How to design your own R/C aircraft guide: Part 2 (Designing the Tail)

PART 2

Designing the Tail Contents

1.

INTRODUCTION. ....................................................... 2

2.

Disclaimer........................................................................ 3

3. Tail design......................................................................... 3 4. T-tails/Conventional tails .................................................. 5 5. V-tails………………………………………………………….................... 6 6. Canards………….................................................................. 7 6. Designing the vertical tail fins ........................................ 10 7. Designing the canard...................................................... 12 8. Afterword………………....................................................... 14 9. Bibliography……………… ................................................... 16

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’thave 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 two to this walkthrough, which is 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.

Disclaimer

I am a student, and what you are reading should be taken as the way in which I go about designing an airplane. A lot of conclusions drawn here should not be taken as rules, they are mere preferences. This walkthrough must not become the only source for designing your own aircraft, hence you should not rely 100% on the information provided here. The information here is taken from the knowledge gained through reading books such as:

• • • •

Mechanics of Flight by Warren F. Phillips The Illustrated Guide to Aerodynamics by Hubert “Skip” Smith Airfield Models (www.airfieldmodels.com) Cunningham on R/C (send an e-mail to me for a copy @ [email protected])

I hope that you enjoy the walkthrough, but again, do not rely 100% on it, just like any other walkthrough that you may read. Gather information from enough sources before designing your own aircraft- that is my suggestion to you, dear reader.

3.

Tail design

The purpose of tail surfaces is to provide stability and control; hence, the siye of the tail surfaces is defined by the degree of stability/control required! The horizontal tail provides longtitudinal stability, whereas the vertical tail provides stabiltiy along the z-axis- in other words, it provides stbaility in the directional sense. Try to imagine a plane with no vertical tail surface- what will direct it in the air? What will keep it flying straight and not wobbling about due to moments from other parts and air currents? If you make your vertical tail too small, you will notice that your plane tends to 'seek' with its noce- left to right, right to left, etc.

Whereas the horizontal tail surface provides longtitudinal stability, an elevator provides pitch control. The same goes for a vertical tail and rudder- the rudder provides yaw control. Aerodynamic forces are proportional to the area of your surface- hence a larger tail will produce more lifting force from the tail. However, stbaility is defined by moments about the aircraft CG- and a moment requires a moment arm. Remember that a moment is defined by: M=Fxd where: M = moment; F = Force d = lever arm length Hence, the distance- the lever arm elngth- betweent he tail aerodynamic center and the airplane's CG is also plays a role in sizing the tail. The tail moment that actually provides longtitudinal stability is the tail lift (i.e. The Force) times the tail moment arm (i.e. the lever arm length). Since force is partially determined by the area, stability will be proportional to the tail area times the tail moment arm. Are is measure in units squared (e.g. cm2, in2, ft2), whereas the tail moment arm is measure in a length unit (e.g. cm, in, ft). Hence the product of these will be a a cubic unitotherwise known as the Volume. Hence, the product of tail area and moment arm is reffered to as the tail volume. An increase in either tail area or the moment arm will result in the increase in stability since stabiltiy is proportional to tail volume. Hence, a long fuselage can have a small tail whereas a short fuselage will have to have a large tail in order to be stable. Tail volume coefficients, which will later aid us in finding the areas for our tail surfaces, are defined by diving the tail volume by another volume- in this case, the wing area, wing chord, and the wing span mainly determine the amount of stability required from the tail. Therefore, a horizontal tail volume coefficient is defined as the actual tail volume divided by the wing area times the mean average chord (M.A.C.):

Vh=(St * lt) / (Sw * c) where: Vh = horizontal tail volume coefficient; St = horizontal tail area; lt = tail moment arm; Sw= wing area; c = MAC.

The volume coefficient for the vertical tail is similar, except that the span is a mroe important value than the chord. Hence, the vertical tail volume coefficient is:

Vv=(St * lt) / (Sw * b) where: Vv = vertical tail volume coefficient; St = horizontal tail area; lt = tail moment arm; Sw= wing area; b = wing span. For model airplane, these coefficients range between:

Vh = 0.35 - 0.50 Vv = 0.02 - 0.035

We will use these to figure out areas of our tailplane later in this part of the tutorial

☺ 4.

Different tail designs 1. T-tails/Conventional tails

Since for our aircraft we will not be using a T-tail configuration, the T-tail will only be discussed briefly in this document. This tail design became gained popularity in the early 1980s after NASA’s research into spin recovery which concluded that a T-tail was the ideal configuration for spin recovery. Another reason for which to have a T-tail is to place the horizontal tail fin out of the wing’s downwash. Downwash has a destabilizing effect on the horizontal tail fin, and this effect increases with alpha (AoA). The low-mounted (normal) tail is immersed in this downwash during horizontal and low alpha flight, whereas the T-tail stays out of the area. However, the disadvantage of the T-tail becomes apparent at high alpha flight. At full stall, zero lift is produced, hence there is no downwash. So, the wing’s wake flows directly aft, immersing the T-tail in itself (fig.1)- whereas the low-mounted tail would now fly below the wake. In the wake, the T-tail experienced a sudden los of effectiveness, and a rapid pitchdown motion puts the aircraft into a deep stall.

Fig.1 T-tail immersed in the wing’s wake at high alpha

Another disadvantage of this tail configuration is the extra weight required for the heavier structure to support the T-tail; the elevator control/linkage also become complicated and adds further weight. However, the T-tail improves the efficiency of the vertical tail by its endplate effect (as it sits on top of the vertical tail), similar to how twin vertical tails mounted on the tips of a horizontal stabilizer improve its efficiency. In one of my previous designs (not this design), I implemented a t-tail where the horizontal stabilizer was mounted midway across the vertical tail fin (fig.2). This structure is usually more rigid with less weight required for supporting the horizontal stabilizer.

Fig.2 t-tail configuration 5.

V-tails

Another infamous tail design is, of course, the V-tail. In this design, a single surface is slanted on either side of the fuselage centerline to serve as both a horizontal and vertical tail fin. The vertical projection of a V-tail provides longitudinal stability, whereas the horizontal project (you guessed it!) provides directional stability. The advantage of this configuration is

that it slightly reduced drag from a conventional tail. This drag reduction actually comes about only from the fewer fin-to-fuselage and fin-to-fin junctures, which reduces the interference drag. There are no savings in skin friction drag since the total surface area of a V-tail must be equal to the total surface area of the horizontal and vertical tail fins in a conventional tail in order to provide equal stability.

Fig.3 Rear view of the 1965 S35 V-tailed Beech Bonanza A great example of a V-tail configuration is the original Model 35 1947 Beech Bonanza (fig.3); it was a common belief of the time that its high performance came from the V-tail, although the tail only slightly added to the low-drag configuration of the airplane. This can be proven if you compare the Model 35 to the Model 33, utilizing a conventional tail with the same powerplant; you will see that their performance is almost identical. 6.

Canards

The canard configuration is what we’ll be using in the airplane design discussed in this walkthrough. Just like with a conventional aft tail, trim and static stability can also be achieved by combining a wing with a forward lifting surface called a canard; it is a horizontal lifting surface mounted forward of the wing, rather than behind it like a horizontal stabilizer in a conventional tail design. The first successful heavier-than-air powered aircraft, the 1903 Wright Flyer, incidentally used exactly this configuration rather than a conventional tail. However, after this most designers abandoned this configuration- although it was most likely not due to aerodynamic disadvantages, but patent difficulties1. As a matter of fact, the canard design holds some significant advantages over the conventional tail, and the T-tail and V-tail for that matter. A good example of such a configuration used in the commercial aircraft industry would be the Beech Starship (fig.4).

1

Phillips, Warren F. Mechanics of Flight. Page 381. Hoboken, N.J.: Wiley, 2004. Print.

Fig.4 Beech Starship demonstrating a forward-mounted canard. The aerodynamic relations between the wing and the canard are very complex and cannot be accurately modeled through formulae; since the canard is mounted forward of the wing, the wing will induce upwash on the canard, just like the canard will induce downwash on the wing. Since the canard is shorter in wingspan than the wing, the wingtip vortices produced by the canard will also travel over the wing, hence creating a very complex flow over the wing. This interaction between the two lifting surfaces can only be correctly modeled by computer simulations and wind tunnel tests; in Part III we will be using the freeware computational aerodynamics software XFLR5 in order to run CFD tests on our canard design. Google Books provides a limited view of the excellent book “Mechanics of Flight” by Warren F. Phillips. Clicking on the link above will take you to the limited preview of the book, where you can read pages 381-394 (pages 386-387 excluded) in which Mr. Phillips takes you through a much more detailed analysis of the canard design; I very much recommend you to read those few brilliant pages about the canard design! Pinpointing main points from Mr. Phillips’ analysis of the canard configuration, here is an outline of the properties of the canard configuration. Please note that no plagiarism is meant, and the following list is a rewording of what is found in the book Mechanics of Flight1: ⇒ The canard is required to always be ahead of the CG to maintain trim; ⇒ The canard has a destabilizing effect on the whole airplane;

1

Phillips, Warren F. Mechanics of Flight. Page 381. Hoboken, N.J.: Wiley, 2004. Print.

⇒ A stable canard configuration required the CG to always be forward of the wing aerodynamic center; ⇒ Therefore, in a stable canard configuration, the CG must always stay in between the wing’s and canard’s aerodynamic centers; ⇒ The main wing is what provides stability in a canard configuration; ⇒ To maintain trim and static stability, the lift coefficient of the canard must always be greater than that of the wing. For trim, the canard volume coefficient (horizontal tail volume coefficient) must be large enough in order to counter the negative pitching moment created by the wing. However, the canard volume coefficient must also be small enough in order to not subdue the stability provided by the wing! Hence, sizing a canard in a canard configuration is much more critical than sizing a horizontal tail fin in a conventional tail design. With an aft tail, pitch stability is always increased by increasing the horizontal tail volume coefficient; but, sizing a canard requires compromising pitch stability and control.1 Since both canard and wing support the aircraft weight, the canard should be designed with a high AR for best efficiency. The fact stated above that a canard must have a higher lift coefficient than the wing is one of the advantages of canard design. As airspeed is reduced, the lift coefficients must be increased in order to support the aircraft in the air. However, since the canard always has a higher lift coefficient, it will reach its stall CL before the wing does. As the canard stalls, it no longer supports its portion of the aircraft weight, and it is no longer possible to generate the pitching moment necessary for a higher AoA to stall the wing; therefore, the airplane pitches to a lower angle of attack, and the canard is once again able to create lift. As it is, the main wing in a canard configuration is unlikely to stall in a gradual pitch-up maneuver; although, the wing can be stalled in a whip stall. 1 The higher lift coefficient of the canard also brings about the disadvantage of the canard design. Should an especially high CL be required for an STOL aircraft, it is useless and destabilizing to fit the wing with high-lift devices unless the same is done to the canardwhich downgrades the configuration’s economy for applications such as STOL. Essentially, the CLmax for the airplane is controlled by the CLmax for the canard since the canard must always have a higher lift coefficient than the wing. When high-lift systems are used, the magnitude of the negative pitching moment coefficient for the wing and the canard is increased- and for the canard configuration, this decreases the ratio of allowable lift coefficients for the wing and canard.1 Therefore, even though the wing is what mainly supports the aircraft’s weight, the canard must have a CL significantly larger than the wing in order to rotate the airplane during take off.1 Hence, the canard configuration is ill suited for purposes such as short take-off and landing where high lift coefficients are required with the aid of high-lift devices; since I’m using the canard configuration, STOL is currently not an option, and a longer take off and landing strip will be required for my aircraft. This was a brief overview of the canard design. If you would like to see the mathematical reasons behind the properties of the canard configuration that were discussed here, follow this link to the limited preview of the book Mechanics of Flight and read pages 381-394! ☺

6.

Designing the vertical tail fins

Okay, so knowing the vertical tail volume coefficient, we can easily rearrange it and get:

Vvertical = Vv * Sw * b Where: Vvertical – vertical tail volume (Vertical tail area * tail arm). We know that the vertical tail volume coefficient would be in the range of 0.02 0.035, and for now I will choose 0.03 to not make the airplane too stable because, as was decided in Part I, we still want some of that aerobatic ability. Of course, this is an estimate and the value is going to most likely change during CFD tests in Part III. We know the wing area and wingspan values from Part I, so we can readily plug these into the equation to get out vertical tail volume:

Vvertical = 0.03 * 506.88 * 61.68” Vvertical = 937. 93 in3 Now, the tail arm is measured from the aerodynamic centre of the airfoil to the aerodynamic centre of the tail surface- which is, for first estimates, considered to be located at 25% chord. Now, in our canard configuration the vertical tails will be tip-mounted, and let us assume that their root chord is equal to the tip chord of the wing, such that:

Vertical tail Same v. tail root chord as wing tip-chord

Fig.5 Vertical tail configuration Therefore, we can consider the vertical tail aerodynamic center to be the aerodynamic center of the wingtip- 25% of the wingtip chord! Hence we can easily approximate the distance of the tail arm by finding the distance between the aerodynamic centers of the wing root and tip (of course this is quite inaccurate, but good for the first estimate- to get an idea☺):

25%

5.265” 25%

Fig.6 Tail arm estimate Therefore, knowing the rough tail arm, we can easily calculate for the vertical area required to achieve stability:

937. 93 in3 = Sv * 5.265” Sv = 178.14 in2 Therefore, if we’re going to have two tip-mounted vertical tails, we should divide the area by two and hence our single vertical tail area is 89.07 in2. Now we will very quickly and unreasonably decide on basic geometry for our vertical tail. We will do this by eye, with no aerodynamics reasoning behind- the geometry of the vertical tail fin will be defined through CFD tests in Part III. Knowing that our wingspan is 61.68” (156.7 cm), I would like the vertical tail fin on each wingtip to be about 13.78” (35 cm) tall. Of course, here I am just judging by aesthetics and the height of the vertical tail fin is bound to change when in Part III I find out how the configuration plays out aerodynamically-speaking. So, we can easily figure out the tip chord of the vertical tail fin with an equation:

((7.878 + x)/2) * 13.78 = 89.07 in2 (7.878 + x)/2 = 6.46 7.878 + x = 12.93 x = 5.05” Therefore, the tip chord of the vertical tail fin is 5.05 inches (12.83 cm). Once again, this is an extremely rough estimate based on nothing but aesthetics- the final geometry of the vertical tail fin will be defined in Part III. Sorry for repeating this so much, it’s just so that you understand the importance of not incorporating wild guesses like this in your very final design that you will actually go on to build. So, these are our final vertical tail fin aspects:

VERTICAL TAIL FIN Vertical tail volume coefficient (Vh) Aft tail arm (lt) Individual vertical fin area (in2) Vertical fin height (in) Vertical fin root chord (in) Vertical fin tip chord (in) Taper ratio 7.

0.03 5.265” 89.07 13.78 7.878 5.05 0.64

Designing the canard

Knowing the horizontal tail volume coefficient equation, it is easy to rearrange it and get:

Vt = Vh * Sw * c Where: Vt – tail volume (Tail area * tail arm). We also know that our horizontal tail volume coefficient would be in the range of 0.35 and 0.5. Remember, we want a stable airplane. So for now, I chose to aim for a coefficient of 0.5. Now, we know our wing area and we know our wing chord- hence, we can figure out the tail volume that we’ll have to alter calibrate our canard area and tail arm to:

Vt = 0.5 * 506.88 * 8.224 = 2084.29 in3 Hence, we now know that our tail arm lt and canard area St have to multiply up to:

lt * St = 2084.29 in3 Now, considering our wingspan, I’d want my fuselage to be in the region of 1210 mm (47.64 in). So, what I did was draw a simple sketch of the fuselage, and then allocated lengths to it. For example, I wanted my nose to be 200 mm (7.87 in), and since I know the overall fuselage length (47.64 in)- by

placing the wing almost at the back of the fuselage (leave some space for the engine!), I could figure out the tail arm between the aerodynamics centres of the wing and the canard (these are located approximately at 25% of the chord from the leading edge). Here is the diagram:

Fig.7 Lengths estimation diagram.

So, knowing the approximate tail arm, I could figure out the area for the canard:

31.39” * St = 2084.29 in3 St = 66.83 in2 Now, we want a high aspect ratio for our canard. Why? It is a rule that in order for a canard configuration to maintain trim and static stability, the canard always has to have a higher lift coefficient than the wing. Looking at a graph borrowed from WorldofAerospace.googlepages.com (Fig. 8), we can conclude that a higher aspect ratio causes a lifting surface to reach its highest lift coefficient at a smaller angle of attack. Hence, with an AR for our canard than that of our wing, we will technically maintain trim and static stability. Therefore, for now I chose an AR of 8.0 for our canard, and solving a simple equation will give us the dimensions for the span and chord of the Fig.8 effect of AR on lift coefficient canard:

x8x = 66.83 in2 8x2 = 66.83

x2 = 8.35 x = sqrt(8.35) x = 2.89 in Therefore, the chord of our canard will have to be 2.89 inches. Knowing that our AR is 8, 2.89*8=23.12 inches is the canard span/length. Quick check:

2.89 * 23.12 = 66.82 in2 Therefore, these are out canard dimensions. Remember though that these are only preliminary estimates that were based largely on vague estimations. Although, they will serve as a base in future computational aerodynamics tests in XLFR5, which will be described in Part III of this rather long walkthrough☺.

CANARD Horizontal tail volume coefficient (Vh) Tail arm (lt) Canard area (in2) Canard span (in) Canard chord (in) Canard AR

0.5

31.39” 66.82 23.12 2.89 8.0

PS. Our canard, unlike our wing, will not have any sweep in order to reduce the complexity of the airplane frame. Plus, at the Reynolds numbers that an airplane on our size will operate, small amounts of sweep will not have a large effect on the airplane’s flight characteristics- we are not building a racing airplane here, where every extra mile per hour matters… ☺

8.

Afterword

Sizing the control surfaces will be discussed in Part III along with CFD/computational aerodynamics tests in XFLR5 (freeware). I sincerely hope that this document helped you in one way or another. I am urged to remind you that this document should be regarded more as a scholarly paper than an aircraft design bible- although the decision is entirely up to you. I put my mind into this walkthrough, and now it is for you to judge. As a final word to those against how I went about creating this, no plagiarism was ever intended and I tried to my utmost ability to

acknowledge everything in this document that isn’t mine- and all that isn’t, I tried to put into my own words, and yet I still acknowledged the original source, for after writing these walkthroughs, I now realize how much work and soul needs to be dedicated. Thank you to all those who continue to write- be it fiction, non-fiction, engineering books, websites, or humble articles such as this.

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

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. .

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

3. “Supermarine Spitfire” 4."Dihedral (aircraft)." Wikipedia, the free encyclopedia. Web. 01 Jan. 2010. . 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.

PLEASE NOTE THAT I AM NOT THE OWNER OF CONTENT WHICH I STATED IS NOT MINE. THAT CONTENT BELONGS TO THEIR LAWFUL OWNER.