Flipping heck, so much for a week! It’s been nearly two months. Balancing work-life things is hard.
I’m still fed up with wings, and it’s been so long since the last post I… kinda forgot where we were on that front. So we’ll be covering something else for this post: stability.
Stability has come up a couple of times without proper explanation, yet it is arguably the second most important element of aircraft design – right behind generating sufficient lift for flight. For what good is lift if we cannot control it?
Stability is the ability of an aircraft to return to a point of equilibrium when disturbed. It sounds confusing, but it’s difficult to describe with words.
There are two types of stability: positive and negative. An aircraft is said to have positive stability if it is stable, and negative stability if it is not. An unstable aircraft may be controllable, but you have to fight the aircraft throughout the entire flight. Imagine driving your car down a poorly-surfaced but busy road where everyone is doing 80mph. Now imagine that your car is constantly trying to turn to the left or right, requiring constant adjustment. Now imagine driving like that for eight hours. Not my idea of fun*.
Static Stability
Imagine a simple curved bowl and ball. Place the ball in the bowl and swish it around. As long as you don’t deliberately throw it out, the ball will inevitably return to the centre of its container after a while. Now turn the bowl upside-down and place the ball on top. If you placed it perfectly, the ball will not roll off. Now poke it. Now no matter what corrective action you take, the ball will always try to roll off the bowl and onto the floor, which is lava.
The former is a useful analogy for a stable aircraft – if you try to knock it off-kilter, it will always return to a point of equilibrium. Example: you’re flying a plane straight and level. You throw the control stick to the left, and in response, the left wing drops, the nose falls, and the aircraft begins to descend and turn to the left. Now let go of the stick. Within a few seconds the wings are level, the nose is pointing straight ahead, and you’re fine again. Note that you haven’t returned to your original course and height, but the aircraft has settled comfortably on a new heading.
The latter situation is perfect for explaining unstable aircraft. If you disturb its path even slightly, it’s going to amplify that tiny push and turn it into something monstrous. And in the grubby, non-ideal universe in which we live, it’s impossible to avoid these disturbances. An unstable aircraft will simply fall off its flight path, and will be both dangerous and stressful to fly (and later crash). Throw that stick off to the left, and the plane won’t stop turning. In fact, the turn is probably going to tighten into a spiral dive, which, while exciting, will result in a very fast crash and a very big bang.
Unless you possess excellent flying skills, a supporting flight computer, or extraordinary luck, you’ll want to have a stable aircraft. Such is static stability.
Dynamic Stability
And now we break our bowl analogy. Imagine you have the ball resting in the cup. You swish it around a bit, and the ball returns to the centre. Problem is, it’s still going. It keeps trying to come back to the centre, but… physics, what are you doing? It flies off to the side, reverses direction and returns to the centre again, but moving moving faster this time. Ball? What? No! Stop! Every time the ball tries to return to the midpoint, it is moving a bit faster. Eventually, it becomes so excited it flies out of the cup and falls into the lava. Good job, ball. You bloody pillock.
For the record, unless you’re surreptitiously waving the bowl around, this won’t happen. It breaks physics, and is wrong.
Anyway, that slightly iffy analogy helps demonstrate dynamic stability. The aircraft wants to return to its equilibrium point so badly it over-reacts and ends up flying in the opposite direction. It tries again, and ends up making things even worse. It does this over and over again until either the ground or the increasingly extreme aerodynamic forces destroy it.
Put them together and what have you got?
Just to be clear, you can’t be statically unstable and dynamically stable. The whole point of static instability is that the aircraft just falls off its flight path, whereas a dynamically unstable aircraft tries so hard to get back on track it goes bananas, and thus is by definition statically stable.
See the graphs below – imagine an aircraft flying along the lines.
Case D is what we’re after – if disturbed, the aircraft will gradually return to normal, non-bumpy flight. Cases E and F are distinctly undesirable, as neither of them help to return the aircraft to normal flight – Case F would actually exacerbate the problem. Case E is known as neutral stability, which involves the aircraft neither stabilising itself nor diverging off into instability. The disturbance just keeps going… like a ripple on a pond that won’t die. It’s not helpful to us, and because you’d need literally perfect balancing (or a flight computer) to achieve it, is largely theoretical anyway.
What Do We Want? How Do We Get It? What Were We Saying?
So, positive static and dynamic stability are the name of the game. But how do we achieve this?
Fortunately, static stability is actually pretty easy to achieve – especially for electric models, which can be built in any size or shape as required without having to worry about safely containing people, fuel or cargo. We just need to employ the simple art of balancing. However, this is achieved in different ways according to the aircraft’s axis – see the picture below.
See, an aircraft can turn in three ways:
- Pointing the nose up or down – PITCH
- Pointing a wing up or down – ROLL**
- Pointing the nose to the left or right – YAW
Each of these so-called “modes” of changing direction require different methods to achieve stability – however, they all relate to one thing: the aircraft’s balance point, or centre of gravity. If you wanted to balance the aircraft on just your fingtertips, you would lift it up from this point. The centre of gravity is absolutely vital in determining the stability of an aircraft in pitch, roll and yaw.
Yaw stability is pretty darned easy to achieve. As long as we have a greater surface area behind the centre of gravity than in front, then we’re good to go. This is what the aircraft’s fin (the bit on the tail that points up) is for – it makes sure the nose is always wanting to face into the wind. And here’s the bonus: as far as I’m aware, dynamic stability is simply not an issue here. Hooray for simplicity!
Static stability in pitch is also super simple to achieve – you just make sure that the aircraft’s neutral point is behind the centre of gravity. What is this neutral point, I hear you saying? Well, voice in my head, it’s… reasonably simple. Remember the aerodynamic centre of the wing, explained in this post? The point which lift acts around like a pivot? Take that concept and apply it to the whole aircraft, including the tail surfaces. It’s a simple idea, but it’s bloody complex to calculate. Fortunately, we have software to figure out that part for us.
Remember: Centre of Gravity in front of Neutral Point. That’s the important bit.
As for dynamic stability… that’s also bloody complex to figure out. It’s all sorts of aerodynamic interactions and lifty shenanigans, and we’ll leave it to the software to figure out.
And now for rolling! This is where my knowledge starts to fall short. As far as I’m aware, it’s just static stability that’s the major issue, and it’s fairly easy to achieve with the following methods:
- Keeping the wings well above the centre of gravity. Imagine holding a swinging pendulum by some string – in this case, the centre of gravity is the pendulum, and your fingers are the lifting force holding the string up. It’s more complex than that, but it’s a reasonably helpful analogy.
- Add dihedral (build the wings with the tips higher than the roots) – also ties in with the previous point
- Sweep the wings (NO. WE ARE NOT DOING THAT.)
Combined Modes
This is where things really start going funny. We won’t go over these in detail in this post, but suffice to say rolling and yawing become intertwined in all sorts of interesting ways, resulting in behaviours like spinning, spiralling, Dutch rolling, etc. These behaviours tend to be impossible to design out of an aircraft, but they can be minimised – often to the extent that nobody would notice them unless you actually pointed them out and showed them. Also, you can get computers to damp them out. You can do a lot of things with computers, you know.
The Only Good Aircraft…
Essentials covered. Keep them in mind, and we should have a stable flying machine. And that’s a massive step forward. Like, seriously. Stability is hard.
There’s some more finnicky stuff to stability, but we don’t need to go over it just yet (and it’s possible we can bypass it entirely). To be honest, I could totally have pushed this section back a ways, but I get bored of writing on the same subject for too long. It’s nice to break this stuff up, and stability takes a lot of processing before it sinks in properly.
Anyway, next time (probably) we return to the glorious thing that is wing design. From wing, to tail; from tail, to structure; from structure, to power and control; from there… flight.
Author away!
* Double points: bears in the car. Good luck.
** I really don’t know how to describe that without saying “roll”. It’s like a really stupid game of Taboo.
Basic Model Aircraft Design 
