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How Fast Does Offset or Helical Fletching Spin Your Shaft?
While this is really only of any concern for the theorist, it may be interesting to others for its curiosity value...
Once the arrows spin has attained its maximum value (which happens very quickly), the arrow then rotates freely without any drag** other than the normal skin friction over the shaft and fletches, and each point on the fletch travels through a helical path.
To complete one revolution, the arrow travels a distance of 2.pi.R/Tan è, where R is the radius of the arrow and è is the amount of offset in degrees and pi is ~ 3.1415926.
The time (t) for one revolution is thus t = 2.pi.R/VTan è, where V is the velocity of the arrow
revs per second = 1/t, revs per minute = 60/t = 60VTan è/(2.pi.R) (just plug in your own values for V, è, and R)
Here is a worked solution for you to compare the accuracy of your value against...
The rate of spin is very nearly 3,200 rpm for a 1/4" diameter arrow travelling at 200 ft/sec with 1 degree of fletch offset, and close to another 3,200 rpm for each extra degree of offset (up to a max of about 10 degrees).
** While the comment regarding drag is exactly true for a true helical fletch, it is really only very close to true for a 'straight offset' fletch, the small differences in drag for the last case only becoming apparent at extreme ranges and when the offset angle is relatively large.
What Does 'True Helical' Fletch Mean?
What it is NOT:
For a start, let us consider what archers mean when they say they have 'helical' fletching. What they are quite often referring to is the fact that they've used a helical clamp on their fletching jig to obtain their so-called 'helical' fletching.
However, we need to get rid of the notion that a helical fletching jig clamp will provide a truly helical 'drag-free' fletch. A helical clamp will very rarely (and then only coincidentally) give a true helical curve to the vane, and this is because the amount of curvature required to give a true helical profile to the vane is entirely dependent on both the:
- diameter of the shaft, and
- offset angle at the base of the vane (the angle which the clamp has been offset).
As a consequence, makers of helical clamps would thus need to specify exactly what diameter shaft and what offset angle their clamp was intended to be used with, and state that it's to be used only with that combination. Each different diameter shaft would thus need a separate helical clamp made with the required offset angle specified (at the very least a range of suitable diameters and angles would need to be given) - the number of different clamps that would need to be made to cater for all possible combinations of shaft diameters and offset angles would make this a very cost-prohibitive exercise indeed.
In point of fact, the most common usage for the ordinary helical clamp is when large fletches are used on hunting arrows with broadheads attached, and it is then most usually the case that the base of the vane is applied so that it has no offset at all, with the base being parallel to the shaft (this is also partly due to constraints imposed by the fact that the extreme length of the vane doesn't permit very much offset because the ends of the vane would then hang off the shaft) the gradual twist of the clamp then giving a 'twist' that becomes apparent near the rear outer edge of the fletch. The surface of the fletch near the base is thus guiding the arrow straight ahead in a non-rotatory fashion while the surface of the fletch nearer to the outer edge is trying to rotate it, the conflicting requirements at all the different parts of the fletch leads to drag - much like the effect a small parachute would have.
The increased drag caused by such an arrangement with a helical clamp certainly gives greater directional stability to the arrow and this usually turns out to be fine for arrows with broadheads (which implies there's an intent to use them for hunting - i.e. at relatively short ranges) but it also causes a fairly large loss in speed that is not the best for arrows that need to be shot accurately at larger distances. In short, if you are not going to be fletching hunting arrows that use broadheads, it pays to forget about the so-called helical clamp altogether, it generally causes unwanted drag - and helical it is NOT.
What it IS: (you can skip this semi-technical bit if you like)
Let us look at a very common object - a bolt. The thread on an ordinary bolt follows a helical path, this thread is offset at a constant angle from the bolt, and is usually referred to in terms of threads per unit length (e.g. in imperial units, threads per inch, or TPI) - you don't need much imagination to guess what would happen if the angle of the thread on a constant diameter bolt changed from where it was (say) 20 threads per inch to 25 threads per inch - friction would very quickly cause any 20 TPI nut to seize up when it got to the 25 TPI section of the bolt. It is this concept of 'a constant angle' for a constant diameter that forms the basis for anything that is helical.
With arrow fletches/vanes we are basically looking at an enormous 'thread' that sticks out very much further than the threads on any bolt do, so to make sure we get it right we need to get an idea of what shape the fletch needs to be for it to turn and screw freely through the air without any friction (other than ordinary skin friction) that may cause it to 'seize' up - note that we can consider the air to be a very large 'nut' for this purpose.
For a start, we need every part of the vane - from base to outer edge - to also follow a helical path that's always in line with the base of the vane i.e. we need to consider the same number of TPI at many different radii, from vane base to outer edge if we want it to turn freely as a unit.
Next we need to look at the fact that the outer edge of the vane is a larger distance from the centre of the shaft and it has thus has much further to travel for each turn than the base of the vane and (if you can follow the next bit of maths) you'll see it thus also needs to be at a greater angle.
For the technically minded... From the previous equations (the distance Vt = 2.pi.R/Tan è and t = 2.pi.R/VTan è) given for the amount of spin in the shaft, we see that for the arrow travels forward any given distance Vt at a fairly constant speed. To simplify things, it help you to consider the distance Vt when it is the distance required for the arrow to complete one revolution. When the arrow completes one revolution, each individual part of it has made one complete turn and if we look at parts of the vane perpendicular to the base (but at all the radii greater than the radius at the base) then the formulae tells us that, at all greater radii (R'), Tan è (and hence the angle è') needs to be greater.
What the previous bit means is that if a short section of vane at the base of the vane is at an offset angle è, then the same short section of vane at the outer edge of the vane perpendicular to the shaft that's moving faster must be at a greater angle than the bases offset angle è so as to eliminate any drag, that is, in its entirety, this short cross-sectional "slice" of the vane perpendicular to the shaft has a twist in it. Note that this is the same consideration that needs to be taken into account when manufacturing aeroplane propellors.
We should now see that the amount of 'twist' or 'curl' or - to coin a term - 'helicurl' the vane needs to have is thus primarily dependent on the offset angle that was given to the base of the vane (which essentially sets the number of TPI for us) and it is then further dependent on the greater radius at which this same number of TPI is later going to be considered, with the curl being such that the angle on the 'outside' of the vane is greater then the initial offset angle on the 'inside'.
While not immediately obvious, it should now be seen that a 'straight-fletch' (that has no offset) applied with a straight fletching clamp can also be described as a helical fletch - it's simply the special case where the offset angle è is zero, and the greater angle required on the outside of the vane is then equal to zero plus zero, which also equals zero, leading to the fact that the required helicurl in this particular case can also be described as a completely flat surface.
We can thus see that depending on the amount of offset angle, a helicurl can look like anything from a completely flat surface on one extreme to a greatly corkscrewed type surface on the other extreme.
I hope this background technical information to this point has not confused you, but you'll see in the next article that obtaining a true helical fletch is not at all difficult - in fact just using a small amount of offset on a straight clamp will provide a helical fletch provided only that a firm pressure is applied to the fletching clamp when gluing the vanes to the shaft.
Obtaining a True Helical Fletch:
While the previous discussion makes helical fletching seem very complicated and technical, in practice it's relatively simple to get a true helical fletch.
To be truly helical, the base of the vane only needs to be in full contact with, and perpendicular to, the shaft at every point that they meet. For small offset angles, when the clamp is pushed down firmly while gluing there is enough flexibility in the vane for this contact to occur, that is, the pressure will force the base of the vane to conform to the shape of the shaft.
But when you go for large offset angles, the front and rear of the vane tends to 'hang off' the shaft and not enough pressure can be applied to remedy this situation. In this case, for the vane to be in full contact with the shaft you need to take to your fletching jig clamp with a round file that's about the same diameter as the arrow, and at the angle you want, and file the clamp down with a straight back and forth motion so that it can then press down equally on the fletch at all points where the base of the fletch (both sides) meets the shaft.In both the above cases, after the glue has set and the clamp has been removed, the vane will then spring back to align itself vertical to its glued base and follow a true helical contour.
This is not a very clear picture, but it gives the idea of what is meant about filing the fletch clamp when you want to offset your fletches at a fairly large angle...
The completed fletch will look something like this...
You can check if it's really helical by following this procedure: View the fletch from directly above and perpendicular to the shaft while slowly rotating the shaft, if it is truly helical, any part of the fletch where it crosses the centre of the shaft should then be directly in line with your eye...
When viewed from near the rear you'll see the distinctive 'helicurl'...
Vanes fletched like this are (given that they are flexible vanes) near enough to a true helical shape and will screw through the air with - quite literally - no more drag than the same vane when it's straight-fletched (with no offset) once the arrow spin's reached its maximum value (which happens very quickly).
Technical Note
Interestingly, while energy conservation theory tells us that there will initially be a small loss in speed because some of the arrows linear kinetic energy is being converted to rotational kinetic energy to get the arrow spinning at its maximum rate, the very same theory also tells us that when it has reached its maximum spin rate and thereafter slows down due to skin friction, the helical fletches then act like a small propellor to actually 'drive' the shaft so a little of the rotational kinetic energy is converted back to linear kinetic energy, reducing the rate at which skin friction slows it down, thus keeping the arrows velocity more constant than it otherwise would be.
Also, by using the formulas for the rate of spin that were given above, it is then a relatively simple matter to calculate the angular momentum and rotational kinetic energy of the spinning shaft and subtract this from the initial linear energy to predict exactly how much the arrow was slowed down by the conversion of linear kinetic energy to rotational kinetic energy. The most difficult part of this calculation would probably be calculating the moments of inertia for the tip and fletches, and for most purposes an approximation should suffice for this.
In Summary
As mentioned before, for small offset angles, moderate pressure on the clamp when fletching will force the flexible base of the fletch to conform to the shape of the shaft without any need to file the clamp and it will still be near enough to helical, of course the helicurl will then be much smaller ('flatter' in shape) but the exaggerated example above helps to show the shape more clearly. Tip: It also helps to have a good quality fletching jig with a strong magnet to hold the clamp so that after removing your fingers the downward pressure on the clamp can be maintained while the glue sets.
For larger offset angles, small (short) fletches are better suited because there will be less overhang to begin with, and it is best to file or machine the fletching clamp as described previously, bearing in mind that any such machining then fixes that part of the clamps as only being suitable for a relatively small range of shaft diameters and offset angles.
Note that if the vane is offset by a large amount similar to that shown in the pictures above without any pressure being applied to the clamp and it ends up being completely flat (i.e. the surface simply 'looks' flat and you don't see the distinctive curve denoting a truly helical fletch) then there most definitely WILL be an increase in drag...
Addendum
For those with an interest in such things, the vanes shown above are 1.5 inch Flex-Fletch vanes and the reason for the chosen offset angle and the two fletch configuration is because these were the result of fairly lengthy tests using a 45 lb compound bow to compare the head-to-head trajectories of various configuration (2, 3, and 4 fletch) helical flex fletches set at increasing angles against a 3 fletch configuration 2 inch red (then the largest available spin) spin-wing vanes that were further offset at a similar angle.
The configuration shown was the first one found where the flex-fletch and the spin-wings had identical trajectories at all distances up to 90 metres. Generally, as the offset angle increased the trajectory became flatter (landing higher on the target face)
Interestingly, the three fletched arrows gave exactly the same result as the two fletched ones, but the four fletched arrows didn't, they had a slightly higher trajectory (i.e. with the same sight setting they landed a couple of inches lower at ninety metres) thus showing that the 'drag' from skin friction clearly becomes a factor when the total surface area of the fletches exceeds the optimum size.
Note that in this final phase of the experiment (a two fletch configuration) we're essentially equating the trajectories of arrows with a total of 3 inches of fletching with the trajectories of arrows that have a total 6 inches of fletching - i.e. the spin-wings had roughly twice the surface area.
Directional Stability
A bare shaft generally has a centre of mass (COM) forward of the shafts physical centre. Because there is more surface area behind the COM than in front of it, the extra skin friction from the greater surface area at the rear acts as a small rudimentary rudder, or 'fletches' if you prefer, that helps a little with the shafts directional stability (which is why it is possible to use bare shafts at all).
Moving the COM further forward by using heavier points increases the proportion of the shafts surface area that is helping with directional stability in this manner - but only by a relatively small amount - much greater stability can be provided by using fletches. However, whether fletches are actually used or we rely on the shafts surface area, this stability is essentially caused by drag, so it is a form of 'drag stability'.
Aside: If we carefully consider the above (regarding COM, surface area, and heavier points) we should be able to see why the factory recommended tip weights of the skinnier carbon shafts (particularly the relatively 'heavy' shafts) are fairly heavy tips that give a COM with a much greater percentage of shaft 'front of centre' than that for comparable aluminium shafts in order just to obtain the same 'inbuilt' or 'basic' stability when the arrow's shot without fletches.
Now if (say for arguments sake) the fletches were to be placed on the front, or (as is more usually the case) if a broadhead is placed on the front, the surface area, and hence the drag, in front of the COG is increased, thus greatly reducing directional stability (this is particularly noticeable when a broadhead is not placed symmetrically on the shaft) and the arrow can easily become directionally unstable and veer off in almost any direction, particularly when it reaches a region where there is wind shear or turbulence. This is the reason why larger fletches at the rear of the shaft are required when using arrows with broadheads - the larger surface at the rear is needed to negate the guidance effect of the broadhead at the front.
Generally, to increase an arrows directional stability the usual thinking is that we need to increase the surface area of the fletches, however the increase in surface area then leads to an increase in skin friction (drag) which acts to slow the arrow down, making it difficult to get enough speed to make accurate long-range shots. As a consequence, the fletch surface area used by an archer usually becomes a compromise between accuracy (high directional stability and some loss of speed due to drag) and efficiency (low directional stabiluty and little loss of speed due to drag).
Obviously some drag stability is not only unavoidable but it's also desirable to give the arrow directional stability. This is particularly so just after the arrow has been launched, where there may be some yaw (fishtailing or porpoising) due either to strong wind, poor tuning, a bad release, or any movement of the bow-arm initiated when the arrow was still on the string. Excessive yawing not only leads to inaccuracy, but because the arrow is partially 'side-on' to the air flow when it's yawing, it also causes the arrow to lose speed, so it is during the early stages of its flight where there is the greatest need for directional stability.
Ideally then, using drag stability of straight fletches only, one obvious solution would be to use fairly large fletches with a large amount of drag during the very first phase of the arrows flight. But after this first phase the increased drag only acts as a parachute that causes loss of speed due to excessive skin friction, so, to reach the longer distances we then need to prevent an excessive loss of speed once any yawing has ceased. So we really need some way of then gradually decreasing drag, for example, by having some way of making the fletches 'shrink' or become much smaller.
Of course the idea of having fletches that vary in size during flight is an utterly impractical and unnecessary idea when we can easily increase drag as much as we like during the initial stages of the arrows flight by the simple expedient of putting the vanes on at an angle (i.e. with an 'offset') which will, before the vanes start spinning, cause the desired extra drag and parachute effects at the initial phase of the arrows flight, then (by design) we find that both the drag and parachute effects decrease steadily as the rate of spin increases.
Moreover, spin in itself also assists with directional stability, this type of stability is due to a small gyroscopic effect that is a result of the arrow spinning, and this is a different stabilizing effect that we can call 'spin stability', and the spin stability helps resist any downrange yawing due to turbulence or wind-shear that may occur there.
Hence, if it is possible (and it is) to have a spinning arrow that has no more drag than a non-spinning arrow, the spin stability resulting from this can only increase the directional stability of the arrow - leading to the fairly well-known and easily verifiable result that spinning shafts give tighter groups than non-spinning shafts, and the greater the spin, the greater the benefits (that is, greater directional stability).It is no accident that most of the worlds top recurvers use either helical, spin-wing**, or curly** vanes. Some of the top compound archers use them also - but there are some associated clearance problems for compound bows that act as a deterrent to others, and there are some that are deterred by the fragility of spin-wing and curly vanes (the easiest and most commonly used method to induce spin) .
**The spin of both 'Spin-wing' and 'Curly' vanes is due to a similar principle to that given above for true helical vanes, that is, they both have some helical offset, but the spin is also assisted with a type of venturi effect caused by the "curl" of the vane, which varies from front to rear.
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