So, slightly worried that the tendency to repeat oneself is a sure sign of senility, I shall commence this festive season uniBlog by re-iterating my comment from last time. Congratulations to Carl (who either laudably read all the way through my “A Margin for Error” uniBlog to find the answer or, less diligently but quite understandably, used “Edit/Find” on the word “novice”!) for winning the special Sigma darts in the little competition I set. And may I say I’m looking forward to witnessing both the resulting domination of the darting world that he’s promised from them and the avian porcines!.
As for Craig’s request for photos of the prize that evaded him by just 8 minutes, sorry, I can’t oblige as I haven’t got any! Of course, we could ask Carl to post some on an internet darts forum, but maybe that would be too much like expecting Darth Vader to gift-wrap blueprints of the Death Star and send them to Princess Leia with love and best wishes (which admittedly would have saved him a lot of trouble in the long run).
But enough of rather forced and geeky similes. Coming down to earth, what I’ll look at this time is a question that’s been touched on in some customer e-mails to Unicorn and was also posted by Bob, who asked “In aerodynamic terms, should the shaft/flight combination be married to the weight of the dart body as well as the shape?”
Going to the uniLab webpage, we can show that the simple answer to this might be “yes” by leaving the “STs and SPs” on their default settings and clicking on “Optimiser”. We now need to choose a specific type of dart that’s available in various weights, and the first in the drop-down “Barrel Range” list that fits the bill is the World Champion Golden (the preceding Phil Taylor Phases only come in one weight). And the first Barrel Name in the drop-down for the World Champion Golden range is the John Lowe, which is available in 21, 23, 25 and 27gms.
If we select the 21gm and click “Optimise Darts”, uniLab recommends an XL+ medium length shaft with a Big Wing polyester flight. However, if we repeat the process for the 23gm version, a CheckOut medium shaft with a CheckOut Xtra flight is recommended. For the 25gm, the same shaft and flight shape is recommended, but this time the flight type has changed to the heavier Maestro. A somewhat similar effect results for the 27gm dart, but with the optimal flight type this time being polyester.
However, not every type of dart will yield different shaft/flight combinations when different weights are “optimised”. This is because there are two main ways in which a dart barrel of a given design can be made heavier, the diameter can be increased or it can be made longer. If the latter method is used, as with the World Champion John Lowes, the effect on the dart’s MI (moment of inertia) is comparatively large, due to the fact that (as I explained at tedious length in my “MI2” blog) the MI of a cylindrical shape like a dart barrel tends to vary as the mass times the length squared.
As the MI of a dart is a key factor in determining that all-important yaw wavelength (see “A Matter of Some Moment” and several other blogs), the increase in it caused by lengthening the barrel will thus often mean that the aerodynamically optimal flight/shafts combination will also change.
On the other hand, if the barrel length is kept fixed and the diameter is increased, as with, eg, World Champion John Parts, the effect on the MI may be less significant. Thus, repeating the above uniLab procedure for these yields the same optimum shaft and flights for both the 21gm and 23gm, with only the 25gm being different. With some other types of such darts, the optimum configuration doesn’t even change at all.
Of course, barrel weight could be controlled by altering both diameter and length, with the former having the greater effect as the mass of a cylinder varies as length times diameter squared. Which means that, for a given density of barrel material, the MI will tend to vary as diameter squared times length cubed (still with me out there?).
And so to the eponymous “magic moments”. That squared/cubed relationship can be applied to increasing barrel diameter while reducing length so that the weight of the barrel goes up but the MI magically stays constant. And that, my friends, is one of the sneaky tricks behind Sigma darts. Unlike normal darts, the heavier weights are actually shorter than the lighter, which means all the weight range can have similar MIs and the same aerodynamic properties for a particular shaft/flights combination.
In fact, there’s a little bit more to it than that because there are more things to consider than just the MI of the barrel (centre of gravity position, etc, etc), but you get the idea.
That’s why, when people ask me what weight of Sigmas is best, I can truly say it’s really just a matter of personal preference as no particular weight of Sigma barrel has any real aerodynamic advantage over any other. Similarly, no significant aerodynamic differences exist between Sigma 950s and 970s as, despite the former using slightly lower density tungsten and thus being a fraction longer on average, the shape and grip has been designed to compensate.
But there is a secondary factor which may just tip the balance between two weights or types of Sigmas (or any other darts) if both feel equally comfortable to throw – lighter darts (or higher density tungsten) mean smaller diameters and hence a tiny (very tiny!) bit more room for three in that treble 20.
And with that pleasant thought, let me sign out of 2008 by wishing everyone, and especially my regular readers and commentators, a Merry Yuletide and a very Happy New Year!
Other Q&As
Ecduzitgood and integrated cone tips
I suppose, instead of being separate or attached to the barrel, a cone could be incorporated into the tip as you suggest. However, this could compromise the operation of extraction tools and, depending on how long the remaining point, possibly even lead to board damage. Still, all these things are worth thinking about!