Hybrid Airfoil Design Method to Simulate Full-Scale Ice Accretion Throughout a Given a Range

Transcription

1 JOURNAL OF AIRCRAFf Vol. 35, No.2, March-April 1998 Hybrid Airfoil Deign Method to Simulate Full-Scale Ice Accretion Throughout a Given a Range Farooq Saeed,* MichaelS. Selig.t and Michael B. Bragg:j: Univerity of Illinoi at Urbana-Champaign, Urbana, Illinoi A deign procedure i preented for hybrid airfoil with full-cale leading edge and redeigned aft ection that exhibit full-cale airfoil water droplet-impingement characteritic throughout a given angle of attack or a range. The deign procedure i an extenion of a previouly publihed method in that it not only allow for ubcritical and vicou-flow analyi in the deign but i alo capable of oft-deign droplet-impingement imulation through the ue of a flap ytem. The limitation of the flap-ytem-baed deign for imulating both on- and oft-deign full-cale droplet-impingement characteritic and urfacevelocity ditribution are dicued with the help of pecific deign example. In particular, thi paper preent the deign of two hybrid airfoil at two different angle of attack, uch that they imulate both the full-cale velocity ditribution a well a droplet-impingement characteritic at the repective deign angle of attack. Both of the hybrid airfoil are half-cale airfoil model with the noe ection matching the full-cale coordinate of the Lear jet 305 airfoil back to 5% chord on the upper urface and 20% chord on the lower urface. The effect of flap deflection and droplet ize on droplet-impingement characteritic i alo preented to highlight the important limitation of the preent method both on- and oftdeign. Thi paper alo dicue important compromie that mut be made to achieve full-cale ice accretion imulation throughout a deired a range and ugget alternative uch a applying a multipoint deign approach. c = T v = v Vz = x,y = a a, = {3 r ')' 8 8! Nomenclature airfoil chord length airfoil urface arc length meaured from the leading edge freetream tatic temperature urface velocity urface velocity normalized by Vz freetream velocity airfoil coordinate angle of attack relative to the chord line effective angle of attack relative to the noe-ection chord line, a - y local impingement efficiency circulation trength normalized by Vzc noe droop angle droplet diameter flap deflection Subcript f = full-cale airfoil I lower urface = ubcale airfoil u upper urface Introduction R ECENT aircraft accident have raied important flight afety iue related to the operation of aircraft under e- Preented a Paper at the AIAA 35th Aeropace Science Meeting, Reno, NV, Jan. 6-9, 1997; received May ; reviion received Sept ; accepted for publication Sept. 17, Copy right 1997 by the author. Publihed by the American Intitute of '\eronautic and Atronautic. Inc., with permiion. Graduate Reearch Aitant, Department of Aeronautical and Atronautical Engineering, 306 Talbot Laboratory, 104 South Wright Street. Student Member AIAA. t Aitant Profeor. Department of Aeronautical and Atronautical Engineering. Senior Member AIAA. tprofeor. Department of Aeronautical and Atronautical Engineering. Aociate Fellow AIAA. 233 vere weather condition.' To improve flight afety a better undertanding of the effect of ice accretion on the aerodynamic performance of modern airfoil i required. One important tep in the proce i to evaluate the aerodynamic performance of the airfoil ection, or the wing a a whole. at the icing condition within the certification icing envelope that reult in the larget performance penaltie.. For aircraft afety one of the mot important performance parameter i the maximum lift coefficient. Therefore. while drag and pitching moment are important. the icing condition that reult in the larget degradation in maximum lift coefficient i the mot critical. The determination of the critical ice accretion and it aerodynamic effect on a et of modern airfoil, typical of thoe in ue on aircraft. i under way at NASA Lewi Reearch Center. The reearch reported here i part of thi larger effort. Becaue of the difficultie and uncertaintie in ice accretion caling, 6-11 teting at full-cale i deirable yet cotly. Moreover, available ice accretion tunnel are too mall to tet fullcale airfoil or wing of mot aircraft of interet. One way to expand the uefulne of exiting icing tunnel and to facilitate teting of aircraft de-icing/anti-icing ytem i to tet hybrid airfoil or ubcale airfoil with full-cale leading edge and redeigned aft ection, to provide full-cale icing condition at the leading edge. The term hybrid method refer to uing a full-cale leading edge to match the full-cale ice accretion. The aft ection of the hybrid airfoil i pecially deigned to provide flowfield and droplet impingement imilar to that on the full-cale airfoil leading edge. One uch approach ued airfoil with full-cale leading edge and truncated aft ection to imulate the tlowfield of the full cale, thereby avoiding altogether the ice-accretion proce on the airfoil leading edge and the aociated caling iue. 12 Interetingly, neither the approach nor it range of application received much attention. depite it numerou merit, uch a permitting an in-depth tudy of droplet impingement and ice accretion on full-cale leading-edge ection within the capabilitie of current icing reearch facilitie. Moreover. the method may alo prove ueful for aircraft company icing certification.

2 234 SAEED. SELIG. AND HRAc;c; In the abence of a ytematic tudy to provide inight into the deign of the aft ection. a recent tudy wa carried out in which a deign procedure for hybrid airfoil wa uccefully developed and demontrated with pecific deign example." The tudy howed that hybrid airfoil could be deigned to exhibit the full-cale velocity ditribution on it noe ection a well a full-cale droplet-impingement characteritic and. therefore. ice accretion. An inherent limitation of the deign procedure outlined in the tudy'' i that the method wa retricted to a ingle-point deign and. therefore. lacked the capability to handle off-deign cae. Moreover. the method ued the matched lift coefficient technique to correct for vicou effect. To overcome thee limitation. the preent tudy wa carried out with the objective of expanding the cope of the inglepoint deign procedure of Ref. 13 to a method that enable the hybrid airfoil to exhibit full-cale velocity ditribution a well a droplet-impingement characteritic and, therefore, full-cale ice accretion throughout a deired a range. The tak of imulating off-deign full-cale droplet impingement. a will be hown later. i uccefully accomplihed by introducing a plain flap on the hybrid airfoil. The ue of a plain tlap. however. fail to imulate full-cale velocity ditribution at the off-deign condition. Becaue difference in the velocity ditribution on the noe ection will affect both the thermodynamic of ice accretion and droplet impingement on the urface, it therefore become neceary to imulate the fullcale velocity ditribution in addition to droplet impingement at the off-deign condition. Thu. to imulate the full-cale velocity ditribution a well a droplet-impingement efficiency on the noe ection of the hybrid airfoil throughout a deired a range. it i neceary to formulate a multipoint hybrid airfoil deign method. To et the tage for the multipoint deign method, thi paper preent the deign of two half-cale hybrid airfoil that are deigned at two different angle of attack. uch that they imulate the full-cale noe-ection velocity ditribution a well a the droplet-impingement characteritic at their repective deign angle of attack. The velocity ditribution and dropletimpingement characteritic of the two hybrid airfoil are then analyzed at an off-deign angle of attack and compared with that of the full-cale airfoil. The reult are then ued to highlight the limitation of the preent method and. therefore. ugget a need for a multipoint deign method. Important compromie that mut be made to achieve a multipoint deign for full-cale ice-accretion imulation throughout a deired a range are alo dicued. Deign Approach The hybrid-airfoil deign procedure for the full-cale flowfield and droplet-impingement imulation ue both validated computational airfoil aerodynamic and droplet-impingement code, pecifically, an invere deign method, 16 the Eppler code, 17 - '" X FOIL. 22 and AIRDROP.' 7 Reference 13 provide a brief dicuion of each of thee code. For a more detailed dicuion, the reader i referred to the aociated literature. Unlike the method preented in Ref. 13, wherein the potential flow i corrected for vicou effect uing the matched lift coefficient technique, the preent method ue a modified verion of XFOIL. The modified verion of XFOIL wa obtained by integrating the droplet-trajectory and droplet-impingement calculation ubroutine from the AIRDROP code into XFOIL. Thi wa done to take advantage of XFOIL' ability to analyze both invicid/vicou flow and incompreible/ubcritical flow (unlike the AIRDROP code, which i baed on an incompreible flow formulation l. In thi paper. the modified verion of XFOIL i referred to a the XFOILIAIRDROPcode. Once the ftowfield i determined uing known flight and icing condition. the droplet-trajectory calculation ubroutine are then ued in conjunction with the flow-olver ubroutine to determine the droplet-impingement characteritic of the airfoil. A conceptual illutration of the hybrid airfoil deign procedure i hown in Fig. I. A brief ummary of thee tep follow. Firt. a full-cale airfoil geometry i elected and the deired flight and icing condition are pecified. In particular. the Lear Jet 305 airfoil (Fig. 2) i ued in thi tudy to demontrate the deign procedure. The XFOILIAIRDROP code i then ued to predict the limit of droplet impingement on the full-cale airfoil. Thee full-cale limit of impingement are then ued to etablih how much of the full-cale upper and lower urface are ued for the ubequent hybrid airfoil hape. A in Ref. 13. thi leading-edge ection. which ue the full-cale coordinate, will be referred to a the noe ection. and the remaining ection of the hybrid airfoil profile will be referred to a the aft ection. The aft ection of the hybrid airfoil i then deigned to provide full-cale flowfield and droplet-impingement characteritic on the noe ection of the hybrid airfoil. An initial geometry for the aft ection i obtained through the ue of PRO FOIL. a multipoint invere airfoil deign code. 16 The deign of the intermediate airfoil. from which the aft ection of the hybrid airfoil i derived, i governed by everal contraint. namely, the cale of the hybrid airfoil. the upper and lower urface thickne and lope at the junction between the noe and aft ection. and a deired form for the preure recovery characteritic. Apart from thee contraint. additional continuity and cloure contraint that form an integral part of the invere deign methodology are alo atified to achieve a phyically realizable deign.'" A multidimenional Newton iteration cheme i employed to atify thee contraint. The flow over the hybrid airfoil i then analyzed uing the XFOILIAIRDROP code. To have a phyically imilar flow in the vicinity of the noe ection of both the hybrid and the fullcale airfoil, the analyi i performed at the ame angle of attack relative to the noe-ection chord of both airfoil. The local velocity ditribution over the noe ection and the tagnation point location on oth the hybrid and full-cale airfoil are then compared. If the deired velocity ditribution over the noe ection and tagnation point location are not achieved, the aft ection of the hybrid airfoil i redeigned and again merged with the noe ection to form a new hybrid airfoil. The Fig. l 0.2 e Flowchart for the hybrid airfoil deign procedure. c- ---== Fig. 2 Learjet GLC 305 airfoil.

3 SAEED. SELIG. AND BRAGG 235 flow over the new hybrid airfoil i then analyzed and compared with that of the full-cule airfoil. The proce i repeated until the deired velocity ditribution over the noe ection i achieved. In the next tep. the droplet trajectorie and impingement characteritic are determined from the XFOIL/AIRDROP code. The individual droplet trajectorie are combined to calculate the droplet-impingement characteritic of the airfoil. The droplet-impingement characteritic of both the full-cale and hybrid airfoil are then compared. If the agreement in the droplet-impingement characteritic i poor, the hybrid airfoil i modified and the deign proce i repeated again until good agreement i reached. At thi tage, the ingle-point deign i accomplihed. To achieve off-deign full-cale ice accretion or droplet-impingement characteritic, a plain flap i employed on the hybrid airfoil. Thu, by deflecting the flap, the deired droplet-impingement characteritic are achieved over the hybrid airfoil for the off-deign cae. The off-deign cae reveal, a will be hown in the next ection, certain important limitation of the deign method. Thee limitation include I) the onet of flow eparation on the hybrid airfoil at moderate to high angle of attack condition. and 2) a mimatch in the velocity ditribution on the noe ection at off-deign angle of attack. The former limitation can be improved either by uing a more ophiticated flap ytem or by applying le conventional technique, uch a boundary-layer control through lot uction 30 ' 31 or circulation control through trailing-edge blowing. The latter, however, i an important limitation of the preent deign method and can be overcome by uing a multipoint deign approach. A mentioned earlier, the current tudy i an extenion of the ubcale airfoil deign method firt preented in Ref. 13. Reference 13 not only indicate that the ubcale airfoil deign method ue validated computational aerodynamic and droplet-impingement code but alo cite additional reference in which thee code have been uccefully applied to the deign and analyi of airfoil for variou application and, thu, etablihe the accuracy of numerical reult it pteent, a well a thoe prented in thi paper. Implementation In thi ection, the effect of variou parameter on two ingle-point airfoil deign are dicued. In particular, two halfcale hybrid airfoil were deigned at different angle of attack uch that they imulated both the full-cale velocity ditribution on the noe ection a well a droplet-impingement characteritic at the deign condition (ingle-point deign). The off-deign full-cale velocity ditribution and dropletimpingement characteritic of each hybrid airfoil are compared to highlight important limitation of the preent method. Single-Point Deign and Simulation The deign of two half-cale model of the GLC 305 airfoil that imulate full-cale velocity ditribution and droplet-impingement characteritic i preented. Of the two hybrid airfoil, hybrid airfoil A i deigned to imulate full-cale ice accretion at a = 2 deg. and hybrid airfoil B i deigned to imulate full-cale ice accretion at a = 6 deg, along with the following icing condition: V, = 90 m/ ( 175 kn), T = - 10 C, Re = 6 X 10 6 M = and VMD = 20 1-Lm (where VMD = volume median droplet diameter). Although it i realized that in flight the condition will change with the angle of attack, the condition for both angle of attack are held contant here to imply illutrate the method. A a firt tep. the droplet-impingement efficiency {3 for the GLC 305 airfoil that correpond to the given flight and icing condition i determined by the XFOIL/AIRDROP code. The reult are hown in Fig. 3. For a = 6 deg, the XFOIL/ AIRDROP code predict the maximum limit of impingement a. = 076 (x/c = 02) on the upper urface and 1 = (:de= 0.174) on the lower urface. Becaue the limit of impingement define the urface over which ice will accrete on the airfoil, only that part of the full-cale airfoil geometry need to be fixed a the noe ection for the hybrid airfoil. Thu, Table 1 Variable V., m/ T. oc Re M c. Ill VMD. IJ.Ill a. deg y, deg a,. deg VN., p 02 -{)2 Deign flight and icing condition Full cale X , Hybrid A Hybrid B X x to Hybrid A 0.5 xlc 0.1 ylc ----> Fig. 3 Droplet impingement efficiency for the Learjet GLC 305 airfoil. c) - x/c Fig. 4 Comparion of full-cale and hybrid airfoil A at deign a = 2 deg: V., {3, and c) tangent droplet trajectorie.

4 236 SAEED. SELIG. AND BRAGG Hybrid B 0.5 Hybrid/j VNtx> p 0.5 :de Fig. 7 Comparion of full-cale and hybrid airfoil A droplet-impingement efficiencie for deign a at 5- and 40-,.un droplet. y/c c) 0.2 Fig. 5 Comparion of full-cale and hybrid airfoil 8 at deign a = 6 deg: V {J, and c) tangent droplet trajectorie. Fig. 6 c - - Hybrid A Hybrid ::-- _- _-=: _- _--===- Two hybrid airfoil and the Learjet GLC 305 airfoil. the noe-ection geometry for both hybrid airfoil wa elected a the full-cale airfoil urface from :de = 5 on the upper urface to x/c = 0.20 on the lower urface. The two hybrid airfoil were then deigned following the procedure illutrated in Fig. 1. Table 1 lit the flight and icing condition for the final ingle-point deign. A companon of the full-cale airfoil velocity ditribution with that of the individual hybrid airfoil velocity ditribution (Fig. 4a and 5 at the ingle-point deign condition how good agreement over the common noe ection. Comparion of the impingement characteritic (Fig. 4b and 5 and tangent droplet trajectorie (Fig. 4c and 5c) alo indicate excellent agreement with thoe of the full-cale airfoil. The tangent droplet trajectorie. although originating from different location uptream. are matched in the vicinity of the leading edge. Thi i conitent with the obervation made during the cae tudie in Ref. 13. At thi point. the ingle-point deign for full-cale velocity ditribution and droplet-impingement im- ulation i complete, and the two hybrid airfoil along with the Learjet 305 airfoil are hown in Fig. 6. Effect of Droplet Size The droplet-impingement characteritic of an airfoil. i.e.. the limit of droplet impingement, {3. and the rnax.imum point on the {3 curve (referred to a f3m,,.), depend to a large ex.tent on the ize of the water droplet in the flow. Por the cae of mall droplet. the droplet drag dominate and the particle are very reponive to the flowfield and. therefore. act almot a flow tracer; wherea. in the cae of large droplet, the droplet inertia dominate and the particle are le enitive to change in the flowfield. Change in flow velocity for contant droplet ize follow a imilar trend. Thu, an increae in the droplet ize or the flow velocity reult in an increae in {3. f3mu and the limit of droplet impingement. It i therefore intereting to examine the effect of different droplet ize on full-cale droplet-impingement characteritic at contant flow velocity. Becaue, in natural icing cloud, the water droplet have volume median diameter ranging from 5-40 J.tiTI. the impingement characteritic of hybrid airfoil A were determined for two different droplet ize. The reult are preented in Fig. 7 and how good agreement where the droplet ize are le than that elected for the ingle-point deign. For larger droplet ize. a good overall agreement can be een, but the limit of {3 and f3m., differ lightly. Similar reult were alo oberved in hybrid airfoil B. Off-Deign Simulation To imulate full-cale ice-accretion or droplet-impingement characteritic throughout a deired a range. a fiap ytem wa employed on each of the hybrid airfoil. The objective wa to match both the velocity ditribution and the droplet-impingement characteritic at any off-deign angle of attack by an appropriate amount of flap deflection. To accomplih thi tak the two hybrid airfoil were analyzed at off-deign angle of attack; in particular. hybrid airfoil A. deigned to imulate condition at a = 2 deg, wa analyzed at a = 6 deg. and hybrid airfoil B. deigned to imulate condition at a = 6 deg, wa analyzed at a = 2 deg. Other tlight and icing condition were kept the ame a hown in Table I. The reult are hown in Fig. 8 and 9, in which the hybrid airfoil velocity ditribution and droplet-impingement characteritic are hown with and without the appropriate flap deflection neceary to imulate full-cale droplet-impingement characteritic. The reult how that, although the ue of a flap on hybrid airfoil can be quite effective in imulating full-cale droplet-impingement characteritic at an off-deign condition (the {3 curve for the

5 SAEED. SELIG. AND BRAGG 237 VN Hybrid A (Sf= 0 dcg) Hybrid A (S/ = 6 dcg) full-cale and hybrid airfoil are cotnctdent), the flap doe not yield the full-cale velocity ditnbutton over the hybrid-airfoil noe ection. To determine the optimum flap etting, the root-mean-quare ( RMS) difference in local impingement efficiency RMS and in normalized urface velocity RvtS.-. were calculated for different a and flap etting. Mathemattcally. RMS 11 and RMSv are defined by (I) RMS., =II V,,(J - V,JJII (2) p '"------\ c 0.5 xlc Fig. 8 Comparion of full-cale and hybrid airfoil A at off-deign a 6 deg: V and /J, with and without flap deflection. where, :S :S. Figure loa and lob how the variation in RMSu and RMS.,, repectively, for different angle of attack and 8 1 for the hybrid airfoil A deigned for a = 2 de g. and Fig. II a and lib how imilar plot for the hybrid airfoil B deigned for a = 6 deg. The optimum flap deflection wa then elected a the one that correpond to the minimum value of RMS 0. The optimum flap etting correponding to each angle-ofattack cae are plotted in Fig. 12a for clarity. Figure 12b. on the other hand, how a comparion of the I' of both hybrid 04 c:o e-- a = 0 deg --e- u = 2 deg --e-- a = 4 dcg --+- a =6deg a =8deg -tt- a =9deg +,. 4 II ' ' Hybrid B (Sf = 0 deg) Hybrid B (Sf = -8 deg) I:.., O.D2 VJI::xr.. _:1 VN / I of, deg Fig. 10 Variation in the RMS value for different angle of attack and flap etting for hybrid airfoil A xlc c:o _-_-_-_-_-_- \ c ===-\ I 4 I: Fig. 9 Comparion of full-cale and hybrid airfoil 8 at off-deign a 2 deg: V and /J, with and without flap defiectioo of,deg Fig. 11 Variation in the RMS value for different angle of attack and flap etting for hybrid airfoil B (ee Fig. 10 for key ymbol).

6 23g SAEED. SELIG. AND BRAGG ""0... c.o I a, deg Deign pomt 1, / _/Hybrid A Concluion From thi work it ha been hown that 11 i poible to deign hybrid airfoil with full-cale leading edge and redeigned aft ection that exhibit full-cale airfoil water droplet-impingement characteritic throughout a given angle-of-attack range. The reult indicate the uefulne of a flap ytem in imulating off-deign full-cale droplet-impmgement characteritic. The ue of a flap for full-cale droplet-impingement imulation i, however, retricted to low and moderate angle of attack, becaue at high abolute angle of attack together with high flap deflection, the hybrid airfoil become uceptible to flow eparation. It hould be poible to overcome thi limitation, however, by the ue of a more ophiticated flap ytem or by the application of boundary-layer control method. The reult of the off-deign imulation alo reveal the exitence of mall difference in urface velocity ditribution within the limit of droplet impingement. Becaue thi difference in urface velocity will affect the thermodynamic of ice accretion and prevent full-cale ice-accretion imulation. the preent method hould be modified to include alo the effect of ice accretion in the deign of hybrid airfoil. Fig. 12 Plot of optimum flap deflection and repective airfoil circulation Hybrid B Fig. l3 Comparion of off-deign /3 for 40-1-'m droplet ize at a = 4 deg and 6 1 = -5 deg. airfoil with that of the full-cale airfoil. The reult indicate that the hybrid airfoil require le circulation than the fullcale airfoil to imulate full-cale droplet impingement, and that the difference between the full-cale and hybrid airfoil circulation i nearly contant until ignificant flow eparation occur on the hybrid airfoil. Beyond thi point the hybrid airfoil circulation tart to fall off gradually and, therefore, ugget the limit to which a hybrid airfoil can be ued to imulate full-cale droplet-impingement characteritic. It i important to note in Fig. 10 and II that the RMS;; value are an order of magnitude higher than the correponding RMS". Although contribution to the RMS value caued by numerical noie cannot be ruled out completely. difference in urface velocity may affect the thermodynamic of ice accretion. Thu, it become neceary to incorporate the ice accretion proce in the deign method, in addition to flow and droplet-impingement analyi. The effect of larger droplet ize on the off-deign imulation i hown in Fig. 13. Similar trend can be oberved a in the on-deign cae. Becaue large-ized droplet reult in an increae in the limit of impingement. they, together with the angle of attack of interet, may dictate the ize of the noe ection and, thu, limit the range of application of the preent method. Acknowledgment Thi work wa ponored by NASA Lewi Reearch Center under Grant NCC We would like to thank Reuben Chanderaekharan of Learjet, Inc.. for providing the NASA Lewi Reearch Center with the Learjet GLC 305 airfoil ued in thi tudy. Alo, helpful dicuion with Gene Addy, Tom Ratvaky, and Tom Bond of NASA Lewi Reearch Center are gratefully acknowledged. Reference 'Anon., "Selected Bibliography of NACA-NASA Aircraft Icing Publication," NASA TM Aug 'Anon., "Icing Technology Bibliography." Society of Automotive Engineer, Aeropace Information Rcpt. 4015, Warrendale. PA. Nov 'Anon., "Aircraft Icing," NASA CP FAA-RD NASA Lewi Reearch Center. Cleveland, OH. July 'Brun, R. J., "Icing Problem and Recommended Solution," AGARDograph 16. Nov 'Perkin. P. and Rieke, W., "Aircraft Icing Problem- After 50 Year," AIAA Paper , Jan Bragg, M. B., Gregorek, G. M.. and Shaw, R. J.. "An Analytical Approach to Airfoil Icing," AIAA Paper g Jan 'Bragg, M. 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7 SAEED. SELIG. AND BRAGG Eppler. R.. and Somer. D. M.. ''A Computer Program for the Deign and Analyi of Low-Speed Aorfoil. NASA fm Aug Eppler. R.. Airfoil Deign and Data. Springer- Verlag. New York. 90. ' 0 Drela. M.. and Gile. M. B.. "ISES: A Two-Dimenional Vicou Aerodynamic Deign and Analyi Code," AIAA Paper Jan "Orela. M.. "Low-Reynold Number Airfoil Deign for the MIT Daedalu Prototype: A Cae Study. lou mal of Aircraft. Vol. 25. No. 8, pp "Orela. M. "XFOIL: An Analyi and Deign Sytem for Low Reynold Number Airfoil. ' Lecture Note in Engineering: Low Reynold Number Aerodwwmic. edited by T. J. Mueller. Vol. 54. Springer- Verlag, New York pp "Taylor. G. 1., "Note on Poible Equipment and Technique for Experiment on Icing on Aircraft." Aeronautical Reearch Council, R&M Jan Giauert. M.. "A Method of Contructing the Path of Raindrop of Different Diameter Moving in the Neighbourhood of (I) a Circular Cylinder, (2) an Aerofoil Placed in a Uniform Stream of Air; and a Determination of the Rate of Depoit of the Drop on the Surface and the Percentage of Drop Caught. Aeronautical Reearch Council. R&M Nov "Langmuir. 1.. and Blougett. K. B. "A Mathematical Invetigation of Water Droplet Trajectorie." U.S Army Air Force, TR 5418, Feb '"Bragg. M. B.. "A Similanty Analyo of the Droplet Trajectory E4uation." AIAA Journal. Vol. 20. No pp "Bragg, M. B... AIRDROP: Aorfoil Droplet Impingement Code," NASA CR (to he publihed). "Bragg, M. B.. and Gregorck. G. M. "An Incompreible Droplet Impingement Analyi of Thirty Low and Medium Speed Airfoil," Aeronautical and A aronautical Reearch Lab., Ohio State Univ., TR AARL Columbu. OH. Feb Gent, R. W.. "Calculation of Water Droplet Trajectorie About an Aerofoil in Steady, Two-Dimenional. Compreible Flow," Royal Aircraft Etablihment. TR Famborough, Hant. UK, June Saeed. F.. and Selig, M. S.. "A Multipoint Invere Deign of Airfoil with Slot-Suction," Journal of Aircraft. Vol. 33, No.5,' 1996, pp "Saeed. F., and Selig, M. S.. "A New Cla of Airfoil Uing Slot Suction," AIAA Paper Jan Flight Perf anna nee of Aircraft S. K Ojha Indian Intitute of Technology Powat Bombay, lndta 1995, 516 pp, illu. Hardback ISBN AIM Member $69.95 Nonmember $89.95 Order #: 13-2(945) Thi important new book decribe the baic force that dictate and decide the performance of an aircraft. Primarily written for undergraduate and graduate tudent of aeronautical and aeropace engineering, thi book will alo erve pilot and flight tet engineer. Flight Performance of Aircraft i an academic book that directly correpond to real-life ituation. Thi elf-contained book preent performance analy1 of almot all the phae of flight including takeoff. climb. cruie. turn. decent, and landing. To enhance the reader' confidence in dealing with thee topic and other. a lit of problem i provided at the end of each chapter to encourage problem olving and theory comprehenion In addition. the book include hundred of figure. ketche. table. chart. and reference that reinforce and complement the text. Content: A1rcraft. Baic Force. and Performance Atmophere and Flying Weather Aerodynamic Force on Aircraft Propulive Thrut by Jet Engine Propulive Power by Piton-Prop Engine Altitude. Airpeed, and Wind Speed Gliding and Unpowered Flight Cruimg Flight of Turbotet Aircraft. Optimization of Cruiing Flight of Turbojet Aircraft Climbing Flight of Turbojet Aircraft Turning Flight of Turbojet Aircraft. Cruiing Flight of P1ton-Prop Aircraft Optimization of Cruiing Flight of Piton-Prop Aircraft Climbing Flight of Piton-Prop Aircraft. Coordinated Turning Flight of Piton-Prop Aircraft. Takeoff and Landing Performance Aerobatic Maneuver and Flight Boundarie Performance Evaluation by Flight Tet Weather Hazard and Flying Weather Obervation. Report. and Forecat to Flying Appendice Subject Index American Intitute of Aeronautic and Atronautic Pubhcaloon Cutomer Servtce. 9 Jav Gould Ci.. PO Box 153. Watdort Fax J.ll159 Phone 800/ am - 5 p m Eatern CA and VA retdent add applicable ale tax For htppmo and l'landhng add S4 75tor 1-4 book (call for rate lor htgher Quan I toe) Alltndtvldual order. tnr:ludtng US. Canadtan. and IOielQil. """lle prepard by peronal or comoany cl'eck. tr...- dwld<. nlernaiic!rjal money order. or credrt card (VISA. MalerCard. AmeriCan Expre_ or Ot""' CluOI All cte:1c mullle fmile payaoie lo AIAA tn US dollar. drawn on au S!lank Order lrom IIOrane. COf]Xllal on.go""""""' aoenr:tes. &"'l un,.,.tly aod college llook Siore muolle accoo'(lallled llv an aulhortled puftllae order All oll1er llookloll! order mullle Prtll'td Pleae allow 4""'"' lor Jettvoery Prtce are ub1ect to cl\anoe wtlflouf nottce Return tn ellable eoodtlton wtl! be acceped Wlttun 30 day Sorry Ytt! can not ret:um of cae tudte. conlerera proceedtrvjs. ale tlem or oftware tunle detecttve) Noo-U S retdent are repootole lor payrrent ol any taxe requ11ed bv ltlelf qovernmen1