7#ba "FBB2tx H*r H+HHrXHHHHHH STEP- BY- STEP DESIGN PROCEDURE FOR FLYING WING R/C MODEL AIRCRAFT WITHOUT ANY VERTICAL STABILISATION AID (NO FIN, NO RUDDER, NO WINGLET) BY JOCHEN HAAS Contents: Page: 1. Choose size and planform: THE FIRST LAYOUT...........................................3 2. Check, whether size and planform will work properly...............................................3 2A.: Estimate C L max................................................................................................3 2B.: Calculate the minimum speed............................................................................4 2C.: Calculate the Reynold Numbers.........................................................................4 2D.: Choose suitable airfoils.......................................................................................5 3.: Washout...................................................................................................................5 Design lift coefficient..................................................................................................5 Airfoils zero moment coefficient.................................................................................5 Stability proportion......................................................................................................5 Sweep angle at _ chord line......................................................................................5 Aspect ratio................................................................................................................ 5 Taper ratio...................................................................................................................5 Spare simple tapered wing.......................................................................................6 4.: Aerodynamics...........................................................................................................6 4A.: The lift distribution...............................................................................................6 4B.: The washout- curves ........................................................................................6 I : Simple tapered wing..........................................................................................7 I a.: Without Flaps..................................................................................................7 I b.: With Flaps.......................................................................................................7 II : Tapered wing with Horten- rump ...................................................................8 5.: Steering and size of Elevons and Flaps...................................................................9 5A.: Elevon design.........................................................................................................9 Elecon chord...............................................................................................................9 Elevon length..............................................................................................................9 SPECIAL ADVICE: STRONGLY RECOMMENDED, PARTED ELEVONS.................9 SPECIAL ADVICE: BRANDNEW RUDDER FUNCTION..........................................10 5B.:Flap design............................................................................................................10 Flap chord (lk/ l) ........................................................................................................10 Flap length (s WK / s) ................................................................................................11 HIGH PERFORMANCE SOLUTION..........................................................................12 6.: Center of gravity ( CG or xs): ..................................................................................12 7.: The procedure without explanations.......................................................................13- 15 8.: Calculation Example...............................................................................................16+ 17 9.: References..............................................................................................................18 DESIGN PROCEDURE FOR FLYING WING MODEL AIRCRAFT WITHOUT ANY VERTICAL STABILISATION AID (NO FIN, NO RUDDER, NO WINGLET) The oftener you run through the procedure, the better the result, I suggest 2 runs, because some values have to be estimated at the first run! 1. Choose size and planform: THE FIRST LAYOUT Wingspan...................................b = _____ m Root Chord...............................l 0 = _____ m Tip Chord...................................l 1 = _____ m eventually other chords, here: at y/s=0.2.................l 0.2 = _____ m at y/s=0.3.................l 0.3 = _____ m Now you are allready able to calculate the Wing area...................................F = _____ m2 ( square meters ) Aspect ratio..............................AR = _____ AR = b2 / F and estimate the Weight........................................G = _____ kg Sheme for a First Layout: y/s 0.9 0.7 0.5 0.3 0.1 y/s 1.0 0.8 0.6 0.4 0.2 0.0 l 0_ PFW l _ H l 0 l 1_ l 1 b_ = s The values of l 0 _, l1 _, H and the PFW l _s will be used later. Remark: The value of l 1 is measured with staight, not curver leading- and trailing edges at the wingtip! 2. Check, whether size and planform will work properly: 2A.: Estimate C L max 2B.: Calculate the minimum speed 2C.: Calculate the Reynold Numbers 2D.: Choose suitable airfoils 2A.: C L max (MAXIMUM LIFT COEFFICIENT) =estimated between 0.7 (0.9) and 1.0 (1.5) Airfoils for flying wing models, which are about 8% to 12% thick and do have a C m 0 at about 0 (MOMENT COEFFICIENT AT ZERO LIFT is about 0) will show a C L max of about 0.7 to 1.0. Thicker airfoils at big Reynolds Numbersmay reach a higher C L max. CALCULATE ROUGHLY: C L max = (THICKNESS [%] * 0.9)+ (ALPHA 0 []* 0.1) If you intend to use camber- changeing = lift- increasing flaps, you may expect a C L max increase of 0.2 to 0.5. The higher the AR (ASPECT RATIO) and the PFW_ (SWEEP- ANGLE at QUARTER CHORD LINE), the more increase you may expect. Estimate: HLG size: C L max- increase: about 0.2 100 Inch class: C L max- increase: up to 0.4 Only Polar Diagrams, which are measured in WIND TUNNEL TESTS give excellent values of C L max. 2B.: Minimum speed: The Formula to calculate the speed (German units of measurements) is: v = 4 * G [ m/sec ] F * CL TAKE C L max instead of C L, so you have v min (Minimum speed). 2C.: Calculate the Reynold Numbers The Formula to calculate the the Reynold Numbers (Again german units of measurements) is: Re =70 000 * v * l So the lowest Reynold Number (at the wingtip) is: Re min (y/s = 1) = 70 000 * v min * l 1 and Re min (y/s = 0) = 70 000 * v min * l 0 (at the root). 2D.: Choose a suitable airfoil: Have a look into Polar diagrams, which airfoil will work with these calculated Reynold Numbers at high/ maximum C L.. Bill Northrop and the Horten Brothers started with symmetrical sections all over the wing. Later the Horten Brothers used symmetrical sections at the wingtip and reflexed airfoils at the root, both with a C m 0 of about 0. Both, Horten and Northrop used thick airfoils at the root, thinning towards the wingtip. I prefer cambered sections all over the wing (MH 45, HQN 1.1 / 10, NACA modifications etc.). I accept an average C m 0 which is zero or slightly negative. Models do not need thicker airfoils at center, but you may use them there. In case you found several suitable airfoils, check performace of these airfoils and select the best, again the polar diagrams will help. Caution: Some modern high performance airfoils do NOT show docile slow speed and stall characteristics, so an oldfashioned airfoil could be the better choice, even for big birds. If you did not find any suitable airfoil (for the wingtip), restart with #1 and change the relevant data (in most cases l 1). More weight could solve the problem as well, but doesnt improve the performance, in general. 3.: Washout: This is a little more difficult formula, but a PC is able to calculate it (the input is done easier in steps): K1 * c m 0 (l 0) + K2 * c m 0 (l 1) - C L* * STM ALPHA s [ ] = -5 1.43 1.4 * 10 * AR *PFW l _ K1 = _ * ( 3+ 2*Z + Z2 ) / ( 1 + Z + Z2 ) K2 = 1 - K1 Z = l 1 / l 0 ALPHA s: The washout from root to wingtip, in degrees [ ]. The washout curve between l 0 and l 1 will be calculated later. C m 0 (l 0): The moment coefficient of the root airfoil at zero lift, out of polar diagramm. C m 0 (l 1): The moment coefficient of the wingtip airfoil at zero lift, out of polar diagramm. C L*: The design lift coefficient: At this lift coefficient the aircraft will fly when the elevator is in neutral position. Full sizes aircraft C L* si selected to meet the cruising speed. We take for our models: C L* = 0.4 for acrobatic aircraft. C L* = 0.6 for allround aircraft. C L* = 0.8 for slow / beginners aircraft. NEVER use a C L* below 0.4, it will cause steering / control problems! NEVER use a C L* above airfoils C L max. STM: The stability proportion: The distance between the center of gravity (x S) and the neutral point (x N), relative to the average chord (l m). Unit of measurement is the meter for all three values, you may use inches here, that will work. Conventional aircraft and flying wings with fin or winglets show a STM of about 0.1 (equals 10%), For our models here, we need a STM of about 0.15 (15%). Start with STM = 0.15, then you do not need to calculate in the first run. Nevertheless, the (x N - x S) formula: STM = , for later more precise calculations. l m PFW l _: The sweep angle of the quarter chord line in degrees [ ]. If this line is curved, take the average sweep angle: It is the straight line from l 0 _ to l 1 _ (see picture). AR: The aspect ratio: The higher the AR, ...the sleeker the wing. ...the lower the induced drag, the better the performance could be. ...the smaller the Reynold Numbers, the worse the (airfoil)performance is. Z: The taper ratio: It is the relation between l 1 and l 0. Formula: Z= l 1 / l 0 The more difference between l 1 and l 0: The less washout you need. + The smaller the Reynold number at the wingtip. -- The worse stall characteristics can be shown. -- A planform with a Horten-rump gives values of Z which are for the formula above not suitable: Calculate a spare simple tapered wing, which has same l 1, b, F and AR but the better l 0 NEW. l 0 NEW If the formula calculates a washout of less than 4 or more than 15, restart with other data in #1 or select another airfoil. A washout of less than 4 gives an unstable ship, more than 15 gives too bad high speed performance. 4.: Aerodynamics: 4A.: The lift distribution: Conventional aircraft and flying wings with fin or winglets show best performance and handling with an (allmost) elliptical lift distribution. Our wing needs a special lift distribution curve. Mr. Prandtl, Germany, published at about 1910 the bell- shaped lift distribution, and in the 30s the Horten brothers picked that up to design their wings. Mr Northrop, I assume, started the same way. This bell- shaped lift distribution shows good handling, stable flight and docile slow speed control but, due to a big amount of induced drag, only medium to poor performance. Several people tried to mix the bell- shaped and elliptical lift distribution or tried other solutions to improve performance and still have the advantages listed above. By the way, the modern Northrop B 2 doesnt fit into this picture, it is an unstable aircraft, flyable only with the aids of computers and gyros, but this way it is a high performance ship. The bell- shaped- and elliptical lift distribution ( no scale) 4B.: The washout curves: To obtain the bell- shaped lift distribution, the washout along a simple tapered wing should look like (theoreticaly) in the diagram below: ALPHA s [ % ] 100% halfspan (s) Depending on wing planform and whether you want to use flaps in the center section, I recommend different washout curves. Expect not as much induced drag as the original bell- shaped lift distribution delivers at higher speeds and a docile handling in slow speeds. I : Simple tapered wing: ( like Ho II, Ho III, N9M...) Without Flap With Flap I a.: Without Flaps: ALPHA s [ % ] 100% halfspan (s) I b.: With Flaps: ALPHA s [ % ] 100% halfspan (s) End of Flap II : Tapered wing with Horten- rump: ( like Ho IV, Ho VI,...) ALPHA s [ % ] 100% halfspan (s) End of Rump and / or Flap 5.: Steering and size of elevons and flaps 5A.: Elevon design: Elevon chord: Normally, high performance aircrafts ailerons- and flaps- chord is between 18% and 25% of local chord. Modern layouts tend towards the smaller values, to obtain a longer laminar flow. These chords were, at the Hortens and Northrops wings, up to 50%, common at their times. I still recommend these high -chords, but not everywhere: 18- 25% of local chord up to 60% of local chord 40- 70% of halfspan (s) Take about 50% of local chord near wingtip. Pulling up the elevator increases washout a lot, thats what a wing needs. For inverted flight, the washout can then be corrected towards the right side. Take between 18% (modern airfoils) and 25% (older airfoils) of local chord at the other side. This gives smooth lift distribution, so better performance. Elevon length: At high aspect ratio wings (more than AR= 10), use elevator length of up to about 70% of halfspan (s), low aspect ratios demand for about only 40% of s,the elevator response is better! SPECIAL ADVICE: STRONGLY RECOMMENDED, PARTED ELEVONS: Part these elevons in 2, both parts about same length; small models may still use one servo each side. Slow speed mode: With the aileron function, the outer elevons move more up, the inner elevons move more down. The wing is better turning, or: turning, not only banking, as many of these wings only do. With a modern transmitter its easy to programm, caution to the pitch moment. Here, the elevator works more smooth than with same travel over full length, the outer elevon always moves more up, the inner one more down. Gives docile handling, even when pushing down elevator, the washout doesnt turn around. One servo linkage: outer elevon inner elevon ELEVATOR, NOSE UP: (all seen from the rear) ELEVATOR NOSE DOWN: AILERON TURN LEFT: Fast speed and acro mode: (2 servos each side,then) Aileron: If you want the wing bank, but not turn, its better to let the elevons travel the same way, eventually the inner one more up, less down. Test it. Elevator: To obtain a docile inverted flight handling and to be able to slow the wing down in inverted flight, the outer elevon moves more up and down, or both the same way. Test it also! SPECIAL ADVICE: BRANDNEW RUDDER FUNCTION My way to turn, without bank ( rudder control). I know no other person useing this: RUDDER LEFT slow and fast mode, 2 servos each side: Butterfly on one side only: 5B.:Flap design Flap chord (lk/ l): Flaps slow down the aircraft by increasing lift (more camber) and increasing washout (higher CA*). They do not necessarily produce more drag: The airfoil is working in an optimum, means low drag, range. These wings need, at high CA, much more lift at the center section, less towards the wingtip. So I give more flap chord towards the center of the wing, less the other side. 30%- 50% 18%- 25% see formula Flap length: The flap length is a very important value at swept flying wings. A too long flap gives a lot of nose down elevator trim, so a too short flap gives nose up effect and not as much additional lift as possible. To correct these effects, the elevon has to be moved, but to the direction which gives no advantage! The optimal flap lengths are these, which give no up or down moment or just a little up moment when deflected down, to have just the correct speed trim, only by flap deflection. Formula for moment free flap (only for flying wing model aircraft without any vertical stabilisation aid): 4 s WK / s= 0.636 BFk * AR * tan PFW_ with some values of BFk: lk/ l: 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.40 0.50 BFk: 0.20 0.18 0.17 0.165 0.16 0.155 0.15 0.12 0.095 A flap, which trims to the correct speed when deflected is a little bit shorter, Im unable to give a formula, test flights will give the correct length only. If the flaps inner end is not the centerline, at the other side you have to shorten the flap, too! corrected length calculated length Start with a deflection of about 10 down, testfly less and more. NOTE: when s WK / s= 0.3 and halfspan s= 60 inches calculate 0.3 * 60 = 18 so the required flap length at this wing is 18 inches HIGH PERFORMANCE SOLUTION: High performance flying wings with a very high aspect ratio and sweep angle give a fine option for elevon and flap design: Here, chose a flap length which is about 15% shorter than calculated moment free, the inner elevon, I call it combi flap now, trims for the correct speed. Possible slow speed trim (smooth lift distribution): Combiflap pitch trim optimum down deflection and better in the slow speed mode is: Elevator nose up: little down defl. lift loss here! to increase lift. and pitch moment! 6.: Center of gravity ( CG or xs): As at all wings the neutral point is at about the _ chord line, but, due to the lift distribution we have to have a look to the location of the CG in wingspan direction. Our wing has to produce a lot of lift in the central part, less lift is produced by the outer panel. So, in direction of wingspan the CG is closer to the centerline than towards the wingtip. The original bell shaped lift distribution places the CG at 33% of halfspan from centerline towards the wingtip. The elliptical lift distribution and the optimum for a wing with winglets place the CG at about 42% of halfspan. That is the reason for a less good performance of wings without fin or winglets (induced drag increase). Trying to mix the bell shaped- and elliptical lift distribution improves performance, but the handlind is probably not so gentle then. Since the formula is not too simple take the geometrical way. It works as well with all kinds of curved _ chord lines, even lines with edges. If the wing is not docile, put more lead into the nose. Later, in test flights, you may try to place the CG in small steps back, but go then forward a little bit, when ascertaining bad behaviors. center of gravity _ of local chord _ chord line 30%- 33% of halfspan 7.: The procedure without explanations: 1. THE FIRST LAYOUT Wingspan...................................b = _____ m Root Chord...............................l 0 = _____ m Tip Chord...................................l 1 = _____ m eventually other chords, here: at y/s=0.2.................l 0.2 = _____ m at y/s=0.3.................l 0.3 = _____ m Now you are allready able to calculate the Wing area...................................F = _____ m2 ( square meters ) Aspect ratio..............................AR = _____ AR = b2 / F and estimate the Weight........................................G = _____ kg 2A.: C L max (MAXIMUM LIFT COEFFICIENT) =estimated between 0.7 (0.9) and 1.0 (1.5) CALCULATE ROUGHLY: C L max = (THICKNESS [%] * 0.9)+ (ALPHA 0 []* 0.1) 2B.: Minimum speed v = 4 * G [ m/sec ] F * CL max 2C.: Calculate the lowest Reynold Number Re min (y/s = 1) = 70 000 * v min * l 1 2D.: Choose a suitable airfoil 3.: Washout: K1 * c m 0 (l 0) + K2 * c m 0 (l 1) - C L* * STM ALPHA s [ ] = -5 1.43 1.4 * 10 * AR *PFW l _ K1 = _ * ( 3+ 2*Z + Z2 ) / ( 1 + Z + Z2 ) K2 = 1 - K1 Z = l 1 / l 0 4B.: The washout curves: For the original bell- shaped lift distribution: ALPHA s [ % ] 100% halfspan (s) I : Simple tapered wing: ( like Ho II, Ho III, N9M...) Without Flap With Flap I a.: Without Flaps: ALPHA s [ % ] 100% halfspan (s) I b.: With Flaps: ALPHA s [ % ] 100% halfspan (s) End of Flap II : Tapered wing with Horten- rump: ALPHA s [ % ] 100% halfspan (s) End of Rump and / or Flap 5A.: Elevon design: 18- 25% of local chord up to 60% of local chord 40- 70% of halfspan (s) Part these elevons in 2, both parts about same length; small models may still use one servo each side. 5B.:Flap design 30%- 50% 18%- 25% see formula Flap length: Formula for moment free flap (only for flying wing model aircraft without any vertical stabilisation aid): 4 s WK / s= 0.636 BFk * AR * tan PFW_ lk/ l: 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.40 0.50 BFk: 0.20 0.18 0.17 0.165 0.16 0.155 0.15 0.12 0.095 6.: Center of gravity ( CG or xs): center of gravity _ of local chord _ chord line 30%- 33% of halfspan 8.: Calculation Example Let us design a Horten II L, scale 1: 6.3, semi scale glider. 1. THE FIRST LAYOUT Wingspan...................................b = 2.540 m 100.000 inches Root Chord................................l 0 = 0.550 m 21.800 inches Tip Chord...................................l 1 = 0.090 m 3.650 inches Now calculate: Wing area...................................F = 0.854 m2 ( square meters ) about 8.8 sq. Feet Aspect ratio..............................AR = 7.55 estimated Weight.......................G = 2.500 kg 5.5 lbs 2A.: C L max (MAXIMUM LIFT COEFFICIENT) estimated = 1.0 2B.: Minimum speed v = 4 * G [ m/sec ] Vmin= 6.8 m/ sec= 24 km/ h= 13.5 kts F * CL max 2C.: Calculate the lowest Reynold Number Re min (y/s = 1) = 70 000 * v min * l 1 = 43100 2D.: Choose a suitable airfoil: Wingtip: NACA 0007 Root: MH 45 or: NACA 0010 but with reflexed centerline of MH 45 ! We may go back and correct V min and Re min, Ca max is only 0.8 with these airfoils. 3.: Washout: C L* = 0.6 c m 0 = 0, all airfoils 0 + 0 - 0.6 * 0.15 ALPHA s [ ] = -5 1.43 = -13.812 1.4 * 10 * 7.55 *25.84 4B.: The washout curve: I : Simple tapered wing, I a.: without Flaps: ALPHA s [ % ] 100% halfspan (s) At y/s = 0.00 = s= 0.000 m ALPHA S (y) = 0.000 = 0.000 At y/s = 0.33 = s= 0.419 m ALPHA S (y) = 0.330 = - 4.560 At y/s = 0.66 = s= 0.838 m ALPHA S (y) = 0.330 = - 4.560 At y/s = 1.00 = s= 1.270 m ALPHA S (y) = 1.000 = -13.812 5A.: Elevon design: As in scale drawings, but part these elevons in 2, both parts about same length; small models may still use one servo each side. Its no difference between fixed wingtip, like at Ho II or elevons all way out, like at the Ho III. 6.: Center of gravity ( CG or xs) : = 0.3357 m =13,2 inches behind nose 0.419 m = 0.2357 m _ of local chord = _ * 0.400 m = 0.100 m 33% of halfspan 9.: References: Some of the knowledge is out of books or magazines, some is based on a lot of test models, it took about 15 years to get these information level. Best book, with superb infornation is Schwanzlose Flugzeuge Ihre Auslegung und ihre Eigenschaften Karl Nickel, Michael Wohlfahrt Birkhuser, 1990 ISBN 3-7643-2502-X Other good books: ON THE WING, Kuhlman bsquared TAILLESS TALE, Gale bsquared FASZINATION NURFLGEL, Unverferth VTH NURFLGELMODELLE, Lichte VTH and magazines: FLUG UND MODELLTECHNIK, many issues VTH MAN RCM FLYING MODELS MODEL BUILDER  J. 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C t   G P R y %&   C !";$=&&&&&p&q&s&u&w''6((()*X*****/-/11112222506B78 9:::::;;;;;=>>s?VX~(HHR[ (hh t2 HK'd!5Sy C/FH-:SP 750 SymbolArialTimes New RomanEDEDX0DESIGN PROCEDURE FOR A FLYING WING MODELAIRCRAFT Jochen HaasBill & Bunny Kuhlman