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Shooting the Breeze

Posted by UniBoffin at 10:33 on 16th January 2012 in UniBlog

Shooting the Breeze

Although I find it hard to believe we’re well into 2012 already, it’s harder still to credit this is my 60th UniBlog - a sort of cut-and-paste Diamond Jubilee of scientific darting missives. But stifle any yawns at the prospect of reading yet another because, after all the excitement of the various World Championships, we’ve got a lot to get through!

So let’s start by congratulating Christian Kist and our own Anastasia Dobromyslova on their BDO victories, as well as, of course, Adrian Lewis on retaining his PDC crown. Also in that event, it’s commiserations but still well played to Unicorn maestros Andy Hamilton and James Wade, The Machine only just missing double 18 to join The Hammer in the final.

Which brings me nicely to my main subject for today, something else from that match against Jackpot, the mysterious air current that peskily interrupted Ally Pally proceedings - and then apparently blew down to Lakeside to aerate both BDO semis, thereby possibly harming Sparky’s chances and helping to put Ted Hankey out for the count (sorry, couldn’t resist!).

Moving quickly on, this timely gift to any dart flight dynamicist seeking a New Year topic has been, rather predictably, christened “Breezegate”. However, I do feel obliged to act the pedantic scientist and dispute that terminology. According to the Beaufort Scale, a “breeze” (light, gentle, moderate, fresh, or strong) has a wind speed between 2 and 14m/s. What we’re talking about was more likely merely a “light air” of around 1m/s. But, whatever we call it, the question is what could it have done to the players’ darts?

Well, the first thing to realise is that a dart is not like a high-sided vehicle – it doesn’t get blown off course simply by the side area (like the flat face of the flight) catching any crosswind. This is because, unlike a vehicle which has the friction between tyres and road trying to keep it straight, a dart can “weathercock” and point into any crosswind. And, once it has done that, the force causing it to move downwind will be frontal drag, not lift.

Now, as I’ve said before, the frontal drag of a dart is small compared to its lift, which means that, if it weathercocks quickly enough, it will not be thrown that much off-course – maybe a millimetre or so - by a 1m/s crosswind. However, if it doesn’t, the larger lift force then has time to act, which would result in a very noticeable deviation, say 4 or 5mm. So what’s important here is not primarily the size of the dart’s flights, or its weight (although that certainly has a direct effect), it’s how quickly it weathercocks - in more scientific parlance, how statically stable and how short its yaw wavelength. And, as larger flights generally make a dart more stable, the high-sided vehicle analogy is made even more inappropriate.

If I haven’t explained that understandably, all I can do is apologise, but if you are merely dubious about it due to healthy scepticism, what I can do is suggest you perform an internet search for “classic crosswind deflection formula”. Then you will (with luck!) find that a projectile’s sideways deviation per unit crosswind can often be approximated by flight time with drag minus flight time without drag. No lift there! (In case anyone’s geeky enough to be genuinely interested in this sort of stuff, I’ll add that this also means rockets will usually deviate upwind while they’re burning as they’ll effectively have negative drag – something you might check out next time you watch fireworks!)

But back with darts, it’s not just the deviation of their centre of gravity in any crosswind that players may notice, there’s also the angle at which they hit the board. A dart thrown at 6m/s that has weathercocked into a 1m/s crosswind will yaw sideways around 10 degrees, which means the point could be 7 or 8mm off-line – in an upwind direction! As the cg might only have drifted downwind half that amount, this means that, to compensate for the effect of a crosswind, a player could have to aim downwind - counterintuitive to say the least!

Of course a dart thrown faster will both weathercock to a smaller angle and deviate less than a slower one, but with all this complex dynamics still affecting exactly where it hits the board even in a “light air” of just 1m/s, it’s no wonder the players weren’t happy!

Finally on this topic, one more confusion: although the draught at both venues did appear to be a crosswind, another time it could be a convection current in an upward or downward direction (hot air rising is usually cited as the cause, although cold air falling would perhaps be a better way of putting it). Fortunately this doesn’t change the basic logic in the above argument, although it does alter the plane of the drift and impact angle effects.

So is that clear? No? Oh, well, I tried! If the words “as mud” just crossed your mind, you’re welcome to post a request for further clarification! And talking of posts, it’s now time for me to thank Warren and Diana, John, Hays, and the inimitable Giraffe, for their seasonal good wishes, and finish shooting the breeze in some Q&As!

Q&As
Giraffe and Round Flights
Yes, Mr G, round flights would work – in fact circular wings and lifting surfaces have long been of interest to aircraft designers, first for their structural advantages and more latterly because of their stealth benefits in dissipating radar reflections. However, stability and vortex-shedding problems tend to beset the concept and would also affect the efficiency of round dart flights. In summary, I reckon the additional lift generated would not be enough to justify the extra width over pears. Still, why not cut a set out of, say, Big Wings, and let me know how you get on with them? I’m all for encouraging some experimental arrerdynamics!

Eoghan and V Wing Flights
Thanks for your question, Eoghan, but I hope you’ll understand it’s not really appropriate for me to pass judgement here on other manufacturers’ products. That said, I believe V Wing are made by Harrows rather than Winmau, who instead offer the Arrowhead. I have no doubt both are quality flights, but you’d have to ask the companies themselves about the thinking behind their design. All I can say is that, although the leading edge sweepbacks of both may bring to mind Sigma Pro flights, when designing those I was very aware of the need to balance aerodynamic performance with practical factors such as reducing bed-blockage and allowing maximum draw-back distance. As I’ve reported before, I rather failed in this regard with The Power as he found the trailing edge on Sigma Pros sometimes hit his cheek, which was why he originally reverted to Slims with his Phase 4s and 5s before moving on to DXMs. I’ll leave it for you to judge how he’d get on with more rear-sloping designs!

Eddie and Barney’s Darts
I must admit, Eddie, that even I have trouble keeping up with Barney’s changes of equipment, but I believe that in the 2010 World Champs he was using the 25gm WC Golden barrel with Sigma Pro flights and shafts (that choice was nothing to do with me, by the way!). This barrel was specifically designed for him (I actually have a copy of a prototype drawing dated 8/5/2009), but is in the Unicorn catalogue (no 10138) and is also made in 21, 23 and 27gm. If you want even weights, there’s also the somewhat similar RvB Hero Golden.

David and The Power’s DXMs
David thinks the Power seemed more consistent with his Slim flights than with his current DXMs and wants to know if I have thought of advising Phil to go back to them. I’ve actually touched on this topic before, notably in “Flights of Fancy” (Nov 2009) when I said “from a flight dynamics point of view I would have considered Phil’s new flights rather too small to give the ideal amount of lift. For a player of his ability, this may well not cause any problems when he is playing well and releasing smoothly, but not doing so could potentially lead to some comparatively wayward darts.” However, I also pointed out that his DXMs did have advantages, notably that they “will cause his darts to land slightly below horizontal on average, something he was used to with his old Purist set-up.” To summarise my thoughts on this, I certainly wouldn’t rule out suggesting Phil try a more “forgiving” set-up if and when he feels he wants a change (as happened before when he switched from his Purists to Sigmas and then his Phase 5s), but I would be reluctant to do so, especially unbidden, when has had such great results with his current set-up in the very recent past.

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