With no wind present then the impact height or total distance travelled
for an arrow is closely connected to the arrow 'roll-over' rate. The wind
effect (headwind/tailwind) on arrow height or distance is similarly related
to the arrow rotational characteristics.
If the arrow is flying 'nose up' then the wind drag force acts to lift
the arrow with a head wind and drive the arrow down with a tail wind. The
reverse applies if the arrow is flying 'nose down'. When you shoot an arrow
its starts off flying nose up and ends up flying nose down. How much of
its flight the arrow spends nose up as opposed to nose down depends on
how fast the arrow rotates. The overall wind drag effect, i.e. does the
arrow hit lower in a headwind and higher in a tailwind or the reverse,
depends on the relative proportion of time the arrow is flying nose up
to nose down.
Suppose you start with an arrow with a high roll-over rate and then
by some means gradually reduce it. Initially the arrow will hit higher
in a tailwind and lower in a headwind. As you reduce the roll-over rate
evenually you will reach a point where the arrow starts to impact higher
in a headwind and lower in a tail wind.
The factors which affect arrow roll over rate (in order of importance)
are:
1. Amount of fletching torque
Increasing the fletching area or arrow FOC will increase the arrow roll-over rate.
2. Arrow Moment of Inertia
As the arrow gets heavier it will rotate more slowly under a given fletching torque.
3. Arrow Speed
The faster the arrow and the flatter the trajectory then the less time the arrow will have to roll
over.
Target arrows invariably carry enough fletching to tighten the arrow
groups (high arrow rotation rate) so they will hit lower in a headwind
and higher in a tail wind.
The effect of a headwind or tailwind on the height variation of where
the arrow hits are not the same. If the wind drag is pushing the arrow
up then the overall downwards acceleration is gravity minus the wind drag.
If the wind drag is pushing the arrow down then the overall downwards acceleration
is gravity plus the wind drag. The amount the arrow hits high for a given
tailwind is less then the amount the arrow hits low with the same wind
as a headwind.
The diagrams simulate how where the arrow hits varies as a
constant wind speed is rotated (at 30 degree intervals) through 360 degrees.
Diagrams are presented for a 'perfect' arrow a stiff arrow and a weak arrow.
In each case it can be seen that the drop in height for a headwind is greater
than the increase in height for a tailwind. For an explanation of the variation in horizontal displacements for the weak/stiff arrows see the section on variable tuning.
If the arrow is flying 'nose up' then the wind drag force acts to lift
the arrow with a head wind and drive the arrow down with a tail wind. The
reverse applies if the arrow is flying 'nose down'. When you shoot an arrow
its starts off flying nose up and ends up flying nose down. How much of
its flight the arrow spends nose up as opposed to nose down depends on
how fast the arrow rotates. The overall wind drag effect, i.e. does the
arrow hit lower in a headwind and higher in a tailwind or the reverse,
depends on the relative proportion of time the arrow is flying nose up
to nose down.
