It is a common practice to fit fletchings at an angle to the shaft or
use fletchings which have a built in angle to cause the arrow to spin in
flight around the shaft axis. Why do this and how does it work?
An individual arrow can have a bias to curve in flight. This may result
from the arrow not being perfectly symmetrical e.g. slightly bent, or from
having a non symmetrical pile e.g. a broadhead. When the arrow flies, any
asymmetry will result in a torque on the arrow increasing the offset angle
and resulting in a curved flight path. By making the arrow spin around
its axis the curved flight path is converted into a helical path as the
'bias' is rotated in all directions. This approach works equally well with
all arrows, all with different biases and tightens the arrow groups. The
diagram illustrates the effect on arrow flight path of arrow spinning.
To describe how angling the fletchings spins an arrow the simple case
of the airflow being directly along the shaft, i.e. the arrow flies perfectly
straight, is used. In this situation the drag force on the fletching surface
does not generate any 'straightening' torque on the arrow, it's already
straight.. Because the fletching is at an angle the direction of the fletching
drag force is no longer at a right angle to the shaft. A component of the
drag force on the fletching acts to slow the arrow down and a component
generates a torque on each fletching at a right angle to the shaft which
acts to rotationally accelerate the arrow i.e. makes it spin. The diagrams illustrate this effect.
The arrow starts off with no rotation and then the spin rate increases
as the arrow is rotationally accelerated. As the arrow flies through the
air it slows down due to drag effects. Initially the direction of the net
air flow onto the fletching is along the arrow shaft. However as the arrow
spins faster and faster the fletching itself is moving faster and faster
at a right angle to the shaft. The net air flow direction is the sum of
the air velocity and the fletching velocity. As the spin rate increases
therefore the net air flow direction rotates until at some combination
of arrow speed and arrow RPM the direction of the net air flow will be
parallel to the fletching at which point the spin acceleration will be
zero. The arrow will have reached a 'terminal' RPM and will spin no faster.
A second effect is that if the arrow is spinning fast enough with respect
to the arrow speed each fletching begins running in the turbulent airflow
of the fletching ahead. This significantly reduces the drag force on the
fletching and hence the spin acceleration.
Attached is a very crude arrow spin calculator. It works
on the basis of the arrow being mounted on bearings in a wind tunnel and offset
flat vanes are used to make the arrow spin.
The above case unfortunately bears little resemblence to what actually
happens to an arrow in flight when you spin it. As usual the real situation
is highly complicated. The two main complications are as follows. Firstly
an actual arrow in flight is never flying straight, it is always oscillating
about. When the arrow has an offset angle a large chunk of the fletching
drag is acting to straighten the arrow up not spin it. The spin acceleration
is constantly changing as the 'spin drag' changes. The second related effect
is that as the arrow oscillates about, the direction of the air flow from
the arrow velocity keeps changing e.g. suppose the arrow swings about from
plus four degrees to minus four degrees and the fletchings are fitted at
2 degrees to the shaft. The air flow on fletching will vary from plus six
degrees to minus two degrees. Not only does the the direction of
the air flow continuously vary, part of the time it is acting on the 'back'
of the fletching braking the spin. For a real arrow the RPM will be considerably
less than for the simple example given above and the RPM will go up and
down in an oscillatory way as the arrow fishtails, though increasing overall.
In the real arrow spinning case the drag on the fletchings has three
effects:
- Straighting the arrow up (normal function)
- Spinning the arrow
- Slowing the arrow down
The following diagrams illustrate how these three different effects
occur.
In the diagram for simplicity (OK I can't draw!) the arrow only
has 2 fletchings attached at 180 degrees to the shaft and we are looking
down on a transparent arrow. Fletchings are marked in red, the drag on
the fletching in purple and the direction of the air flow onto the fletching
in blue. Because of the angle at which the fletching is attached to the
shaft the angle at which the air flow impinges on the lower shaft is bigger
than the equivalent angle on the upper shaft. As a consequence the total
drag on the bottom fletching is bigger than the total drag on the top fletching.
Because the fletchings are at an angle to the shaft the direction of
the fletching drag is no longer at a right angle to the shaft. This results
in a component of the drag force acting through the arrow's centre of gravity
which acts to move the arrow as whole. Note that in the above diagram this
drag force component acts to accelerate the arrow in the case of the top
fletching and decelerate the arrow in the case of the bottom fletching.
The net effect is to decelerate the arrow as the lower fletching drag component
is bigger than for the upper fletching. Whether the fletching drag component
acts to accelerate or decelerate the arrow depends on the fletching angle
and the arrow offset angle. For a good flying arrow with small offset angles
in general these drag components will subtract rather then add. The end
result is that the overall drag effect from angling the fletchings in terms
of slowing the arrow down is much smaller then might be envisaged.
With the top fletching the drag force component at a right angle to
the shaft acts to rotate the arrow in an anti-clockwise direction
(looking at the arrow from the front). The equivalent drag force component
on the bottom fletching acts to rotate the arrow in a clockwise direction.
This drag force component is larger on the bottom fletching then on the
top fletching.
The drag force torque on the top fletching is balanced by an equal an opposite torque on the bottom fletching. The net result is a drag force
rotating the arrow about a rotation axis - the normal fletching action, straightening the arrow up. There remains some drag force torque on the bottom
fletching with with no counterbalancing torque from the top fletching and this acts to spin the arrow in a clockwise direction as viewed from the front. As you
increase the angle the fletching is attached to the shaft you increase the difference between the total drag on each fletching. The net result as the angle
increases is that less fletching drag is used for the normal fletching action and more to spin the arrow.
The division between drag that is used to straighten the arrow and drag
that is used to spin the arrow is determined by the fletching to shaft
angle (fixed) and the arrow's offset angle (variable). The following graph
illustrates how the ratio of 'fletching' drag to spin drag varies with
arrow offset angle.
Until the arrow offset angle reaches the fletching angle all the drag
goes into spinning the arrow (were ignoring the drag that slows the arrow
down) and none into straightening it. (Note this only applies to a straight
fletching fixed at an angle, fletchings that are mainly straight but have
a 'bent' section like spin-wings always provide some straighting drag).
Once the offset angle exceeds the fletching angle drag is shared between
the fletching and spin functions. What is fortuitous is that as the offset
angle increases the proportion of drag used for fletching action increases
over that for spinning. It's like having an onboard pilot saying 'Hey guys
were at a hell of angle here, lets switch drag from spinning us to straightening
us up'. A consequence of this effect is that the design of the 'spin fletching'
affects the arrow fishtailing period so in theory it can be used for a
fine tuning of arrow groups at specific distances. This variation in spin
drag as the arrow fishtails also impacts on the ocillatory nature in the
growth of of the arrow spin RPM over time.
Spinning an arrow requires energy. The energy source for arrow spinning comes from the fletching
potential energy not from the arrow linear kinetic energy. So spinning an arrow has no direct
impact on the speed of an arrow. If anything you get a benefit because by draining off fletching
potential energy into spin energy you reduce the fishtailing amplitude of the arrow. There is an indirect
effect of arrow spinning on arrow speed and this is one of the areas where curved vanes give better
performance than flat vanes. Of course with an offset flat vane you do lose kinetic energy as the fletching is at an angle to the shaft
All the above discussion relates to using flat vanes set at an offset to the shaft to generate
spin. Curved vanes like spin wings use a different mechanism to generate spin. Instead of varying the
angle of the air flow onto different fletchings (flat vanes) to get different drag forces between
fletchings, curved vanes use the variation in drag efficiency between fletchings (different drag coefficients)
to vary the drag force between fletchings. Curved vanes do not require an offset to the shaft to generate
spin. As a consequence curved vane surfaces do not necessarily generate any drag slowing the arrow down.
To get the 'right amount' of spin with a curved vane, not too slow and not to fast, you can either use
a large vane area or combine a smaller curved vane with some offset. The latter is the usual option as
very large vane surfaces become sensitive to wind variations. However for the same amount of spin, less
offset will be required for the curved vane than for a flat one (and the larger the curved vane the lower
the required offset) so for equivalent sized vanes curved vanes generate less drag slowing the arrow up
then flat vanes.
You often get the comment that an arrow does not start to spin until
its x metres away from the bow as though at some point a 'start to spin'
switch is thrown. Not exactly true, the arrow starts to spin as soon as
it leaves the string. What happens is that the archers paradox effect drastically
reduces the growth in spin rate. When the arrow leaves the bow its flexing
back and forth at a fairly high rate and with a considerable degree of
bending. It takes a while/distance for drag to damp this vibration out.
The effect on spin is the same as for the arrow fishtailing described above
(alternating spin acceleration and spin braking) only at a much higher
frequency. The net result is that initially there is only a very slow growth
in the arrow rate of spin.
The graph illustrates how the overall spin RPM of the arrow would
grow over time/distance based on the previous discussion; an initial slow
growth rate (archers paradox effect) and then increasing overall with occasional
drops resulting from fishtailing initiated spin braking. Ultimately, if
the flight was long enough, the arrow would reach a terminal spin RPM for
the reasons described above.
Most of the top archers using spin wing fletchings. We can assume that
the arrows they use are as perfect as they can make them so what is the
point of spinning them. Hold an arrow sideways with the (straight) fletchings
in front of your face and slowly rotate the arrow. You see a variation
in the 'effective area' of the fletchings as you rotate the arrow. The
overall area varies, sometimes there is more fletching above the shaft
then below and vice versa. The 'third' fletching when pointing towards
you varies in angle and how much it screens the fletching behind it. All
these variations result in how the fletching works in straightening the
arrow being dependent on what orientation the arrow has. When more fletching
area is one side of the shaft then the other some of the fletching
drag goes into rotating the arrow not straightening it. How much and at
what angle one fletching is screened by another will effect the overall
drag. The end result is that with straight fletchings there is an inherent
unpredictability about how the fletchings will act and therefore how the
arrow will fly which makes a contribution to increasing arrow group size.
When you spin the arrow these variations are smoothed out so overall the
behaviour of the fletchings is more consistent leading to better arrow
groups.
There are a number of negative aspects to spinning an arrow. Experience
has shown that the benefits outweigh the negatives even for target arrows
for the case where you want to shoot with less than perfect arrows.
Using fletching drag to spin the arrow means you are not using it to
straighten the arrow. The net loss of arrow speed due to additional drag
is an accepted consequence of spinning.
The behaviour of the air flow over a spinning shaft generates a sideways
force from an effect called the Magnus effect. This is assumed to have a relatively minor effect on the arrow behaviour.
The spinning arrow will generate gyroscopic effects (ref).
If the arrow is at an angle and the fletching torque tries to straighten the arrow up then any gyroscopic effect will try to prevent the fletchings
doing their job and instead try to rotate the arrow at a right angle to
what the fletching is trying to do. In practice the fletchings are much
stronger than any gyro effect. The net effect would be to put a bit of
a wobble on the arrow which would get lost in the helical flight path.
The direction of rotation of the spinning arrow makes no difference
to the flight of the arrow. The direction of rotation does affect the clearance
between arrow and rest/bow when being shot which is why it is generally
recommended to have the fletchings orientated so that the arrow spin is
clockwise when viewed from the rear. The most likely fletching to contact
the bow is the lower fletching on the bow side. Bearing in mind that the
rear of the arrow is bending away from the bow as it goes past it then
the front of this fletching is the most likely contact point with the bow.
The diagram illustrates that for a straight fletching attached
at an angle, the clearance between the front of this fletching and say
the arrow rest is larger if the fletching is angled away from it. (clockwise
rotation viewed from the back). In the case of spin wing type vanes (attached
straight on the shaft) having the 'curly bit' going away from the bow gives
more clearance (again clockwise rotation viewed from the back).
It is sometimes stated that it is the physical rotation of the arrow
(and fletching) that provides better clearance with one direction of rotation
over the other. While the arrow does start to spin as soon as it leaves
the string the actual amount the fletchings rotate between leaving the
string and passing the bow is so small as to be irrelevant. The following
calculation illustrates this:
Supppose the distance the arrow travels between leaving the string and
passing the bow is 20 centimetres (roughly the bracing height)and the arrow
speed is a typical 55 metres/sec. Suppose the distance from the arrow axis
to the top of the fletchings is 3 centimetres (the radius of fletching
rotation).
The time between the arrow leaving the string and passing the bow
= distance/speed = 20/5500 = 0.004 seconds.
The extra clearance we get from arrow rotation is the amount the top
of the fletching rotates. Let's take 0.5 millimetre of movement as being
the smallest amount that is worth considering as 'extra clearance'.
The amount of arrow revolution needed for 0.5mm displacement
(circumference = 2*Pi*radius) = 0.05/2*Pi*3 = 0.0027 revolutions
Remembering your school physics that distance = acceleration*time*time/2,
the required arrow angular acceleration to give 0.5 millimetres of movement
= 2*revolutions/time*time = 2*0.0027/(0.004*0.004) = 337.5 revs/sec squared
As velocity = acceleration*time the required arrow spin revolutions
per second as the fletchings pass the bow to give 0.5 mm clearance
= 337.5*.004 = 1.35 revolutions per second ( or 81 RPM)
In other words to get 0.5 millimetres extra clearance from arrow rotation
the arrow would need to be spinning at 81 RPM as the fletchings pass the
bow. In practice the arrow RPM is much lower than this. The actual amount
of fletching movement is so small that it cannot be seen on most generally
available high speed films of arrows being shot.
An individual arrow can have a bias to curve in flight. This may result
from the arrow not being perfectly symmetrical e.g. slightly bent, or from
having a non symmetrical pile e.g. a broadhead. When the arrow flies, any
asymmetry will result in a torque on the arrow increasing the offset angle
and resulting in a curved flight path. By making the arrow spin around
its axis the curved flight path is converted into a helical path as the
'bias' is rotated in all directions. This approach works equally well with
all arrows, all with different biases and tightens the arrow groups. The
diagram illustrates the effect on arrow flight path of arrow spinning.
To describe how angling the fletchings spins an arrow the simple case
of the airflow being directly along the shaft, i.e. the arrow flies perfectly
straight, is used. In this situation the drag force on the fletching surface
does not generate any 'straightening' torque on the arrow, it's already
straight.. Because the fletching is at an angle the direction of the fletching
drag force is no longer at a right angle to the shaft. A component of the
drag force on the fletching acts to slow the arrow down and a component
generates a torque on each fletching at a right angle to the shaft which
acts to rotationally accelerate the arrow i.e. makes it spin. The diagrams illustrate this effect.
The arrow starts off with no rotation and then the spin rate increases
as the arrow is rotationally accelerated. As the arrow flies through the
air it slows down due to drag effects. Initially the direction of the net
air flow onto the fletching is along the arrow shaft. However as the arrow
spins faster and faster the fletching itself is moving faster and faster
at a right angle to the shaft. The net air flow direction is the sum of
the air velocity and the fletching velocity. As the spin rate increases
therefore the net air flow direction rotates until at some combination
of arrow speed and arrow RPM the direction of the net air flow will be
parallel to the fletching at which point the spin acceleration will be
zero. The arrow will have reached a 'terminal' RPM and will spin no faster.
A second effect is that if the arrow is spinning fast enough with respect
to the arrow speed each fletching begins running in the turbulent airflow
of the fletching ahead. This significantly reduces the drag force on the
fletching and hence the spin acceleration.
In the diagram for simplicity (OK I can't draw!) the arrow only
has 2 fletchings attached at 180 degrees to the shaft and we are looking
down on a transparent arrow. Fletchings are marked in red, the drag on
the fletching in purple and the direction of the air flow onto the fletching
in blue. Because of the angle at which the fletching is attached to the
shaft the angle at which the air flow impinges on the lower shaft is bigger
than the equivalent angle on the upper shaft. As a consequence the total
drag on the bottom fletching is bigger than the total drag on the top fletching.
With the top fletching the drag force component at a right angle to
the shaft acts to rotate the arrow in an anti-clockwise direction
(looking at the arrow from the front). The equivalent drag force component
on the bottom fletching acts to rotate the arrow in a clockwise direction.
This drag force component is larger on the bottom fletching then on the
top fletching.
The division between drag that is used to straighten the arrow and drag
that is used to spin the arrow is determined by the fletching to shaft
angle (fixed) and the arrow's offset angle (variable). The following graph
illustrates how the ratio of 'fletching' drag to spin drag varies with
arrow offset angle.
The graph illustrates how the overall spin RPM of the arrow would
grow over time/distance based on the previous discussion; an initial slow
growth rate (archers paradox effect) and then increasing overall with occasional
drops resulting from fishtailing initiated spin braking. Ultimately, if
the flight was long enough, the arrow would reach a terminal spin RPM for
the reasons described above.
The diagram illustrates that for a straight fletching attached
at an angle, the clearance between the front of this fletching and say
the arrow rest is larger if the fletching is angled away from it. (clockwise
rotation viewed from the back). In the case of spin wing type vanes (attached
straight on the shaft) having the 'curly bit' going away from the bow gives
more clearance (again clockwise rotation viewed from the back).