Although particularly trusting readers may fondly imagine that this series of blogs is all carefully planned out with properly scientific forethought and precision, the truth is I’m always on the lookout for newsworthy darting topics upon which to pontificate.
Of course, I’m not saying that somewhere in the background there isn’t a sneakily subliminal college course on projectile aerodynamics that I return to when nothing much else is happening, but whenever possible I try to cover events, comments, or questions of the moment.
And this time I haven’t had to look far for such inspiration, thanks to two people – Sid Waddell and Joe Pearce.
First to our Sid. In his recent “Record-breaking Taylor” UniBlog, Sid writes that The Power is “…more relaxed than ever in his career. He has also ignored the Uniboffin theory that he should always land the dart parallel with the floor. He likes a dip of about three degrees in some shots into the 60 bed. So in fact he is using the old muscle memory of the old ‘knitting needle’ darts to good effect”.
This is great stuff which relates to the smaller flights which Phil now uses. As it happens, it echoes my “Flights of Fancy” blog in which I wrote that, from a purely flight dynamics point of view, I would have thought these flights were “rather too small to give the ideal amount of lift.” and “will cause his darts to land slightly below horizontal on average, something he was used to with his old Purist set-up”.
I then went on to say how Phil’s success with his new flights – now underlined by further achievements such as his recent record 118.66 average - has modified some of my thinking on dart design for very good players and made me re-examine some work I did on small flights in the 1980s. The question now is might the results of this be seen in the shops in the near future? Well, that’s one only The Big Boss can answer!
On that buck-passing note, I’ll move on from the legends that are Phil Taylor and Sid Waddell to Joe Pearce, who may not be quite such a legend (humble apologies if you are, Joe!), but to whom I’m nonetheless grateful for taking the trouble to post an interesting comment to my last blog. Joe asks if the tendency for the tail of his darts to “whip around violently” unless he spins them is because he uses smaller flights. He also wonders whether larger flights “with a little more drag” would work better with his natural low-spin throw.
Well, first I’m afraid this has provoked the pedant in me to take some time to correct a common misconception about flights and drag. Yes, bigger flights have more drag, but for most players that’s not the real issue. It’s more important that they have greater lift.
To explain further, for a dart which is flying straight the only drag forces acting on the flights are tiny amounts of what aerodynamicists call forebody and base drag (tiny because flights are so thin) and a bit more – although still not much in the grand scheme of things - skin friction drag.
However, for a dart not flying straight but at an “angle of incidence” (a term those who read my early blogs might recall), another, much larger, force comes into play as soon as the incidence becomes significant. This force acts at right-angles (“normal” in maths-speak) to the axis of the flights (and thus also, hopefully, the shaft and barrel) in the direction of the incidence and is called, unimaginatively, the normal force.
Now, to be honest, I’ve been a bit lax with my terminology in the past by saying that the lift acting on the flights stabilises a dart. To be precise, I should have said it’s the normal force. I didn’t for two reasons – firstly more people would understand the term “lift” and, secondly, at moderate incidence there isn’t numerically much difference.
If I can indulge in a bit of third-form trigonometry here for a second (and with due apologies for wielding the Cosine of Damocles again so soon after my last blog!), in this case lift pretty much equates to normal force times cosine of the incidence. As anyone with a set of trig function tables handy will confirm, at 20 degrees incidence – quite a lot – this implies lift is 94% of the normal force. At 10 degrees it’s 98.5%.
But the normal force doesn’t just give rise to lift. It also causes drag (known, rather annoyingly for the clarity of my explanation, as lift-induced drag). And this drag is equal to the normal force times sine (what else?) of the incidence. This means that, at that 10 degrees, drag is only 17% of the normal force – and less than 18% of the lift. Even at 20 degrees, it’s still little more than a third of the lift.
In fact, only if you’re in the habit of throwing your darts with more than 45 degrees of incidence is their drag of as much significance as their lift.
Now that’s cleared up, back to Joe’s question (just hope he hasn’t got bored and cleared off by now!). Yes, bigger flights will most probably help his darts to impact straight, but (unless he is in the habit of playing with very bent shafts or flights) spin in itself probably isn’t much of a factor in what’s causing them not to do so with smaller flights. A more likely explanation is that there is a flicking action in his release which causes his darts to yaw but which diminishes when he deliberately spins them.
So over to you, Joe – I’d be very interested to get some feedback on whether my guess is right or wrong.
Which reminds me, Joe also asked about “beta testing” any new stuff I’ve been working on. Can’t promise about that (as you can imagine, there’s already quite a queue!), but here’s a beta-related fact. Projectile aerodynamicists lazily tend to equate incidence to yaw, but those working on aeroplanes and such like generally spilt it into up-and-down pitch and side-to-side yaw, with the former sometimes being denoted by the Greek letter alpha and the latter by – guess what? Which means that Joe checking out my theory on his throw could well involve a sort of “beta testing”.
And that makes me wonder if he thus might not even stumble across some sort of secret of darts. Phil Taylor tends to land his darts pretty straight side-to-side, but, as we’ve discussed, with a distinctive angle in the vertical plane. Maybe that’s why, as far as darts is concerned, he’s definitely a bit of an alpha male!