So how is everyone getting on with our wade into the murky depths of dart flight dynamics? The water’s getting a bit deeper now, but, judging by your comments (as last time, I’ve answered some of them in a Q&A session at the end), at least a few of you are staying with me! For those others who want to learn more but feel that all this stuff about static margins and yaw wavelengths is starting to go a bit over their head, don’t give up yet! If referring back to my earlier uniBlogs doesn’t clear things up, just use the comment facility to ask a question. And don’t worry if you think it might be too simple to be worth posting - I’ve always preferred easy questions to difficult ones!
Right, where did I get to last time? Oh yes, transverse moment of inertia. Well, simply put, moment of inertia, or MI, is the rotational equivalent of mass (which I’m going to prattle on about for a minute, so if you already know about it, just skip the next para).
Now the mass of an object is defined by the amount of force needed to accelerate it. When that force is gravity at the Earth’s surface, the mass becomes numerically the same as the weight, but the two shouldn’t be confused. Darts with a mass of 24 grams might also weigh 24 grams in everyday life, but if Neil Armstrong had taken them to the moon he would have found that there they only weighed around 4 grams. Their mass would still have been 24 grams, though, and it would have taken the same force as on Earth to throw them at a given speed (not that they would stick in a lunar board straight – no air on the moon means no lift on the flights and hence no stability).
So the mass of an object is, unlike its weight, a universal constant quantity (unless you’re Einstein, but that’s another story) defined by the difficulty of accelerating it. And moment of inertia, or MI, is the equivalent for spinning it. But there’s a catch. Mass is independent of direction, MI isn’t. When unsupported, as it is in flight, a dart will tend to rotate about its CG, but that could mean around the axis which runs down the middle of the barrel or around an axis which goes through the CG from the side.
As it’s much easier to spin a dart around the former than the latter, a dart has two very different MIs. The one which goes down the barrel axis is called the polar or, more unimaginatively, the axial MI and isn’t of much interest to us. The one I’m going to talk about is the one which goes across and this is called the transverse MI.
We saw last time how the yawing of a dart could be likened to a pendulum. And, just as a longer pendulum swings more slowly, so a longer dart tends to yaw more slowly, not just because it’s longer, but because its transverse MI is greater. Now those of you who have been paying attention might have thought that the yaw wavelength on a longer dart would be shorter because the flights will be further behind the CG, giving it a bigger static margin. However, although the static margin of a dart might tend to increase with its length, the MI tends to increase with the square of the length and can thus outvote the static margin when it comes to determining yaw wavelength.
So the MI of a dart is an important factor in determining how it flies. Next time we’ll see how the weight of the shaft and even the flights can make a big difference to the MI of the much heavier barrel. Until then, Merry Christmas and Happy New Year!
Q & As!
Chris and Warren and dimpled flights:
You guys have opened a bit of a Pandora’s box here! I’ll be looking at the aerodynamics of flights in the future, so for the moment I’ll just confirm that Chris is right in suspecting that the dimples won’t do much for the drag. Without getting too technical and going on about super and sub-critical Reynolds numbers and other aerodynamicist jargon, it’s worth explaining that spheres in general (and golf balls in particular) are a very special case where, under the right circumstances, surface roughness can make a huge difference to drag by minimising the extent of the low-pressure wake. This can reduce the drag coefficient by as much as a factor of four, which is why a golf ball without dimples wouldn’t go very far.
For darts, on the other hand, aerodynamic drag is actually not that significant a factor - rigidity and flatness of the flights are much more important, as Warren seems to have been told. At the risk of confusing the situation, I could add that some past research had suggested that roughness might help the air flow over insect wings, which are similar in scale to dart flights, whereas on aircraft wings, for example, it generally makes it worse. However, more recent work has not really supported that theory.
Warren and Phil Taylor and yaw:
When a dart hits the board with a relatively small angle of yaw, it’s easier to see if it’s sideways than if it’s vertical because there’s no trajectory angle due to gravity to confuse the situation. Thus any darts which are not released smoothly will be more obvious if they yaw sideways. Let’s suppose the yaw wavelength of Warren’s darts is somewhat greater than his throwing distance (which is usual) and his errant finger sometimes causes one to start off yawing to the right, say. The dart’s yaw “pendulum” will first swing straight and then the dart will hit the board yawing with the point to the left. Phil Taylor may occasionally do this as well, but I would say that the main characteristic of his throw is that he starts his darts yawing downwards, which means that they hit the board yawing upwards, which compensates for the downward angle of the trajectory and makes them land nearly horizontally, perhaps helping him to have a better view of the bed for the next dart.
Tall Eric and his long darts again:
I have a little Christmas present for Eric – a sneak preview of a uniLab result. For a tall person of good standard and fairly conventional style who throws 18 gram (44mm) Stretch 80% tungsten soft tip darts, my pre-release version of uniLab suggests using a CheckOut medium length shaft (eg no 78565 in the Unicorn catalogue) with Q Slim flights (eg no77343 in the last year’s catalogue). However, as the latter are not at the moment supplied from the factory separately but only as part of a set (for example with Striker soft tip darts), you might have some difficulty in getting them, in which case Checkout Xtras (eg no 77485) would be a good alternative. Warren will no doubt be interested both that these are the shape he was suggesting and that his long dart/short shaft and vice-versa argument is linked to the moment of inertia topic discussed in this uniBlog and due to be looked at further in the next one.