Take for example an arrow stuck in
a target with a wind blowing across the shaft as illustrated in the following
diagram. As the air flows around the top of the shaft the pressure of the
flow decreases to zero. At this point the air flow separates from the shaft.
Further round the shaft the pressure gradient is in the opposite direction
and so the air flow is in the opposite direction creating an eddy or air
vortex behind the shaft. The same thing happens with the air flow round
the bottom of the shaft. These air vortices drop off the back of the shaft
creating the wake behind the shaft, the main source of drag. This is the
effect known as vortex shedding. Frequently these vortices drop off
the shaft alternatively from top and bottom.(For a nice photo of this effect
click here ). When a vortex is shed it creates a
'push' across the shaft at right-angles to the overall wind direction.
The shedding of vortices alternatively from each side of the arrow therefore
generates a vibrational effect on the arrow shaft. If the frequency of
this vortex shedding is close to the natural vibration frequency of the
arrow shaft then the shaft can begin vibrating in sympathy. You often see
arrows in a target nodding up and down on a windy day. This the effect
of vortex shedding induced vibration.
When an arrow is in flight you get this vortex shedding effect from the air flow across the shaft but, if the shaft is not spinning, it has no effect on the overall arrow flight behaviour.
You can change the point at which the air flow separates from the surface either by changing the roughness of the surface, by changing the shape of the surface or by rotating the surface. The attached diagram shows the effect of changing the shape of
a cyclist's helmet. By reducing the rate of curvature at the back of the
helmet the air flow separates from the helmet much later reducing the size
of the wake and hence the drag force.
A special case of the above effect is where the separation of the air flow is not symmetrical around the back of the object. In this case the alternating 'pushes' generated when the vortices are shed do not cancel out and you get a net sideways force. The
most familiar examples of this effect are spinning a ball (e.g. tennis)
or roughing one side of a ball (cricket) to make it swerve as it flies
through the air. With a long thin object the net effect is the generation
of a torque on the object in the direction to rotate the front away from
the direction of the airflow. The effect is popularly known as the 'leaf-fall'
effect as it is this vortex shedding induced torque that makes falling
leaves oscillate back and forth as they fall. The attached diagram shows
how this effect is generated at the nock of an arrow. In this case it is
because if the arrow is at an angle to its direction of flight the effective
rate of curvature on one side is steeper than the other. As the force
is being generated at the back of the arrow it generates a significant
torque as the 'lever arm' is long, say around half a metre.
The phenomenon is easily observed if you shoot a bare shaft arrow with a very low FOC. The arrow flies in an unpredictable curve. (note: if you do this with
real arrows then take proper safety precautions). For a simple practical example of this effect I suggest shooting plastic straws with an elastic band and varying
a +ve small FOC.
The first requirement of the fletching action on an arrow (FOC or physical fetchings) is stabilize the arrow against this effect.
Vortex shedding induced torque varies with arrow velocity and offset angle in exactly the same way as the torque produced from drag on the shaft. The higher the
arrow velocity or the higher the offset angle then the higher the torque.
The lateral force from vortex shedding will also effect an arrow if the arrow is spun in flight using the fletchings. In this case a sideways force is generated
along the arrow shaft at a right angle to the plane of the air flow. This topic is discussed on the
Magnus effect page.
Take for example an arrow stuck in
a target with a wind blowing across the shaft as illustrated in the following
diagram. As the air flows around the top of the shaft the pressure of the
flow decreases to zero. At this point the air flow separates from the shaft.
Further round the shaft the pressure gradient is in the opposite direction
and so the air flow is in the opposite direction creating an eddy or air
vortex behind the shaft. The same thing happens with the air flow round
the bottom of the shaft. These air vortices drop off the back of the shaft
creating the wake behind the shaft, the main source of drag. This is the
effect known as vortex shedding. Frequently these vortices drop off
the shaft alternatively from top and bottom.(For a nice photo of this effect
click here ). When a vortex is shed it creates a
'push' across the shaft at right-angles to the overall wind direction.
The shedding of vortices alternatively from each side of the arrow therefore
generates a vibrational effect on the arrow shaft. If the frequency of
this vortex shedding is close to the natural vibration frequency of the
arrow shaft then the shaft can begin vibrating in sympathy. You often see
arrows in a target nodding up and down on a windy day. This the effect
of vortex shedding induced vibration.
You can change the point at which the air flow separates from the surface either by changing the roughness of the surface, by changing the shape of the surface or by rotating the surface. The attached diagram shows the effect of changing the shape of
a cyclist's helmet. By reducing the rate of curvature at the back of the
helmet the air flow separates from the helmet much later reducing the size
of the wake and hence the drag force.
A special case of the above effect is where the separation of the air flow is not symmetrical around the back of the object. In this case the alternating 'pushes' generated when the vortices are shed do not cancel out and you get a net sideways force. The
most familiar examples of this effect are spinning a ball (e.g. tennis)
or roughing one side of a ball (cricket) to make it swerve as it flies
through the air. With a long thin object the net effect is the generation
of a torque on the object in the direction to rotate the front away from
the direction of the airflow. The effect is popularly known as the 'leaf-fall'
effect as it is this vortex shedding induced torque that makes falling
leaves oscillate back and forth as they fall. The attached diagram shows
how this effect is generated at the nock of an arrow. In this case it is
because if the arrow is at an angle to its direction of flight the effective
rate of curvature on one side is steeper than the other. As the force
is being generated at the back of the arrow it generates a significant
torque as the 'lever arm' is long, say around half a metre.