By offsetting (angling) the fletches by a millimeter or so, an arrow is induced to spin on its axis. Spin has three main advantages:
a small gyroscopic stabilizing effect,
averaging aerodynamic imbalances,
drag increase when advantageous.
The gyroscopic effect can be shown to be real but small - so small as to probably be not contribute significantly.
The spin's averaging effect on aerodynamic imbalances ensures minimal random path deviation while fish-tailing or in gusting crosswinds.
Once an arrow is up to spin speed, the arrow experiences almost no extra drag as the spinning vanes are aligned with the air flow. The arrow is acting like a turbine anemometer's impeller, spinning at a rate directly proportional to the airspeed.
However, while the arrow is coming up to spin speed, it does experience increased drag. This drag occurs at time when some fish-tailing is likely immediately on launch. Such rear-end drag will increase the dampening effect on this oscillation just when it is required, then back off when on longer needed.
Spin can have some negative effects although generally these are minor compared to the advantages:
a spinning shaft can add asymmetry to the vortex shedding,
spinning a broadhead will generally increase drag,
typically, 0.5% of arrow energy is used to spin the arrow.
A fishtailing arrow will develop a vortex wake which when combined with spin will produce a small lateral force. This force is usually much smaller than shaft lift and like shaft lift, tend to cancels out over the flight of the arrow.
The impact on broadheads is more serious. A broadhead tends to act like a fletch without offset, so when combined can work against one another. The net effect is increased drag and a possible forward movement of the center of pressure. Ideally both broadhead and fletches would have the same helical form and angular offset. One compromise is to use standard offset fletches with and "offset sharpened" broadhead, ensuring both offsets are in the same direction.
There would seem to be an opportunity to match the spin speed-up to the dampening time constant of the fish-tailing for optimal impact.
The spin up rated could be adjusted by the vane area and the arrow's rotary moment of inertia.
Like any sprung mass, an arrow will resonate when stimulated. The spring is the arrow's shaft stiffness and the mass its distributed mass plus the point, inset, fletching and nock masses.
You can get a feel for the resonance by holding the arrow vertically between the thumb and forefinger at about a 20% down from the nock and flick the shaft at its midpoint. You will feel the vibration last for several seconds. By moving you hold point up or down the resonance may be more pronounced and last longer. Your hold point is then close to a null, where your fingers can have very little dampening effect. Invert the arrow and repeat - and you will find this null closer to the point due to its extra mass. In both cases you will feel the same vibration frequency - it is the arrow's fundamental, probably in the range 5 to 20 Hz**.
The arrow's fundamental resonant frequency is closely related to the arrow's dynamic spine. Tuning the system's (i.e. bow + arrow) spine is about gainfully using the arrow's induced oscillation to avoid hitting the riser on launch and then getting the arrow traveling along the bow's center line to target.
You may have noticed the vibration is quite long lasting indicating the resonant vibration will probably last for the entire flight duration. Air flow may dampen the oscillation more quickly than the static case, but this has not been established.
The magnitude of the oscillation may be enough to induce turbulent flow over the arrow's shaft. Wind-tunnel tests have shown that lamina flow is to be expected in steady state arrow flight, however free flight drag measurement have indicated the contrary. This may be an explanation.
There are other interesting considerations with arrow spin. As the arrow spin speed increases it is likely to pass through the arrow's fundamental resonant frequency (and its harmonics). The arrow is very likely to be vibrating from the launch when this occurs. The impact is difficult to predict, but it could result in increased oscillation amplitude, even sustained oscillation and/or increased drag.
With further speculation, a three-way system may happen under the right conditions - spin + resonance + fishtailing.
Resonant systems stimulated by a synchronized driving force can sometimes have totally unexpected consequences.
**Note: Measuring Arrow Resonance
A smart phone's microphone may be used to measure the arrow's fundamental
resonant frequency ...