As a mathematician, I suppose it’s predictable that the apparent illogic behind some English words would bother me – why does inflammable mean the same as flammable, for example? In the words of a learned student of grammar I once knew, “it just don’t make no sense”.
I mention this because another such lexicographic dichotomy (great phrase – wonder what it means?) reared its head this month when I decided to recapitulate the salient features of dart aerodynamics. This was not only because I haven’t really explained some of them properly since near the start of these blogs four years ago, but also because, when I did the first time, I fear I may have over-cooked the flight dynamics jargon a little too much for some tastes.
I’m not really going to apologise for that, though – it was a question of scientific credibility. If I hadn’t started off sounding like an escapee from a NASA Incomprehensibility Unit, the rumours that I was just an invention of Unicorn’s marketing department might have gained an even larger following!
But back at my linguistic concerns over “recapitulating”, that means, of course, “restating the main points of”, in other words “giving out – again”. That’s as opposed to “re-capitulating”, which I suppose must mean “giving in - again”. And I want to make it quite clear that, despite my recent abject surrender to a sneaky pincer attack from within and without Unicorn over designing Sigma 4s, my steadfast intention here is to do the former and not the latter.
Now we’ve cleared that up, time to turn from etymology to the rather more logical (IMHO) world of “arrerdynamics”. Whilst a dart in flight has lots of different aerodynamic forces and moments acting on it, understanding the effect of just a few of them can give you a good idea of how things work. So here goes with a handy (and relatively low jargon-count) list:
1: Drag: Easy one this. Don’t worry about it - at least not in itself. Due to pure aerodynamic drag a dart going straight will lose less than 1% of its speed on its way to the board and you won’t notice that. But, before you write this statement off as rubbish, let me qualify it by saying that what you may notice is the drag effect of the lift acting on a dart that wobbles in flight – and that can increase the velocity drop to observable levels. A scientific purist might argue that I actually mean “normal force” and not “lift” here and what I’m describing is still a drag effect, but that’s just being pedantic (“normal” in maths-speak means “at right angles”, by the way).
So my advice on drag as far as darts are concerned is to worry about lift instead!
2: Lift: Yes, it’s something to worry about. Not so much for its still small effect on the velocity drop of a wobbling dart, but for it’s ability to throw that dart off line. The vast majority of a dart’s lift comes from the flights and, in general terms, the bigger the more the lift, although “delta” flights like Sigmas are a bit of an exception in that they may not have as much lift as bigger flights at low wobble angles, but don’t lose it so easily (“stall”) as the wobble gets bigger.
So does all that mean everyone should use small flights to minimise lift? Well, no because of:
3: Overturning Moment: The aerodynamic effect that makes a dart try to fly straight after it’s released at an angle or with a “flick”. Largely a function of the lift and the distance of the flights behind the centre of gravity and without it the dart would just tumble end over end. So reduce the lift to reduce the effect of any wobble and the lower overturning moment just means more wobble! S(omeb)od(y)’s Law in action! Of course, if you’ve got a really smooth “unflicky” throw there won’t be much wobble in the first place and you may be able to get away with small flights – hence Sigma Super Pros and The Power’s DXMs.
So why not get lots of overturning moment (in magnitude – it’s negative in sign) by using small flights and a REALLY long shaft? Nice idea, but Somebody’s Law comes into action again because of:
4: Moment of Inertia: MI for short, it’s rotational motion’s equivalent of mass but with an additional length squared term in it. That length squared bit means even a little scrap of mass like a flight at the end of a long shaft can have as much MI as the far heavier barrel. And the bigger the MI the longer a dart will take to correct itself in flight, so using a long shaft to increase the overturning moment can end up being counterproductive.
So MI makes long darts with heavy shafts (and even flights!) straighten in flight more slowly.
5: Yaw wavelength: A key aerodynamic parameter of a dart, it’s a function of MI divided by overturning moment and is the distance taken to wobble first one way and then the other. Within limits it’s not dependent on the size of the wobble (it’s like a pendulum swing in this regard) or on the speed of throw. Thus, from a dart designer’s point of view, relating the yaw wavelength to the throwing distance in some way (as is done with Sigmas) can give the dart specific desirable flight characteristics over a wide range of players.
OK, reckon that’s enough aerodynamics stuff for one blog. The question now is what, in practical terms, can you take from it to help you find your perfect dart set-up? Well, the proper scientist in me would contend there are just too many complicating factors to answer that simply. However, if you really insist, I’ll give in and say you should try to achieve the right yaw wavelength for you using flights no larger than necessary to achieve that aim.
If your impact angles vary a lot from dart to dart, the right yaw wavelength will usually be the one that gives the smallest variation in them. In this case, especially if you like a long and/or heavy barrel with high MI, you’re probably best off with a light plastic shaft and larger flights such as Plus or Big Wing.
On the other hand, if your impact angles are always fairly consistent dart to dart irrespective of your flight/shaft set-up, you may find, especially if a shorter and/or lighter barrel suits you, that you get better accuracy with a heavier metal shaft and/or smaller flights.
Of course, those statements are horrible generalisations and I’m already regretting that I was so weak-willed as to give in and write them. I’m clearly getting a bad habit of doing exactly what I said I wouldn’t. First I design Sigma 4s and now, instead of sticking to recapitulating, I re-capitulated.
Yep, I gave in – again!