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I give in – again!

Posted by UniBoffin at 15:30 on 6th October 2011 in UniBlog

I give in – again!

As a mathematician, I suppose it’s predictable that the apparent illogic behind some English words would bother me – why does inflammable mean the same as flammable, for example? In the words of a learned student of grammar I once knew, “it just don’t make no sense”.

I mention this because another such lexicographic dichotomy (great phrase – wonder what it means?) reared its head this month when I decided to recapitulate the salient features of dart aerodynamics. This was not only because I haven’t really explained some of them properly since near the start of these blogs four years ago, but also because, when I did the first time, I fear I may have over-cooked the flight dynamics jargon a little too much for some tastes.

I’m not really going to apologise for that, though – it was a question of scientific credibility. If I hadn’t started off sounding like an escapee from a NASA Incomprehensibility Unit, the rumours that I was just an invention of Unicorn’s marketing department might have gained an even larger following!

But back at my linguistic concerns over “recapitulating”, that means, of course, “restating the main points of”, in other words “giving out – again”. That’s as opposed to “re-capitulating”, which I suppose must mean “giving in - again”. And I want to make it quite clear that, despite my recent abject surrender to a sneaky pincer attack from within and without Unicorn over designing Sigma 4s, my steadfast intention here is to do the former and not the latter.

Now we’ve cleared that up, time to turn from etymology to the rather more logical (IMHO) world of “arrerdynamics”. Whilst a dart in flight has lots of different aerodynamic forces and moments acting on it, understanding the effect of just a few of them can give you a good idea of how things work. So here goes with a handy (and relatively low jargon-count) list:

1: Drag: Easy one this. Don’t worry about it - at least not in itself. Due to pure aerodynamic drag a dart going straight will lose less than 1% of its speed on its way to the board and you won’t notice that. But, before you write this statement off as rubbish, let me qualify it by saying that what you may notice is the drag effect of the lift acting on a dart that wobbles in flight – and that can increase the velocity drop to observable levels. A scientific purist might argue that I actually mean “normal force” and not “lift” here and what I’m describing is still a drag effect, but that’s just being pedantic (“normal” in maths-speak means “at right angles”, by the way).

So my advice on drag as far as darts are concerned is to worry about lift instead!

2: Lift: Yes, it’s something to worry about. Not so much for its still small effect on the velocity drop of a wobbling dart, but for it’s ability to throw that dart off line. The vast majority of a dart’s lift comes from the flights and, in general terms, the bigger the more the lift, although “delta” flights like Sigmas are a bit of an exception in that they may not have as much lift as bigger flights at low wobble angles, but don’t lose it so easily (“stall”) as the wobble gets bigger.

So does all that mean everyone should use small flights to minimise lift? Well, no because of:

3: Overturning Moment: The aerodynamic effect that makes a dart try to fly straight after it’s released at an angle or with a “flick”. Largely a function of the lift and the distance of the flights behind the centre of gravity and without it the dart would just tumble end over end. So reduce the lift to reduce the effect of any wobble and the lower overturning moment just means more wobble! S(omeb)od(y)’s Law in action! Of course, if you’ve got a really smooth “unflicky” throw there won’t be much wobble in the first place and you may be able to get away with small flights – hence Sigma Super Pros and The Power’s DXMs.

So why not get lots of overturning moment (in magnitude – it’s negative in sign) by using small flights and a REALLY long shaft? Nice idea, but Somebody’s Law comes into action again because of:

4: Moment of Inertia: MI for short, it’s rotational motion’s equivalent of mass but with an additional length squared term in it. That length squared bit means even a little scrap of mass like a flight at the end of a long shaft can have as much MI as the far heavier barrel. And the bigger the MI the longer a dart will take to correct itself in flight, so using a long shaft to increase the overturning moment can end up being counterproductive.

So MI makes long darts with heavy shafts (and even flights!) straighten in flight more slowly.

5: Yaw wavelength: A key aerodynamic parameter of a dart, it’s a function of MI divided by overturning moment and is the distance taken to wobble first one way and then the other. Within limits it’s not dependent on the size of the wobble (it’s like a pendulum swing in this regard) or on the speed of throw. Thus, from a dart designer’s point of view, relating the yaw wavelength to the throwing distance in some way (as is done with Sigmas) can give the dart specific desirable flight characteristics over a wide range of players.


OK, reckon that’s enough aerodynamics stuff for one blog. The question now is what, in practical terms, can you take from it to help you find your perfect dart set-up? Well, the proper scientist in me would contend there are just too many complicating factors to answer that simply. However, if you really insist, I’ll give in and say you should try to achieve the right yaw wavelength for you using flights no larger than necessary to achieve that aim.

If your impact angles vary a lot from dart to dart, the right yaw wavelength will usually be the one that gives the smallest variation in them. In this case, especially if you like a long and/or heavy barrel with high MI, you’re probably best off with a light plastic shaft and larger flights such as Plus or Big Wing.

On the other hand, if your impact angles are always fairly consistent dart to dart irrespective of your flight/shaft set-up, you may find, especially if a shorter and/or lighter barrel suits you, that you get better accuracy with a heavier metal shaft and/or smaller flights.

Of course, those statements are horrible generalisations and I’m already regretting that I was so weak-willed as to give in and write them. I’m clearly getting a bad habit of doing exactly what I said I wouldn’t. First I design Sigma 4s and now, instead of sticking to recapitulating, I re-capitulated.

Yep, I gave in – again!

There are 6 comments to this post

Posted by Jeff Cruz at 11:46 on 8th October 2011

Wow, this read is really a scientific piece...I hope I can apply this into my arrows and style of play...

Here's a pint for you Uniboffin!!!

Posted by Hays Paterson at 18:49 on 8th October 2011

Wow, your erudition and prowess with prose are a marvel to read, digest aswell as decipher in our mere attempts at bettering ourselves, our games and our limited yet (now)expanding vocabulary.

We who are about to do battle, appreciate the efforts! No endeavor! No undertaking! Well you get the idea.

Keep up the good work, love reading what's next.

Posted by Mad John at 10:25 on 11th October 2011

Good Blog. Certainly more use than hearing how honeybees
would tile Rick Wakeman's floor.

Posted by Giraffe at 12:56 on 11th October 2011

A very interesting blog, I think I'll have a tinker with flight and stem combinations.
I have purchased and tried the sigma 4 dart and found them a nice dart but they are not the dart for me. I am using 23g gripper darts and at the moment think these are the ones.
Is there no way that you could design a straight barrelled sigma dart?

Posted by Warren Ackary at 10:43 on 20th October 2011

Well, interesting indeed & as you know alot of the latter blog pertains to my situation UB!

Great barrels, I tried many combinations in 2 different venue's during the day, I even used the uniLab Optimiser (going on barrel 3 gripper) most came out with the same setup, I tried the Aliflex & teardrop flight.. all I got was wobble through the air and the nose dropping down critically enough to be way under the target!

At the moment I have gone to medium Gripper11 stems & Standard (B) White Unicorn Polyflights. Interesting as I was taking a liking to the phase 5 stems & standard core flights (alot of flexability in that setup) but alas.. I had to give the stems back, so gripper11's it is and (B) stanard polyflights!

I wonder how I would fare if I could get some Unicorn Big Wings but I am afraind they will strain the back of the Gripper11 stems, make the prongs weak and shatter (again). I dont want to go to a long stem as I like to keep my glasses on my face!

See what you think & let me know:)

regards

Warren

Posted by Matt Hastwell at 22:44 on 28th October 2011

Uniboffin..... Oh great one (bows)

I have a question regarding the aerodynamic's of phase 5's with dxm flights

When designing the darts do you factor the grip and positioning of the grip into the darts design? Rightly or wrongly I covered the variables in my blog

http://matthastwell.blogspot.com/2011/10/uniboffin-in-disguise.html?m=1

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