Designing Smooth Symmetrical Airfoil Wings

Hello everyone,

This article discusses the design considerations I use in designing Smooth Curved Surface Symmetrical Wings made from DTFB using modified Flite Test building methods.

Many different wing shapes and sizes can be designed and built using these methods.  You can do tapered or straight, with or without dihedral, varying thicknesses, with or without wash-out, various aileron designs, etc. The possible combinations are endless.

The first model that I designed with a symmetrical wing was the subject of my most recent article, "Making Fully Symmetrical Curved Wings from DTFB". The subject model, the Blue Streak has a low mounted tapered wing.  Here is a picture of the resulting model with its wing in the foreground:

The article showed how to build the wing but did not go into a lot of detail about how the design was developed.  You can see the other article here:

http://flitetest.com/articles/making-fully-symmetrical-w-ings  

PURPOSE: 

The purpose of this article is to delve into the minutia of wing design.

I will use my Stout Trainer as a second example since I currently have only flat bottomed wings designed for it.  To fully investigate the upper end aerobatic potential for this aircraft a fully symmetrical wing option makes sense.  My current wing designs for the Stout Trainer are both flat bottomed.  One has dihedral and one does not. Here is Stout Trainer with the more aggressive of those two, the straight flat bottomed wing:

DESIGN CONSIDERATIONS: 

There are a number of factors to consider when designing a wing.  Here are the main ones I use:

1. Wing mounting position: Low, mid, shoulder, high or parasol.

2. Wing Shape: Rectangular, tapered, elliptical, delta, swept back, forward swept, flying wings (various). 

2. Wing Span / Wing Cord / Aspect Ratio.

3. Wing Area / Wing Loading

4. Airfoil Shape.

5. Wing Thickness.

6. Spar Design.

7. Aileron design.

8. Dihedral Angle.

9. Wash Out.

10. Tip Design.

11. Angle of Incidence.

12. Wing Mounting details.

Wing Mounting Position:

Wings can be mounted in various positions which then effect other wing design considerations.  The higher a wing is mounted the less dihedral is needed.  The weight of the fuselage on a parasol wing serves the same righting affect as a high dihedral value does for a low wing. The wing position can strongly affect overall airplane performance.  High wing designs are generally easier to fly because of the inherent stability of the pendulum effect but have more difficulty with aerobatics such as inverted or knife edge flight than ones with mid or low wings. Many high performance aerobatic airplanes have mid mounted wings so they can perform equally well in any position.

Here are sketches of various wing positions from Wikipedia:

Low wing

Mid wing

Shoulder wing

High wing

Parasol wing

Wing position has a large impact on the design of the rest of the aircraft as well as directly on the wing itself. The position of the main wing can have an impact on the placement of tail surfaces.  High wings can put low mounted tail surfaces in turbulence at high angles of attack during slow flight when tail surface effectiveness is most important. Low or mid wings can affect the position of the cockpit for visibility greatly affecting the overall appearance of the airplane

The wing position for Stout Trainer is High Wing.  Most trainers are high wing due to the inherent stability of the design.   

Wing Shape:

The shape of the wing is probably the most important decision in designing an airplane.  It pretty much determines the character of the aircraft.  All other features are generally dependent on the wing shape. Here is a graphic I found on-line showing the most common wing shapes:

For the purpose of this discussion, most of the above wing types can be made as fully symmetrical using foam board.  The main exception is elliptical.  Forming symmetrical airfoils when the leading and/or trailing edges are curved would require making compound curves that are not possible when using a rigid sheet product.

The example in this article, the Stout Trainer, uses a Rectangular Straight Wing which can be made easily with a symmetrical airfoil.   http://flitetest.com/articles/stout-trainer-mid-to-advanced-trainer-preview

The example used in my previous article "Making Fully Symmetrical Curved Wings from DTFB" is a Tapered Straight Wing which can also be made easily with a fully symmetrical airfoil as the article shows:    http://flitetest.com/articles/making-fully-symmetrical-w-ings

All of the other wing shapes shown above can be made with symmetrical sections.  The compound delta would present the most challenges. It would have to be done in sections with segmented leading and trailing edges.

Some of my earlier articles feature No Waste Flying Wings.  Any of these could be done with symmetrical airfoils as could my Twin Tail Boom series. 

Most of the designs in the Flite Test hanger could be modified to have symmetrical airfoils.  Some would be practical.  Some would not.

Wing Span / Chord / Aspect Ratio:

 After wing shape the next design consideration is the basic wing dimensions.  We have to determine the wing span and chord length.  The relationship between Span and Average Chord Length is called the Aspect Ratio.  

The example in this article, the Stout Trainer has a 64" wing span and a chord length of 11".  The aspect ratio (AR) is 64 : 11 or 5.82 : 1.  It is sometimes expressed as just AR = 5.82.

The aspect ratio for the Stout Trainer is well within the averages of common general aviation aircraft.  A Piper Cub has an Aspect Ratio of 7:1.  A Cessna 172 has an AR of 7.32: 1.  A Beech Craft Bonanza has AR = 6.2. A Piper Cherokee has AR = 5.63.

The shape and size of the wing are chosen according to the performance requirements of the aircraft being designed.  Different wing proportions cause aircraft to behave differently. High Aspect Ratio wings for aircraft such as gliders and the U-2 are designed to have highly efficient long glide slopes and to be capable of long duration flights.  Low Aspect Ratio wings for aircraft such as supersonic jet fighters are designed for extreme speed and maneuverability.

The Stout Trainer design began with the wing.  I wanted a larger trainer to rebuild my flying skills after a 15 year break from the hobby.  I designed the largest wing that was possible to be made from two sheets of DTFB with no waste.  That concept started with a wing span of 60" based on using the 30" sheet dimension for the wing half length.  The wing cord was established at 10 3/4" based on a 2" aileron width and using the remaining 18 "to make the wing including top and bottom surfaces. I checked the Aspect Ratio and found it to be well within the range I wanted for the trainer I had in mind.  The rest of the aircraft design grew from that wing.

Here is a graphic from NASA showing Span, Chord and Aspect Ratio:

Wing Area and Wing Loading:

Wing Area and Wing Loading are important design consideration but more for deciding other aspects of the overall design than for determining the wing design itself.  For example, there are formulas and rules of thumb for determining tail surface sizes based on the wing area and tail length.  For the sake of this design I started with the wing and used formulas for tail surfaces.  Wing loading is more a result than a design consideration.  I usually build as light as possible consistent with structural integrity and then calculate power requirements based on the final weight including various motor and battery combinations. I frequently back into wing loading just as a check measure. A nice light wing loading goal for a trainer is in the 8 to 9 oz per SF neighborhood.  

Airfoil Shape: 

There is a vast amount of information available online regarding airfoils. One data base I looked at has 1629 individual airfoils listed (link below).  This information is interesting to view if for no other reason than to gain some understanding of how complicated aeronautical engineering can be.  I have used similar airfoil information in the past designing airplanes for balsa. It is simply not possible to control foam board to the degree necessary to reproduce airfoils taken from data bases accurately. The best we can do is approximate the general shape of known successful designs.  In reviewing symmetrical airfoils from data bases I noted that many of them have the maximum thickness of about 12% at about 30% of the chord.  I used those parameters for my airfoil design.

Here is a picture showing the three most basic airfoil types used in RC modeling, Flat Bottom, Semi-Symmetrical and Symmetrical:

The link below will take you to an airfoil database with over 1600 airfoils: 

http://airfoiltools.com/search/index?m%5BmaxCamber%5D=0&m%5Bsort%5D=5  

We are not likely to use the detailed information given in this database for these simple foam board designs but it is interesting to see how much information is available out there. 

Maximum Thickness:

Maximum thickness is the thickness of the wing at the thickest point, frequently at the spar. It is expressed as a percentage of the chord.  Maximum thickness has a considerable effect on airplane performance. Generally thicker wings fly more slowly and produce a higher amount of lift at a given speed.  Many other factors go into the results including airfoil shape, angle of incidence, speed, wing loading, etc.  In the end it all ties together.  Among airfoils the "Clark Y" is perhaps the best known.  It was used on many of the traditional general aviation airplanes and is probably the most common one used on RC models.  It has a thickness of 12%.  I generally use it as the standard and decide whether I want to be thicker or thinner than "Clark Y" for the performance I want.  For the Stout Trainer symmetrical wing I stayed with 12% maximum thickness which was the same value I had used for the flat bottom wing.

For conventional airfoils the maximum thickness most commonly occurs at 25 to 35% of the wing chord.  In laminar flow wings the maximum thickness usually moves further back most often between 40 and 50%. I used 30% for this example, which was again the same value I had used for the flat bottom wing.

Note: Maximum Thickness is shown as "Thickness" in the NASA graphic above.

The maximum thickness for this design can be seen corresponding to the double spar location in the next photo below.

Spar Design:

As Josh Bixler often says, the strength of the typical FT style wing is not in the spar.  The strength is in the top and bottom wing panels.  The spar in these very light foam board designs usually simply acts as web bracing to keep the two surfaces in alignment. Instead of each surface flexing separately the spar makes them act as a unit so that the lower wing panel is in tension and the upper one is in compression in normal flight.  The panels are much stronger in tension and compression than in flexure.  For this design I am using a simple spar at the point of maximum thickness.  It is made from two thicknesses of DTFB 1" wide laminated together.  I use an additional 1/2" single layer spar toward the trailing edge of the wing to control the angle between the upper and lower wing panels at that point.  Without the second spar it would be impossible to keep the airfoil uniform.

Additional strength is sometimes needed if a wing is expected to be used in high G force conditions such as high speed aerobatics.  Foam board is stronger in tension than in compression.  On normal flight the bottom of the wing is in tension and the top is in compression.  When a FT style wing fails it is usually because the upper surface develops creases and then collapses accordion style causing the tips to fold upwards.  If a stronger component such as a wood dowel is added to the top wing panel it can help resist the compression force.  On this wing it would make sense to add two 3/16 dowels about 18" long to each wing half.  They would be placed at the intersection of the upper wing panel and the spar from the wing root to about mid span, one on each side of the spar.  This would greatly increase the strength of the middle half of the assembled wing.  For even greater strength make one of them 30" and run the full length of the wing. The ends of the dowels should be flush with the wing root so that there is no portion in the middle that is not reinforced.  Since the upper wing surface will be in compression rather than tension there is no need to have the dowels continuous through the joint. The glued joint will perform well in compression.     

Spar design can be used to help avoid tip stalls.  A thinner airfoil will stall before a thicker airfoil of similar shape.  This principle can be utilized in two ways.  A tapered wing can be given a constant thickness spar instead of tapering the spar down toward the tip.  This makes the measured thickness the same for two airfoils with different chord lengths.  However the Maximum thickness at the tip is actually higher than at the root because the chord is less.  

The same effect can be accomplished in a rectangular wing by increasing the measured spar thickness at the tip. The Maximum Thickness will be higher at the tip and the stall speed will be slower.  In the example of the Stout Trainer the spar thickness measures 1".  Adding the two wing panels yields a net thickness 1.375".  The wing chord including ailerons is 11".  The maximum thickness is the measured thickness divided by the chord length over 100, or 12.5%.  If you increase the spar at the tip to 1 1/4" the net thickness becomes 1.625" and the Maximum Thickness is 14.8%.  The wing tip will stall later because of the higher Maximum Thickness.  

Here is the airfoil that resulted from this design:

Note the double 1"spar at the point of maximum thickness and the single 1/2" spar further back.

Aileron Design:

Traditional ailerons vary from up to 25% of the cord for 1/2 width ailerons down to as low as 5% of cord for full width ailerons. For 3-D airplanes these sizes are increased considerably. 

On the Stout Trainer prototype the first wing had full length 1" wide ailerons (9% of chord).  I found them to not be as responsive as I wanted. It was a nice and easy Sunday flier but I wanted a fairly high roll rate for aerobatics.  I added an extra inch to the width for a net of 2" (18% of chord).  The roll rate was much better with pretty modest throw rates. For this wing I am using 1 3/4" wide full length ailerons (16% of chord).  With moderate throw rates this wing should be equally as responsive.  I can go to higher throw rates if I want more extreme performance.

Here is the aileron that resulted:

Dihedral Angle:

Dihedral angle is the angle the wing is mounted compared to a horizontal surface.  The purpose of dihedral is to stabilize the yaw of an airplane in flight.  When one wing is raised the opposite wing rotates toward level creating more lift.  Lift is reduced on the wing that is at a higher angle.  The reduced lift causes the high wing to drop and level flight is resumed.

Airplanes without ailerons rely on this principal for return to level flight after making a turn. Their dihedral angles are generally higher and need to fall within a certain range to function properly. Dihedral angles for these airplanes range from 7 degrees for high wing models to 9 degrees for low wing. These airplanes should return to level flight if the controls are released.

General use airplanes with ailerons usually have lower dihedral angles ranging from 3 degrees for high wing to 6 degrees for low wing.  These aircraft have some tendency to return to level flight if the controls are released but will need aileron assistance if too far out of level.

High performance aerobatic airplanes such as pattern and 3D models usually have mid-mount wings with no dihedral.  These airplanes need constant aileron input to maintain level flight.

The Stout Trainer prototype was made with 3 degrees of dihedral.  As I regained my flying skills I shifted to 0 degrees for better aerobatic performance.  That is the wing shown in the picture at the beginning of the article.

Washout:        

Washout is a design feature where the wing tip is at a lower angle of attack than the root.  The reason for this is to avoid tip stalls. When approaching a stall you want the wing root to stall first.  If the inner part of the wing is stalled and the tip is still flying you maintain control.  If the tip stalls before the root the stalled tip drops and a snap roll results.  This usually happens on landings with disastrous results.

Washout can be built into wings by twisting the wing from end to end.  The ability of DTFB to twist is limited.  On straight rectangular wings you can usually get 2 degrees of so without wrinkles. Tapered wings can be built in such a way to use the taper to force a twist. The details of this method are given in my previous article, "Making Fully Symmetrical Curved Wings from DTFB":   http://flitetest.com/articles/making-fully-symmetrical-w-ings

Wing Tip Design:

Wing tip design is a complex issue that I do not intend to delve into here.  According to the graphic below my tip is a "Sharp" which is used on many RC designs.  This graphic is by no means compete.  For example it does not show the undercambered tip used in many FT designs. I just wanded to show some of the many options available. 

Here are completed wing tips for Stout Trainer (bottom) and Blue Streak (top):

Angle of Incidence:

The angle of incidence is the angle a wing is mounted from horizontal as compared to the line of flight.  The angle of incidence varies depending on the use and performance expectations of the aircraft design.  

Entry level trainers and Sunday fliers typically have 2 to 3 degrees positive on the wing or 2 to 3 degrees negative on the vertical stabilizer.  There is really no difference between them.  The important thing is to have a difference between the two.  In practice the wing will be at a positive angle of a degree or two and the vertical stabilizer will be a degree or two negative.  If the tail is low the downwash from the wing can reduce the need for negative on the tail.  Small adjustments can then be made in the elevator trim to accomplish level flight.

Aerobatic aircraft including pattern and 3D typically have mid mounted wings and no angle of incidence on either the wing or tail so that they perform the same inverted or right side up.          

Wing Mounting:

Wings can be mounted in various ways.  The most common method for FT style foamies is rubber bands.  That method is fine for simpler designs where the details of appearance are not as important as convenience.  For more detailed models it becomes more important to use concealed structural methods similar to those traditionally used on balsa / Monokote models.

I use rubber bands and dowels to mount the wing on the Stout Trainer.  For the more finished "Blue Streak" featured in my previous article I used a mostly concealed system of dowels, wood blocks, plywood bulkheads and a nylon bolt.

Here is the wing mount for my Blue Streak:  

The two dowels are inserted into the two holes in the bulkhead at the front of the wing and the nylon bolt is screwed into the tapped hole in the wood block near the trailing edge.  The holes are positioned to make a snug fit. 

SPECIFIC MODEL DESIGN CRITERION: 

Design Criterion for This Example (Stout Trainer): 

1. Wing mounting position: High

2. Wing Shape: Rectangular. 

2. Wing Span 64" / Wing Cord 11" / Aspect Ratio. 5.8 - 1 (or simply 5.8)

3. Wing Area 4.81 SF / Wing Loading 10.3 oz / SF

4. Airfoil Shape. Symmetrical

5. Wing Thickness.  1.375 / 11  = 12.5%

6. Spar Design. 1" foam board vertical doubled at 30 % of chord, 3/8 " foam board vertical at 65% of chord

7. Aileron design. Full length X 1 3/4" wide.

8. Dihedral Angle. None

9. Wash Out.  2 Degrees (by twisting during assembly)

10. Tip Design: Sharp.

11. Angle of Incidence. None 

12. Wing Mounting details. Dowels and rubber bands.

DRAWINGS - THE DESIGN: 

With the design criterion established the plan can now be developed.

Here is the drawing I developed to satisfy this set of design criterion:  

(Click on drawing to print - jpg file)

Here is the full sized wing tip pattern:

 (Click on drawing to print - jpg file)

The design concept is based on using a full sheet of DTFB to make each wing, the same as was done with the original Stout Trainer wing design.  This wing is actually about 4" longer than the original because the wing tips are added instead of being cut from the full sheet.  That should help compensate for the lower efficiency of the symmetrical airfoil.

The wing assembly method for this wing would be the same as for the tapered symmetrical wing detailed in my earlier article:  "Making Fully Symmetrical Curved Wings from DTFB".  If an experienced builder is interested in actually building this wing they could use this set of plans and follow the assembly method in the link below:   

http://flitetest.com/articles/making-fully-symmetrical-w-ings

The only "twist" is the different method needed to develop wash-out.  Since the wing is not tapered the wash-out does not develop automatically by building the top surface flat as in the tapered example.  We have to actually develop a twist in the wing as we assemble it.  That is done by misaligning the trailing edges by 1/8" on one side. That is why the top panel at the tip end measures 1/8" more (9 1/8") than the other three locations (9").  The misalignment forces the leading edge of the wing tip to pull up.  The leading edge measures about 3/8" more from the building board at the wing tip than at the root when the wing is upside down.  The tip leading edge ends up drooped when the wing is right side up yielding about 2 degrees of washout.

CONCLUSION:

It is not my intention to show how to build the wing described above in this article but simply to discuss the factors that go into the design process.  There are other considerations related to the building process which I have not discussed here. Those would be dealt with in a build article.  Hopefully this will give the reader an appreciation of the complexity of information that should be considered in developing a wing design.