Above are some wing recipes. They have been prepared using John Hazel's wing LIFTROLL design tool. You can download this tool as a zip file from here:

If that doesn't work for you then you could try this link: http://briefcase.yahoo.com/jebbushell and look in the "public" directory. An unzipped version of Liftroll can be downloaded from there. Remember that Yahoo gets busy during the U.S. evening, so please be patient. You may need to make several attempts.

Liftroll simulates a generic wing. This wing has no definite size and no definite airfoil section but you can configure it into many different shapes and Liftroll will instantly predict a lift distribution and a lift coefficient (CL) distribution.

You may need to spend a few hours experimenting before you get a feel for how to make your designs approach the quality of the originally supplied design. If you happen to find one that's better, or you wish to make any comment or ask a question or especially if you spot a mistake then e-mail me, Jeb Bushell. I am sorry that I am not an Aero Engineer and cannot answer questions about the math of the tool, but if you really must know then John Hazel recommends Bertin and Smith "Aerodynamics for Engineers". For a beginner I recommend Martin Simon's "Model Aircraft Aerodynamics".

Each of the designs given above illustrates something different about Liftroll. In particular, the 3-piece 120 shows how to hack the input parameters and the Mantis shows a non-hacked way to represent a 3-panel wing in a 4-panel tool. You may want to look at them all at least once in order to get some ideas for solutions to the problems of your design. You may also find the Cookbook much easier to read if you print it first.

Here are some definitions that you may find helpful, followed by some remarks by knowledgeable commentators. Also included is the most complete table of airfoil zero-lift angles on the web.

Not all parts of a wing are equal when it comes to generating lift. The ideal lift distribution is elliptical and the tool allows you to see how you're doing against a perfect ellipse - if you need to know why then be aware that the issue is subtle and that getting to understand it may take considerable effort. Mark Drela has provided the most elegant explanation that I know of in a response to a question in RCSE. Remarks by Mark Drela

The CL is a measure of how hard the section is working. Some parts of the wing may work harder than other parts so there is a CL distribution. A flat CL distribution means the wing is being worked equally hard everywhere. A high point in the CL distribution tells you where the wing will stall first (because it's working too hard) so a flat CL distribution means that the wing stalls all the way across at the same time. For good handling, sailplanes really need to avoid a stall that begins at a tip, so they generally use a conservative CL distribution that is very slightly higher at the center. (They also favor the Schuemann Planform but see John Hazel's critique of the Schuemann Planform.)

Twist is the change in AOA of a panel from one end to the other. You can vary the twist of the wing to simulate either a real twist or an aerodynamic twist caused by a change of airfoil section. A twist that makes the leading edge lower than the trailing edge as you move away from the fuselage is called wash-out. Wash-in is a twist in the opposite direction. Wash-out is generally a good thing. Wash-in is generally a bad thing. You should refer to the Lilan design to see a crude but effective way for the dimwits among us (alas, that's me again) to work out whether a difference in zero-lift angle amounts to washout or washin.

Before addressing wing twist (wash-out) you should be aware that there are at least two ways to define angle of attack (AOA):

Geometric AOA is referenced to the airfoil chord line. At zero geometric AOA the chord line is pointed directly in line with the flight path. The problem with defining AOA this way is that the lift is not the same for different airfoils at zero AOA. A symmetric airfoil will have zero lift at zero geometric AOA. A cambered airfoil will have some amount of lift at zero geometric AOA. Usually, higher cambered airfoils will have higher lift at zero geometric AOA.

A more sensible AOA is what I'll call aerodynamic AOA. Aerodynamic AOA is referenced to the zero lift line. For a symmetric airfoil the zero lift line and the chord line are the same. On a cambered airfoil they are not the same. A cambered airfoil that has zero lift at -1 degree geometric AOA has 1 degree aerodynamic AOA when it is at 0 degrees geometric AOA.

Calculating the correct inputs to model a wing in LIFTROLL (LR) is easy if you are using a single airfoil. Just keep in mind that for LR the AOA and twist inputs are relative to the zero lift line of the airfoil.

For example if you have an untwisted wing with a SD7037 airfoil the AOA for zero lift is about -3.4 degrees. The appropriate AOA input for LR to model this condition is 0 degrees. You would model zero geometric AOA in LR by typing 3.4 degrees in the AOA input cell. Five degrees of geometric AOA would be modeled by typing 8.4 degrees in the AOA cell. When using LR it is best to just think in terms of AOA relative to the zero lift line.

Wings with airfoil transitions are a little more complicated. A minimally complicated example is a single taper wing with linear airfoil transition and twist.

For this illustration let's say you choose airfoils using a thick, low camber root and thin, high camber tip. This gives strength in bending at the root and typically reduced tip stall tendency from the more cambered tip's better max Cl. Higher max Cl at the tip allows a more tapered wing. Hopefully more taper will reduce induced drag for lower sink speed and higher L/D. Smaller tips will also reduce polar moment of inertia in yaw which will make the ship track better and improve rudder response. However as the taper is increased there will be more danger of tip stalls. Negative twist (wash-out) would help prevent tip stall but it could hurt performance, especially at high speed.

So, in this over simplified example, the task now is to choose the taper and twist for best performance while retaining acceptable stall behavior.

One approach you might take is to look at the maximum lift of the root and tip airfoil from wind tunnel data. (be sure to estimate flying speed at stall, calculate Reynolds number at the root and tip and then look for the Cl max.) Guess at the max lift of the in-between airfoils by interpolating between root and tip. (remember this is an over simplified example!)

Just to get some numbers to work with let's specify the following: The root airfoil has 10% thickness, zero lift at -1 degree geometric AOA, and max CL 1.0. The tip airfoil has 6% thickness, zero lift at -2 degrees geometric AOA, and max Cl 1.2.

Again, just to get numbers to work with, assume you find two possible max performance wings: (1) Taper of 0.65 (tip is 0.65 as large as root chord) with no twist. (2) Taper of 0.4 with -3 degrees of twist (wash-out).

To build these wings you now need to adjust the twist to account for the differences in zero lift AOA.

If you build the first wing with zero geometric twist (chord lines parallel) you will actually end up with a wing that has 1 degree of wash-IN. This is the effect of the difference in zero lift lines. To get the desired untwisted wing you would have to twist the tip by -1 degree (wash-out) to compensate for the difference in zero lift lines.

To get the second wing you would need to give the tip -1 degree of twist for the zero lift line difference and then -3 more for the wash-out, a total of -4 degrees twist.

Remember that these wing specifications were made to help explain the relationships of zero lift lines, twist, and LR. They are not recommended for RC sailplanes.

This business is easy to get mixed up with. There at least one widely published design that mistakenly specifies twist in the wash-in sense to compensate for the transition from low to high camber from root to tip. I hope the author catches this and writes a correction letter to the publisher.

For an example of a well executed (and wonderfully documented!) example of a wing with thick low camber root transitioning to a thin more cambered tip, check out Drela's Allegro at the CRRC web site. Be sure to compare the composite version to the more recently designed built up Allegro.

John Hazel

A good rule of thumb: The zero-lift angle for most airfoils is about -1 degree per percent of airfoil camber.

The airfoil camber line is the line midway between the upper and lower surface. The airfoil camber is the distance between the highest point on the camber line and the chord line, divided by the chord.

The chord line is the line that connects the leading and trailing edge.

Example using the rule of thumb: The zero-lift angle of a 3% camber section is -3 degrees.

The following table is taken from the instructions for Plane Geometry (see: Plane Geometry). These values in turn come from the Soartech wind tunnel measurements by Dr. Michael Selig. [Some additions, taken from the "Summary of Low-Speed Airfoil Data Volume 3" have been added by me, Jeb.]

The columns of the table are: Airfoil designation, % camber, pitching moment coefficient (Cmo), angle of attack at zero lift, and thickness to chord ratio.

Airfoil | % camber | Cmo | AOA @ zero lift | thickness ratio |

AG35 | -3.64 | |||

AG36 | -3.40 | |||

AG37 | -3.21 | |||

AG38 | -2.94 | |||

Clark-Y | 3.55 | -0.0873 | -3.840 | 11.72 |

DAE51 | 3.98 | -0.1081 | -5.418 | 9.37 |

DF101 | 2.3 | -0.0582 | -2.260 | 11 |

DF102 | 2.3 | -0.0521 | -1.944 | 11 |

E205 | 3.01 | -0.0543 | -2.278 | 10.48 |

E214 | 4.03 | -0.1382 | -4.069 | 11.1 |

E374 | 2.24 | -0.0556 | -2.435 | 10.91 |

E387 | 3.8 | -0.0817 | -3.333 | 9.06 |

FX60-100 | 3.55 | -0.1201 | -2.587 | 9.97 |

HQ2/9 | 1.99 | -0.0821 | -1.792 | 8.97 |

MB253515 | 2.43 | -0.0495 | -2.327 | 14.96 |

RG14 | -2.000 | |||

RG15 | 1.76 | -0.0578 | -1.502 | 8.92 |

S2048 | 1.94 | -0.0676 | -2.095 | 8.63 |

S2055 | 1.66 | -0.0483 | -1.478 | 7.99 |

S2091 | 3.91 | -0.0817 | -4.105 | 10.1 |

S3014 | 2.57 | -0.0508 | -3.793 | 9.46 |

S3016 | 2.09 | -0.039 | -0.822 | 9.52 |

S3021 | 2.96 | -0.0597 | -2.379 | 9.47 |

S4061B | 3.9 | -0.0915 | -4.438 | 9.6 |

S4233 | 3.26 | -0.0758 | -3.280 | 13.64 |

S6063 | -1.400 | |||

S7075 | -3.700 | |||

SA7035 | -2.800 | |||

SA7036 | -3.100 | |||

SD5060 | 2.3 | -0.0529 | -2.163 | 9.45 |

SD6060 | 1.84 | -0.0386 | -1.814 | 10.37 |

SD6080 | 3.74 | -0.0822 | -4.491 | 9.18 |

SD7003 | 1.46 | -0.0347 | -1.532 | 8.51 |

SD7032 | 3.66 | -0.0989 | -4.757 | 9.95 |

SD7032 | -3.100 | |||

SD7037 | -3.400 |

(Note: AG35-38 A0's by VisualFoil at Re 1,000,000. Thanks Tony Estep.)

That's all for now.

Blaine Beron-Rawdon Envision Design San Pedro, California USA http://members.home.net/evdesign/

The following question was asked in RCSE: "I'm working with some talented youngsters on aerodynamics and glider design and am having a hard time explaining exactly WHY elliptical lift distribution (and the resulting elliptical planform) is a theoretical ideal. Does anyone have a great simple way of thinking about it?"

Mark Drela replied as follows:

An elliptical loading has a constant downwash angle across the span, so each spanwise station has its local lift force rotated aft by the same angle. The aft component of this local lift is the local induced drag:

Di = downwash_angle * L

If the angle is NOT uniform, you can reduce the total induced drag by reducing L at the stations where the angle is larger and correspondingly increasing L where the angle is smaller. The total lift would be the same but the total induced drag would drop. The optimum situation occurs when no further improvement is possible, which in turn requires that the downwash angle is constant across the span, which in turn requires that the loading is elliptical.

-- Mark Drela

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