After a tumultuous few months, I found my mind pondering the bizarrely wonderful… noun… that is Nyan Cat. This triggered a trip down internet memory lane, which among other amusing or dreadful things, reminded to to update the bloody blog. Deep breath; focus… here goes.
So hey, does anyone else remember the whole arrow in the knee thing?
False start. I’m so sorry.
Aerofoils! Flying! No aerofoils, no flying. Unless we count rockets, which while fun, would be cheating.
Last time, we basically explored the idea that there is no perfect aerofoil; we’re just going to have to pick the one that does our job the best (or least terribly, if you’re that way inclined).
To recap, we want:
- High Lift (for going and staying up)
- Low drag (for moving forwards with great haste)
- Low pitching moment (for keeping the stabilising tail surfaces as small and light as possible)
- High stall angle and predictable stall behaviour (for pointing the nose higher for maximum lift, and not immediately falling like a rock)
And the formula for governing how much lift our wing is producing:
Lift = 0.6125 x Coefficient of Lift x Wing Area x (Airspeed^2)
Simple, right? right?! Yes. Yes it is. But allow me to muddy the waters ever so slightly, because it’s fun.
Remember when I said that the coefficient of lift allows us to calculate the actual lifting force generated by the wing, regardless of airspeed and wing area? Well, I oversimplified a little bit. Compared to what we’ve covered so far, the coefficient of lift is not a simple thing to calculate. It is strongly governed by something called Reynolds numbers.
If you don’t care for the technical stuff, the following few paragraphs can be summarised thus:
BIGGER REYNOLDS NUMBER = BIGGER LIFT COEFFICIENT & LOWER DRAG COEFFICIENT = MORE LIFT & LESS DRAG
For the even less technically-inclined:
BIGGER REYNOLDS NUMBER = BETTER PERFORMANCE
or BIGGER REYNOLDS NUMBER = GOOD
These statements are pretty darned generalised, but we won’t be flying even remotely fast or high enough to invalidate them.
Reynolds numbers are the ratio of inertial forces to viscous (sticky) forces. Ideally, this means we want to be moving at high speeds through a low-viscosity fluid. Imagine an oil tanker chugging through the water. For the purposes of the scenario, the powertrain is unbreakable*. The ship is big, heavy, and takes a long time to speed up or slow down. At cruising speeds, it would have a huge amount of inertia. Now let’s take that tanker and plop it in a sea of honey, pushing it along so it hits its normal cruise speed. Honey is thicker and stickier (i.e. more viscous) than water, so as the resulting viscous forces against the ship increase, the Reynolds number would fall dramatically. If we stop pushing the ship forwards and the tanker were to rely entirely on its own engines for movement, the increased viscosity of the honey would gradually slow the ship down, lowering the Reynolds number further still, until the ship came to a halt and got stuck, at which point it would be 0.
Another key aspect of Reynolds numbers are their impact on flow style. See, there are three ways air (or any fluid) can flow:
- Laminar – order. The liquid/gas forms ordered layers. This smooth flow regime allows our aircraft to slice through the air with minimal drag.
- Transitional – a highly unpredictable state in which parts of the flow switch erratically between laminar and turbulent flow. Modelling this state is a nightmare.
- Turbulent – chaos. The flow breaks down into random vortices (think hurricanes) and other random swirly formations. Drag goes through the roof, and lift all but ceases to be. All pretences of order are discarded as the true nature of fluids is unmasked – sorry, I think I went a little off-topic there…
Under normal flying conditions, air will typically move over the wing’s upper surface under laminar flow conditions, with hints of transitional flow developing towards the trailing edge as the angle of attack is increased. Keep pointing that wing further up, and the transitional flow will gradually become turbulent and move forwards along the chord. At the stall point, the transitional/turbulent air moves far forward enough to completely disrupt the laminar flow, at which point the air becomes ‘unstuck’ and lift suddenly drops. Perhaps counter-intuitively, increasing the Reynolds number makes the air more prone to ‘sticking’ to the wing and remaining laminar.
So what controls these mighty magical** numbers? We won’t go into the maths this time, but suffice to say, there are a few factors which affect the Reynolds number (and thus our coefficient of lift). Air temperature and density affect Reynolds numbers due to their influence over viscosity, but since we can’t control them, it’s largely a moot point. The ones we can control are:
- Our airspeed – the faster we go, the greater our inertial forces.
- The chord length of our wing (how long our wings are from leading to trailing edges) – air is less well-behaved around smaller objects, which imposes size limits on our aircraft. If we make our model too small, its performance will drop off rapidly. This is less of a problem for larger aircraft, as models sit on the proverbial brink of reasonable size limits (which is part of the reason why we see plenty of palm-sized multirotors, but very few similarly-sized fixed-wing aircraft).
It’s important to note here that drag forces also increase with both of these factors – we have a larger, draggier wing, and our speed means we’re bumping into more air particles per second. Like many things in engineering, it’s a compromise thing. However, as we’re building a simple, easy-to-fly model, drag isn’t really a massive priority.
Thus Concludes the Basic Wing Theory Stuff!
Well, look how far we’ve come. And look what I’m moving to the next post. Next time we’ll actually be covering aerofoil selection like I said we would. If we were covering a full-sized aircraft design I probably wouldn’t even have mentioned Reynolds numbers, but models lie on the tipping point where even small shape changes can have dramatic impacts on performance; brilliant aerofoils become useless, useless ones become feasible, and we get weird effects like aerodynamic hysteresis. Bigger really is better in some ways. Still, it’s also more expensive and dangerous. Compromise is our friend!
And now we part ways. Rest assured, there is much more to come quite soon. With many more pretty pictures.
* To clarify: explaining even simple engineering concepts is made MASSIVELY easier by creating thought experiments which rely on certain simplifying assumptions being made, even when the situation becomes impossible to achieve in reality. Remember the scene in Life of Brian where Brian, in misery and frustration, orders his obsessed followers to “politely leave” and the crowd asks “how shall we politely leave?” If we make a number of reasonable and well-informed assumptions which remove certain factors from a problem, we are left with the important stuff.
** No, magic is not a valid analysis or design tool.
Basic Model Aircraft Design 