Wing Design 3: Do You Even Lift?

I’ve been waiting to use that title for some time now. Packing references into these blog posts makes them so much less dull to write, you know. Anyway…

Penultimate post on wing design! Turns out the wing couldn’t lift quite as much as I had hoped for, and it needs a redesign. Let’s find out why. Onwards!

Why Lift at All?

Oh yeah, I forgot to explain why lift was really important in the first place. It’s the force that keeps aircraft from falling down. There are four forces acting on an aircraft:

Forces on an Aircraft. NASA (http://www.grc.nasa.gov/WWW/k-12/airplane/Images/forces.jpg)

• Thrust is the force pushing the aircraft forwards, and is produced by the engines. Usually, thrust is generated by spinning things at hair-raising speeds.
• If thrust is Holmes, then drag is Moriarty. As the aircraft moves forwards, it collides with air molecules, which exert frictional forces which try to pull it to a stop. Go away. Moriarty. You’re ruining everyone’s fun again.
• Weight doesn’t really need an explanation. It is the anchor that tethers us to this rock; our Magikarp, if you will.
• Lift fights against weight to keep us up. The Garydos to our Magikarp.

In short, to keep flying, our plucky aircraft will have to produce enough lift to counter or exceed its weight. If its weight is even slightly greater than its lift, the aircraft will accelerate downwards, which (unless you intend to land) is generally considered a bad thing.

Given its size, our aircraft will probably have a mass of around 0.8kg, give or take a few hundred grams. Weight is a force, so Force = Mass x Acceleration becomes Weight = Mass x Gravitational Acceleration. Gravitational Acceleration at sea level is 9.807m/s^2, so:

Weight = 9.807 x Mass = 7.846 Newtons

Therefore our aircraft should be producing around 7.8 Newtons of lift.

Bear in mind, the figure is just an estimate, based on previous experience and guesswork. We’ll only start to get an accurate idea of the aircraft’s weight once we start working on its structure. But hey, it’s a start.

Wing Lift Curve

We left off with the necessary formula for calculating our wing lift curve. This is very important, as it will allow us to track just how much lift our wing is producing, which is itself very important for balancing our aircraft, designing the tail, and predicting how fast our stall speed (i.e. minimum flying speed) is going to be.

Wing Lift Curve = 0.7485 x Foil Lift Curve

Clark-Y Lift Curve. Modified from Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=clarky-il#polars)

Where that red line is the foil lift curve. The foil lift curve can be represented mathematically as:

Foil Lift Curve = Change in Aerofoil’s Lift Coefficient ÷ Change in Angle of Attack.

By comparison, the wing lift curve will look something like this when plotted on the same graph:

Clark-Y Lift Curve, complete with approximations of Foil Lift Curve and Wing Lift Curve. Note the intersecting points at the Zero-Lift Angle of Attack. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=clarky-il#polars)

I’m going to do the heavy lifting here and determine just what the foil lift curve is for you. To be more precise, I’ll be using aerodynamic data generated by the previously-introduced XFLR5, and running some of it through Excel. Here’s why:

It’s okay to cry.

It’s going to involve some fiddling in the previously-introduced XFLR5, some data transfer to Excel, and simple maths – I can’t really explain without a video or a long, boring wall of text. Wish me luck.

Ok, it looks like the lift curve is pretty much straight from 0 to 7 degrees angle of attack. The coefficient of lift at Alpha=0 is 0.3605, and at Alpha=7 is 1.109.

Applying maths to the problem, we have:

Foil Lift Curve = Change in Aerofoil’s Lift Coefficient ÷ Change in Angle of Attack.

So:

Foil Lift Curve = (Final Lift Coefficient – Initial Lift Coefficient) ÷ (Final Angle of Attack – Initial Angle of Attack)

Foil Lift Curve = (1.109 – 0.3605) ÷ (7-0)

Foil Lift Curve = 0.7485 ÷ 7

Foil Lift Curve = 0.1069

And judging from the graph I can’t be bothered to include, it looks like the Zero-Lift Angle of Attack is -2.257.

We’re on! So the Wing Lift Curve must be:

Wing Lift Curve = 0.75 x Foil Lift Curve

Wing Lift Curve = 0.75 x 0.1069

Wing Lift Curve = 0.08018

Woo! This means we can finally calculate the amount of lift our wing is producing!

Wing Lift Coefficient = (Wing Lift Curve x Angle of Attack) + Y Intersect

Wing Lift Coefficient = (0.08018 x Angle of Attack) + Y Intersect

Ah… forgot that step. We need to find the lift coefficient when the angle of attack is 0 (the so-called Y Intersect). Fortunately, we already know the zero-lift angle of attack, so if we use this as a baseline, we can solve the formula. We set the parameters:

• Angle of Attack = -2.257
• Coefficient of Lift = 0

And we plug these numbers back into the formula:

Wing Lift Coefficient = (0.08018 x Angle of Attack) + Y Intersect

0 = (0.08018 x -2.257) + Y Intersect

0 = -0.1810 + Y Intersect

Y Intersect = 0.1810

Which finally combines to make:

Wing Lift Coefficient = (0.08018 x Angle of Attack) + 0.1810

Dihedral

Since dihedral only has positive effects for stability, there’s no way of knowing how much we’ll need to use before moving into the later stages of design. Based on previous experience, I reckon we would be prudent to design the wing with 3 degrees of dihedral already built in. If we don’t need it, we can remove the dihedral and gain a little extra lift. If we need more, then we won’t lose a lot of lift in the process.

If 0 degrees of dihedral leaves us with 100% lift, and 90 degrees dihedral leaves us with 0 lift, then a single degree of dihedral reduces lift by 1.111%.

Therefore, the 3 degrees of dihedral we want for stability reduces total lift available by 3.333%.

Wing Tips

We’ll be working some rounded tips into our wing. They shouldn’t add more than 5% to the span, and will give us a small increase in lift – both from the increased wing area and the reduction in wasted lift. They might be a little challenging to design in XFLR5, but they’re not too hard to build in practice. Also, it looks better – models like ours tend to benefit from looking old-school.

Heavy Lifting

We can now calculate our wing lift coefficient for a given angle of attack. Note: this formula only applies if the wing is behaving normally – a wing approaching the stall will perform very differently! Fortunately, we only really need the formula to calculate what’s going on in cruise conditions.

So how much lift is our wing actually producing in the cruise? We’ve already worked out the lift formula, so let’s dredge it back up:

Lift = 0.6125 x Coefficient of Lift x Wing Area x (Airspeed^2)

Since we’ve already set the dimensions of our wing, we can calculate the wing area.

Wing Area = Wing Span x Wing Chord

Wing Area = 1.25m x 0.21m = 0.2625 metres squared

Plugging this back into the lift formula:

Lift = 0.6125 x Coefficient of Lift x 0.2625 x (Airspeed^2)

Lift = 0.1608 x Coefficient of Lift x (Airspeed^2)

This is the simplest form of the formula, but it’s not all that useful unless we can relate the lift to the angle of attack our aircraft will be flying at. Plugging in the formula for coefficient of lift vs angle of attack:

Wing Lift Coefficient = (0.08018 x Angle of Attack) + 0.1810

Lift = 0.1608 x [(0.08018 x Angle of Attack) + 0.1810] x (Airspeed^2)

A few lines of maths, and now the formula is looking much less wordy and more numbery. Let’s plug in the cruise condition figures and see what comes out. Since we’re only figuring this out for the wing, we don’t have to take an angle of incidence into account (if you have no idea what’s going on: see the last post or alternatively think about your place in the universe).

• Angle of Attack = 0 degrees
• Airspeed = 6m/s

Lift = 0.1608 x [(0.08018 x 0)+0.1846] x (6^2)

Lift = 0.1608 x 0.1846 x 36

And taking the 3.333% loss in in lift:

Lift = 0.1608 x 0.1846 x 36 x 0.9666

Lift = 1.033 Newtons

Divide by gravitational acceleration at Earth’s surface (9.81 metres per second squared) and we have a wing that can lift 108.9 grams. This wing could potentially lift a pear.

Tower, this is Ghost Rider requesting a flyby…

Physics, if you were a person, I would rub tabasco into your eyeballs and call you a horrible creature who should be ashamed for even being alive. But I think that act would make me a horrible creature, and hypocrisy is something that really rustles my jimmies. Besides, we love physics really. It’s just so very clever.

At first I thought I got the maths wrong, but no. It’s just the way the formulae worked out, and numbers don’t lie (I have been informed that hips also do not lie, but have yet to confirm this). But this is a key step in the learning process – making the really, really annoying mistakes that make you really stroppy, then kind of bummed out, before realising it’s not so bad and fixing it with a few adjustments. As William Blake once said: “there is no mistake so great as the mistake of not going on.” And go on we must. I have too much invested in this alcove of the internet; turning back now would be an outrageous act of moral turpitude. And you, dear reader; you, who have invested your precious time in this dusty abode in pursuit of the understanding of aerial vehicles – your attention must not be allowed to go to waste. We shall walk this perilous road of learning, through the treacherous wastelands of ignorance, to stand together in the glorious light of knowledge. We shall!

But not quite yet, because this one has already gone on for far too long. And spoiler alert: I’ve already figured out how to squeeze out that extra lift. Also, the wing kills Dumbledore on page 314.

Well this has been amusing. I suppose I will get on with the next post; hopefully we’ll have this wing thing sorted before the end of the week. In the meantime, consider this: what exactly was the purpose of Magikarp?

Wing Design Part 2: Chiselled Features

Today we’ll be going over the second half of our wing design – sculpting that plank into an efficient and beautiful surface of great majesty and grace… sort of. And what’s more, unlike the last two posts, this will actually be important! So unglaze those eyes and look sharp.

Last time we established that our wing will be 1.25m in span and 0.21m in chord, and use a Clark-Y aerofoil. We have a wing-shaped plank.

Our wing! Hooray!

We’re going to make it so much more; more efficient, more stable, and… slightly more difficult to build. Worth it. This post will cover the aspects of wing shape that need to be taken into account when designing the optimal flying surface. Size isn’t everything, you know…

Sweep

NO. We’re not doing that! Stanford University (http://adg.stanford.edu/aa200b/potential3d/images/x29.jpg)

There will be no sweeping of wings in this blog, whether this way, that way, forwards or backwards, and certainly not over the Irish sea. Sure, it looks cool, but we’re not building models for hipsters here. There would simply be no point, as our aircraft will not be flying even remotely fast enough to benefit from it.  Sweep also makes the wing harder to design and build. No sweep!

Dihedral

Imagine a bird flapping its wings – preferably something tasty, such as chicken or pheasant. Now that you’re hungry, allow me to explain the concept of dihedral.

Dihedral explained. It really is that simple. AvStop (http://avstop.com/ac/flighttrainghandbook/stability.html)

See the picture above. It’s like a bird’s wings just before starting the downstroke. There isn’t really any other efficient way of explaining with words. We point the wings up a bit, and we have dihedral. It is one of the easiest ways to make an aircraft stable.

Junior 60. Buckets of dihedral makes this model super stable. King’s Lynn Aero Model Club (http://www.klamc.co.uk/Pages/ClubNews.aspx)

But wait! Surely pointing the wings straight up would lose us lift, right? Absolutely right, voice in my head. You clever thing. Have a bird.

Extremes of Dihedral. On the left we fly with the wings flat (0 degrees dihedral), and on the right we fly with the wing pointing straight up (90 degrees dihedral). You wouldn’t be pointing your wings straight up unless you were showing off or trying to outmanoeuvre something.

Pointing the wing straight up gives us 0% useful lift, and pointing it flat horizontally gives us 100% – we have all the lift. Using dihedral will lose us some lift, so we typically only dial in a few degrees to improve stability – more than 5 degrees is unusual in full-scale aircraft.

Of course we’re building a model and can go wild, but every degree of dihedral means either a bigger wing or a higher stall speed, neither of which are particularly desirable – a bigger wing will make handling in windy conditions trickier, and a higher stall speed makes landing and launching less safe.

Unfortunately dihedral does make the wing less easy to design and build, as well as making it slightly weaker. You’ll find out why when we try to design the thing.

Angle of Incidence (AKA “Cheating A Bit”)

Thought experiment: we want to produce a fixed amount of lift at a fixed speed. To reduce drag and increase maximum speed, we want the wing to be as small as possible. We’ve already fixed our aerofoil, so what can we do to eke more lift out of our wing?

Well, you know how wings produce more lift when you point them higher? What if we were to mount the wing to the aircraft… with the wing already pointing slightly upwards? We now have a wing that can produce the same amount of lift at the same speed, but is smaller – and as a result, it’s less draggy, stronger, and less expensive to build.

Boom. Mind blown. Absolute genius. This angle between the aircraft’s body and its wing is called the Angle of Incidence.

Only problem is that we’re stretching the wing’s performance. Let’s imagine our wing stalls at 12 degrees. We bolt our wing to the aircraft with a 3 degree angle of incidence. The aircraft is now happier on the straight-and-level, but now it stalls at 9 degrees (for the maths: 12-3 = 9).

Using an angle of incidence is very handy tool for increasing the fuel-efficiency of aircraft – if you’re trying to get somewhere fast and with the minimum of fuel, using a smaller wing with a slight angle of incidence will get you there faster and save you a fair bit of money in the long run. You don’t want to push it too far though – drag increases sharply with angle of attack, so you could well end up with an aircraft that stalls more easily and yet is less efficient than one with a wing mounted with 0 degrees angle of incidence. And that’s just embarrassing. Just imagine what your friends would think – everyone would point and laugh, and you’d look like a buffoon. Hmm… Good word, “buffoon”…

An angle of incidence of 3 degrees is very common for aircraft of this type.

However, it also creates an extra level of detail that we could really do without for a starter aircraft. Our aircraft could be at 0 degrees, but our wing would be at 3, and our tailplane… I forget what a typical angle of incidence for a tailplane might be. I am kind of torn…

Given that we’ve already fixed our wing size, we’ve got a simple trade-off:

• Mount wing with a positive angle of incidence and get reduced stall speed, but reduced maximum angle of attack (aircraft is also slightly harder to design and build)
• Mount wing with 0 angle of incidence and get higher stall speed, but increased maximum angle of attack (aircraft is easier to design and build)

In theory, the first option might make for slower, easier landings, but could make for trickier slow-speed manoeuvring – particularly when trying to turn. The second option would make the aircraft easier to control when flying at speed, but would make for faster landings. It would, however, make low-speed handling slightly safer.

I suppose we’ll cross that bridge when we come to it. As it is, we only need to set it once we start pinning the tail design down.

Tip Losses and Wing Tips

This is going to be a bore, but it’s very important. Remember how we established that a wing creates lift by lowering the pressure on its upper surface, causing the pressure on the lower surface to push it up?

Unfortunately, that pressure differential can be… lossy. See, fluids don’t really like differentials. They want to be uniform; the higher-pressure air on the bottom wants to fill the space left by the low-pressure air on top. There are two ways it can do this:

• The good way: rejoining the low-pressure air behind the wing as it passes on (see image below):

  

  Airflow Past a Wing. Wikipedia (https://i1.wp.com/upload.wikimedia.org/wikipedia/commons/9/99/Karman_trefftz.gif)

• The bad way: rejoining the air on the upper surface by sneaking around the wing tips (see image below):

  

  Tip Losses. So very frustrating. Q’s Corner (http://www.dwave.net/~bkling/rc/howto/wingtips.htm)

  Yep. Our hard-won pressure differential is literally slipping away from us. Our precious lift is being stolen from us. And what do we get in return for our lost lift? Drag, that’s what. Also, horrible vortices trailing behind the wing tips (this is the reason airliners have to keep their distances between each other during landing – the trailing vortices would toss them around like ragdolls otherwise). Thanks a bunch, physics.

Tip losses, as they are called, are the reason why most airliners have some form of winglets on their wing tips – these quite literally block the air from the lower surface from the joining air on top. Some air still gets across, but the effects of tip losses are reduced.

Effects of Different Wing Tips. Q’s Corner (http://www.dwave.net/~bkling/rc/howto/tipfig2.gif)

Simply shaping our wing tips can have a similar (if diminished) effect without requiring us to build fragile winglets. We’ll probably go with some simple rounded tips, as these are simple and look pretty.

Note: I didn’t mention this when explaining wing theory because we had been looking at wings from a 2D perspective. Air falling off the sides complicates things – that extra dimension really can give the universe some very bad habits.

Aspect Ratio

If you read the section above, you’ll have seen from the pictures that a wing of greater span is a wing of lesser losses. As it happens, a wing of smaller chord is also less prone to tip losses. A crude explanation might be that since there is a shorter distance between the front of the wing and the back (aka leading and trailing edges), the air has less time under the wing to slip off to the sides.

Tip losses are thus directly linked to aspect ratio – a higher aspect ratio means a less lossy, more lifty wing.

To recap: aspect ratio is the ratio of wing span to wing chord. Looky below.

Aspect Ratios. Science Learning (http://sciencelearn.org.nz/var/sciencelearn/storage/images/media/images/flt_sci_art_04_wing_aspect_ratio_lowtohighratios-nc2/529619-1-eng-NZ/FLT_SCI_ART_04_Wing_aspect_ratio_LowToHighRatios-NC.jpg)

Unfortunately, we can’t build a wing of infinite aspect ratio – it would need to be of infinite span and infinitesimally (i.e. really, really small) thin. It would be impossible to build, impossibly fragile, and would experience collisions from anything from trees to celestial bodies. And just imagine trying to turn… no, don’t do that. It’s just too awful.

A high aspect ratio wing is also prone to flutter – have you ever watched the wings flex in an airliner? Too much of that flexing will rip the wings apart. Even if they stay in one piece, the constantly-shifting shape of the wing sends your lift vectors all over the place, and the aircraft becomes difficult to control. Building wings from exceptionally stiff materials such as carbon fibre is essential for flutter-resistant, high-aspect ratio wings.

Flutter. Mesmerising on structural simulations, but OH GOD MAKE IT STOP in real life. Flow Solutions (http://www.flowsol.co.uk/products/newpan/dynamics.php)

A high aspect ratio wing is more fragile, prone to flutter, and more difficult to design and build.

However, low-aspect ratio wings have some advantages – their short, stubby flying surfaces provide high manoeuvrability, take up less hangar (or car) space, and are WAY stronger than their more efficient brethren.

Either way, we opted for an aspect ratio of six, simply because it’s typical for models of this type. It strikes a balance between reasonable efficiency and reasonable strength and manoeuvrability.

So why did I write this section, dear reader, if we have already set the aspect ratio? Because we need to figure out just how lossy our wing actually is. Our tail design and stall speed depend on knowing how much lift we’ve lost.

So how can we count our losses and figure out just how much lift our wing is actually producing? With maths, of course!

I’ll try to keep this as simple as I possibly can. If you read the last post (and I won’t blame you if you haven’t), you may recognise our friend, the Clark-Y lift plot. If you haven’t, then this graph shows how our aerofoil’s lift changes with its angle of attack. Increase the angle of attack (point the nose up), and you get increased lift up to around 12.5 degrees; decrease the angle of attack (point the nose down) and you get a decrease in lift (though apparently not below -7 degrees, which is weird).

Clark-Y Lift Coefficient vs Angle of Attack at Re=100000. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=clarky-il#polars)

See how the lift tends to rise evenly with increased angle of attack between -5 to +7.5 degrees? We can be a little rough and approximate that to a straight line.

Clark-Y Lift Curve. Modified from Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=clarky-il#polars)

Okay, very rough. I’m sorry, but I really don’t want to get into Excel in this post and I no longer have a MATLAB licence. Plus I’m using MS Paint here.

Anyhoo, let’s call our pretty red line the Foil Lift Curve for now (it’s not really called that, but it’s easier to remember). We’ll get something more accurate for the next post, in which we’ll actually be designing the blessed wing.

Aspect ratios lower the gradient of the foil lift curve, resulting in smaller lift gains for increased angles of attack. They do have the handy bonus of increasing the stall angle, though. Anyway, to illustrate:

An illustration of how aspect ratios affect the lift curve. The higher the aspect ratio, the steeper the lift curve of the 3D wing. NASA (http://history.nasa.gov/SP-367/fig56.jpg)

The infinite aspect ratio wing is the ideal. See how you get more lift for your increased angle of attack? We want that. Let’s call the 3D wing’s lift slope the Wing Lift Curve. Note how both lift curves intersect at the zero-lift angle of attack. At this angle, both the aerofoil and the wing generate 0 lift. If you scroll up, you’ll see the Clark-Y’s zero-lift angle is roughly -2.5 degrees.

Anyhoo, the formula for determining the Wing Lift Curve:

Wing Lift Curve = (Aspect Ratio x Foil Lift Curve) ÷ (Aspect Ratio + 2)

Our aspect ratio was 6, but since we rounded up the wing chord to 0.21m, it’s actually 5.952. Plugging this figure into the formula, we can simplify down to:

Wing Lift Curve =  (5.952 x Foil Lift Curve) ÷ (5.952+2) = (5.952 x Foil Lift Curve) ÷ 7.952

And finally:

Wing Lift Curve = 0.7485 x Foil Lift Curve

So when we figure out the Foil Lift Curve in the next post, finding the Wing Lift Curve will be a cinch. And from there, we will have no problem calculating just how much lift our will will be producing. Whoop whoop.

Parting Words

Right, I think that about covers it. We’ll design the flappy bits (ailerons, flaps and spoilers) much later on in the design process – in truth, we could probably get away with not having them at all. But hey, we will cross that bridge when we come to it.

Next time: actually completing the wing design (minus flappy bits)!

K, I’m done. Bye.

Wing Design 1: Throwing Shapes

Triumph! We are now sufficiently clued-up to start designing our wing. Feeling pumped? Yes you are.

No, I will not source this.

Unless you’re not, in which case one of us is doing something seriously wrong. Personally, I’m so pumped I’ve started sprinkling doge references into the headings. Don’t ask why. Either way: pretty pictures!

Note: if you’re not feeling the technical vibes, you can probably skip this post. You’ll miss out on an important design step, but many aeromodellers just go with a Clark-Y aerofoil and move on. Your call.

Remember the Reynolds number post, where I mentioned how our aerofoil selection would depend on Reynolds numbers? I’ve just had to dump five days’ worth of draft post because I couldn’t explain it succinctly without an extra line or two of maths. Let’s just breeze through it now and be on our merry way.

Reynolds Number = Density of Air x Airspeed x Chord Length ÷ Kinematic Viscosity of Air = 1.225 x Airspeed x Chord Length ÷ 0.00001456 = (Airspeed x Chord Length) x (1.225 ÷ 0.00001456) ≈  Airspeed x Chord Length x 84130

Success! To find the Reynolds number of the air flowing over the wing, we need to (roughly) determine:

• Our wing chord length (front-to-back length of wing)
• Our airspeed

Take a deep breath, people! This is where we step from the socks-with-sandals of theory to the MIGHTY WELLINGTON BOOTS OF DESIGN! YEAAAAH!

Such Airspeed

Low-flying Tornado. No, our wing will not look like this. At all. Daily Wales (http://dailywales.net/2014/08/01/sonic-booms-and-the-welsh-military-playground/)

For our purposes, the cruise speed is going to be the airspeed at which our aircraft will normally be flying. It shouldn’t need to be pointing its nose in the air to maintain flight at this speed, but will be perfectly happy pootling around on the straight-and-level. Bear in mind that “airspeed” is the aircraft through the air – if we have a strong headwind, the aircraft could be stationary  from the ground but have 10m/s airspeed. This is VERY important for any operations involving the ground, most notably landing and taking off. If we pick an aerofoil based on high-speed flight, it might perform terribly at slow flight, and would be a nightmare to get on and off the ground. We want our aircraft to be slow enough to enable easy and safe take-offs and landings, and to allow us to keep track of it from the ground. Being slow also gives us more room for manoeuvre, allowing us to fly in smaller spaces. Please note that it is imperative that you give yourself enough space to fly safely, and stay away from people, cars, and… pretty much anything that could object to being hit by small, speeding airborne objects. However, if we cruise too slowly, our aircraft will be swatted off course by the merest sparrow’s fart of wind. Believe me, trying to control an aircraft under excessively windy conditions is not fun at all. It’s a balance thing.

Your average human walks at about 1.4 metres per second (m/s). Usain Bolt managed a top speed of 12.4m/s, which is incredible. Experience has taught me that 5-7m/s is a pretty good target for reasonably easy flight. Let’s compromise at 6m/s (13.4mph). At this speed, our aircraft will cover a football stadium in 15 seconds. Sounds reasonable… at least on paper. You have to get a feel for this thing from experience.

To summarise: we’ve set a cruise speed of 6m/s.

Much Wing Chord

Since we’re at the earliest stage of design, we’re going to be doing this quite roughly. We’re creating a simple, easy-to-fly model, which generally puts us in the small-to-medium category – we’re talking 0.7-1.6m wingspans. Model size is often determined by the desired wingspan, as it generally determines how big the rest of your aircraft needs to be. If we go too small, the wind will destroy our hard work. If we go too large, we’ll get an overly complex, expensive, awkward aircraft which won’t even fit in a car. Again based on experience, let’s go with a 1.25m wingspan.

Now that we’ve chosen our span, we can figure out what our chord will be. For a model of this type, let’s go with an aspect ratio of 6 – this means the wingspan will be 6 times as great as the wing chord. Divide the wingspan by the aspect ratio, and we get: 1.25 ÷ 6 = 0.208m – let’s round that up and go with a wing chord of 0.21m.

To summarise: our aircraft’s wing will have a span of 1.25m and a chord of 0.21m.

Must Pick Aerofoil, Wow

With a wing chord and a cruise speed set, we can calculate our target Reynolds number (see last post here). Let’s skim through it and be done.

Reynolds Number = Airspeed x Chord Length x 84130 = 6 x 0.21 x 84130 = 106000

Yay! Our Reynolds number is higher than I expected, which is great! Aerofoil performance tends to degrade erratically and dramatically below this point. The aerofoil selection site I use can rank aerofoils based on their maximum lift/drag ratios at Re=100000, so we’re pretty well set. We can’t measure the suitability of an aerofoil based exclusively on lift/drag ratio, so we’ll dip into lift vs alpha graphs. The process for picking aerofoils for full-scale aircraft is much more involved and complex, but frankly I can’t be bothered to go into that level of detail.

Before we begin, just a refresher: the angle of attack (aka ‘alpha’) is the angle at which the aerofoil hits the incoming airflow. See image below.

Angle of Attack. Wikipedia (https://upload.wikimedia.org/wikipedia/commons/0/02/Airfoil_angle_of_attack.jpg)

Picking the best aerofoil requires a baseline to compare against. The Clark-Y aerofoil is the go-to section for most modellers, so let’s go with that.

Clark-Y Aerofoil. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=clarky-il#polars)

It might not look particularly interesting, but this aerofoil has been the mainstay of many models and full-scale aircraft alike. Its flat bottom makes it easy to build with, and it’s thick enough to use on small models without being paper-thin.

Clark-Y Lift Coefficient vs Angle of Attack at Re=100000. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=clarky-il#polars)

Dat lift curve, amirite? So let’s see what makes this one so handy and dandy:

• Long, drawn-out stall – once the aerofoil starts to stall at about 13 degrees, the lift curve drops off… slowly. Hell, the thing is still flying at ~18 degrees. That’s fantastic for our purposes – our aircraft will give us plenty of warning when we approach the stall.
• Reasonable stall angle (~13 degrees) – see where the curve reaches its peak? Most aerofoils stall around 12 degrees, so this is fairly average.
• Good maximum lift coefficient of ~1.38

Now that we have a baseline, let’s go with the chart-topping aerofoil: the Eppler 376.

Eppler 376. Airfoil Tools
(http://airfoiltools.com/airfoil/details?airfoil=e376-il#polars)

Skinny as a beanpole, isn’t it? The most efficient aerofoils for models operating under our conditions tend to be like this. Anyhoo, the lift curve:

Eppler 376 Lift Coefficient vs Angle of Attack at Re=100000. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=e376-il#polars)

• Very, very high maximum lift coefficient at ~1.65. Grand!
• Stall angle of 10 degrees. Less grand. The 376 stops flying at ~16 degrees.
• Shorter, bumpier, less predictable stall. Hmm.

So we have an aerofoil which is pretty darned lifty. Problem is, it really won’t give us much warning of a stall. Bigger problem is: how the bloody hell are we supposed to actually build the thing? You’d need a microscope to shape the trailing edge (back end). And when it hits the ground (and it will, believe me) it will simply cease to exist. Poof. Gone. There’s no way we can use this. NEXT!

… yeah, most of them have paper-thin trailing edges. We can’t use them.

Found one! The Sokolov aerofoil:

Sokolov Aerofoil. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=sokolov-il)

Better. Not perfect, but better. Let’s take a peek at the lift curve graph.

Sokolov Lift Coefficient vs Angle of Attack. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=sokolov-il)

• Pretty good maximum lift coefficient of ~1.58
• Stall angle of ~11.7. Not so good, but we could work with it. Ceasing to fly at ~12.4 degrees… that’s pretty bad.
• Unpredictable stall behaviour. There really isn’t much room between the aerofoil hitting its maximum lift coefficient and ceasing to fly.

So we have an aerofoil we could potentially build… but flying it won’t be much fun. If we were building an efficient aerofoil for thermal soaring, then we could totally go for it… but we’re not, so we won’t. Harrumph. NEXT!

SG6043 Aerofoil. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=sg6043-il#polars)

Huh. Apparently this one is designed for wind turbines. Interesting…

SG6043 Lift Coefficient vs Angle of Attack at Re=100000. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=sg6043-il#polars)

• Maximum lift coefficient of ~1.6.
• Stall angle of ~13 degrees. Aerofoil stops flying at ~17 degrees. Not bad at all…
• Reasonably drawn-out stall behaviour. Could be better (especially on the drop-off), but it peaks fairly slowly.

It took me a minute, but snooping around at the rest of the associated graphs showed the downside – the pitching moment coefficient is unusually high, and we would need a bigger tail to compensate – partially negating the extra lift this aerofoil provides. I haven’t included the graph because then we’d have to compare pitching moments between aerofoils, and I still can’t be bothered. We’ll keep it in mind either way.

Before we continue, let’s go over what the last batch of candidates have taught us:

• We can’t work with aerofoils that are too thin to build, no matter how lifty they are.
• The only good stall is a long stall.
• Be wary of high pitching moments (this one is more for me than you).

Thus we move onto the Eppler 67.

Eppler 67 Aerofoil. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=e67-il)

Looks better, right? Thick enough not to fall apart if you look at it funny.

Eppler 67 Lift Coefficient vs Angle of Attack at Re=100000. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=e67-il)

• Maximum lift coefficient of 1.38. Huh.
• Stall angle of ~13 degrees. Aerofoil stops flying at ~17 degrees.
• Reasonable warning of stalls past ~7.5 degrees. If we push it, this aerofoil will let us know.

This is an interesting one. The maximum lift coefficient is roughly even with the Clark-Y section, but the behaviour is very different. It wants to flatten out at about 7.5 degrees, giving us ample warning of an approaching stall at 13 degrees. This would give us some breathing room to lower the nose and return to level flight. On the other hand, we might need that lift during slow flight. If we know we can squeeze that little bit of extra lift out at 13 degrees, we might risk pushing our luck – and past that point, the lift drops off pretty quickly.

At any rate, the number of aerofoils we’re comparing is just becoming silly. There are hundreds (possbibly thousands) out there, so I found a list of ones commonly used for model aircraft. Among them was the Eppler 214:

Eppler 214 Aerofoil. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=e214-il)

Thinner on the trailing edge than its sibling, but let’s run with it for now and see how it goes. Graphs!

Eppler 214 Lift Coefficient vs Angle of Attack at Re=100000. Airfoil Tools (http://airfoiltools.com/airfoil/details?airfoil=e214-il)

• Maximum lift coefficient of ~1.41
• Stall angle of ~13 degrees. Stops flying at ~16 degrees.
• Curiously predictable stall behaviour – the lift curve flattens out at a respectable lift coefficient when the angle of attack hits 8 degrees. The aerofoil is giving us about 9 degrees of breathing room to pick up on the stall and point the nose back down.

We could work with this. The trailing edge will be fragile, but the wing is thick enough to have some semblance of strength. The only thing we have to note is that the E214 aerofoil is noted as a “low-Reynolds aerofoil”. These can suffer from the peculiar problem of aerodynamic hysteresis – once stalled, there will be a more pronounced delay between getting the angle of attack within a reasonable angle of attack and the aerofoil beginning to fly again. I believe it’s more of a problem in smaller aircraft at slower speeds, but it’s worth bearing in mind.

We must curtail our exploration of further aerofoils here, because this post is taking forever to write. I suspect it doesn’t make the most exciting reading, either. Let us study what is already before us.

Our list of aerofoils thus far:

• Clark-Y (average lift, excellent stall characteristics, easy to build, strongest)
• Eppler 376 (very high lift but too skinny to build)
• Sokolov (thicker than the 376, high-lift but naff stall characteristics)
• SG6043 (not too hard to build, handy for high lift, but iffy for very high moments)
• Eppler 64 (average but strangely-distributed lift, good long stall, not too hard to build, not too fragile)
• Eppler 214 (slightly better lift, thinner trailing edge, but good indication of stall)

I reckon we’ve got three options here: The Clark-Y, the SG6043, and the Eppler 214. The Clark-Y is probably going to be the easiest to build and fly with, the SG6043 enables us to fly with a smaller wing but requires a bigger tail to compensate, and the Eppler 214 trades high maximum angle of attack for the possibility of a slightly better warning on the stall and marginally higher lift. I didn’t mention this before, but the 214 also has a higher pitching moment than the Clark-Y, so will require a slightly bigger tail to compensate.

You know what? I think we were fine with the Clark-Y all along. It keeps on flying at high angles of attack, has relatively low pitching moments, and is the easiest of the six to build. Now to write it in bold, so all of us can occupy the same page:

We’ll be using the Clark-Y aerofoil for our wing.

SO MUCH BLOG

I spent three weeks of sporadic work writing this post, so to resort to the most popular and immediately obvious solution is ever so slightly embarrassing. In truth, I have partially failed in my attempts to keep this non-engineer friendly, as I could have simply said “we’ll use a Clark-Y because that’s what most models use anyway”, and avoided both this post and the Reynolds number one. Accidentally expanding the scope of my projects is one of my greater personal weaknesses. Oh well, we live and we learn. Again and again. Sigh.

Still, that’s the first step of the design process done. We’ve actually done reasonably well – we have the aerofoil, target cruise speed and basic dimensions of our wing pinned down. We might need to tweak them a little later, but we’re good for now.

To summarise:

• Our aircraft will cruise at 6m/s
• The wing will have a span of 1.25m, and a chord of 0.21m.
• The wing will use the Clark-Y aerofoil.

Let’s take a lot at our work thus far.

Our wing! Hooray!

Boom. We put good work in, and get good results out. This is what many aeromodellers refer to as a “plank”. Next time we’ll refine it to allow for easier, more stable (and possibly efficient) flight. Until then!