So, folks, this is where I casually give away some of Unicorn’s hard-earned lead in darts’ technology by explaining just how a dart can be designed to be aerodynamically more accurate. (I can now almost imagine villainous competitor darts manufacturers in black frock-coats and top hats twisting their conceptual waxed moustaches in evil anticipation!). Still, perhaps fortunately for my future employment prospects, neither the theory nor the practice is as easy as all that, so I reckon I’ll take my chances that the darts world will soon be awash with copycat Sigma Pros!
Unfortunately this protective complexity means that all you genuine darts technology enthusiasts out there are probably going to need a quiet place to read this and maybe some headache pills handy. Well, warning over, off we go.
Last time we looked at two types of dart, a “good” aerodynamic design like a Sigma One that has a yaw wavelength of around 2 metres, which is similar to the flight path length from a 2.37m oche, and a “bad” aerodynamic design which has a yaw wavelength of twice that. We saw how, when thrown with just a “yawing rate”, although both designs hit the board with low yaw (ie “pointing straight”), the yaw during flight creates lift which causes the “bad” design to deviate far more than the “good” One (in the example I gave, the actual numbers were 30mm instead of 8mm).
If, on the other hand, the same darts were launched at a yaw angle, the higher “yaw damping” of the more stable “good” design reduced the undesirable impact angle considerably (and yes, Bob, you’re absolutely right – yaw damping is linked to the lift on the flight and the length of the shaft – a bit more on that in the Q&As at the end).
So, whether launched with yawing rate, yaw, or both, a dart with a yaw wavelength of around 2m, which therefore goes through a whole yaw cycle on its way to the board, is likely to be preferable to one which only goes through a half-cycle. But what about a dart that goes through three-quarters of a cycle? How good would that be?
Well, at first glance it doesn’t look too great because when, as is most usual, it is thrown with a yawing rate, it will hit the board at a yaw angle in the opposite direction to that rate. So, if the initial yawing rate is upwards, say, the dart will hit the board pointing down, with its tip below the thrown trajectory of its CG. But there’s a trick here, because, for the first two-thirds of its trajectory, the dart will have been yawing up and lifting in that direction. Since both the distance the dart’s tip is below the trajectory and the upward lift will be proportional to that initial yawing rate, with a bit of careful design, we can arrange it so those two factors always cancel each other out.
If you managed to follow that, well done! I hope you agree that it’s really pretty sneaky to arrange for any initial yawing rate imparted to the dart causing it to hit the board at an angle which actually compensates for the lift deviation that would otherwise have been a source of inaccuracy. That’s what I call a smart dart!
But what about if our smart dart is thrown with a yaw angle? Well, that’s sneaky too, because it will go through its three-quarters of a yaw cycle and hit the board with no yaw. And the lift effect won’t be much because the yaw, and therefore the lift, will be in one direction for the first third of the flight and then in the opposite direction for the next two-thirds. Since lift is an acceleration which needs time to take effect, the lift deviation from these two yaw phases will tend to cancel out (as all you keen students of the double integrals of trigonometrical functions will testify!). In fact, we might even control the amount of yaw damping in our dart to make them cancel out exactly.
So there we are. Design a dart with a three-quarter yaw cycle and then further optimise the yaw damping, mass, lift, and distance between the tip and the CG, and we can virtually eliminate the inaccuracy caused by variations in the combination of yaw and yawing rate with which it is thrown. We could then call it a Sigma Pro and have good reason to claim it to be the most aerodynamically accurate dart ever produced.
But there is a potential problem. If a Sigma Pro is thrown with too great a yawing rate, it will not only hit the board at an angle which might cause bounce-outs and bed-blocking, its in-flight yaw could also exceed the level where the flights lose lift. In aerodynamics this is “stalling” and, should it happen, it would mess-up that nice yaw cycle. Fortunately, though, really good players don’t usually throw with a yawing rate that high, which is why the Sigma Pro is meant for them. For the rest of us with rather more wayward throwing styles, a more “forgiving” Sigma One may be a better choice.
Next time maybe I’ll look at stalling a bit more and explain how the design of the Sigma flights helps in this regard. Until then, how about a bit of sleuthing for you – the title of this uniBlog is from a detective story, but what’s the missing word?
Q & As!
Bob and Grips and Yaw Damping:
Last time I talked about the importance of individual preferences in the bio-mechanics of a dart and the “ideal” grip is a case in point. The current Sigmas were designed so that a finger-thumb grip could push them against an upward taper from just behind the CG whilst a stabilising finger rested just ahead. This is mechanically efficient and was intended to overcome some of the fine grip disadvantage of possible slipperiness and obviate the need for a coarser grip which could cause variable release. However, no one type of grip will suit everyone and this arrangement is no exception, so any future Sigma developments could well take account of the Phil Taylor mods and offer a coarser-gripped variant. In the meantime, Bob, you could try putting your choices of barrel shape and grip into uniLab to help with your search for new darts.
As for yaw damping, as I’ve said, you’re right in thinking that it’s a function of lift from the flights and the static margin (which is related to shaft length). But there’s also the moment of inertia and other complications which I’ll deal with another time.
Tony Warne, Nick Steenstra, Warren, et al:
Thanks for your feedback, guys, and for Nick’s recollections from half-a-century of darts!