Following my last blog, which centred around Neily B’s question on how Sigma darts can help the average player, I’ve got into the swing of responding at length to your comments, so this time I’m taking a look at a subject Red has raised. To paraphrase, he wants to know the relative importance of bio-mechanics and aerodynamics in darts – and that’s a great question (and not the only good one I was asked – more from Red, Chris, Kev, Valspar11, Jon, and Bob, in the Q&A section at the end).
Now you won’t need a scientist to tell you that the skill of the player is a lot more important then the aerodynamics of the dart, but it does help to have a flight dynamicist handy if you want to quantify by how much. So here goes.
As I explained to Neily, Sigma Ones are very stable darts with a yaw wavelength close to their flight path length of around 2m. Let’s say these are an example of a “good” aerodynamic design and that you’re a reasonable player who throws them with a “yawing rate” so that they peak at a not unreasonable 15 degrees of yaw and then hit the board when they’re pointing straight again. The yaw during flight will nonetheless create lift and cause the Sigmas to deviate about 8mm from the thrown trajectory.
I also mentioned last time that designing a dart with a very long yaw wavelength of 4m, which thus only goes through half-a-cycle, wouldn’t be a great idea. But if you did throw such “bad” darts like your “good” Ones, they’d still hit pointing straight, but that 15degs peak of yaw would rise to 32degs and the deviation increase to 30mm.
Now if that yaw were totally consistent, this 30mm wouldn’t be an inaccuracy, just a constant bias for which you could allow. In the real world, however, the yawing rate you impart will have some variability and a moderate 20% variation would cause 6mm inaccuracy with the “bad” darts, but less than 2mm with the “good” Ones.
Now some players (as Red suggests and Bob has asked about) throw their darts not just with a yawing rate, but also with a yaw angle. The “bad” darts would then go through their half-cycle to hit the board yawing opposite to the way they were released, but not by as much due to something called “yaw damping”. More about that another time, but if the darts were released with, say, 30degs of yaw they would hit the board with maybe 23degs – quite an angle. On the other hand, the “good” Ones would go through a whole cycle and, although they would also hit the board with yaw, this time in the same direction as when they were released, their extra stability would give them more “yaw damping” and the impact angle would be a more tolerable 13degs.
Thus, for a reasonable player, a fair estimate of the difference in accuracy between a “good” aerodynamic design of dart and a “bad” one is in the region of 4mm. For someone less competent, who might impart both more and more variable yaw and yawing rate to their darts, this difference could easily double or triple. Moreover, for any standard of player, there would also be a tendency for the “bad” darts to have large impact angles that would induce increased bounce-outs and bed-blocking.
And now to answer Red’s question. If, for example, those “good” darts had a barrel shape that our reasonable player found ungainly, and that caused the 20% of yaw variability to increase to 30%, that would lead to an extra 4mm inaccuracy (and more wayward impact angles), negating the aerodynamic benefits. Or the barrel might have, say, a slippery grip which led to 20% variability in speed of throw. That would cause 17mm change in impact height, much more than the aerodynamic inaccuracy.
So, Red, I wouldn’t recommend that you, Phil Taylor, or anyone, changes their darts for aerodynamically superior ones if that involves significantly less favourable bio-mechanics. That’s why evolution – the best designer I know – has led to there being so many types of dart. And it’s also why uniLab allows the user to specify the type of barrel they prefer – even if the preference is arbitrary, with much of the game being in the mind players must feel comfortable with, and have confidence in, their equipment.
On that note, a final thought. How much confidence could a player gain from knowing they were using the most aerodynamically advanced darts in the world? I’ve talked about “good” aerodynamic designs of dart and used Sigma Ones as an example. But I reckon, for better players, the Sigma Pro can be more than just “good”. With luck, next time I finally get to explain what’s so special about it – hope you’ll join me then!
Q & As!
Chris (but not Chris R!), Red, Kev and Phil Taylor:
If you’ve read my “Sigma to the Power of One” blog, Chris, you’ll know that Phil changing to Sigmas was entirely his own idea and might have caught my hint that I didn’t think Unicorn were actually that happy about it! I also mention that Phil, who (as Red eloquently evidenced in his last comment!) is very much his own man, has modified the barrels and uses a shaft/flights set-up that I personally wouldn’t recommend. Strictly speaking, his darts aren’t proper Sigmas at all, but he’s happy with them (at least as I write!) and is reportedly playing well in practice. The last phrase in my penultimate paragraph above applies here and neither I nor Unicorn would presume to tell a 13-times World Champion what darts to use!
On a similar theme, I’m glad Kev also likes Sigma barrels, even if he too has forsaken the Pro set-up. Nonetheless, I’m sticking to my guns about it being hard to achieve a set-up as aerodynamically accurate as the Pro by trial and error. The key point is that, unlike ordinary darts, with Pros a player shouldn’t tune out impact yaw angles unless they’re excessive – they’re part of how the aerodynamics works to provide accuracy.
Valspar11 and Pitch:
Sounds to me like you’ve just got a good “arm” throwing style, Valspar, which doesn’t impart any sideways yaw. Are you sure that “up and down” pattern isn’t just the dart following the curve of the trajectory? If you are getting too much vertical yaw (pitch, to aeroplane designers), you might try extending your arm out straighter – you could be imparting an upwards yawing rate by pulling your arm down as you release.
Jon and Sigma Pro sideload shafts:
The difference between Sigma Pro and SlikStik+ Al shafts, Jon, is that the former uses (very expensive!) titanium instead of aluminium for better balance and strength.
More from Red and Bob:
You’ve got a good memory, Red. The basic design for Sigma darts was formulated nearly a quarter of a century ago and the flights you saw John Lowe use on TV were indeed prototypes for those now used on the Sigma Pro – although I don’t think they were ever on sale (not even in pink!). As I explained last time to Chris, the long wait since is because the technology wasn’t then available either to mass-produce the barrel and shaft designs economically or promote the product properly – if it weren’t for the internet allowing me to explain the theory to healthily-sceptical darts players, Sigmas might be unfairly labelled as just sports-marketing hype and pseudo-science!
As for Red’s well-thought-out points about uniLab – yes, there are assumptions that have to be made, but these aren’t as restrictive as you might think. As you know, personal preferences on barrel grip are catered for (even if shaft length isn’t!), as are differences in style, stance and speed of throw – within limits, obviously. The fact is none of these significantly affect the aerodynamic characteristics of the dart, only the release conditions it has to cope with and the distance it has to travel. If a dart yaws a lot, whether it’s up, down or sideways is irrelevant, it’s still not a good idea!
As to the difference between releasing with yaw and yawing rate, I’ve dealt with that a bit today (and hopefully answered Bob in the process), but more about it next time.
Finally, Red, using the longer aluminium SlikStiks and Maestro Xtra flights your 21gm John Lowe Golden World Champions is not (in the terminology of today’s blog) a “bad” set-up and, if you’ve tuned it to give you very little impact yaw, you’re obviously not going get much improvement in this parameter by switching to something else. However, if (as I suspect) you’ve asked uniLab to recommend a dart for a “good” player (as opposed to an “average” one or a “novice”, who would have trouble tuning their darts), it will have paid more attention to maximising accuracy and less to minimising impact angle. Hence the set-ups it recommended might be more accurate, but not fly quite so straight, as your normal one. Why this is I’ll look at next time in the context of Sigma Pros, but all I can say is give the recommendations a fair try and don’t just dismiss them after a few throws just because the impact angles aren’t what you’re used to. Nonetheless, they are only recommendations and, as we’ve seen, it’s not worth changing if you don’t feel comfortable with them.