And we’re back to the dry stuff! It’s good to be posting again. I tried to bite off more than I can chew (imagine your average cat trying to consume a bowling ball), and had to break this post down into… a number of parts. Anyhoo, we should now be familiar with the posts covered below:
- Part 1: The basic theory of how wings produce lift
- Part 2: The fact that this lift acts through a point called the centre of pressure
- Part 3 (yes, that one): The centre of pressure moves around a point called the aerodynamic centre. The distance between the two is dependant on the angle at which the wing meets the incoming airflow
Right, let’s get down to business. The business of awesome. Right now, that involves determining our aerofoil (or airfoils, if you live across the pond). The aerofoil is basically the shape of the wing viewed from a side-on perspective, like it’s in 2D. Or if it’s easier, think of a wing as an aerofoil stretched into the third dimension. There are huge numbers of aerofoils, each optimised for certain tasks. Some are designed for wings, tail surfaces, or even helicopter rotors, which are basically really long, thin wings spinning around super fast (don’t touch).
An aerofoil’s shape governs how air flows around it. It’s worth mentioning that the physics that govern the behaviour of gases is shockingly complicated (we still only have a very limited grasp on it), and we simply can’t have an aerofoil that does everything. Depending on whether you’re flying fast or slow, the air could behave as if it were incompressible or compressible. Chubby aerofoils tend to perform fairly well here, but if you go really slowly, you’ll be wanting something thinner. When you’re going fast enough to approach the sound barrier, air starts changing its behaviour again and forms shockwaves. Needle-thin wings are the order of the day here. And it changes again if you go even faster – the Americans flew a number of hypersonic aircraft to see what happens at this speeds, but they were all destroyed by the aerodynamic stresses. Air also behaves differently at different temperatures and heights. It’s… like… wow. Seriously. Beyond us. For now.
Fortunately, we have had well over a century to gather reams of experimental data and form some pretty good theories and observations. People will crack the problem eventually, but until then we know enough about it to make some pretty efficient wings.
I think it’s fair to say we’ve gathered by now that we simply can’t have an aerofoil that does it all. We have to specialise; we must pick an aerofoil that provides good performance under specific conditions. This goes back to the last post: What Do We Want Our Aircraft To Do? We must begin to define our flight envelope. And no, not the envelope you stick letters in. At this stage, it’s mostly just estimating what the air will be like, and how fast our aircraft will be moving through it. Under normal circumstances, we would need to estimate the temperature, viscosity (pretty much a measure of stickyness) and density of the surrounding air through which our aircraft will probably be flying. However, this whole process is MASSIVELY simplified by the fact that we’re flying a simple model aircraft at low height and low speed, which enables us to take some (admittedly cheap) shortcuts. And believe me, this saves a hell of a lot of work.
So we know we’re flying low and (relatively) slow. And with this information in hand, we need to choose our aerofoil. I’ll skip the more complex analytical stuff (but if you’re curious, look up Reynolds numbers) and just compare a group of aerofoils against each other at the appropriate conditions. But first: what are we looking for in our wing’s aerofoil?
- High Lift
- Low drag
- Low pitching moment
- High stall angle and predictable stall behaviour
The pitching moment above harks back to the Basics of Wings: Part 3. An aerofoil with a large pitching moment will feature a centre of pressure that has a greater tendency to wander around, which is generally considered to be distinctly unhelpful quality in a wing.
Stalling
Put simply, stalling is what happens when the wing stops working properly. Put slightly less crudely, the stall occurs when increasing the wing’s angle of attack ceases to provide any more lift. It is generally regarded as being A Bad Thing.
Contrary to what you might think, air has an element of stickiness to it. Remember how the wing accelerates air over its top surface to generate lift (see Basics of Wings: Part 1)? Keeping a layer of air stuck to that top surface is absolutely critical to that process. This can only happen when the wing is flying within a certain range of angles relative to the incoming air. See the graph below:
That red line (known as the lift slope) shows how lift increases with the angle of attack. The wing stalls when the air over its top surface starts to unstick. Just before this point, the wing is producing its absolute maximum amount of lift. This is known as the stall angle, because you’ll start losing lift if you point any higher. See the very end of this line? That’s where the air has become completely unstuck. Physics suddenly becomes astronomically complex, but the effect is much more noticeable to the lay person: you start falling very fast. The decline in lift slope is pretty gentle here, but not many actual aerofoils behave like this. Many will stall with less predictability than an excitable cat – one second we’re generating buckets of lift, the next we’re plummeting. We would rather avoid such things.
Keeping the stall angle as high as possible makes flying a little less dangerous and allows for greater manoeuvrability. Remember, we’ve got at least one engine fixed to our aircraft – the higher you can point that propellor (or jet), the more thrust you have available to pull you up. Imagine holding the engine in your hand – point it straight ahead of you, and it will pull you forward; point it higher and higher, and it will increasingly try to pull you upwards (for the love of your own existence, do not attempt this experiment outside of the theroretical confines of your own imagination). Depending on airspeed and local conditions, some aerofoils can keep flying unstalled past 20 degrees. However, a high stall angle doesn’t necessarily mean high maximum lift, and drag also tends to increase sharply with angle of attack. There’s always a balance to be struck, and in many cases it’s simply experience which allows us to make the best choice.
Lift Coefficients
Notice how the graph measures something called the Coefficient of Lift, rather than lifting force? This coefficient is useful as a scaling tool, as it doesn’t change with the size, shape or speed (mostly) of our wing. Think of a standard equilateral triangle – no matter how big you make it, it will always have angles of 60 degrees in its corners. Same deal with the coefficient of lift. The actual formula for calculating lift from the coefficient of lift might look scary to the uninitiated, but it’s actually super simple:
Lift = (Coefficient of Lift x Wing Area x (Airspeed^2) x Air Density)/2
Search the internet for air density at sea level (which we set earlier) and you’ll find it’s listed as 1.225 kg/m^3. So the formula becomes:
Lift = (Coefficient of Lift x Wing Area x (Airspeed^2) x 1.225)/2
Dividing the 1.225 by 2, we simplify the equation down to:
Lift = 0.6125 x Coefficient of Lift x Wing Area x (Airspeed^2)
Wing Area is simply the surface area of the wing – Lenght x Width, or in this case, Span x Chord. And since WordPress won’t let me type in superscript, I must explain that Airspeed^2 represents Airspeed squared, i.e. Airspeed x Airspeed.
Until Next Time…
This post has already gotten far out of hand, so I’ll leave the actual aerofoil selection process in the next post. I expect to have wing design covered within the next arbitrary time period. I mean two posts. Once we’ve chosen our aerofoil, it’s pretty much a matter of deciding how big we want our wing to be. In the meantime, let me illustrate what happens if you stick a sufficiently powerful engine in the front and point it straight up.
Prop hanging, i.e. hanging an aircraft on the propellor. Those wings are completely stalled, and are all but dead weight. Model Flying (http://www.modelflying.co.uk/sites/3/images/member_albums/30015/kat_reincarnation.jpg)
Basic Model Aircraft Design 
