl Ocenic nd Atmospheric Administrtion, Ntionl Aeronutics nd Spce Administrtion, United Sttes Air Force, 1976. 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33 N.N., ATOS Softwre User Mnul, Institut für Flumechnik und Reelun, University of Stuttrt, Auust 1996. 34 N.N., GESOP (Grphicl Environment for Simultion nd Optimiztion), Softwresystem für Bhnoptimierun, Institut für Robotik und Systemdynmik, DR, Oberpfffenhofen, 1993. 35 http://etircrft.zoecom.com/index.htm Fiure 3 Extension of jet strem (from Ref. 30). Fiure 1 Dynmic sorin trjectory of lbtross. Fiure 4 Geodetic coordinte system nd speed vectors for fliht of silplne in horizontlly movin ir. Fiure Sher wind ssocited with jet strem (dt from Ref. 9). Fiure 5 ift-to-dr rtio of silplne ( C1, C,... C5 : cmber flp settins). Win spn: 30 m, win re: 18.56 m. TECHNICA SOARING 17 VOUME 31, NO. 1 - Jnury 007
Fiure 6 Optiml enery-neutrl dynmic sorin cycle requirin minimum sher wind strenth (dv W /dh)min=0.01 s. Fiure 9 Time histories of lift coefficient nd bnk nle of optiml enery-neutrl dynmic sorin cycle requirin minimum sher wind strenth (dv W /dh) min =0.01 s. Fiure 7 Altitude time history of optiml enery-neutrl dynmic sorin cycle requirin minimum sher wind strenth (dv W /dh) min =0.01 s. Fiure 10 od fctor time history of optiml enery-neutrl dynmic sorin cycle requirin minimum sher wind strenth (dv W /dh) min =0.01 s. Fiure 8 Speed time histories of optiml enery-neutrl dynmic sorin cycle requirin minimum sher wind strenth (dv W /dh) min =0.01 s VOUME 31, NO. 1 - Jnury 007 18 TECHNICA SOARING