Joe Tapley
One of the common discussion topics in target archery is the benefit you
gain from a higher speed arrow. If you remember the Sydney Olympics
where high wind speeds were expected a lot of work was spent by
archers looking for a high wind speed solution. Many archers for example
increased their draw weight. The main benefit to be gained from higher arrow speed is the increased fletching action i.e. with the correct fletching size the arrow weathervanes faster into the net wind direction reducing lateral drift under constant or gusting winds. However other benefits from higher arrow speeds are sometimes suggested.
One frequently suggested benefit of
higher arrow speed is that the arrow spends less time in flight so the wind on it is acting for a shorter time and as a result
the arrow will experience less wind drift. At 70m distance a change in arrow speed
of 10fps will decrease the typical recurve arrow flight time by around
0.06 seconds (~5%) and reduce the absolute wind drift by something like
1cm. However as mentioned many times absolute wind drift is meaningless
as in theory the archer always aims off. One has to look at at the
variation of group size with arrow speed. There will be a benefit to
group sizes but any such benefit is going to be arrow specific and fairly small.
The
second frequently suggested benefit of higher arrow speed is that you
have a flatter trajectory. The wind speed increases with height so the
argument goes that the flatter the trajectory the lower the overall wind
speed acting on the arrow and the lower the arrow wind drift. A perfectly logical
theoretical argument but one which is never supported by any actual
data. Not surprising as when you add thermals, air turbulence, surface
conditions etc. into the mix you are in "as long as a piece of string
territory". While you can't be specific about actual wind speeds at
various heights you can give some indicative numbers.
The
variation in arrow height above ground in recurve target archery is in
the region of say 1.5 meters to 6 meters above the ground (determined
basically by distance shot and arrow launch speed).
Estimation of
variation of wind speed with height is a requirement for many
applications. The pattern is to define a reference height for
measurement/specification and use an algorithm to adjust any measured
wind speed to that reference height. For example in the UK the
Meteorological Office reference height is 10 meters above ground level
and this is the "published" wind speed on weather forecasts etc. If wind
speed is measured (instrumentally) at a different height then this it is adjusted to the
10 meter reference height via a published algorithm. The wind speed
reference height (of 2 meters) used by the UN FAO for agricultural (crop
related) purposes is probably the best suited one to use for archery
purposes.
The following chart is based on the FOA wind speed v height algorithm FAO Wind Speed Reference. It suits the arrow height range well and includes the 10 meter (Met. Office) reference height.
So for example from the chart if you multiply the Met. Office published wind speed by 0.75 it gives the 2 meter height wind speed reference value. You can then use the appropriate coefficient, read from the chart, to estimate the wind speed at any height up to 10 meters. (If you want to calculate the wind speed variation with arrow height, e.g. for inclusion in a trajectory calculation, then the algorithm is in the above FAO reference document).
For example if the Met. Office wind speed is 5 m/s then the FAO 2 metre wind speed reference is 5*0.75 = 3.75 m/s. For say 5 meters in height the coefficient from the graph is 0.84 so the wind speed at a height of 5 meters is 3.75/0.84 = 4.46 m/s.
To make a quick guess at the effect of arrow speed on arrow wind drift in terms of a flatter trajectory then lets do the following comparison between arrows launched at 190fps and 200fps. Both arrows start at a height of 150 cms above ground. The 190fps arrow maximum height is around 360cms and let's take the average height above ground as 255cms. The 200fps arrow maximum height is around 330cms and let's take the average height above ground as 240cms.
If the Met. office wind speed is 8 m/s then the estimated wind speed at 255cms height is 6.32m/s and the wind speed at 240cms height is 6.19m/s. So let's apply these two values as average wind speeds over the 70m flight of the arrows for both launch speeds removing the effect of.gravity. Putting these two wind speeds into the arrow flight simulator gives a consequent difference in absolute wind drift between the two arrows at 70m relating to the height variation of around 1cm or less. Again absolute wind drift is really irrelevant and difference in group size is going to be small and arrow specific.