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Sigma Squared

Posted by UniBoffin at 00:00 on 7th August 2008 in UniBlog

Sigma Squared

As you may already know, the Unicorn 2009 catalogue is now available (not much plot, but still many good points!) and includes my latest excursion into the mystic art of dart design, the Sigma 950. This should come as no surprise to dedicated readers (those determined souls who don’t actually nod off at the very mention of moment of inertia!) who will have caught my past hints about the coming of “Son of Sigma”.

For example, Lonnie probably guessed why I suggested he wait awhile before buying soft tip darts similar to the 19gm Sigma but meeting US league rules by being no more than 18gm. Similarly, I expect Clarence, John P, Chris R, Bob and Warren will not be surprised at the new Sigmas’ longer, more aggressive grip, slight nose taper, and choice of even weights, even though I had to be a bit non-committal when answering pleas for such changes.

These modifications have in fact been long-planned, but another wasn’t decided until fairly recently – changing the barrel material from the original’s 97% tungsten to 95%. Now the cynical will no doubt be suspicious that this is merely an exercise in cost-cutting, but in fact almost the opposite is true – the change was needed to provide the best quality product without incurring too much of a cost penalty.

To explain, 97% tungsten is quite brittle and the design of the original Sigmas had to take this into account by having a front flat on the barrel nose to facilitate precision machining and point insertion. Even so, it had to be accepted that this brittleness means that a percentage of manufactured barrels will not pass Unicorn’s rigorous quality control procedures. Unfortunately the cost of such quality must eventually be passed on to the customer, who may not always be that happy about it!

With the new Sigmas, I wanted to have a more tapered nose to help prevent flight damage during close grouping. However, with 97% tungsten this would have caused even greater machining difficulties and quality control issues. In a world where raw material costs have already risen hugely and keep on rising, the consequences of this on the retail price of the product would have been very severe, so it was decided to use 95% alloy, which, for very little less density, has significantly better machinability.

My task was then to ensure that the slight reduction in density didn’t compromise the aerodynamics - which is, after all, the main focus of Sigma darts. Improving on the aerodynamic performance of the original Sigmas was not possible (if I say so myself), so my aim was to match it using the same Pro and One shaft/flights combinations.

Now this meant designing barrels with comparable moments of inertia (wake up at the back there!). However, to allow close grouping, I didn’t want to increase the diameter of the heaviest dart and that factor, together with my desire to offer a more aggressive grip (which obviously involves taking material off), implied that the 95% Sigmas would be longer than the 97% for the same weight.

Although I saw this length increase as no bad thing in terms of fitting in with the majority of player’s grips, it did mean that a moment of inertia match with the original Sigmas could only be achieved if the weight range didn’t extend quite so far up.

Fortunately (with apologies to any players who were waiting for a 28gm plus version of Sigma), I didn’t see the need for a small weight reduction as a huge problem as I’d already intended merely to “fill in the gaps” in the Sigma steel tip weights on offer by taking a gram off the original’s choice of 21, 23, 25 or 27gms. Unicorn also asked me to add an 18gm steel tip to match the new 18gm soft tip (although the soft tip barrel is actual much lighter as, by convention, its nominal weight includes the shaft and flights whereas the nominal weight of a steel tip dart just refers to the barrel).

So “Son of Sigma” darts were born. Mind you, despite all my calculations to ensure they were just as good aerodynamically as the originals, they still had to pass a crucial test. And, luckily for me, they did so with literally flying colours when, after some judicious throws, the Big Boss pronounced they had “that characteristic Sigma feel”.

So now only one problem remained - what to call them? Sigma 2 was dull, but I still couldn’t resist suggesting it would be nice to write it as Sigma squared, which in statistics is called “variance” and can be a measure of accuracy. This idea, although appealing to a sad scientist like me, met with pitying stares all round, and, although I desperately tried again with a “Sigma Variants” pun, the Big Boss wisely went for the rather less esoteric Sigma 950, at the same time renaming the originals Sigma 970.

Marketing-wise I know when I’m beaten – the new name is clearly one in a thousand!

Q&As

John and Dilithium
Thanks for the advice, John, but the places you mention only do regular dilithium – as I said, I was looking for free-range organic!

Paul and Troy and 2, 3 and 8 “Panel” Flights
Paul (whom I must also thank for the feedback on his curved flights) and Troy want to know why most flights have 4 “panels” and not 3, or 2, or even 8. The answer to this is linked to the lift “non-axisymmetry” I was talking about in my “The Spin Doctor” blog. Whereas 4-panel flights have, as I explained, only around 10% difference in lift between the “x” and the “+” configuration, 3-panel flights have maybe 20% between the “Y” and “Upside-Down Y”. Players who spin their darts a lot might not notice this, but for the rest of us it could create some inconsistent yawing motion. 2-panel flights would need yet faster spin to work even vaguely properly because, of course, in one direction they produce no lift at all.

As for flights with more than 4 panels, for each added panel aerodynamic interference between the panels will cause a slight loss of lift efficiency for a given total panel area. For a set length (chord is the technical term) of flight and amount of lift required, this means that there will be more “total length of panel back” to affect following darts. This wouldn’t be helped by the lower width (span) of individual panels resulting in a reduction in “aspect ratio” (basically span divided by chord), which also causes lift per unit area to fall. Apart from all that, they would also be a bit harder to make and fit!

Clarence and Replacement Sigma Soft Tips
Sorry you’re experiencing difficulties in getting these, Clarence – at the risk of being accused of passing the buck, try e-mailing assist@unicorngroup.com.

Dylan and Sigma 970 25gm
It’s hard to make a recommendation without knowing more about your style, etc, Dylan, but my first thought is that you should have found the Sigma One set up better than the Gripper/Q combination you are using. However, if you have already tried the former without success, you could give CheckOut medium shafts (cat nos 78565-8) and Maestro Xtra flights (eg cat no 68195) a go. Good luck!

There are 11 comments to this post

Posted by Red at 15:56 on 8th August 2008

Here are a few thoughts on UniLab and the future.
There are a couple of things I would like to see in the development of the UniLab.

First I would love to see a feature where you could enter the parameters of your current Unicorn dart so that you could see a comparative analysis of accuracy between what you have chosen and the UniLab recommendations.
It''s fine saying "this is the best" but by how much?

Another thing would be to have the optimisation data represented by other means than a percentage score. What is this percentage anyway? I don''t believe that it is properly explained in UniLab at all. What does that 97.26% mean? Is 100% perfect? Can 100% be achieved? I would doubt it, theoretically possible maybe but in practice unachievable due to many factors.
I would very much like to see factors such as wavelength and percentage deviation being shown to give a much more all round impression of performance and to see these in comparison to personal choices.

Posted by Red at 16:11 on 8th August 2008

Future Perfect
What does the future hold for dart optimisation? What if we consider other sports and the kind of personalisation of equipment that takes place? What could the future hold if we look at optimisation and pursue it to its logical conclusion? (well I hope I am being logical with my conclusion).

The UniLab as it stands, as has been discussed before is limited for a number of reasons. It cannot take into account the yaw imparted by the thrower or the rate of spin, velocity, angle at the moment of release etc. Now although some of these factors can be to an extent discounted or are less important than others in determining the performance of a dart in a general sense what about the specific player?
What if we could have complete information about the way an individual dart player throws?

It certainly should be technically possible to obtain this information with current technology. Tracking the movement of an object in four dimensions is not a huge problem. And tracking this information repeatedly should reveal both average and extremes of variation in throw.
Now lets add to this bio-mechanical information about the player.

Then it should be possible to design a dart and its attendant flight and shaft combination to provide not just a generally great dart but the best possible dart for that player.

One day maybe this will happen as players take more and more note of undeniable scientific advantage and rely less and less on gut feeling.

Posted by Red at 19:15 on 8th August 2008

"BACKWARDS"
How much is our grip and throw created to deal with the darts we buy rather than the darts we buy the best suited to our throw.
It occurs to me that the way we select darts is backwards. Often the first darts we buy are a) ones we like the look of. b) the ones used by our favourite player. c) chosen for some other equally random and illogical reason. We then learn to throw with these darts. The dart itself must then surely inform the way our throw and especially our grip develops.
Logic seems to play very little part in our selections.
For instance I myself currently use a John Lowe dart, and why not I very much admire John and think the darts themselves excellent. They are not however my favourite darts of all time, that accolade goes to the Unicorn Big Cliff Lazarenko dart. I liked the shape balance feel grip and everything about those darts. I am still trying to get another set! Is this however logical?
Let''s say that the Sigma dart is the very best dart that you can possibly buy, the best quality the most accurate, most likely to hit the target dart in the world!
Logically shouldn''t I want a set of them and then learn to throw with them as I know for a certainty that they will yield a better result, fly truer, deviate from the target less than any other dart.
And yet I still want a set of Big Cliff darts, sorry but I do, even though I know I am not being logical and not giving myself the best possible darts to play with.
I wonder why I am being so illogical?

Posted by Red at 15:02 on 9th August 2008

As an interesting exercise I thought I would see how many different darts I have used over the years. Helped by looking through the various Unicorn Books of darts available on the site. So I compiled a list, as this is something of a turning point it being both my 40th birthday and 29th year as a darts player (yes I stated when I was 11). Also I have what is popularly known as ''dartitis'' - in my case it''s not a mystery ailment it is a focus dystonia affecting my right hand and wrist.
I am therefore having to re-learn playing darts using my off hand. Probably a perfect moment to change darts once again for the best possible logical choice (a set of Sigma Pro 950s when they become available) as a birthday present to myself. So looking back I have had 1 set of brass darts and 22 sets of Unicorn Tungsten darts in the last 28 years, starting with a set of John Lowe collection torpedoes in 1980 and finishing this year with a set of John Lowe Golden World Champion darts who knows how many flights and stems have gone west in that time too.

Posted by bob at 02:48 on 10th August 2008

Great news abut the 2009 Sigmas, thanks! How does a poor fan in the USA get his hands on a set of those new 24 Pros before the fall season is half over?

Posted by Red at 11:05 on 10th August 2008

I wonder how long ago we first saw the hand of the UniBoffin in the Unicorn range? I was having a look through the heritage section working out what Unicorn darts I have bought over the years and as close as I could when they were available and saw a set of darts that I used to own called the Modus in the 1986 catalogue. I remember these darts especially as they were very different looking to any dart I had seen before and just had to try them. They felt very odd at first but were undeniably a great dart. So - Were these the first UniBoffin designed dart in the range? The shape and also the name are highly suggestive that the UniBoffin was at work in 1985-86. In fact these darts wouldn''t look out of place against the new Sigmas. The Sigma 800 perhaps? The Sigma Modus? Or maybe the Sigma Classic? Well I could be wrong of course, but somehow this feels like a Sigma designed with the materials available at the time to work with slik stiks and pear shaped flights, and as physics hasn''t changed in the meantime I would suggest just as good a dart now as then.

Posted by bob at 05:24 on 13th August 2008

Reading your current blg again, I wonder about the aerodynamic issues of altering the grip. Did the addition of extra and more aggressive cuts change the way air flowed over the surface in a meaningful way such that compensations had to be made?

Posted by Warren at 22:57 on 14th August 2008

G''Day uniBoffin! Yes I know, been awhile since I have been in here. havent been the best health wise but am on the mend.
I have been getting some feedback from a few Sigma users here in Australia of late and it seems they have found just one thing wrong with the product... the square cut on the nose!
I know that is a trademark of Unicorns designs but for those who have talked to me they have found due to the very deep tapered nose (compared to other darts) the square cut tends to smash thier flights on the way through to the board. Both said players have had the sharpe edge rounded off on the barrels and are now happy chappies!

That was something I had never thought of until they told me, can be devastating when close grouping all the time unless you have a big supply of flights!

Hope this may be of some help for future reference.

Posted by Red at 23:02 on 16th August 2008

Hey Bob - going on the previous UniBoffin articles and some basic reading up, it would seem that aerodynamic drag is not that significant a factor for darts. Picking up on another comment that aerodynamically we are in the same sort of range as insect wings, I would guess that boundary layer flow over the barrel is completely laminar and you would need some very serious grooving (big and wide in one groove) to cause turbulent flow on a object this size. Interestingly enough it has been speculated that insect wings i.e. the dragonfly wing which has a saw tooth surface forms eddies in the troughs that help form turbulent flow more quickly and keep the airflow from separating. This would perhaps somewhat counter intuitively suggest that the grooves would improve airflow and not reduce it. If I''m wrong here I''m sure the Boffin will set things right. My main point here is that I think the grooves are probably not a factor.

Posted by Dave Burgess at 12:55 on 18th August 2008

Can you confirm the dimensions of the Sigma barrels? Also, for that matter, the new "Gripper" barrels. It seems the only way to find this out currently is on the Unilab selector.

Posted by Carey Bock at 13:37 on 26th August 2008

What''s with the Phil Taylor "phase 5" darts? Does he actually use these?? To me, they simply look like a longer version of an old John Lowe barrel????

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