Flying Wing Calc July 2009

[email protected] of the this spreadsheet on a website is only authorized with the permission of the author/designer. Email: [email protected] out is only as accurate as data in. This is not a thousand dollar program that takes into effectall of the complexities of flight in determining the results. The use of these predictive values work well enough to build and fly a better model airplane. It has proven to be quite accurate and is better than guessing. However, further flight testing and trimming is required. Before you change a manufacturers recommendation please consult someone who has flown the model. Please don't hesitate to email for questions, concerns or suggestions. The author is not responsible for the loss of your model.General Information- All that's required is a weight scale and ruler.- The only measurements required are in "Inches" and "Ounces".- Fill in ALL the yellow rectangles.- If you see a Red triangle in the upper right of a rectangle, hover your mouse over it to read the instruction.What does it do?This spreadsheet will calculate wing and tiplet areas, aspect ratios, taper ratios and required twist for flying wings. It'll calculate the percent Mean Aerodynamic Chord and Neutral Point to help determine a center of balance location for a first test flight.The information does not take into effect, spanwise flows, etc. However, this is a very good starting point for a new model or verifying manufacturer's supplied information.I originally started programming this spreadsheet because I crashed a new model on its first flight. The cause of the crash was that the manufacturer had calculated the balance point incorrectly, over 2" aft! They since submitted a change to the plans. This spreadsheet will allow simple measurements with a ruler that will perform complicated formulas to determine where the neutral point is and thus where the center of balance should be for an initial test flight.Wing TabWith the sole use of this tab you can determine Wing Area, Wingspan, Wing Loading, Sweepback Angle, Aspect Ratio, Taper Ratio and Mean Aerodynamic Chord.Balance Point TabTo determine a balance point (CG) for a first flight, a static margin of 5-10 percent is generally accepted as a good starting point for a safe test flight. Flight testing can then narrow the actual balance location by removing noseweight. I personally prefer the dive test method for refining the balance location.Panknin Wing Twist TabMethod formulated by Dr. Walter Panknin for determining wing twist, or washout, for required stability of tailless aircraft.Changing Reynold's number, airfoils, taper ratio, aspect ratio, sweepback, design lift coefficeint and static margin gives the designer wide latitude so far as final design.The idea is to have the elevons in trail with the wing i.e. zero elevon deflection at designed cruise airspeedHow to Find Airfoil DataThis is a tutorial on how to determine the zero lift angle and pitching moment of an airfoil from wind tunnel polar data by either graphs or tables.Results TabSingle page printing of results from all of the above tabsGlossary TabCredits TabPlease read the credits tab.Current Version July 2009. Pass Solo all letters.

WingModel Weight (ounces)20.01/4 ChordSweepback Angle0.0Root Chord1/4 Chord9.0Sweepback Angle28.0degrees1/4 ChordSweepback AngleTip Chord0.0degrees1st Panel Span9.04.5Tip Chord4.57Tip Chord2nd Panel Span0.019.53rd Panel Span0.0SpanChordSpanChordSpanChord0.005924-2Total Wing Results0.0924-224-2Total Span48.00in.4.5924-724-2Total Area345.62in24.505024-7Wing Loading8.33oz/ft20.00.0Effective Wing Loading10.83oz/ft2Mean Chord (area/span)7.20in.AC0.03.21Mean Aerodynamic Chord (length)7.49in.Wing Aspect Ratio6.67MAC distance10.635.08MAC LengthWing Taper Ratio0.60MAC distance10.63-2.40MAC LengthLocation of 0% point3.99in.Location of 25% point5.79in.Red Dashed LineMAC distance from root10.63in.0.0010.63Average .25 chord sweep angle14.00degrees3.213.21Note: Red Triangle is Aerodynamic Center (AC) of the WingBlue line is MAC location and lengthWhere Blue MAC line and Red dashed line intersect is the Aerodynamic Center of the WingSweepback ConverterTo find 1/4 chord angle for a wing panel enter the following information:Root Chord10.47Tip Chord5.41Span47.7Then enter either known dimension or angle:1/4 Chord AngleDistance Tip Leading Edge is aft of Root Leading Edge10.23inches10.64degreesLeading Edge Angle0.0degrees-1.52degreesRequired Calculations, please ignore.Panel 1 ResultsArea (dS1)40.50in225% MAC (x1) from R.L.E.2.25in.MAC for this panel9.00in.Sweep distance at MAC0.00in..25 Chord Sweep Angle0.0degreesMAC distance from root2.25in.Sweep Distance at Panels Leading Edge Tip0.00in.Sweep Angle at Leading Edge0.00degreesPanel 2 ResultsArea (dS1)132.31in225% MAC (x1) from R.L.E.6.87in.MAC for this panel7.03in.Sweep distance at MAC5.11in..25 Chord Sweep Angle28.0degreesMAC distance from root13.19in.Sweep Distance at Panels Leading Edge Tip11.48in.Sweep Angle at Leading Edge30.48degreesPanel 3 ResultsArea (dS1)0.00in225% MAC (x1) from R.L.E.0.00in.MAC for this panel0.00in.Sweep distance at MAC0.00in..25 Chord Sweep Angle0.0degreesMAC distance from root0.00in.Sweep Distance at Panels Leading Edge Tip0.00in.Sweep Angle at Leading Edge0.00degrees

Wing

NPMACInchesInchesDoes your wing look like this?

Balance PointSpanChordSpanChordSpanChord0.00.05924-20.09.024-224-24.59.024-724-24.50.05024-70.00.00.03.210.03.210.0010.633.213.2110.635.0810.63-2.40Note: Blue Dash is the balance location with the static margin specified in Row 38Red Triangle is Aircraft's Neutral Point at the Wings RootBlue Line is the MAC location and lengthWhere Blue MAC line and Red dashed line intersect is the Neutral Point of the WingWarning!: For the first flight of a model the red Triangle, (neutral point of the plane) should NEVER be forward of the blue Line, (CG).Static Margin (%)Distance (inches)% MACNeutral Point (%MAC)0.05.7925.0Enter Static Margin0.05.7925.0Static Margin ConverterStatic MarginEnter actual CG from L.E.7.00inches-16.8%Enter % MAC21.0%4.0%Required Calculations, please ignore.Neutral Point (%MAC)25.00percentNeutral Point from R.L.E.5.79in.Neutral Point from R.T.E.3.21in.

Measured aft from Leading edge at wing root.Measured aft from Leading edge at wing root.This is assumed to be 30% greater than normal since part of the wing is acting as the tail.Measure from Root Leading Edge.

Balance Point0.0

MACInchesInchesDoes your wing look like this?

Panknin Wing TwistWhat Affects Geometric Twist?The Reynolds number.The wings sweepback, aspect and taper ratios.The airfoils zero lift angle and pitching moments and the design lift coeffecientThe Static Margin i.e. Balance PointReynolds NumberSpeed35mphDesign Parameter TablesResult196568Table 1Table 2Airfoil DataRequired Twist vs ClRequired Twist vs SMRoot Zero Lift Angle-3.650Static Margin8.0CL0.14Root Cmo-0.097CLTwist (degrees)SM (%)Twist (degrees)CGTip Zero Lift Angle1.7300.10.000.50.005.75Tip Cmo0.0250.20.001.00.005.72CL Manually Calculated0.00Note: Enter the number "zero" to have Cl automatically calculated0.30.001.50.005.68CL Automatic Value0.1660.40.002.00.005.64Static Margin8.00%0.50.002.50.005.61Aerodynamic Twist-20.06degrees0.60.003.00.005.570.70.003.50.005.540.80.004.00.005.50REQUIRED WING TWIST0.90.004.50.005.46Geometric Twist-14.68degrees1.00.005.00.005.43Geometric Twist1.20inchesSpeed CalculatorEstimated Speed35.0mphCl =0.166CL =0.136Speed =38mphRequired Calculations, please ignore.K10.58K20.42Geo Twist-2.49degreesCl=-0.574

Measured aft from from Root Leading Edge.

This is the RED triangle.This is the BLUE dash on the graph.Measured aft from from Root Leading Edge.For a fast slope model you would set a low Cl for the design point - say 0.2. For a thermal model you would use a fairly high Cl - maybe 0.7Affected by Weight, Speed and Wing area on the Wing TabNegative value is Wash-out Positive value is Wash-insee GlossaryTwist measured in Profile view at the wingtip with the leading edge stationary and the trailing edge moving accordingly.Ensure the Wing Tab is completed.For help on how to determine this data see the "How to Find Airfoil Data" Tab.Inches measured aft from Root Leading Edge.Standard Day:- 59 degrees Farenheit- Sea Level Altitude- Barometric Pressure 29.92 in hgAffected by Weight and Wing AreaAffected by Weight, Wingspan and Mean Chord.

How to Find Airfoil DataHow to find airfoils zero lift angles (ZLA) and moment of coefficient (Cmo)Graph Method* The values for ZLA and Cmo must be obtained from published wind tunnel airfoil data (polars) with such programs as Xfoil, XFLR5, and Java Foil among many others. See the Links Tab* To obtain the necessary polar data I'll use XFLR5 as an example as I'm familiar with it's use* I've copied data from the SD7037 airfoil below:* The polars we're interested in are Cl/Alpha and Cm/Alpha* To find the Zero Lift Angle refer to the Cl/Alpha graph. The Vertical y-axis is the lift coeffiecient (Cl) and the horizontal x-axis is the alpha or angle attack (AoA). We're interested in where the green line crosses the Alpha at a Cl of zero, in this case it's -2.5 which is our ZLA. This means that this airfoil will not produce any lift with its leading edge pointed down -2.5 degrees.* To find the moment of coefficient enter the Cm/Alpha graph with the ZLA found in the step above, move down to the green line then to the right to find the Cm which in this case is -.07Direct Reading Method* Shown below is the operating points view. Specify Cl and enter zero for Start and End and select Viscous then click Analyze. After the airfoil is analyzed viscously, uncheck the Viscous box and then click analyze again and the data will be automatically calculated in the lower center of the screen. If the CL = 0 then read the Alpha and Cmo. This data matches exactly what I find with published airfoil data.Note:* Viscous or Non-viscous (inviscid)-- It's important to note that I have no practical experience with polars or designing my own tailless swept wings. To obtain polar information for an airfoil a Reynolds number must be specified which is Viscous data. However, after comparing data with other modelers published work, Non-viscous or Inviscid data matches exactly with their published ZLA and Cmo data. Reynolds numbers aren't applicable with Inviscid airfoil data. This is why you see different values from Viscous in the Polar/Graph Method versus the Direct Reading Method that used Inviscid.

ZLACmoCl = 0Alpha = -3.31Cm = -.078

ResultsDecimalMetricTOTAL WING RESULTSTotal Span48.00in.1219mmTotal Area346in222.30dm2Wing Loading8.33oz/ft225.42gr/dm2Effective Wing Loading10.83oz/ft233.04gr/dm2Mean Chord (area/span)7.20in.183mmMean Aerodynamic Chord (length)7.49in.190mmWing Aspect Ratio6.676.67Wing Taper Ratio0.600.60Location of 25% AC5.79inches aft of root leading edge147millimeters aft of root leading edgeWing Sweepback at .25 Chord Point14.00degrees14.00degreesBalance PointLocation of Neutral Point5.79inches aft of root leading edge147millimeters aft of root leading edgeNote: Balance model forward of this locationStatic Margin Specified0.00%0.00%Balance point with above Static Margin5.79inches aft of root leading edge147millimeters aft of root leading edgePercent of MAC with above balance location25.00%25.00%Required Wing TwistTwist Required-14.68degrees-14.68degreesTwist Required1.20inches measured in profile view30millimeters measured in profile viewReynolds Number196568196568Designed Cl0.170.170.00mm aft of root leading edge0.00%0.00mm aft of root leading edge

GlossaryAerodynamic Center (AC)The place on the glider where all aerodynamic forces may be assumed to act as a single force, i.e 25% MACAerodynamic TwistThe angle between the zero-lift angle of an airfoil and the zero-lift angle of the root airfoil." In essence, this means that the airfoil of the wing would actually change shape as it moved farther away from the fuselageAirfoil Moment Coefficients (Cmo)A number that gives you a relative measure of how much nose-over torque the airfoil is generating. It is typically measured about the 25% of the chord. A negative sign implies that the airfoil wants to naturally rotate nose-down.Airfoil Zero Lift Angles (ZLA)The angle of attack of the airfoil that produces zero lift. The zero lift angles of the root and tip airfoils influence the geometric wing twist required.Angle of Attack (AoA)Angle between the chordline of an airfoil and the oncoming wind. It's the difference between where you are pointed and where you are going. Not referenced to horizon, but direction of travel.AreaThe total surface area of a wing, tail or finAspect Ratio (AR)The ratio of the wings span to the wings average chord. The greater the aspect ratio, the less twist is required. However, as aspect ratio increases, and the wing chord gets proportionally smaller, it becomes more difficult to build a strong stiff wing.Center of Gravity (CG)For modeling purposes, this is the point at which the glider balances fore and aftChordA line connecting the leading edge to the trailing edge of a surfaceCoefficient of Lift (Cl)Is a number associated with a particular shape of an airfoil, and is incorporated in the lift equation to predict the lift force generated by a wing using this particular cross section. The greater the design coefficient of lift, the more wing twist will be required. The design coefficient of lift should be the coefficient of lift at cruise speed so that trim drag is minimized. Some amount of up trim is expected to be necessary for thermalling.Drag Coefficient (Cd)A unitless number for estimating the effective force produced by drag on an object.Geometric TwistAn actual change in the airfoil angle of incidence, usually measured with respect to the root airfoil.Lift Coefficient (Cl)A number that tells you a relative measure of how much lift an airfoil is producing at a given angle of attack. It grows linearly by about 0.10 per degree of angle of attack until stall; typically around 15 degrees.Mean Aerodynamic Chord (MAC)The average chord length of the wingNeutral Point (NP)This is the aerodynamic center of the whole aircraft. It's the position through which all net lift actsReynolds' Number (Re)The most important parameter in aerodynamics. This number has no dimensions, but it encompasses almost everything about a certain flight condition; among these parameters are chordlength, flight velocity and air density. Low-Reynolds Numbers, 200,000 or less, refer to smaller chordlengths or slower flight speeds such as those found on R/C Models.SpanThe distance from wingtip to wingtipStatic Margin (SM)The distance between the aerodynamic center and the center of gravity as measured in percent of the mean aerodynamic chord. A measure of the amount of static stability possessed by a glider. Increased static stability (CG further ahead of the neutral point) dictates increased wing twist.Sweep Back AngleThe angle in degrees the leading edge is swept aft from root to tip. The greater the sweep back angle, the less twist will be required. However, angles of sweep in excess of 20-degrees adversely affect air flow over the wing and may lead to control problemsTaper RatioThe ratio the wings chord tapers from root to tip. The greater the taper ratio, the more twist will be required. This is due to the loss of airfoil efficiency as the wing tip chord gets smaller.Wing LoadingThis is the amount of gross weight that each square foot of wing must support in flight to provide lift, expressed as "ounces per square foot"Wash-outLeading Edge of Wing twists nose down when going from wings root to tipWash-inLeading Edge of Wing twists nose up when going from wings root to tip

CreditsHerk StokelyI've never met Herk in person but he helped me understand terms such as the Mean Aerodynamic Chord, Static Margin etc. Thanks so much to Herk for all his excellent knowledge and patience with my numerous questions.Martin SimonsMartin's book "Model Aircraft Aerodynamics" is a must read for any model airplane designer or wanting to understand more about aerodynamics.OthersThere are to many others to name that have answered my questions throughout the years. Many have come from the internet newsgroups. I highly recommend reading these groups and other periodicals as there is a wealth of information on the design and flying of R/C sailplanes.MyselfI started this spreadsheet in the early 1990's as I got interested in sailplanes, I was previously a "wet" flyer. As I trained for my full size fixed wing pilots certificate I found that I enjoyed the learning of the aerodynamics involved in what makes airplanes fly. Reading Martin's book I thought it'd be nice to input this data for quick comparison between models. It's grown into what you see today. All I have done is take others knowledge and placed their formulas into a spreadsheet.I encourage constructive comments to improve this work. Please email [email protected] Suter, Designer.

LinksSoarTech Aero PublicationsUIUC Applied Aerodynamics GroupHERK STOKELY'S HANDLAUNCH FLYING WINGXFLR5 Airfoil and Wing Analysis Tool

SoarTech Aero PublicationsUIUC Applied Aerodynamics GroupHERK STOKELY'S HANDLAUNCH FLYING WING