Well, my last uniBlog, in which we followed my imaginary pal Nigel the Novice as he chose a set of darts, has rewardingly provoked so many comments that I’ve decided to make this an extra-long effort by responding to some of the points raised at the end of my scheduled dissertation. Apologies for taking a rain-check on a few of the questions, though – it’s not that they don’t deserve answers, it’s more because the issues raised will be covered in my future uniBlogs. I’m afraid the keen students at the front will just have to possess their souls in patience as the rest of the class progress at a steady pace - no sneaky peeking at the next chapter of the text-book yet!
So, back to the course for a while, we left good old Nigel having bought a set of Peter Manley Maestro Tungsten steel tip darts and then customised them with XL+ shafts and Big Wing flights. He did this to increase their “static margin” of stability so that they flew straighter and were forgiving of his inconsistent throwing. Now, as I said, he actually made a good choice, but he needed a bit of luck so to do. This is because choosing the dart which is aerodynamically best for a beginner - or, indeed, any player - is far more complicated than just being a question of the static margin.
I’ve previously mentioned that the angle between the direction a dart is pointing and its direction of flight is known as incidence. For aeroplanes and other flying things which have an obvious “right way up”, incidence is split into two components – upwards “pitch” and sideways “yaw”. But for things like darts which don’t really have a “right way up”, we flight dynamicists are too lazy to bother with this distinction (or to say the tiring three syllables in “incidence”), so we call both components yaw.
Now the stabilising effect of the flights means that a dart flying at an angle of yaw will not only straighten up, but also overshoot to yaw in the opposite direction. It helps to think of this motion being like a pendulum (in technical terms, a “simple harmonic motion”) because, for every dart, its yaw “pendulum” has a characteristic time which it takes to swing back and forth. And, as any clock designer knows, this time is conveniently pretty much unaffected by the size (amplitude) of the pendulum’s swing,
But, if you’re a dart designer, there’s something else which is convenient. Because the lift on the flights increases with speed through the air (it actually goes up nearly as the square), the characteristic time it takes for the dart to yaw back and forth reduces if the dart is thrown faster. However, a faster dart travels further in any given time and these two factors nicely cancel each other out so that a dart, no matter at what speed it is thrown, tends to take a more-or-less fixed characteristic distance to yaw back and forth. This distance is known as the “yaw wavelength”. If you look at the slow-motion shots of dart throws on TV, you can see the yaw wavelength in action.
In the unlikely event that our Nigel was playing darts on TV, we might see that, like many beginners, he throws with an erratic, staccato action. His darts leave his hand pointing almost in the direction of his throw, but then yaw one way and the other in varying amounts. However, if his darts have a yaw wavelength that matches his throwing distance, they’ll still tend to straighten up just as they hit the board. If they don’t, they’ll hit the board at an angle to their direction of travel.
Now, although the static margin is important in determining the yaw wavelength (the more static margin, the shorter yaw wavelength), it’s by no means the only factor. The actual amount of lift again comes into the equation, as does the transverse moment of inertia. And that’s why Nigel was a bit lucky when he chose his customised Peter Manley darts only on the basis of static margin, it just happened that they had the right amount of lift and transverse moment of inertia as well.
So if, like Nigel, you’re none too sure about what a “transverse moment of inertia” is, you might want to join me again next time.
Q & As!
Red, Chris and Warren and Centres of Pressure and Gravity:
Red has made many good points when pointing out that the CP can’t be determined by Chris’s method, but Chris is not entirely wrong all the same. His vaguely remembered technique will actually find the centre (hope you’re getting used to my UK spelling, guys!) of area of a “side elevation” of the dart, which would approximate to the CP if it were going sideways. Of course, in practice that isn’t of much interest and finding the CP at realistic yaw angles is much more difficult (and is one reason why wind tunnels are still so popular with aerodynamicists!). However, it also needn’t always be quite as complex as Red makes it sound because of something called linearised aerodynamics – but more on that another day.
As to Warren’s comments, it might help to explain that the term Centre of Pressure sensibly relates to the pressure from air flow whereas Centre of Gravity is really a misnomer as a body has a CG even if it were in space without any gravity – it’s simply the point the body tends to revolve around when unsupported. It could therefore be argued that Centre of Balance is actually a better term, but unfortunately it’s not the one that’s used!
Troy and large static margins:
As you can see from this uniBlog, Troy is right in saying that a large static margin isn’t always a good thing, but remember I said Nigel’s darts “tend to hit the board at a variety of angles”, therefore Troy’s point about “a wobble in the dart as it travels through the air is not a problem as long as it’s consistent” may be true but doesn’t apply to Nigel! As to the question about whether the dart should be held at the CG, that will be something I’ll be looking at in future uniBlogs.
Tall Eric and long darts:
uniLab will be just be the very thing to help solve Eric’s wobbly long dart problem – watch this space!