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How to design your own R/C aircraft guide: Part 1 (Setting Specifications and Designing the Wing)

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Use this guide as a source of info on how to design your own radio controlled aircraft. In this informative guide, I will walk you through how to design an entirely new R/C aircraft.In Part 1 we set the specifications and design the wing of our aircraft.Search for Part 2 after readings this!

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Page 1: How to design your own R/C aircraft guide: Part 1 (Setting Specifications and Designing the Wing)

1 | P a g e Copyright © 2009 the Malyuta Avionics logo is reserved

Page 2: How to design your own R/C aircraft guide: Part 1 (Setting Specifications and Designing the Wing)

2 | P a g e Copyright © 2009 the Malyuta Avionics logo is reserved

Contents

1. Introduction………………………………………………………………... 3

2. Setting specifications………………………………………………………. 3

3. Establish vertical performance and airspeed envelope……. 4

4. Wing design…………………………………………………………………….. 5

4.1 What affects what?...................................................................... 5

4.2 Wing area………………………………………………………………………………… 6 4.3 Wing loading……………………………………………………………………………. 7 4.4 Aspect ratio (AR) ………………………………………………………………. 7 4.5 Wing taper……………………………………………………………………………….. 8 4.6 Wing sweep……………………………………………………………………………… 10 4.7 Wing dihedral…………………………………………………………………………… 12 4.8 Washout………………………………………………………………………………….. 13 4.9 Aileron sizing……………………………………………………………………………. 13 5.0 Our wing specifications………………………………………………………. 14

6.0 Conclusion………………………………………………………………………….. 16

Bibliography…………………………………………………………………………….. 17

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1. Introduction. I am a modeler, just like you probably are, dear reader. This tutorial is intended for those of you,

who are just getting started in this wonderful hobby- and obviously, need lots of advice on how to

design, build, fly. Looking through the web, I did not find one full, comprehensive walkthrough for

designing an aircraft, where the author would set himself guidelines and talk through until the final

design. I will be a pioneer in doing this- and excuse me if I do not succeed in some areas.

Here, you will find references to software (almost all freeware, and those that aren’t- have many

freeware substitutes), many pictures, explanations, aerodynamics and what-not. I am writing this

walkthrough for everyone- beginners will understand, and those of you that are advanced will profit

as well.

This is part one to this walkthrough, which will be broken up into four parts (part I: setting

specifications and designing the wing, part II: designing the fuselage and tail, part III: virtual

prototype tests, Part IV: extras on flight mechanics).

2. Setting specifications Setting your design specifications is crucial- even if you in the end design a successful, flying,

aircraft, you would have been designing to make it fly, not make it fly the way you want, and

just making it fly is only half the job…

This is a guideline for those who will be designing your own airplanes, here is a guideline taken

from the awesome site http://www.airfieldmodels.com/index.html (to clear myself, I am not the

owner of this list- check the bibliography):

o Purpose of the model

o Style — Modern, Old Timer, Scale, Sleek, etc.

o Powerplant class

o Flight time

o Stability — Should the model be self-

stabilizing, neutrally stable or somewhere in

between?

o Airspeed envelope

o Vertical performance

o Control response

o Stall characteristics

o Construction methods — Traditional wood,

composite, etc.

o Control system

o Landing gear system

o Break-down for transportation

o Etc.

Fig. 1 Canard aircraft

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For this walkthrough, I want to design a sports, pusher-prop, canard aircraft which

has a very short take-off distance and is able to perform mild aerobatics is needed. I

will also be using an OS .46 gas engine which I already purchased- so as to save money. So, I list my own guidelines for this design:

Single-engine, two-seater sports aircraft

Should be able to switch between docility and mild aerobatics, and have a low

stall speed

Power plant- OS .46 gas engine

Flight time ≈60 minutes

Stability- self stable (tendency to go back to 0 pitching moment (more on this

later))

Airspeed envelope 10-60 mph

Vertical performance- medium climb rate (let’s say about 15 ft/s)

Control response- relatively solid, but not like on a 3D aircraft

Tricycle landing gear setup (main gear + nose gear)

Should have detachable wings

Weight should be kept under 2 kg

Build type- traditional, but maybe foam-core canard and vertical tail fins

The airplane should have a small take-off distance- about 30 feet, although

I’m not sure yet

CANARD CONFIGURATION

Maximum allowable wingspan- 1600mm

Now that I set myself these specifications, I can confidently go on to start thinking

up dimensions which I will later with the use of software (freeware, mentioned

later) refine to get a flight-able prototype which will suit almost all of my above

listed specifications.

I think it is right to mention now that the design process for aircraft is a process of

constant compromises and unavoidable tradeoffs- for example, I may have to

break up my aircraft into more than a detachable wing, because my car won’t fit

the airplane, so I will be forced to create detachable canrds- but the joints that

result will add weight and force me to go above the 2 kg weight mark- and

perhaps sacrifice some aerobatics and takeoff distance for the ability to transport

the airplane.

3. Establish vertical performance and airspeed envelope

Again, I must mention that a lot of what I write is inspired by the Airfield Models website- please visit it, great website.

“Rate of climb is determined by the powerplant , propeller and the aircraft's ready-to-fly weight.”1- Airfield Models (it is also defined by your wing’s lift slope which is determined by the airfoil, downwash angles and what not- but, let’s keep it simple here, shall we?)

Think of: Do you want your aircraft to climb straight up like a crazy 3D monster? Or, do you want a heavy-weight sumo sort of airplane which climbs slowly, but confidently? These options become pretty much defined when you choose your engine- a 3D monster with a one and a half meter span and only a .40 size engine? I don’t think so…

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―Airspeed (minimum and maximum) is determined by the engine,propeller and wing.‖ 1

-Airfield Models

Let’s fill in a table with some values and definitions we want for our aircraft (again, the table is taken from Airfield Models):

Weight ready-to-fly ≤ 2 kg

Min. airspeed ≈ 10 mph

Max. airspeed ≈60 mph

Climb rate A confident, rapid, climb rate, let’s say about 15 feet per second

4. The wing design

4.1 What affects what?

The wing is by far the toughest component to design and pretty much the most critical. The wing’s design defines the induced drag (a large problem on sailplanes), the neutral point (the point about which all moment coefficients are 0), the needed size of the tail, and many other things.

Choosing an airfoil family like NACA 4 digit airfoils or 5 digit airfoils, or Eppler self-stable airfoils, etc. is a good starting point. You can then begin scratching airfoils out of the list depending on if you want an airfoil which is easy to stall in order to get exciting aerobatics out of the airplane- but an easy to stall airplane may not be a good choice for a trainer because it will challenge the inexperienced pilot and mean a short life for his model. In our design we wanted mild aerobatics to stand along docile flight- which means compromises will have to be made to attain a plane that will allow us to perform aerobatics when we feel like it, but also be able to please us in a calm flight without unexpected stalls happening in an average turn.

Here is a table, again from Airfield Models1, which shows what affects what in a wing (I am no the creator of this table):

Flight

Characteristic

Design Parameters

Airfoil Wing

Loading

Aspect

Ratio

Dihedral Washout Aileron

(Area/Style)

Airspeed

Roll Rate

Stall

Stability

Lift Capability

Lift/Drag

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Ratio

Aerobatics

Affects characteristic

Here is also a useful table from NextCraft2 website (check bibliography) which shows characteristics apparent in different types of model aircraft:

Type Wing

Span

Aspect

Ratio

Overall

Length

Wing

Area

(sq.

inches)

Weight Wing

Loading

Power

Loading Power Skill Level

Trainer 60" 6 50" 600 to

700 4 lbs.

15 to 20

oz/sq.ft.

110 to 160

oz/cid .40 to .60 Low

Sport 60" 4 to 6 50" to

60"

500 to

600 5 lbs.

20 to 25

oz/sq. ft

110 to 160

oz/cid .40 to .60 Medium

Aerobatic 60" 4 to 6 50" to

60"

500 to

600 5 lbs.

15 to 25

oz/sq. ft

75 to 120

oz/cid

.40 and

up

Medium to

High

3D/IMAC 60" 4 to 6 50" to

60"

700 to

800 4 lbs.

10 to 15

oz./sq.ft

50 to 100

oz/cid

.60 and

up

Medium to

High

Glider 60" 8 to

12 40"

400 to

500 1 lb

5 to

15oz./sq. ft N/A N/A

Medium to

High

Turbine 60" 3 to 4 80" 850 to

1100 25 lbs.

40 to 50

oz/sq. ft

Thrust >=

wt.

25 lbs.

thrust High

* "cid" in the "Power Loading" column stands for "cubic inches displacement". (a .40

engine is .40 cubic inches displacement) The idea of using "Power Loading" as a design

criteria is mentioned in Andy Lennon's book, "The Basics of RC Model Aircraft Design".

See the High Lift Page for info on how to obtain the book.

4.2 Wing loading Wing loading is a critical parameter in the design phase and should be built towards. Wing loading affects, “low speed flight, predictable landing approach, rate of climb (lift from the wing, not pull from the engine), control response, and how easily the plane is upset in flight.” 1

A plane with a light wing loading will be more affected by air pockets, and hence be more difficult to spot land because during landing, air currents will move the plane about a lot. A lighter wing loading also means that the plane’s top speed will be decrease in order to prevent the wing’s to break during high-G maneuvers which come which come with maneuvers at high

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speeds. A higher wing loading wing, on the other hand, will be less affected by air currents and will also be less responsive to controls- it will also have to fly faster in order to stay aloft.

Looking at our table above, since we are building a sport-type aircraft with the possibility of docile flight like that of a trainer, we’ll chose the shared by both 20 oz/ft^2. In the next subchapter, we will work out the required wing area using the wing loading we just set for our plane and the previously determined weight.

4.3 Wing area

We previously stated that the weight of our plane will be in the 2 kg region. We’ll convert 2 kg to lb, which turns out to be 4.4 lbs. Using some simple algebra, we solve for wing area (the original wing loading equation is wing loading = weight / area):

Wing loading (oz/ft^2) = weight (lb) / area (ft^2)

20 = (4.4 * 2304) / Sw

Sw = (4.4 * 2304) / 20

Sw = 506.88 in^2

Perfect! As per the table, our wing area falls into the wing area range for sports aircraft whilst having a wing loading allowable for a trainer- which will give our plane some trainer characteristics. Well… in reality everything is much more complicated than that…. But that is a discussion for another day.

4.4 Aspect Ratio (AR)

Before I say anything, the AR ratio is calculated as AR=span/MAC(mean aerodynamic chord)

Aspect ratio is a fun topic to discuss- and as you can see from the table above, it strongly affects many flight characteristics- such as roll rate, lift to drag ratio, pitch sensitivity, etc. In XFLR5, a program we’ll discover later when testing our wing ;), I did an analysis on the aspect ratio of a wing planform- if you, dear reader, want the file for this study, just e-mail me at [email protected].

The AR also affects the wing’s tip stall characteristics. In a bank, the outer wingtip will travel at a faster speed than the lower wingtip. At the lower airspeed, the inner wingtip will stall sooner- but when it does, the outer wingtip would continue lifting as it did not stall yet. Effectively, the plane will turned upside-down and put into a spiral it may or may not recover from- basically, a

big sad face for the pilot of that plane.

Higher AR wings produce lift more effectively- their Cl (lift coefficient) is higher. In the specifications I said that I want a short takeoff distance and also wanted aerobatics and stall-free docile flight… so, for our plane we’ll break the rules of that table I showed before (and, I want to say, that that’s perfectly OK, those tables are very general and don’t allow for creativity)and aim

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for an AR of something around 7.5- which will give me a gorgeous, not too chubby, wing which will suit my purposes more than a standard wing of AR 6:1. Here, it is important to note that low aspect ratio wings are more maneuverable in roll- but this is one of those compromises I have to make- downgrade aerobatic abilities of my design for the sake of a short takeoff distance. You can see by now that trying to design a plane to be docile and aerobatic at once is not an easy job- one always has to compromise, and here I traded some aerobatics for docile flight- because I know that I will be spending most of the time just flying around, so it would make sense to optimize my design for calm flight! Here is an excerpt from Airfield Models:

For example, short, stubby wings are not even considered an option for these types:

Sailplanes

Go a long way using very little fuel.

Airlines

Money spent on fuel is less money in the bank.

Voyager by Burt Rutan.

It's sole purpose was to fly non-stop around the world without refueling and then

retire.

A high aspect ratio wing has a better lift to drag ratio and is generally more efficient than a

low aspect ratio wing. If the aspect ratio is too high the plane will have a sluggish rate of roll

and is easier to break.

As the aspect ratio of a wing becomes lower the aircraft becomes more maneuverable in roll

and less efficient in lift. That's why you never see fighter aircraft having high aspect ratio

wings and you don't see bombers with low aspect ratio wings with some special exceptions.

3

Fig. 2 The Supermarine Spitfire is an excellent

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If the aspect ratio is too low the plane may be

twitchy about the roll axis and slow down

excessively in turns. Low aspect ratio wings have tremendous drag as angle of attack

increases. Low aspect ratio wings are inefficient and not good for load lifting.

” 1

4.5 Wing taper

Wing taper is, basically, the variation in chord between the root and tip of the wing. Taper ratio is the chord of the tip divided by the chord at the root and, obviously, varies between 0 and 1. Taper decreases the MAC- the wing chord, and therefore increases the AR ratio, so you must be careful when designing a wing for one AR ratio prior to taper, and then apply taper to the wing- you’ll effectively get a higher AR wing, and overshoot your preliminary parameter!

Elliptical wings are the most efficient, but they are the hardest to build- especially so because you will have elliptical thickness as well. The most efficient, and cheapest for modern aircraft manufacturers, way to increase efficiency from a plain rectangular wing is to apply taper to your wing - but this depends on the AR ratio again….

Wings with high AR ratios must not have a low taper ratio (a more ‘pointy’ tip) because such a configuration is extremely prone to tip stall. If you want a high taper ratio, keep your AR ratio down!!!

Above, I decided that my wing should have an AR ratio of around 7.5:1. But, I want to have some taper, because I want my plane to look cool! I also plan on using some sweep in order to make my aircraft more stable and more likely to recover from a tip stall (described later).

So, since taper tends to increase AR, I think that my wing will have originally an AR of 7 before taper- and then I will need a taper ratio which will give me a M.A.C. which will give me an overall AR of 7.3 to 7.5! I think that at this stage it is important for me to set a wingspan for my wings… I will have the standard wingspan of 60”, and my car will fit this length anyway! Perfect, I set my wingspan- now, I will figure out the required chord to give my rectangular wing an AR of 7, and then I will figure out the tip chord which I’ll need to yield an AR of ≈7.4, and then I will figure out the resulting taper ratio…

b- span; Sw- wing area; AR- aspect ratio; c- chord; M.A.C.- mean aerodynamic chord; Rt- taper ratio;

1. b / MAC = AR 60 / MAC = 7 rectangular planform MAC = 8.57”

→ hence, the root chord will have to be 8.57” (21.77 cm)

→now, we’ll have to find a MAC which will give us an AR ratio of 7.5

2. 60 / MAC = 7.5 MAC which will give us the desired AR

example of an elliptical wing

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MAC = 8

→Now we need to find the appropriate tip chord to give us that M.A.C.

→But now I realized that this won’t give me the wing area I want, so I need to figure out how I can increase the span and MAC proportionally to give me the wing area that I want…

3. 60x * 8x = 506.88 480x^2 = 506.88 So, we need to scale the span and MAC by a factor of 1.028… X^2 = 1.056 x = 1.028

→This gives us a span of 61.68” and a M.A.C. of 8.224”!

4. (8.57” + x) / 2 = 8.224” 8.57” + x = 16.448” So then this is the tip chord length x = 7.878”

→So, now knowing out root and tip chords, we will find the taper ratio for our wing

5. 7.878” / 8.57” = Rt So, then 0.919 the taper ratio! Not too bad…

0.919 = Rt

So now we figured out the root and tip chords, the taper ratio- which is pretty

close to 1, so our design won’t allow any nasty tip stalls to spoil our tranquil bank into the setting sun

… Armed with this knowledge, we move on to wing sweep!

4.6 Wing sweep

In a swept wing, the center of lift is much more aft of the main spar of your wing than if you had a plain rectangular planform. Because of this, the lift from the wing will twist the TE (trailing edge) upwards, which will make the wingtip have a natural tendency to twist to a lower AoA than the rest of the wing. As we increase the AoA, the lift of the wing will increase (until the stall alpha, of course), which will twist the TE and the wingtips to a more and more negative AoA. This will place a natural washout into our wing design and somewhat protect it from tip stall.

Sweep also makes an airplane look smooth- which is, in essence, what the general public will want to see- cool-looking aircraft! I’m sure that a modern grumpy teen will not be impressed by a jet fighter with rectangular wings. Just look:

To the spectator… To the engineer…

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Ugly duckling OMG!!!!! Awesome!!!!! The brainchild of

engineering genius Brilliant, but so financially inefficient that it’s not even funny…

Sweep also puts the CG back and broadens the CG range- more room to locate the CG at.

Figs. 3 & 4 show the graphs I produced after a study of wing sweep vs. lift and drag (done in XFLR5,

which we’ll be using to model out design prototype for CFD/computational aerodynamics tests in

part III).

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I decide to have 10 degree sweep, because from looking at the graph it is evident that I can decrease

drag by x without too much lift loss. Plus, 10 degrees provides plenty of that extra stability that

comes in with the sweep package!

4.7 Wing dihedral I will say now that I will not be adding dihedral to the wing- for the reason that will now be described.

The dihedral package comes with two advantages- it provides increased stability and allows a model aircraft to be flown with rudder-only. Dihedral provides stability about the aircraft’s roll axis- when an airplane is disturbed from flying straight, its weight and lift will pull it to the side. With dihedral, if the plane was to bank left, the left wing will be set at a higher AoA because of

non-zero sideslip. I do not want to go into the details of sideslip at the moment… but basically:

In the case of setting a dihedral angle for a wing, what one essentially is doing is affecting the amount of dihedral effect (more dihedral, more dihedral effect). Dihedral effect is simply the amount of roll moment per degree of sideslip. What is sideslip? Sideslip is the rotation of the aircraft from relative wind. Think about it, when the airplane banks, the outer wingtip travels faster than the inner wingtip- which effectively puts the airplane at an angle towards the free-stream air… this is sideslip! With dihedral, the larger dihedral effect- which is a weighty topic to

Fig. 3 Alpha vs. total drag for sweeps between 0 and 30° with 5° iterations (sorry about the watermark- it’s

the print screen program)

Fig. 4 Alpha vs. total lift for sweeps between 0 and 30° with 5° iterations (as you see, the lift decreases as sweep increases- again, we encounter compromise).

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discuss another time- will put the wing corresponding to the inner wingtip at an ever higher alpha, which will create a positive rolling moment that’ll rotate our plane so that it faces back into the wind again! That’s dihedral in a nut shell …

*image from Wikipedia.org

*image from Wikipedia.org

Fig. 5 “Uncompensated lift component produces a side force Fy, which causes the aircraft to sideslip.” 4

Fig. 6 “Non-zero sideslip sets the lower, upwind wing to a higher angle of attack, resulting in a stabilizing roll moment P.” 4

The negative effect of dihedral is that it causes control coupling- when a control causes the aircraft to rotate about a different axis than intended, such as pitching when rudder is applied. Aerobatic aircraft should avoid control coupling as much as possible, which is one reason I will not have dihedral angle on my wings… I still want some aerobatic ability after all the compromise that I’ve done above, don’t I?!

From Airfield Models, as Done Lowe will tell you, “As Don Lowe will tell you, if you want your ship to be tuned for competition you need to be willing to cut the wing apart to adjust the dihedral.” 1

As I will tell you, “Make compromises!”

Cutting wings for dihedral when you want an aerobatic aircraft that you want to keep as neutral in flight as possible is not the best thing that could come to your mind! If not done carefully, this cutting can lead to weak spots in the wing structure and what-not…

So, I won’t have any dihedral on my plane- although you might want it on yours if it is a trainer or a slow flyer.

For your rudder-only models, 5° of dihedral is an excellent choice- too little will make turns sluggish and your airplane will have a pitching down tendency in turns, while too much can make the wing inefficient.

Good link on dihedral: http://en.wikipedia.org/wiki/Dihedral_(aircraft)#How_dihedral_angle_creates_rolling_moment_from_sideslip_.28dihedral_effect.29

4.8 Washout

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Washout is an intended twist given to the wing towards the wingtips. What washout does is it sets the wingtips at a negative angle to the root of the wing- which means that at high alpha, the tips would actually be flying at a lower alpha than the root- which prevents a tip stall from

ruining your day.

Washout is a bad move on aerobatic models which should fly as neutrally as possible, and inverted flight will cause wash-in (the opposite of washout)- which means an inverted loop will

likely tipstall your aircraft, and ruin your day. But, it will be a fun show for your buddies.

Washout is useful on trainers, utility aircraft, high aspect ratio aircraft such as gliders, jumbo-sized model aircraft- if only for extra safety after you spend 4000+ on them beauties, heavy-scale aircraft, airliners (my favorites). Rectangular-planform wings do not really need washout because the rectangular planform is naturally very resistant to tip stalls- I guess that’s one of the reasons why almost every trainer has a rectangular planform!

Again, I want my design to be somewhat aerobatic- so I won’t have any washout- it’s just not necessary and may even harm things, but cheer up my friends…

4.9 Aileron sizing

―Strip ailerons are easier to build and in my experience have a better roll rate than

barn door ailerons. Tapered strip ailerons tend to work best with the least possibility of flutter.‖ 1 – Airfield Models

I don’t know anything about taper strip ailerons, and I do not know if strip ailerons really

do have a better roll rate- although they might. It is important to know that the most

efficient area for ailerons is at the very wingtip because the moment arm from the

ailerons to the fuselage would be the longest- and hence, an aileron of any size would

cause a large roll rate if placed at the tip than at the root- which means that less aileron

area is required! Barn door ailerons are placed at the tips for most efficiency, strip

ailerons are placed along the entire wing- and the most efficient use of strip aileron area

is towards the tip! If you ask me, I prefer barn door ailerons because they give you the

ability to place flaps as well (we won’t be discussing flap sizing in this part). Although, some say strip ailerons are easier to build…

Strip ailerons are typically 10% of wing chord and each aileron is 4% of the total wing area. On the other hand, tip-mounted barn door ailerons are usually 25%of wing chord and one aileron is 6% of total wing area.

For my aircraft, I will use a standard barn door aileron 25% of chord, located at the very tips. I cannot put down any aileron dimensions right now- the aileron, because the wing has taper, will also have taper. I should say that tapered ailerons are less likely to stall!

5. Our wing specifications

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This table is taken from Airfield Models, and all we will do is fill in the blanks for our wing dimensions.

1

*One of my specifications was a short takeoff distance, and I chose an airfoil with a high Cl. Initially, I chose the NACA 6414 with a Clmax of 1.907- but I realized that it would be hard to build the wing straight, and I compared it to other airfoils (I used the websites www.worldofkrauss.com and http://www.ae.illinois.edu/m-selig/ads/coord_database.html#N for finding airfoils)- and ended up choosing the GOE 611 with a relatively flat bottom for it had a high Clmax of 1.834. Again- this is compromise.

Fig. 8 A visual sketch of the wing. Beautiful!

Wing Loading 20 oz./ft2

Wing Area 506.88 in2

Aspect Ratio 7.5:1

Taper Ratio 0.919

Root Chord 8.57‖

Tip Chord 7.878”

Wing Sweep 10°

Dihedral 0°

Stall performance

(description)

Unlikely to tip stall because of

high aspect ratio

Washout 0°

Airfoil (root) GOE 611*

Airfoil (tip) GOE 611*

Wingspan 61.68‖

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6. Conclusion

And this concludes Part I of this walkthrough, dear reader. I hope that it was useful to you, Part II will be coming soon.

Good luck and good flying! Daniel Malyuta, Malyuta Avionics.

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Bibliography

1. "Airfield Models - Step-By-Step Radio Control Model Aircraft Design." Airfield Models - Radio Control Flying Aircraft and Display Models. Web. 01 Jan. 2010. <http://www.airfieldmodels.com/information_source/math_and_science_of_model_aircraft/rc_aircraft_design/step_by_step_model_aircraft_design.htm>.

2. "NextCraft" Aircraft Design Concepts, by Mike James." NextCraft. Web. 01 Jan. 2010.

<http://www.nextcraft.com/aircraftdesignconcepts.html>.

3. “Supermarine Spitfire” <http://images.google.com/images?hl=en&um=1&q=supermarine+spitfire+mk1&sa=N&start=20&ndsp=20>

4."Dihedral (aircraft)." Wikipedia, the free encyclopedia. Web. 01 Jan. 2010. <http://en.wikipedia.org/wiki/Dihedral_(aircraft)>.

5.Phillips, Warren F. Mechanics of Flight. New York: Wiley, 2004. Print.

6. Hubert, Smith,. Illustrated guide to aerodynamics. Blue Ridge Summit, PA: Tab Books, 1985. Print.

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