Dihedral

iD7 mow dral THREE BASIC MANEUVERS volve roll axis straight level flight state circling rolling article will steady-state roll predict roll rate will detail effect hedral arrangemen properties will also Part three cuss steady-state relationship stability ransitlons ers disci time induce thim p wing ml tt NO OCR TEXT 0 -I-7/ -----~1 / Figure 1 RoIl damping caused opposing change angle attack figure de picts wing flying right executing right-hand axial roll phantom lines trace motion wing left wing sees negative angle attack right wing sees positive angle attack change angle attack opposes dampens right-hand roll Note change angle attack diminishes zero center wing damping-moment balance steadystate roll achieved roll damping can cels out roll moment due yaw useful compare relative sensitivity roll damping roll moment varia bles discussed above instance roll damping roll moment equally af fected change variable say wing area variable does affect balance point two moments can cel Normally balance point interest roll rate Lets look time variables Wing area Equal effect moment damping no effect roll rate means fixed span aspect ratio has no effect roll rate other variables being equal Wingspan Affects damping momentroll rate inversely proportional wingspan means big airplanes will slower roll Airspeed Roll rate proportional air speed Airspeed increases roll damping proportion airspeed roll moment creases square alrspeed roll mo ment wins Yaw angle Roll moment proportional yaw angle damping affected yaw roll rate proportional yaw angle Dihedral angle Equivalent Dihedral An gle Roll moment proportional EDA damping affected EDA roll 80 UAJ 003 flfl .. rate proportional EDA sum up roll rate proportional air speed yaw angle equivalent dihedral angle inversely proportional span Example Say nice plane want double roll rate could making fly twice fast put ting rudder yaws twice much bending wings up its EDA twice great could chop wings down span halved Calculating steady-state roil rate Since works out roll rate proportional versely proportional important var iables really need calculate roll rate single known roll rate given set variables need ra tio roll rate proportion ratio various variables Rather make work too hard Ive included several plots should speed up process Figure 3 shows roll rate 100-in-span airplane 100 EDA 100 yaw variety airspeeds Say have 80-in-span airplane 150 EDA want know its roll rate 20 ft/sec yawed 100 Since plane has 8/10 span 15/10 dihe dral know will roll 10/8 x 15/10 times fast Looking up roll rate bigger plane Figure 3 find 70 ---7 -J -- - - - right roll V -I -08 -06 -04 -02 0 02 04 06 06 left tipCLright tip WING STATION fraction semi span Figure 2 Change lift distribution forcibly rolled wing oppo ses roll Figure plots change lift distribution along ellip tical planform wing being forcibly rolled say physically twisting fuselage example span 100 area 1000 sq airspeed 20 ftIsec roll rate 1420/sec right 60 50 Roll Rate deg/sec 40 30 20 10 0 10 20 30 40 50 60 70 Airspeed Cf t/sec Figure 3 An airplanes roll rate proportional its airspeed Plot ted roll rate 100-in-span plane 10 EDA yawed 100 98 Model Aviation ultimate rolling machine High speed very small span powerful ailerons com bine provide 2-ft-span slope airplane very high roll rate does ex pense good thermaling abilities though GELTA LIFT lbIO05 span 001 -001 -002 -003 -004 80 90 100 70 60 50 Roll Rate deg/sec 40 30 20 10 0 255075100 12550175200 Spaninches EDA s 50 0246 80 12 1461820 Yaw Angle degrees Figure 4 Left Roll rate inversely proportional wingspan figure plots roll rate planes 100 Equivalent Dihedral Angle yawed 1O airspeed 30 ftIsec Figure 5 Right Roll rate proportional Equivalent Dihedral Angle yaw angle figure plots roll rate three differed 100-in-span planes flying 30 ft/sec planes have Equivalent Dihedral Angles 50 10 150 --71g- 50 Li - - 08 -06 -04 -02 0 02 04 06 08 CL Wing Station fraction semispan Figure 6 Left Yawed rolling change angle attack parabolically curved wing proportional wing station Equivalent Dihedral Angle EDA yaw angle Three wings shown EDAs 50 100 150 yawed parabolic wing analogous helical pitch propeller amount twist vary ing wing yaw angle EDA Figure 7 Above Local dihedral determines change angle attack yawed wing V-dihe right tip dral wings have constant change angle attack along wing yawed parabolic wing changes proportionate wing sta tion polyhedral wing approximation parabolic wing has roll rate about 14 degrees per second airspeed 20 ft/sec Clearly plane will roll 14 x 1875 degrees per second could also have figured out Figure 4 shows roll rate plane 100 EDA 100 yaw airspeed 30 ft/sec variety spans Since plane has 15/lOs EDA 20/30 airspeed same yaw angle plane plot know Continued page 174 300 200 100 000 -100 -200 Parabolic: :~ lyhedral hedral -300 CL -08 -06 -04 -02 u 02 04 06 08 1 left tipWING STATIONright tip fraction semispan 200 150 100 DELTA ALPHA deg 050 000 -050 -100 -150 -200 iiI~~IV-Dihedral \ ISO0 Ad4e NI -06 -04 -02 0 02 04 06 08 CL WING STATIONfraction semispan Figure 8 Left plot Idea represented Figure 7 yawed rolling wing change angle attack delta alpha varies continuously tip tip parabolic wing two- four-panel wings change angle attack occurs two four steps particular plot represents wings Equivalent Dihedral Angles 10 yawed 100 right Figure 9 Right Increasing number wing panels reduces range angle attack rolling wing plot combines effects shown Figure 1 Figure 8 change angle attack along length steadily rolling yawed wing shown parabolic polyhedral V-dihedral types parabolic wing achieves roll equilibrium entire wing same angle attack inboard 60% V-dihedral wing push ing outboard portion wing fighting itself rolling Polyhedral wing compromise between two other types data shown 100-ln-span plane 10 Equivalent Dihedral Angle yawed 100 flyIng 30 ff/sec rolling 2201sec right September 1988 99 100 go 80 70 60 Roll Rate deg/sec 50 40 30 20 I0 0 DELTA ALPHA deg 5 4 3 2 0 -2 3 -4 -5 left tip DELTA ALPHA deg double-sided tape Wait until after initial test flights before permanently attaching 6 dowel motor nacelle braces lightly glue Ambroid first adding radiators vacuformed engines will enable make minor thrust adjustments needed easily Lastly carve some foam pilot figures add much rigging control ca bles like flying Make sure surfaces un warped balance point shown plans first test flights should very calm weather over softest sur face can find green grass ideal Test charge flight battery several times get feel long charge needed get 8- 10-sec motor run Since really cant test glide model will use short runs sort things out initially Put tweak about /16 right rud der Charge motor 8- 10-sec run carefully launch model Re move noticeable turn dive stall ten dency rudder elevator surfaces large make small changes time Shoot straight power glide almost level flight no tendency slow down hang props short hops satisfactory gin lengthen charge get five 10 additional seconds power Remember lengthen charge initial power level will increase somewhat time reach 20 30 seconds power should getting very slight initial climb level cruise Keep turns very wide gentle power exhausted model will descend slow steep glide isnt thermal soarer allow model climb nosehigh near stallespecially gusty weather Trim relatively shallow pen etrating climb satisfied short power runs charge up enjoy prettiest Free Flight sights youre ever likely see Dihedral/Beron-Rawdon Continued page 99 will roll 15/10 x 20/30 same roll rate Going plot Figure 4 80-in-span planes find roll rate should about 26 degrees per second Good thing plots agree Figure 5 also contains same informa tion three EDAs function yaw angle NEW IMPROVED * * LIjila WiMit todd wilk wouli Pow *US Pcte,tNx Des ** WANDIT * 2763 * * ies exited * eveamarramiPo1OftCORDJ * * elorOry * ick Abrasives * * Machine gives exceptional * ing control excellent tinixh * * 5 easic mci 1 fiat Wand aed 1 * nisantsp * ulde Specel iint 2 fIat 1 hail* rauma wand 5 xl grits * ehsiie ricxdes3liai2 hail 10uSd xi * gits * ditional Wandx Abraxivex available * *WANDIT MANUFACTURING 214 2885789 PO Box 266 uite Texas 75149 MINIJET SERIESOhs Proud gird thePreiLd Sun Onese planes feature xii balsadesigned meet rxnstructlon Designed ciththe g/7 0SPRA Furmula intccnedlate flyer xindthey clii 120 rulesnhis 1/u accept 2025 sizeenginefuse scale wedel ciii accept rear eahaust engine fur xx 60i20 cl size engines ccptionai perforxanceOet p glass fuselageclth uf tIe thrill jet cithoutoo wing cxnstructixn full kit $15000 ccv hassles nutted fanSkphack Semikit alma axailable Ins cund $02100 Special Introdactocp PricePlease add $1000 shipping handling $4000 plus $300 flu hes Send check Mdadd 5% sales tax Mastercard hisS C0D add $3003001 15lA477 PARRISH AIRCRAFT c SCALE cOAStS Toy Turkyp Fornula lDart Experimental o SW 49lkTer $9100 $5 SIRtigershurkceoplace full size aircraft antalien FIx 33317 Prototypical dihedral arrangements Al though different dihedral schemes same Equivalent Dihedral Angle will roll same rate actual localized flow air over wing will vary considerably sake illustrating behavior less rudder yaw near stall fly speed margin stall rapid maneuvers required Polyhedral Breaking wing up four sections instead two V-dihedral re duces range angle attack variations across wing during steady-state roll illustrated Figure 9 saw tooth line reduces possibility leaving drag bucket during maneuvers can imagine number wing panels increased sawtooth becomes progressively finer until equivalent elliptical wing reached Discussion see above designer rudder-elevator airplane has few options play order control maximum roll rate plane RC Sailplane applications desire achieve high roll ratemore almost al ways better Span airspeed powerful variables usually determined higher prior ity requirements such glide ratio 174 Model Aviation AND PRINTING SERVICE QUICK SERVICE OVER 300 ORDINATE SETS ON FILE SEND 5200 xodS1SEloogeonelopeforsuoooplea tlxs list xf niefuil xx isuod xxxv SEP10 S500 SASE bag fur plot ta chord irogIlo suet oxooples oxooc scvezxl xixfuds lox ocdcc pocfccruccc IncludE pLots copy thc thepe rod die dhta possible SEND $1011 fur doe PLOT SHAPE CATALOG xfcbe 100 plus olotuds loc St ditch plots pius lustsoicxi xoofcol iofnzxoxloon sdsec osefxdl aicfod duos roan/many puges STANDARD PLOTSander Oliorhex ISLE poge Lorge docoda noriloble no coDs cost cssopcopscdoorlox clssod bxogob 20 chord tosice coat sf10 p1st CUSTOM PLOTnEG AVAILABLE Can modifr oanbcx olijobosass mdi pieces Osgather coos slow vanous also thocboocSScs top & bottom ilifrorot TAPERED 1NO PLOTS $1000 Secop pbua 50 roots pci rib oven 10 slightly higher THIS MONThS HOT PLOTS MACA 6100 MACA 0000 Orcut foc stabs EPPLER 102 205 SIOil Oxsd chE cod af Mooch magsoioe issue date Can slow Slid oh no tltdiSlsixnldclooess NO EXIThIL CHARGE Hot plots Osly $100 over 10 $101 THE PTERANOOOH PRESS 0N PODOSS0 OAE ANn CA 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Write free catalog SVNASA patches flight suits pictures astronaut food much VISA/MC 1-800-426-1354 sink rate leaves yaw angle Equivalent Di hedral Angle big vertical stabilizer large-percentage-chord rudder can used achieve high yaw angles large yaw angles problematic Unless fuse lage very small inefficient fly airplane high angles yaw because fuselage will making lot drag Also large yaw angles take lot time achieve plane depends high roll rate will lack precision different dihedral arrangements roll mode will describe two prototypical arrangements intermediate arrange ment prototypical arrangement wing smoothly curving dihedral curve shape parabola has property having slope propor tional distance centerline smaller angles dihedral less 300 fair approximation say its dihedral angle increases propor tion distance airplane center line also fair approximation say parabolas very similar circles angles small say less 20 degrees can see Figure 2 changing angle attack delta alpha such curved wing yawed increases linearly toward tip progressive change angle attack also visible front view yawed wing illustrated Figure 7 An approximate formula curva tare wing Z 0296/b X2 EDA equivalent dihedral gle Z vertical height wing function wingspan b wing station X other prototypical arrangement sinijile V-dihedral scheme wing has same dihedral angle everywhere yawed has same change angle attack positive negative along wing Figure 8 illustrates delta alpha yawed dihedral wing well other types Figure 7 also illu strates property intermediate arrangement fourpanel wing panel breaks 05 semi span wing intended approxi Step future AVIATION Become Aviation Electronics Technician learn repair maintain electronic equipment used aboard aircraft Actual planes used training Hangar runway campus Train just 19 months Jobs waiting CALL NOW 1-800-634-7972 CLOVER PARK Vocational Technical institute 4500 Steilacoom Blvd SW Tacoma WA 98499-4098 FAA Rupair Slation #4466 mately mimic behavior curved wing setting dihedral angle propor tion distance centerline Since center outer panel three times far centerline inner panel its dihedral angle three times SAFE FLYING ISNO ACCIDENT YXKI great Figures 7 8 also illustrate type wing Parabolic dihedral yawed wing parabolic dihedral presents change angle attack along wing pro portional distance airplane centerline See Figure 6 again di rectly analogous helical-pitch propeller forcibly rolled angle attack along wing varies proportion distance airplane centerline Note change angle attack exactly matched presented parabolicdihedral wing means parabol ic-dihedral wing reaches its steady-state roll rate net change angle attack reaches zero along wing illus trated Figure 9 horizontal line delta alpha ans entire wing work ing uaisonno part wing work ing against other September 1988 175 Continue4 page 176 TWO NEW FLIGHT BOXES Cowylefely assewbied snd finished Mode USA Bofh ore top qualify wood constroction Two large drawers Unique drawer locks Swoll boo 0 plus shipping Large boo $1 2500 pius shipping includes fuel cowparfwenfbatferypower panel cowportmeofadjustable fuselage cradles Money back gsaraefee Send $1 specs call 415 3637732 Inane wesuaqe Flights Fancy eruwodefiog P0 Boo f La f4oedo Ca 94020 0070 n,yi 0UU sq II Wfl9 ares Power 15-28 cu gn weight 3-3% lbs Wing loading 34 lbs z Kit Features easy building balsa constructioni Maple Engine Raiis isoisted Tank Compartment Formed MusIc WIre Landing Gear THE FLORIO FLYER 837 Johnsonburg Rd 814 834-2586St Marys PA 15857 V-dihedral yawed V-dihedral wing has constant change angle attack along length half-wing roll ing change angle attack proportional distance centerline im posed constant change What end up inboard 60% wing trying make plane roll faster outboard 40% resisting illus trated Figure 9 large zig-zag line really doesnt matter much since wing still rolls same rate except possibility As can see Figure 9 near root upgoing wing fairly large positive change angle attack Near tip similar nega tive change angle attack Keep mind delta alphas proportional dihedral angle yaw angle wing has narrow drag bucket range angle attack low drag possible high-yaw largedihedral steady-state roll could take part wing outside low-drag range gle attack might also happen basic lift coefficient already near edge drag bucketrolling could move re gions wing out bucket might occur instance during low-speed flight rolling thermal plane already near stall maximum lift co efficient rolling up might stall board portion upgoing wing tip portion downgoing wing con sequence might need maneuver PROPULSION SYSTEMS VI-iliB$2495 Includes HY-71B Motor 8-62 Battery 2 Props Charge P10g Coooector Accessory Pkg screws spacers etc VL-l1lBR$2795 Same VI-lilS hot HY-7IBR Motor aod Remote Flight Battery Holder t 88 176 Model Aviation THERMAL CHARGER what looking electric sailplane good looks easy build fun fly great perfor mance Thermal Charger % PRECISION PRODUCTS INC 714 592-5144 510 E Arrow Highway San Dimas CA 91773 n F GUESS THE NIA S3ERIOU5 FtBOUT ThE NEW REQDENCIE5j / 11 ~1 POWER AT ITS BEST t Weight l P-30 Size Modelo k Gear Ratio t ant Start cost Battery Power ner MOTORS HY-lOB$1495 An improved HY-7t Featores reinforced prop shaft neoprene sleeve engage disengage Free-wheeling HY7OBR$1795 Same HY-7tB hot eqoipped Remote Flight Battery Holder er has 7Y leads quick disconnects Slide hattery FLIGHT BATTERIE 8-62 2n50 mAHr 9 gins . 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576Serendipityt ndeer EZA record-holder spans l7A in$325 No 577HallIlte CL /aA Combat plane has teem wing spans 30 in$225 No 578Schwelzer 1-26B 80 Oaarter-scale Sailplane spans 125 Two plan sheets$1475 No 579Lockheed P38 CL Precision Scale 98W II fighter tsr twin 45s spans 55 Fowler flays etc Thme plan sheets$1898 No 580Parnall Pixie PP Robber Scale Golden Age British biplane la 112 scala spans 31l/u in$375 No S81Gee Bee Model Y AC Golden Age Aucer spans 72 1k scale fur 60 power Three plan sheets$1175 No 582Heinkel 100 CL Sport Scite 9898 II fighter 40 engine spans 611/u stmctare mostly cardboard Two plan shts$1250 No 583Sportwsgon AC Radio-tied sport PP model spans 54 oses 10115 engine$798 No 584Happy Days CL Intermediate trainer/Stunter spans 42 uses 29135 engine$575 No 985Dragonfly PP High-performance P-30 Robber ship spans 35 weighs 50 grams$498 No 586Snapdragon AC Pan-fly/sportster 25/30 engines spans 45 in$6 98 No 587Pilatus PC-Sr CL Prable Scale/Stunten/sportster spans 56 oses 29/35 engine$550 No 586Marlah AC Slope-Scaring Sailplane spans 41 oses 2 80 channels$425 No 589Vickera Welleeley AC Sport Scale PdW II bomber spans 89 uses 40 4-cycle eegine Two plan shnets no dec$1250 No 550Bud Lite Laser Stunter CL Stunter scalelike spans 63 uses 60 engine Two eets$1050 No 591Focke-Wulfi PW 190-A AC Sport Scale WVd II fighter spans 98 uses 35/45 2-steske engine Two plan sht no doc. $13Sg No 592ET CL trainer/sportster oses 35 electric power 6-cell buOury pack Wingspan 24 in$475 No 593Taylorcratt AC Sport Scale lightylane builds sandard 2-placer clipped-wing air show stunter Spans either 701/n 98 Par 30/40 two-strake 40148 foar-strake engine Two plan sheets no docamentatlon$1098 No 554 P61 Black Widow CL Profile Scale WW II twin-engine night fighter uses 19125 engine spans 481/0 in $ 0 98 6 03 0 N N ee E2 -cs 082 8230 U 6zo 82 - C gao Em en -2 V - 82s es82 mob 00 2 3 82 82 0 V so82 0003 98 VI toI 08 o1 I I 003 00 gs I 110 i3 82STREET 82 ITY C 0 Circle numbers plans wish orderI Ga 0 6 oi o oE ZZ 0 98 193 414 490 531 554 572 582 590 239 440 506 533 555 575 583 591 262 447 512 534 559 576 584 592 310 454 514 53 563 577 585 593 314 457 521 539 568 578 586 594 326 460 522 541 569 579 587 595 332 465 525 544 570 580 588 596 Plan pdce includes first Class postage US delivery Air Mail over 300 miles 386 478 528 549 571 581 589 597 rs non-US address please add $250 Air Mail postage handling Bach plan Make check money order payable US funds drawn US bank Model Aviation AMA 1810 Samuel Morse Dr Reston VA 22090 Please allow 3 6 weeks delivery Please print carefullyEnclosed $ ______________________ ___________________________________________ AMA No ______________ immediacy control leaves Equivalent Dihedral Angle large EDA good way achieve high roll rate minimum penalty penalties several minor First wings high EDAs pay minor penalty drag due extra area per projected span facet will discussed Part Four series High EDAs require slightly larger vertical stabilizers order avoid Dutch roll problems will dis cussed briefly Part Three Lastly dis cussed above high EDAs may require cer tain piloting finesse flying close edge drag bucket clear rolling maneuvers parabolic polyhedral dihedral arrange ment superior V-dihedral whole story Part Three series discusses behavior steady-state circling flight such used working ther mal turns out circling V dihedral wing enjoys advantage over other two types reasons similar ar gument rolling case opposite So dont go running off half-cocked build yourself parabolic-dihedral wing un til youve read Part Three anyway series has assumed wings have elliptical planform rea sons discussed Part Wings other planforms may have different roll rates V-dihedral wings sensitive planform because during roll board portion wing pushing outboard portion wing smaller inboard bigger outboard roll rate will reduced would case constant-chord low-taper wing op posite true wella highiy tapered wing will roll faster major effect howevera constant-chord wing will still roll 89% fast elliptical roll rate parabolic-dihedral wings insensitive planform because parabolic wings constant angle attack along wing during steady-state roll Since wing fighting itself chord distrib ution does matter Summary conclusions Steady-state roll achieved roll moment due yaw equaled opposing roll damp ing moment Roll moment due yaw function wing area wingspan airspeed yaw angle Equivalent Dihedral Angle Roll damping moment function wing area wingspan roll rate airspeed Steady-state roll rate proportional air speed yaw angle EDA inversely proportional wingspan Roll rate can estimated basis graphs presented Figures 35 Two prototypical dihedral types intermediate type described dis cussed Dihedral schemes approaching parabolic curvature best rolling maneuvers because display small range angle attack variation across wing during steady-state roll 178 Model Aviation L STATE ____________________________________________________________[v32][b88830667200]]]ZIP ____________________________________________________________[v32][b161530697200]]I

iD7 mow dral THREE BASIC MANEUVERS volve roll axis straight level flight state circling rolling article will steady-state roll predict roll rate will detail effect hedral arrangemen properties will also Part three cuss steady-state relationship stability ransitlons ers disci time induce thim p wing ml tt NO OCR TEXT 0 -I-7/ -----~1 / Figure 1 RoIl damping caused opposing change angle attack figure de picts wing flying right executing right-hand axial roll phantom lines trace motion wing left wing sees negative angle attack right wing sees positive angle attack change angle attack opposes dampens right-hand roll Note change angle attack diminishes zero center wing damping-moment balance steadystate roll achieved roll damping can cels out roll moment due yaw useful compare relative sensitivity roll damping roll moment varia bles discussed above instance roll damping roll moment equally af fected change variable say wing area variable does affect balance point two moments can cel Normally balance point interest roll rate Lets look time variables Wing area Equal effect moment damping no effect roll rate means fixed span aspect ratio has no effect roll rate other variables being equal Wingspan Affects damping momentroll rate inversely proportional wingspan means big airplanes will slower roll Airspeed Roll rate proportional air speed Airspeed increases roll damping proportion airspeed roll moment creases square alrspeed roll mo ment wins Yaw angle Roll moment proportional yaw angle damping affected yaw roll rate proportional yaw angle Dihedral angle Equivalent Dihedral An gle Roll moment proportional EDA damping affected EDA roll 80 UAJ 003 flfl .. rate proportional EDA sum up roll rate proportional air speed yaw angle equivalent dihedral angle inversely proportional span Example Say nice plane want double roll rate could making fly twice fast put ting rudder yaws twice much bending wings up its EDA twice great could chop wings down span halved Calculating steady-state roil rate Since works out roll rate proportional versely proportional important var iables really need calculate roll rate single known roll rate given set variables need ra tio roll rate proportion ratio various variables Rather make work too hard Ive included several plots should speed up process Figure 3 shows roll rate 100-in-span airplane 100 EDA 100 yaw variety airspeeds Say have 80-in-span airplane 150 EDA want know its roll rate 20 ft/sec yawed 100 Since plane has 8/10 span 15/10 dihe dral know will roll 10/8 x 15/10 times fast Looking up roll rate bigger plane Figure 3 find 70 ---7 -J -- - - - right roll V -I -08 -06 -04 -02 0 02 04 06 06 left tipCLright tip WING STATION fraction semi span Figure 2 Change lift distribution forcibly rolled wing oppo ses roll Figure plots change lift distribution along ellip tical planform wing being forcibly rolled say physically twisting fuselage example span 100 area 1000 sq airspeed 20 ftIsec roll rate 1420/sec right 60 50 Roll Rate deg/sec 40 30 20 10 0 10 20 30 40 50 60 70 Airspeed Cf t/sec Figure 3 An airplanes roll rate proportional its airspeed Plot ted roll rate 100-in-span plane 10 EDA yawed 100 98 Model Aviation ultimate rolling machine High speed very small span powerful ailerons com bine provide 2-ft-span slope airplane very high roll rate does ex pense good thermaling abilities though GELTA LIFT lbIO05 span 001 -001 -002 -003 -004 80 90 100 70 60 50 Roll Rate deg/sec 40 30 20 10 0 255075100 12550175200 Spaninches EDA s 50 0246 80 12 1461820 Yaw Angle degrees Figure 4 Left Roll rate inversely proportional wingspan figure plots roll rate planes 100 Equivalent Dihedral Angle yawed 1O airspeed 30 ftIsec Figure 5 Right Roll rate proportional Equivalent Dihedral Angle yaw angle figure plots roll rate three differed 100-in-span planes flying 30 ft/sec planes have Equivalent Dihedral Angles 50 10 150 --71g- 50 Li - - 08 -06 -04 -02 0 02 04 06 08 CL Wing Station fraction semispan Figure 6 Left Yawed rolling change angle attack parabolically curved wing proportional wing station Equivalent Dihedral Angle EDA yaw angle Three wings shown EDAs 50 100 150 yawed parabolic wing analogous helical pitch propeller amount twist vary ing wing yaw angle EDA Figure 7 Above Local dihedral determines change angle attack yawed wing V-dihe right tip dral wings have constant change angle attack along wing yawed parabolic wing changes proportionate wing sta tion polyhedral wing approximation parabolic wing has roll rate about 14 degrees per second airspeed 20 ft/sec Clearly plane will roll 14 x 1875 degrees per second could also have figured out Figure 4 shows roll rate plane 100 EDA 100 yaw airspeed 30 ft/sec variety spans Since plane has 15/lOs EDA 20/30 airspeed same yaw angle plane plot know Continued page 174 300 200 100 000 -100 -200 Parabolic: :~ lyhedral hedral -300 CL -08 -06 -04 -02 u 02 04 06 08 1 left tipWING STATIONright tip fraction semispan 200 150 100 DELTA ALPHA deg 050 000 -050 -100 -150 -200 iiI~~IV-Dihedral \ ISO0 Ad4e NI -06 -04 -02 0 02 04 06 08 CL WING STATIONfraction semispan Figure 8 Left plot Idea represented Figure 7 yawed rolling wing change angle attack delta alpha varies continuously tip tip parabolic wing two- four-panel wings change angle attack occurs two four steps particular plot represents wings Equivalent Dihedral Angles 10 yawed 100 right Figure 9 Right Increasing number wing panels reduces range angle attack rolling wing plot combines effects shown Figure 1 Figure 8 change angle attack along length steadily rolling yawed wing shown parabolic polyhedral V-dihedral types parabolic wing achieves roll equilibrium entire wing same angle attack inboard 60% V-dihedral wing push ing outboard portion wing fighting itself rolling Polyhedral wing compromise between two other types data shown 100-ln-span plane 10 Equivalent Dihedral Angle yawed 100 flyIng 30 ff/sec rolling 2201sec right September 1988 99 100 go 80 70 60 Roll Rate deg/sec 50 40 30 20 I0 0 DELTA ALPHA deg 5 4 3 2 0 -2 3 -4 -5 left tip DELTA ALPHA deg double-sided tape Wait until after initial test flights before permanently attaching 6 dowel motor nacelle braces lightly glue Ambroid first adding radiators vacuformed engines will enable make minor thrust adjustments needed easily Lastly carve some foam pilot figures add much rigging control ca bles like flying Make sure surfaces un warped balance point shown plans first test flights should very calm weather over softest sur face can find green grass ideal Test charge flight battery several times get feel long charge needed get 8- 10-sec motor run Since really cant test glide model will use short runs sort things out initially Put tweak about /16 right rud der Charge motor 8- 10-sec run carefully launch model Re move noticeable turn dive stall ten dency rudder elevator surfaces large make small changes time Shoot straight power glide almost level flight no tendency slow down hang props short hops satisfactory gin lengthen charge get five 10 additional seconds power Remember lengthen charge initial power level will increase somewhat time reach 20 30 seconds power should getting very slight initial climb level cruise Keep turns very wide gentle power exhausted model will descend slow steep glide isnt thermal soarer allow model climb nosehigh near stallespecially gusty weather Trim relatively shallow pen etrating climb satisfied short power runs charge up enjoy prettiest Free Flight sights youre ever likely see Dihedral/Beron-Rawdon Continued page 99 will roll 15/10 x 20/30 same roll rate Going plot Figure 4 80-in-span planes find roll rate should about 26 degrees per second Good thing plots agree Figure 5 also contains same informa tion three EDAs function yaw angle NEW IMPROVED * * LIjila WiMit todd wilk wouli Pow *US Pcte,tNx Des ** WANDIT * 2763 * * ies exited * eveamarramiPo1OftCORDJ * * elorOry * ick Abrasives * * Machine gives exceptional * ing control excellent tinixh * * 5 easic mci 1 fiat Wand aed 1 * nisantsp * ulde Specel iint 2 fIat 1 hail* rauma wand 5 xl grits * ehsiie ricxdes3liai2 hail 10uSd xi * gits * ditional Wandx Abraxivex available * *WANDIT MANUFACTURING 214 2885789 PO Box 266 uite Texas 75149 MINIJET SERIESOhs Proud gird thePreiLd Sun Onese planes feature xii balsadesigned meet rxnstructlon Designed ciththe g/7 0SPRA Furmula intccnedlate flyer xindthey clii 120 rulesnhis 1/u accept 2025 sizeenginefuse scale wedel ciii accept rear eahaust engine fur xx 60i20 cl size engines ccptionai perforxanceOet p glass fuselageclth uf tIe thrill jet cithoutoo wing cxnstructixn full kit $15000 ccv hassles nutted fanSkphack Semikit alma axailable Ins cund $02100 Special Introdactocp PricePlease add $1000 shipping handling $4000 plus $300 flu hes Send check Mdadd 5% sales tax Mastercard hisS C0D add $3003001 15lA477 PARRISH AIRCRAFT c SCALE cOAStS Toy Turkyp Fornula lDart Experimental o SW 49lkTer $9100 $5 SIRtigershurkceoplace full size aircraft antalien FIx 33317 Prototypical dihedral arrangements Al though different dihedral schemes same Equivalent Dihedral Angle will roll same rate actual localized flow air over wing will vary considerably sake illustrating behavior less rudder yaw near stall fly speed margin stall rapid maneuvers required Polyhedral Breaking wing up four sections instead two V-dihedral re duces range angle attack variations across wing during steady-state roll illustrated Figure 9 saw tooth line reduces possibility leaving drag bucket during maneuvers can imagine number wing panels increased sawtooth becomes progressively finer until equivalent elliptical wing reached Discussion see above designer rudder-elevator airplane has few options play order control maximum roll rate plane RC Sailplane applications desire achieve high roll ratemore almost al ways better Span airspeed powerful variables usually determined higher prior ity requirements such glide ratio 174 Model Aviation AND PRINTING SERVICE QUICK SERVICE OVER 300 ORDINATE SETS ON FILE SEND 5200 xodS1SEloogeonelopeforsuoooplea tlxs list xf niefuil xx isuod xxxv SEP10 S500 SASE bag fur plot ta chord irogIlo suet oxooples oxooc scvezxl xixfuds lox ocdcc pocfccruccc IncludE pLots copy thc thepe rod die dhta possible SEND $1011 fur doe PLOT SHAPE CATALOG xfcbe 100 plus olotuds loc St ditch plots pius lustsoicxi xoofcol iofnzxoxloon sdsec osefxdl aicfod duos roan/many puges STANDARD PLOTSander Oliorhex ISLE poge Lorge docoda noriloble no coDs cost cssopcopscdoorlox clssod bxogob 20 chord tosice coat sf10 p1st CUSTOM PLOTnEG AVAILABLE Can modifr oanbcx olijobosass mdi pieces Osgather coos slow vanous also thocboocSScs top & bottom ilifrorot TAPERED 1NO PLOTS $1000 Secop pbua 50 roots pci rib oven 10 slightly higher THIS MONThS HOT PLOTS MACA 6100 MACA 0000 Orcut foc stabs EPPLER 102 205 SIOil Oxsd chE cod af Mooch magsoioe issue date Can slow Slid oh no tltdiSlsixnldclooess NO EXIThIL CHARGE Hot plots Osly $100 over 10 $101 THE PTERANOOOH PRESS 0N PODOSS0 OAE ANn CA 0160 0 0 StarBase Exchange 1902 Walnut Montgomery AL 36106 dee. Write free catalog SVNASA patches flight suits pictures astronaut food much VISA/MC 1-800-426-1354 sink rate leaves yaw angle Equivalent Di hedral Angle big vertical stabilizer large-percentage-chord rudder can used achieve high yaw angles large yaw angles problematic Unless fuse lage very small inefficient fly airplane high angles yaw because fuselage will making lot drag Also large yaw angles take lot time achieve plane depends high roll rate will lack precision different dihedral arrangements roll mode will describe two prototypical arrangements intermediate arrange ment prototypical arrangement wing smoothly curving dihedral curve shape parabola has property having slope propor tional distance centerline smaller angles dihedral less 300 fair approximation say its dihedral angle increases propor tion distance airplane center line also fair approximation say parabolas very similar circles angles small say less 20 degrees can see Figure 2 changing angle attack delta alpha such curved wing yawed increases linearly toward tip progressive change angle attack also visible front view yawed wing illustrated Figure 7 An approximate formula curva tare wing Z 0296/b X2 EDA equivalent dihedral gle Z vertical height wing function wingspan b wing station X other prototypical arrangement sinijile V-dihedral scheme wing has same dihedral angle everywhere yawed has same change angle attack positive negative along wing Figure 8 illustrates delta alpha yawed dihedral wing well other types Figure 7 also illu strates property intermediate arrangement fourpanel wing panel breaks 05 semi span wing intended approxi Step future AVIATION Become Aviation Electronics Technician learn repair maintain electronic equipment used aboard aircraft Actual planes used training Hangar runway campus Train just 19 months Jobs waiting CALL NOW 1-800-634-7972 CLOVER PARK Vocational Technical institute 4500 Steilacoom Blvd SW Tacoma WA 98499-4098 FAA Rupair Slation #4466 mately mimic behavior curved wing setting dihedral angle propor tion distance centerline Since center outer panel three times far centerline inner panel its dihedral angle three times SAFE FLYING ISNO ACCIDENT YXKI great Figures 7 8 also illustrate type wing Parabolic dihedral yawed wing parabolic dihedral presents change angle attack along wing pro portional distance airplane centerline See Figure 6 again di rectly analogous helical-pitch propeller forcibly rolled angle attack along wing varies proportion distance airplane centerline Note change angle attack exactly matched presented parabolicdihedral wing means parabol ic-dihedral wing reaches its steady-state roll rate net change angle attack reaches zero along wing illus trated Figure 9 horizontal line delta alpha ans entire wing work ing uaisonno part wing work ing against other September 1988 175 Continue4 page 176 TWO NEW FLIGHT BOXES Cowylefely assewbied snd finished Mode USA Bofh ore top qualify wood constroction Two large drawers Unique drawer locks Swoll boo 0 plus shipping Large boo $1 2500 pius shipping includes fuel cowparfwenfbatferypower panel cowportmeofadjustable fuselage cradles Money back gsaraefee Send $1 specs call 415 3637732 Inane wesuaqe Flights Fancy eruwodefiog P0 Boo f La f4oedo Ca 94020 0070 n,yi 0UU sq II Wfl9 ares Power 15-28 cu gn weight 3-3% lbs Wing loading 34 lbs z Kit Features easy building balsa constructioni Maple Engine Raiis isoisted Tank Compartment Formed MusIc WIre Landing Gear THE FLORIO FLYER 837 Johnsonburg Rd 814 834-2586St Marys PA 15857 V-dihedral yawed V-dihedral wing has constant change angle attack along length half-wing roll ing change angle attack proportional distance centerline im posed constant change What end up inboard 60% wing trying make plane roll faster outboard 40% resisting illus trated Figure 9 large zig-zag line really doesnt matter much since wing still rolls same rate except possibility As can see Figure 9 near root upgoing wing fairly large positive change angle attack Near tip similar nega tive change angle attack Keep mind delta alphas proportional dihedral angle yaw angle wing has narrow drag bucket range angle attack low drag possible high-yaw largedihedral steady-state roll could take part wing outside low-drag range gle attack might also happen basic lift coefficient already near edge drag bucketrolling could move re gions wing out bucket might occur instance during low-speed flight rolling thermal plane already near stall maximum lift co efficient rolling up might stall board portion upgoing wing tip portion downgoing wing con sequence might need maneuver PROPULSION SYSTEMS VI-iliB$2495 Includes HY-71B Motor 8-62 Battery 2 Props Charge P10g Coooector Accessory Pkg screws spacers etc VL-l1lBR$2795 Same VI-lilS hot HY-7IBR Motor aod Remote Flight Battery Holder t 88 176 Model Aviation THERMAL CHARGER what looking electric sailplane good looks easy build fun fly great perfor mance Thermal Charger % PRECISION PRODUCTS INC 714 592-5144 510 E Arrow Highway San Dimas CA 91773 n F GUESS THE NIA S3ERIOU5 FtBOUT ThE NEW REQDENCIE5j / 11 ~1 POWER AT ITS BEST t Weight l P-30 Size Modelo k Gear Ratio t ant Start cost Battery Power ner MOTORS HY-lOB$1495 An improved HY-7t Featores reinforced prop shaft neoprene sleeve engage disengage Free-wheeling HY7OBR$1795 Same HY-7tB hot eqoipped Remote Flight Battery Holder er has 7Y leads quick disconnects Slide hattery FLIGHT BATTERIE 8-62 2n50 mAHr 9 gins . Snap place motor No wiring reqoired B-52 2x80 mAHr 13 gina Same 8-62 hot motor-ron 11/2 minutes 8-63 3x50 inAHr 13g... S135 shorter motor-an WINGS SCRATCH BUILDERS ! PRECISION CUT FOAM WING CORES WIDE VARIETY OF WING SPANS TAPERS AND SECTIONS TO CHOOSE FROM SEND $200 FOR BROCHURE FLIGHT COMPONENTS POBOX 39366 ST LOUIS MO 63139-8366 No 595 Sparrow$650 RO Sportster 25 engines spans 43 No 596 Tomahawk It$500 CL Profile Stunter uses 35 engine spans 46 No 597 Handley Page W-8b$300 FF SruIls mini-Electric twin spans 30 No 193Stiletto CL Stunt model McDonald winner 1976 1980 1982 PAl Word Champs$375 No 239Btue Birds AC Ken Willards formation plane 4-channel 10/15 power$375 No 262Crashmaster CL Crash-proof trainer two sizeo1S30 35/40 power$125 No 3101930 Fleet Biplane RC Sport Scale ton 35140 4-channel Wtngspan 56 scale Two sheets$625 No 314Drake II AC Keo Willards flying boat 3-channel 15-power Fly land mmonable gear$375 No 326Taylor Cub fiC Don StsIls Scheelyard-Scale 0490 2-3 channel Spans 50 in$350 No 332Zephyr AC Small 2-channel glider hand-launch tow thermal slope soaring$298 No 386Laser 200 AC Sport Scale replica championship Aerobatic flier Uses 40 power 4-5 channel Two sheets$1075 No 414ElectrIc Sparky RC Electric ton flier 05 motor 3-channel RC scaled-op 1 939 istiber-pewer taoodte$850 No 440Cavaller- AC Old-Timer-like new design has huge wing slow easy flights 35 pwr 3 cO Two sheets$1725 No 4471/2A Miss America AC Old-Tinwr 1/rA Texaco model 048 glow 2-channels$650 No 454Sweet P-3D FF Neat stick-and-tissae Outdoor Rubber P-3t1-class model contest-wener$2 98 No 457Specsna 80 Electric-power 85-san motor asos 3 diffemnt nongs sport soaring aembatics$798 No 4604-40 80 Shoulder-wing sport flier 4-cycle 40-see engine 4 channels$650 No 465Blue Max II AC Pun-fly spontater 40-size engines spans 52 Lightweight stescram$798 No 478Buttercup 80 Cute elfin sportater usos micra 2-ch fiC polee-radder Spans 27 O2fY035 power$398 No 490Weekender 80 Low-wing sport flier 20-sloe 4-stroke engine spans 471/u in$575 No 506Playmate 80 Sport flier far 3 80 channels 15/25-size engines spans 50 in$650 No 512Extra 230 80 Giant Scale acrobatic plane spans 6 6 asos Quadra engine Two plan sheets$t6SO No 514Henry T 80 Sporlster /uA 2-3 channel AC spans 52 has adostahle wing flaps$475 No 521Comet Jr Clipper Plus 35% 80 Old-Timer sportoter far bA engine 2-ch AC spans 48 in$650 No 522Sorts PAts Ac Reminder-scale bipe ton 40/60 engines spons 43 Two plan sheets$1050 No 525Hi-Tech 2002 AC Canard ducted-fan ton 45 engines spaso 39 Two sheets$1000 No 528Swallow AC Lightweight hotriogger 40-size foor-strake engines spans 50 in$025 No 531Tenible Coupe FF Rubher-powemd Coupe riHiser spans 48 coetest-winner$475 No 533Cessna C-37 AC Schoolyard Scale famous 30s plane 049/10 power 2-ch spans 401/u rn$598 No 5341938 Challenger AC /uA Teraco Old-Timer spans 47 049 engine 2-channel AC5550 No 535Atrix 80 AMA Class 0 Sailplane spaso 110 eras 4-channel AC system$725 No 539Simitar Slow-Motion 15 AC Tailless flying wing 15 engines spans 60 uses 3-ch AC$350 No 541Parakeet AC Sport biplane 1 5/25 engines 3-channel AC eguipesent spans 42 in$675 No 544Heron AC Winters sport Electric tsr geared 075 motor 3 AC ch spans 65 in$575 No 549Cricket Ac Sport scalelike 20-size two- foor-strake engine spans 48 in$675 No 554Super Doubler II AC Sport Aemba0cnfylon 40146 four-stroke engine spans 57 in$575 No 555Double Duty AC flasic/adoanced trainer tsr 10/15 engines spans either 67r/a 59 Two plan sheets$1875 No 559Low Voltage AC Electric-power sportster far 035 motor spans 44 in$475 No 563lo AC tifidA Class 8 2-Meter Sailplane has 705/u-in-span faum wing$725 No 588AVrO 560 FP Mini-electric Scale 23 British ultralight spans 30 in$298 No 569Electrostreak AC Electric aembatic plane spans 44 uses 35 motor$550 No 570Busy Bee FF Pee Wee-30 plane 02 power spans 30 has either uheet-balsa burt-up surfaces$498 No 571Voyager CL Sorts-Scale A-powomd sersion around-the-wurid plane spans 48 in$225 No 572TR-260 AC Sport Scale Aembatic plane fnr 4-strake 60165 power spans 66 in$1198 No 575Scorpion 60 AC Pun-fly aerobatic plane 60 power spans 58 in$1150 No 576Serendipityt ndeer EZA record-holder spans l7A in$325 No 577HallIlte CL /aA Combat plane has teem wing spans 30 in$225 No 578Schwelzer 1-26B 80 Oaarter-scale Sailplane spans 125 Two plan sheets$1475 No 579Lockheed P38 CL Precision Scale 98W II fighter tsr twin 45s spans 55 Fowler flays etc Thme plan sheets$1898 No 580Parnall Pixie PP Robber Scale Golden Age British biplane la 112 scala spans 31l/u in$375 No S81Gee Bee Model Y AC Golden Age Aucer spans 72 1k scale fur 60 power Three plan sheets$1175 No 582Heinkel 100 CL Sport Scite 9898 II fighter 40 engine spans 611/u stmctare mostly cardboard Two plan shts$1250 No 583Sportwsgon AC Radio-tied sport PP model spans 54 oses 10115 engine$798 No 584Happy Days CL Intermediate trainer/Stunter spans 42 uses 29135 engine$575 No 985Dragonfly PP High-performance P-30 Robber ship spans 35 weighs 50 grams$498 No 586Snapdragon AC Pan-fly/sportster 25/30 engines spans 45 in$6 98 No 587Pilatus PC-Sr CL Prable Scale/Stunten/sportster spans 56 oses 29/35 engine$550 No 586Marlah AC Slope-Scaring Sailplane spans 41 oses 2 80 channels$425 No 589Vickera Welleeley AC Sport Scale PdW II bomber spans 89 uses 40 4-cycle eegine Two plan shnets no dec$1250 No 550Bud Lite Laser Stunter CL Stunter scalelike spans 63 uses 60 engine Two eets$1050 No 591Focke-Wulfi PW 190-A AC Sport Scale WVd II fighter spans 98 uses 35/45 2-steske engine Two plan sht no doc. $13Sg No 592ET CL trainer/sportster oses 35 electric power 6-cell buOury pack Wingspan 24 in$475 No 593Taylorcratt AC Sport Scale lightylane builds sandard 2-placer clipped-wing air show stunter Spans either 701/n 98 Par 30/40 two-strake 40148 foar-strake engine Two plan sheets no docamentatlon$1098 No 554 P61 Black Widow CL Profile Scale WW II twin-engine night fighter uses 19125 engine spans 481/0 in $ 0 98 6 03 0 N N ee E2 -cs 082 8230 U 6zo 82 - C gao Em en -2 V - 82s es82 mob 00 2 3 82 82 0 V so82 0003 98 VI toI 08 o1 I I 003 00 gs I 110 i3 82STREET 82 ITY C 0 Circle numbers plans wish orderI Ga 0 6 oi o oE ZZ 0 98 193 414 490 531 554 572 582 590 239 440 506 533 555 575 583 591 262 447 512 534 559 576 584 592 310 454 514 53 563 577 585 593 314 457 521 539 568 578 586 594 326 460 522 541 569 579 587 595 332 465 525 544 570 580 588 596 Plan pdce includes first Class postage US delivery Air Mail over 300 miles 386 478 528 549 571 581 589 597 rs non-US address please add $250 Air Mail postage handling Bach plan Make check money order payable US funds drawn US bank Model Aviation AMA 1810 Samuel Morse Dr Reston VA 22090 Please allow 3 6 weeks delivery Please print carefullyEnclosed $ ______________________ ___________________________________________ AMA No ______________ immediacy control leaves Equivalent Dihedral Angle large EDA good way achieve high roll rate minimum penalty penalties several minor First wings high EDAs pay minor penalty drag due extra area per projected span facet will discussed Part Four series High EDAs require slightly larger vertical stabilizers order avoid Dutch roll problems will dis cussed briefly Part Three Lastly dis cussed above high EDAs may require cer tain piloting finesse flying close edge drag bucket clear rolling maneuvers parabolic polyhedral dihedral arrange ment superior V-dihedral whole story Part Three series discusses behavior steady-state circling flight such used working ther mal turns out circling V dihedral wing enjoys advantage over other two types reasons similar ar gument rolling case opposite So dont go running off half-cocked build yourself parabolic-dihedral wing un til youve read Part Three anyway series has assumed wings have elliptical planform rea sons discussed Part Wings other planforms may have different roll rates V-dihedral wings sensitive planform because during roll board portion wing pushing outboard portion wing smaller inboard bigger outboard roll rate will reduced would case constant-chord low-taper wing op posite true wella highiy tapered wing will roll faster major effect howevera constant-chord wing will still roll 89% fast elliptical roll rate parabolic-dihedral wings insensitive planform because parabolic wings constant angle attack along wing during steady-state roll Since wing fighting itself chord distrib ution does matter Summary conclusions Steady-state roll achieved roll moment due yaw equaled opposing roll damp ing moment Roll moment due yaw function wing area wingspan airspeed yaw angle Equivalent Dihedral Angle Roll damping moment function wing area wingspan roll rate airspeed Steady-state roll rate proportional air speed yaw angle EDA inversely proportional wingspan Roll rate can estimated basis graphs presented Figures 35 Two prototypical dihedral types intermediate type described dis cussed Dihedral schemes approaching parabolic curvature best rolling maneuvers because display small range angle attack variation across wing during steady-state roll 178 Model Aviation L STATE ____________________________________________________________[v32][b88830667200]]]ZIP ____________________________________________________________[v32][b161530697200]]I

iD7 mow dral THREE BASIC MANEUVERS volve roll axis straight level flight state circling rolling article will steady-state roll predict roll rate will detail effect hedral arrangemen properties will also Part three cuss steady-state relationship stability ransitlons ers disci time induce thim p wing ml tt NO OCR TEXT 0 -I-7/ -----~1 / Figure 1 RoIl damping caused opposing change angle attack figure de picts wing flying right executing right-hand axial roll phantom lines trace motion wing left wing sees negative angle attack right wing sees positive angle attack change angle attack opposes dampens right-hand roll Note change angle attack diminishes zero center wing damping-moment balance steadystate roll achieved roll damping can cels out roll moment due yaw useful compare relative sensitivity roll damping roll moment varia bles discussed above instance roll damping roll moment equally af fected change variable say wing area variable does affect balance point two moments can cel Normally balance point interest roll rate Lets look time variables Wing area Equal effect moment damping no effect roll rate means fixed span aspect ratio has no effect roll rate other variables being equal Wingspan Affects damping momentroll rate inversely proportional wingspan means big airplanes will slower roll Airspeed Roll rate proportional air speed Airspeed increases roll damping proportion airspeed roll moment creases square alrspeed roll mo ment wins Yaw angle Roll moment proportional yaw angle damping affected yaw roll rate proportional yaw angle Dihedral angle Equivalent Dihedral An gle Roll moment proportional EDA damping affected EDA roll 80 UAJ 003 flfl .. rate proportional EDA sum up roll rate proportional air speed yaw angle equivalent dihedral angle inversely proportional span Example Say nice plane want double roll rate could making fly twice fast put ting rudder yaws twice much bending wings up its EDA twice great could chop wings down span halved Calculating steady-state roil rate Since works out roll rate proportional versely proportional important var iables really need calculate roll rate single known roll rate given set variables need ra tio roll rate proportion ratio various variables Rather make work too hard Ive included several plots should speed up process Figure 3 shows roll rate 100-in-span airplane 100 EDA 100 yaw variety airspeeds Say have 80-in-span airplane 150 EDA want know its roll rate 20 ft/sec yawed 100 Since plane has 8/10 span 15/10 dihe dral know will roll 10/8 x 15/10 times fast Looking up roll rate bigger plane Figure 3 find 70 ---7 -J -- - - - right roll V -I -08 -06 -04 -02 0 02 04 06 06 left tipCLright tip WING STATION fraction semi span Figure 2 Change lift distribution forcibly rolled wing oppo ses roll Figure plots change lift distribution along ellip tical planform wing being forcibly rolled say physically twisting fuselage example span 100 area 1000 sq airspeed 20 ftIsec roll rate 1420/sec right 60 50 Roll Rate deg/sec 40 30 20 10 0 10 20 30 40 50 60 70 Airspeed Cf t/sec Figure 3 An airplanes roll rate proportional its airspeed Plot ted roll rate 100-in-span plane 10 EDA yawed 100 98 Model Aviation ultimate rolling machine High speed very small span powerful ailerons com bine provide 2-ft-span slope airplane very high roll rate does ex pense good thermaling abilities though GELTA LIFT lbIO05 span 001 -001 -002 -003 -004 80 90 100 70 60 50 Roll Rate deg/sec 40 30 20 10 0 255075100 12550175200 Spaninches EDA s 50 0246 80 12 1461820 Yaw Angle degrees Figure 4 Left Roll rate inversely proportional wingspan figure plots roll rate planes 100 Equivalent Dihedral Angle yawed 1O airspeed 30 ftIsec Figure 5 Right Roll rate proportional Equivalent Dihedral Angle yaw angle figure plots roll rate three differed 100-in-span planes flying 30 ft/sec planes have Equivalent Dihedral Angles 50 10 150 --71g- 50 Li - - 08 -06 -04 -02 0 02 04 06 08 CL Wing Station fraction semispan Figure 6 Left Yawed rolling change angle attack parabolically curved wing proportional wing station Equivalent Dihedral Angle EDA yaw angle Three wings shown EDAs 50 100 150 yawed parabolic wing analogous helical pitch propeller amount twist vary ing wing yaw angle EDA Figure 7 Above Local dihedral determines change angle attack yawed wing V-dihe right tip dral wings have constant change angle attack along wing yawed parabolic wing changes proportionate wing sta tion polyhedral wing approximation parabolic wing has roll rate about 14 degrees per second airspeed 20 ft/sec Clearly plane will roll 14 x 1875 degrees per second could also have figured out Figure 4 shows roll rate plane 100 EDA 100 yaw airspeed 30 ft/sec variety spans Since plane has 15/lOs EDA 20/30 airspeed same yaw angle plane plot know Continued page 174 300 200 100 000 -100 -200 Parabolic: :~ lyhedral hedral -300 CL -08 -06 -04 -02 u 02 04 06 08 1 left tipWING STATIONright tip fraction semispan 200 150 100 DELTA ALPHA deg 050 000 -050 -100 -150 -200 iiI~~IV-Dihedral \ ISO0 Ad4e NI -06 -04 -02 0 02 04 06 08 CL WING STATIONfraction semispan Figure 8 Left plot Idea represented Figure 7 yawed rolling wing change angle attack delta alpha varies continuously tip tip parabolic wing two- four-panel wings change angle attack occurs two four steps particular plot represents wings Equivalent Dihedral Angles 10 yawed 100 right Figure 9 Right Increasing number wing panels reduces range angle attack rolling wing plot combines effects shown Figure 1 Figure 8 change angle attack along length steadily rolling yawed wing shown parabolic polyhedral V-dihedral types parabolic wing achieves roll equilibrium entire wing same angle attack inboard 60% V-dihedral wing push ing outboard portion wing fighting itself rolling Polyhedral wing compromise between two other types data shown 100-ln-span plane 10 Equivalent Dihedral Angle yawed 100 flyIng 30 ff/sec rolling 2201sec right September 1988 99 100 go 80 70 60 Roll Rate deg/sec 50 40 30 20 I0 0 DELTA ALPHA deg 5 4 3 2 0 -2 3 -4 -5 left tip DELTA ALPHA deg double-sided tape Wait until after initial test flights before permanently attaching 6 dowel motor nacelle braces lightly glue Ambroid first adding radiators vacuformed engines will enable make minor thrust adjustments needed easily Lastly carve some foam pilot figures add much rigging control ca bles like flying Make sure surfaces un warped balance point shown plans first test flights should very calm weather over softest sur face can find green grass ideal Test charge flight battery several times get feel long charge needed get 8- 10-sec motor run Since really cant test glide model will use short runs sort things out initially Put tweak about /16 right rud der Charge motor 8- 10-sec run carefully launch model Re move noticeable turn dive stall ten dency rudder elevator surfaces large make small changes time Shoot straight power glide almost level flight no tendency slow down hang props short hops satisfactory gin lengthen charge get five 10 additional seconds power Remember lengthen charge initial power level will increase somewhat time reach 20 30 seconds power should getting very slight initial climb level cruise Keep turns very wide gentle power exhausted model will descend slow steep glide isnt thermal soarer allow model climb nosehigh near stallespecially gusty weather Trim relatively shallow pen etrating climb satisfied short power runs charge up enjoy prettiest Free Flight sights youre ever likely see Dihedral/Beron-Rawdon Continued page 99 will roll 15/10 x 20/30 same roll rate Going plot Figure 4 80-in-span planes find roll rate should about 26 degrees per second Good thing plots agree Figure 5 also contains same informa tion three EDAs function yaw angle NEW IMPROVED * * LIjila WiMit todd wilk wouli Pow *US Pcte,tNx Des ** WANDIT * 2763 * * ies exited * eveamarramiPo1OftCORDJ * * elorOry * ick Abrasives * * Machine gives exceptional * ing control excellent tinixh * * 5 easic mci 1 fiat Wand aed 1 * nisantsp * ulde Specel iint 2 fIat 1 hail* rauma wand 5 xl grits * ehsiie ricxdes3liai2 hail 10uSd xi * gits * ditional Wandx Abraxivex available * *WANDIT MANUFACTURING 214 2885789 PO Box 266 uite Texas 75149 MINIJET SERIESOhs Proud gird thePreiLd Sun Onese planes feature xii balsadesigned meet rxnstructlon Designed ciththe g/7 0SPRA Furmula intccnedlate flyer xindthey clii 120 rulesnhis 1/u accept 2025 sizeenginefuse scale wedel ciii accept rear eahaust engine fur xx 60i20 cl size engines ccptionai perforxanceOet p glass fuselageclth uf tIe thrill jet cithoutoo wing cxnstructixn full kit $15000 ccv hassles nutted fanSkphack Semikit alma axailable Ins cund $02100 Special Introdactocp PricePlease add $1000 shipping handling $4000 plus $300 flu hes Send check Mdadd 5% sales tax Mastercard hisS C0D add $3003001 15lA477 PARRISH AIRCRAFT c SCALE cOAStS Toy Turkyp Fornula lDart Experimental o SW 49lkTer $9100 $5 SIRtigershurkceoplace full size aircraft antalien FIx 33317 Prototypical dihedral arrangements Al though different dihedral schemes same Equivalent Dihedral Angle will roll same rate actual localized flow air over wing will vary considerably sake illustrating behavior less rudder yaw near stall fly speed margin stall rapid maneuvers required Polyhedral Breaking wing up four sections instead two V-dihedral re duces range angle attack variations across wing during steady-state roll illustrated Figure 9 saw tooth line reduces possibility leaving drag bucket during maneuvers can imagine number wing panels increased sawtooth becomes progressively finer until equivalent elliptical wing reached Discussion see above designer rudder-elevator airplane has few options play order control maximum roll rate plane RC Sailplane applications desire achieve high roll ratemore almost al ways better Span airspeed powerful variables usually determined higher prior ity requirements such glide ratio 174 Model Aviation AND PRINTING SERVICE QUICK SERVICE OVER 300 ORDINATE SETS ON FILE SEND 5200 xodS1SEloogeonelopeforsuoooplea tlxs list xf niefuil xx isuod xxxv SEP10 S500 SASE bag fur plot ta chord irogIlo suet oxooples oxooc scvezxl xixfuds lox ocdcc pocfccruccc IncludE pLots copy thc thepe rod die dhta possible SEND $1011 fur doe PLOT SHAPE CATALOG xfcbe 100 plus olotuds loc St ditch plots pius lustsoicxi xoofcol iofnzxoxloon sdsec osefxdl aicfod duos roan/many puges STANDARD PLOTSander Oliorhex ISLE poge Lorge docoda noriloble no coDs cost cssopcopscdoorlox clssod bxogob 20 chord tosice coat sf10 p1st CUSTOM PLOTnEG AVAILABLE Can modifr oanbcx olijobosass mdi pieces Osgather coos slow vanous also thocboocSScs top & bottom ilifrorot TAPERED 1NO PLOTS $1000 Secop pbua 50 roots pci rib oven 10 slightly higher THIS MONThS HOT PLOTS MACA 6100 MACA 0000 Orcut foc stabs EPPLER 102 205 SIOil Oxsd chE cod af Mooch magsoioe issue date Can slow Slid oh no tltdiSlsixnldclooess NO EXIThIL CHARGE Hot plots Osly $100 over 10 $101 THE PTERANOOOH PRESS 0N PODOSS0 OAE ANn CA 0160 0 0 StarBase Exchange 1902 Walnut Montgomery AL 36106 dee. Write free catalog SVNASA patches flight suits pictures astronaut food much VISA/MC 1-800-426-1354 sink rate leaves yaw angle Equivalent Di hedral Angle big vertical stabilizer large-percentage-chord rudder can used achieve high yaw angles large yaw angles problematic Unless fuse lage very small inefficient fly airplane high angles yaw because fuselage will making lot drag Also large yaw angles take lot time achieve plane depends high roll rate will lack precision different dihedral arrangements roll mode will describe two prototypical arrangements intermediate arrange ment prototypical arrangement wing smoothly curving dihedral curve shape parabola has property having slope propor tional distance centerline smaller angles dihedral less 300 fair approximation say its dihedral angle increases propor tion distance airplane center line also fair approximation say parabolas very similar circles angles small say less 20 degrees can see Figure 2 changing angle attack delta alpha such curved wing yawed increases linearly toward tip progressive change angle attack also visible front view yawed wing illustrated Figure 7 An approximate formula curva tare wing Z 0296/b X2 EDA equivalent dihedral gle Z vertical height wing function wingspan b wing station X other prototypical arrangement sinijile V-dihedral scheme wing has same dihedral angle everywhere yawed has same change angle attack positive negative along wing Figure 8 illustrates delta alpha yawed dihedral wing well other types Figure 7 also illu strates property intermediate arrangement fourpanel wing panel breaks 05 semi span wing intended approxi Step future AVIATION Become Aviation Electronics Technician learn repair maintain electronic equipment used aboard aircraft Actual planes used training Hangar runway campus Train just 19 months Jobs waiting CALL NOW 1-800-634-7972 CLOVER PARK Vocational Technical institute 4500 Steilacoom Blvd SW Tacoma WA 98499-4098 FAA Rupair Slation #4466 mately mimic behavior curved wing setting dihedral angle propor tion distance centerline Since center outer panel three times far centerline inner panel its dihedral angle three times SAFE FLYING ISNO ACCIDENT YXKI great Figures 7 8 also illustrate type wing Parabolic dihedral yawed wing parabolic dihedral presents change angle attack along wing pro portional distance airplane centerline See Figure 6 again di rectly analogous helical-pitch propeller forcibly rolled angle attack along wing varies proportion distance airplane centerline Note change angle attack exactly matched presented parabolicdihedral wing means parabol ic-dihedral wing reaches its steady-state roll rate net change angle attack reaches zero along wing illus trated Figure 9 horizontal line delta alpha ans entire wing work ing uaisonno part wing work ing against other September 1988 175 Continue4 page 176 TWO NEW FLIGHT BOXES Cowylefely assewbied snd finished Mode USA Bofh ore top qualify wood constroction Two large drawers Unique drawer locks Swoll boo 0 plus shipping Large boo $1 2500 pius shipping includes fuel cowparfwenfbatferypower panel cowportmeofadjustable fuselage cradles Money back gsaraefee Send $1 specs call 415 3637732 Inane wesuaqe Flights Fancy eruwodefiog P0 Boo f La f4oedo Ca 94020 0070 n,yi 0UU sq II Wfl9 ares Power 15-28 cu gn weight 3-3% lbs Wing loading 34 lbs z Kit Features easy building balsa constructioni Maple Engine Raiis isoisted Tank Compartment Formed MusIc WIre Landing Gear THE FLORIO FLYER 837 Johnsonburg Rd 814 834-2586St Marys PA 15857 V-dihedral yawed V-dihedral wing has constant change angle attack along length half-wing roll ing change angle attack proportional distance centerline im posed constant change What end up inboard 60% wing trying make plane roll faster outboard 40% resisting illus trated Figure 9 large zig-zag line really doesnt matter much since wing still rolls same rate except possibility As can see Figure 9 near root upgoing wing fairly large positive change angle attack Near tip similar nega tive change angle attack Keep mind delta alphas proportional dihedral angle yaw angle wing has narrow drag bucket range angle attack low drag possible high-yaw largedihedral steady-state roll could take part wing outside low-drag range gle attack might also happen basic lift coefficient already near edge drag bucketrolling could move re gions wing out bucket might occur instance during low-speed flight rolling thermal plane already near stall maximum lift co efficient rolling up might stall board portion upgoing wing tip portion downgoing wing con sequence might need maneuver PROPULSION SYSTEMS VI-iliB$2495 Includes HY-71B Motor 8-62 Battery 2 Props Charge P10g Coooector Accessory Pkg screws spacers etc VL-l1lBR$2795 Same VI-lilS hot HY-7IBR Motor aod Remote Flight Battery Holder t 88 176 Model Aviation THERMAL CHARGER what looking electric sailplane good looks easy build fun fly great perfor mance Thermal Charger % PRECISION PRODUCTS INC 714 592-5144 510 E Arrow Highway San Dimas CA 91773 n F GUESS THE NIA S3ERIOU5 FtBOUT ThE NEW REQDENCIE5j / 11 ~1 POWER AT ITS BEST t Weight l P-30 Size Modelo k Gear Ratio t ant Start cost Battery Power ner MOTORS HY-lOB$1495 An improved HY-7t Featores reinforced prop shaft neoprene sleeve engage disengage Free-wheeling HY7OBR$1795 Same HY-7tB hot eqoipped Remote Flight Battery Holder er has 7Y leads quick disconnects Slide hattery FLIGHT BATTERIE 8-62 2n50 mAHr 9 gins . Snap place motor No wiring reqoired B-52 2x80 mAHr 13 gina Same 8-62 hot motor-ron 11/2 minutes 8-63 3x50 inAHr 13g... S135 shorter motor-an WINGS SCRATCH BUILDERS ! PRECISION CUT FOAM WING CORES WIDE VARIETY OF WING SPANS TAPERS AND SECTIONS TO CHOOSE FROM SEND $200 FOR BROCHURE FLIGHT COMPONENTS POBOX 39366 ST LOUIS MO 63139-8366 No 595 Sparrow$650 RO Sportster 25 engines spans 43 No 596 Tomahawk It$500 CL Profile Stunter uses 35 engine spans 46 No 597 Handley Page W-8b$300 FF SruIls mini-Electric twin spans 30 No 193Stiletto CL Stunt model McDonald winner 1976 1980 1982 PAl Word Champs$375 No 239Btue Birds AC Ken Willards formation plane 4-channel 10/15 power$375 No 262Crashmaster CL Crash-proof trainer two sizeo1S30 35/40 power$125 No 3101930 Fleet Biplane RC Sport Scale ton 35140 4-channel Wtngspan 56 scale Two sheets$625 No 314Drake II AC Keo Willards flying boat 3-channel 15-power Fly land mmonable gear$375 No 326Taylor Cub fiC Don StsIls Scheelyard-Scale 0490 2-3 channel Spans 50 in$350 No 332Zephyr AC Small 2-channel glider hand-launch tow thermal slope soaring$298 No 386Laser 200 AC Sport Scale replica championship Aerobatic flier Uses 40 power 4-5 channel Two sheets$1075 No 414ElectrIc Sparky RC Electric ton flier 05 motor 3-channel RC scaled-op 1 939 istiber-pewer taoodte$850 No 440Cavaller- AC Old-Timer-like new design has huge wing slow easy flights 35 pwr 3 cO Two sheets$1725 No 4471/2A Miss America AC Old-Tinwr 1/rA Texaco model 048 glow 2-channels$650 No 454Sweet P-3D FF Neat stick-and-tissae Outdoor Rubber P-3t1-class model contest-wener$2 98 No 457Specsna 80 Electric-power 85-san motor asos 3 diffemnt nongs sport soaring aembatics$798 No 4604-40 80 Shoulder-wing sport flier 4-cycle 40-see engine 4 channels$650 No 465Blue Max II AC Pun-fly spontater 40-size engines spans 52 Lightweight stescram$798 No 478Buttercup 80 Cute elfin sportater usos micra 2-ch fiC polee-radder Spans 27 O2fY035 power$398 No 490Weekender 80 Low-wing sport flier 20-sloe 4-stroke engine spans 471/u in$575 No 506Playmate 80 Sport flier far 3 80 channels 15/25-size engines spans 50 in$650 No 512Extra 230 80 Giant Scale acrobatic plane spans 6 6 asos Quadra engine Two plan sheets$t6SO No 514Henry T 80 Sporlster /uA 2-3 channel AC spans 52 has adostahle wing flaps$475 No 521Comet Jr Clipper Plus 35% 80 Old-Timer sportoter far bA engine 2-ch AC spans 48 in$650 No 522Sorts PAts Ac Reminder-scale bipe ton 40/60 engines spons 43 Two plan sheets$1050 No 525Hi-Tech 2002 AC Canard ducted-fan ton 45 engines spaso 39 Two sheets$1000 No 528Swallow AC Lightweight hotriogger 40-size foor-strake engines spans 50 in$025 No 531Tenible Coupe FF Rubher-powemd Coupe riHiser spans 48 coetest-winner$475 No 533Cessna C-37 AC Schoolyard Scale famous 30s plane 049/10 power 2-ch spans 401/u rn$598 No 5341938 Challenger AC /uA Teraco Old-Timer spans 47 049 engine 2-channel AC5550 No 535Atrix 80 AMA Class 0 Sailplane spaso 110 eras 4-channel AC system$725 No 539Simitar Slow-Motion 15 AC Tailless flying wing 15 engines spans 60 uses 3-ch AC$350 No 541Parakeet AC Sport biplane 1 5/25 engines 3-channel AC eguipesent spans 42 in$675 No 544Heron AC Winters sport Electric tsr geared 075 motor 3 AC ch spans 65 in$575 No 549Cricket Ac Sport scalelike 20-size two- foor-strake engine spans 48 in$675 No 554Super Doubler II AC Sport Aemba0cnfylon 40146 four-stroke engine spans 57 in$575 No 555Double Duty AC flasic/adoanced trainer tsr 10/15 engines spans either 67r/a 59 Two plan sheets$1875 No 559Low Voltage AC Electric-power sportster far 035 motor spans 44 in$475 No 563lo AC tifidA Class 8 2-Meter Sailplane has 705/u-in-span faum wing$725 No 588AVrO 560 FP Mini-electric Scale 23 British ultralight spans 30 in$298 No 569Electrostreak AC Electric aembatic plane spans 44 uses 35 motor$550 No 570Busy Bee FF Pee Wee-30 plane 02 power spans 30 has either uheet-balsa burt-up surfaces$498 No 571Voyager CL Sorts-Scale A-powomd sersion around-the-wurid plane spans 48 in$225 No 572TR-260 AC Sport Scale Aembatic plane fnr 4-strake 60165 power spans 66 in$1198 No 575Scorpion 60 AC Pun-fly aerobatic plane 60 power spans 58 in$1150 No 576Serendipityt ndeer EZA record-holder spans l7A in$325 No 577HallIlte CL /aA Combat plane has teem wing spans 30 in$225 No 578Schwelzer 1-26B 80 Oaarter-scale Sailplane spans 125 Two plan sheets$1475 No 579Lockheed P38 CL Precision Scale 98W II fighter tsr twin 45s spans 55 Fowler flays etc Thme plan sheets$1898 No 580Parnall Pixie PP Robber Scale Golden Age British biplane la 112 scala spans 31l/u in$375 No S81Gee Bee Model Y AC Golden Age Aucer spans 72 1k scale fur 60 power Three plan sheets$1175 No 582Heinkel 100 CL Sport Scite 9898 II fighter 40 engine spans 611/u stmctare mostly cardboard Two plan shts$1250 No 583Sportwsgon AC Radio-tied sport PP model spans 54 oses 10115 engine$798 No 584Happy Days CL Intermediate trainer/Stunter spans 42 uses 29135 engine$575 No 985Dragonfly PP High-performance P-30 Robber ship spans 35 weighs 50 grams$498 No 586Snapdragon AC Pan-fly/sportster 25/30 engines spans 45 in$6 98 No 587Pilatus PC-Sr CL Prable Scale/Stunten/sportster spans 56 oses 29/35 engine$550 No 586Marlah AC Slope-Scaring Sailplane spans 41 oses 2 80 channels$425 No 589Vickera Welleeley AC Sport Scale PdW II bomber spans 89 uses 40 4-cycle eegine Two plan shnets no dec$1250 No 550Bud Lite Laser Stunter CL Stunter scalelike spans 63 uses 60 engine Two eets$1050 No 591Focke-Wulfi PW 190-A AC Sport Scale WVd II fighter spans 98 uses 35/45 2-steske engine Two plan sht no doc. $13Sg No 592ET CL trainer/sportster oses 35 electric power 6-cell buOury pack Wingspan 24 in$475 No 593Taylorcratt AC Sport Scale lightylane builds sandard 2-placer clipped-wing air show stunter Spans either 701/n 98 Par 30/40 two-strake 40148 foar-strake engine Two plan sheets no docamentatlon$1098 No 554 P61 Black Widow CL Profile Scale WW II twin-engine night fighter uses 19125 engine spans 481/0 in $ 0 98 6 03 0 N N ee E2 -cs 082 8230 U 6zo 82 - C gao Em en -2 V - 82s es82 mob 00 2 3 82 82 0 V so82 0003 98 VI toI 08 o1 I I 003 00 gs I 110 i3 82STREET 82 ITY C 0 Circle numbers plans wish orderI Ga 0 6 oi o oE ZZ 0 98 193 414 490 531 554 572 582 590 239 440 506 533 555 575 583 591 262 447 512 534 559 576 584 592 310 454 514 53 563 577 585 593 314 457 521 539 568 578 586 594 326 460 522 541 569 579 587 595 332 465 525 544 570 580 588 596 Plan pdce includes first Class postage US delivery Air Mail over 300 miles 386 478 528 549 571 581 589 597 rs non-US address please add $250 Air Mail postage handling Bach plan Make check money order payable US funds drawn US bank Model Aviation AMA 1810 Samuel Morse Dr Reston VA 22090 Please allow 3 6 weeks delivery Please print carefullyEnclosed $ ______________________ ___________________________________________ AMA No ______________ immediacy control leaves Equivalent Dihedral Angle large EDA good way achieve high roll rate minimum penalty penalties several minor First wings high EDAs pay minor penalty drag due extra area per projected span facet will discussed Part Four series High EDAs require slightly larger vertical stabilizers order avoid Dutch roll problems will dis cussed briefly Part Three Lastly dis cussed above high EDAs may require cer tain piloting finesse flying close edge drag bucket clear rolling maneuvers parabolic polyhedral dihedral arrange ment superior V-dihedral whole story Part Three series discusses behavior steady-state circling flight such used working ther mal turns out circling V dihedral wing enjoys advantage over other two types reasons similar ar gument rolling case opposite So dont go running off half-cocked build yourself parabolic-dihedral wing un til youve read Part Three anyway series has assumed wings have elliptical planform rea sons discussed Part Wings other planforms may have different roll rates V-dihedral wings sensitive planform because during roll board portion wing pushing outboard portion wing smaller inboard bigger outboard roll rate will reduced would case constant-chord low-taper wing op posite true wella highiy tapered wing will roll faster major effect howevera constant-chord wing will still roll 89% fast elliptical roll rate parabolic-dihedral wings insensitive planform because parabolic wings constant angle attack along wing during steady-state roll Since wing fighting itself chord distrib ution does matter Summary conclusions Steady-state roll achieved roll moment due yaw equaled opposing roll damp ing moment Roll moment due yaw function wing area wingspan airspeed yaw angle Equivalent Dihedral Angle Roll damping moment function wing area wingspan roll rate airspeed Steady-state roll rate proportional air speed yaw angle EDA inversely proportional wingspan Roll rate can estimated basis graphs presented Figures 35 Two prototypical dihedral types intermediate type described dis cussed Dihedral schemes approaching parabolic curvature best rolling maneuvers because display small range angle attack variation across wing during steady-state roll 178 Model Aviation L STATE 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