Archery is all about reliably achieving small groups on target. This pane visually and numerically assists in determining your grouping skill and the impact of various kit changes.
The target display shows the grouping and a score at a nominated range. By default, the range and face of the target is set to the current round's longest range. This display is scored independently of the Current Round, so its range may be changed without impacting the current rounds score.
The archer's form is maintained as a horizontal and vertical angular spread. This can be derived in several ways:
Whichever method is used it can be "Applied" to become the Current Form and from there, saved as "My Form". The concepts of the "Current Round" and "Current Form" is applied throughout FlyingSticks.
FlyingSticks' shot simulator places arrows on the target based on a 2D random normal distribution. There is strong evidence to suggest this is valid, although it is possible that some archers might not be "normal" due to variations in technique. It is also assumed the horizontal and vertical distributions are independent, and if this is not the case, groups will be skewed. Overall, the random normal approach provides a realistic simulation and "feel" which can be enhanced with sound effects, enabled the Preferences panel.
This simulation approach can be run many times to gather statistically significant data and build up a score. This is the preferred method used to calculate most scores as it handles offsets and non-round groups well.
The second method for score calculation is by the rating method. Here the standard deviation for a centered round group is calculated by relatively simple algorithm, and from there this is applied to the face geometry to calculated a score. This is a fast and noise free method compared to the numeric method
Visually, FlyingSticks represents a group as an oval which on average is likely to contain five out of six shots, assuming arrows of zero shaft diameter. This becomes FlyingSticks' statistical definition of group size. This is considered a more intuitively meaningful definition and no less scientifically sound than the "one standard deviation" commonly used in the literature. The FlyingSticks group as a 2D normal distribution corresponds to ± 1.382 standard deviations, or 2.764 standard deviations from side to side.
Group oval definition
There are just two parameters that define your groups - vertical (δ in the above figure) and horizontal angular spreads. See Graphical Grouping below for more discussion.
An alternate way of describing archer's form is the World Archery 1440 Round score. This effectively summarizes everything into a single number, and it allows direct comparison to Olympians. The down side is that statistically, there are not enough arrows fired in a single 1440 Round to avoid a significant spread in the score.
Various Ratings systems are also employed and tend to be logarithmic. FlyingSticks supports the UK and Australian Ratings methodologies.
This part of the panel maintains the archer's "Current Form", the working values for use by the calculator as a whole. The form is retained as two angular spreads, horizontally and vertically.
The group horizontal angle is the angle subscribed from the left side of the group, the archer's eye and right side of the group.
The group vertical angle is the angle subscribed from the group's top, the archer's eye and group's bottom.
The units may seem confusing. The default metric is milli-radians (mrad) and the default imperial is minute of arc (MOA, a unit common in gun ballistics), which approximates to 30 mm at 100 m (1 inch at 100 yd). You can change to degrees if you wish.
These fields are loaded when an Apply button (below) is clicked or can be manually entered.
These angular spreads are the sum of wobble or shaking in the arms, variations in the anchor point, release variability, bow internal ballistics, wind gust, wind gradients, temperature and humidity "bubbles" and the many other things that contribute to an archer's Form. Many of these are separately added using the "Include:" options, the details of which are setup in the Ballistics>Atmosphere, Bow>Dimensions and Ballistics>Internal panels.
A small complication to the archer's form is the so-called Range Squared Law. This is concept that combines many uncertainties into simple model.Skew is a measure of the difference between the vertical and horizontal grouping and is equal to the vertical divided by the horizontal angles. Most novice archers begin with a high skew which progressively moves to 1 as skills are acquired.
Skew is calculated whenever an Archer's Form (Group Angular Spread) is changed but can be set manually in the range 0.1 to 10.0. The latter will automatically adjust the Archer's Form angles accordingly.
This is a logarithmic scale measure of Current Form (based on the Australian rating system). See the Rating info for details. Entering a new value changes the Width and Height fields while attempting to maintaining the Skew. The Rating calculation assumes a skew of 1.0 (i.e. a circular group), so the mean of horizontal and vertical group dimensions is used. Provided the skew is not too great the results are reasonable.
Saves the Current Form as My Form that is stored in FlyingSticks' database.
Loads My Saved Form as the new Current Form.
The round simulation takes the current archer form (i.e. the group angular standard deviations) and Range Square Law (if enabled, and uses numerical techniques to estimate the score of a full current round as selected in Groups>Round. The Current Round name is shown followed by the total number of arrows and the maximum possible score separated by a "/".
The Current Round score based on Current Form with Range Square Law (if enabled) but without wind drift or other "Includes". Also show the possible ± spread from round to round with 95% confidence. This means the score will be within the tolerance limits for 95% of rounds.
Estimated number of X's associated with the above basic score. Note: for rounds that do not have a X concept, the field will be disabled.
An estimate of your Current Round score with wind drift uncompensated for each range.
This score is estimated with the impact of selected "Includes". Ideal conditions would have all includes unchecked, including wind drift and gust, in which case it should match the Basic score above.
An estimate of the number of X's to be expected with above score along with the ± spread from round to round with 95% confidence. Note: for rounds that do not have a X concept, the field will be disabled.
The number of rounds averaged is derived from the "Max. Iteration Loops" value as set in Preferences which defaults to 500 rounds (implying 144 x 500 shots). For this reason, there is an extra decimal place of precision as the value is an average many rounds. This can be useful in statistically quantifying the impact of small changes on the score.
Recalculate a new score. As the score is evaluated using a statistical simulation, each recalculation is likely to be a little different to the previous, but usually well within the calculated confidence limits.
Direct, Round, Rating, Comprehensive and Theory. These tabs provide options for calculating your form. They are a calculator in their own right, with the results only transferred to Current Form when one of their Apply buttons is clicked.
When the Current Archer's Form is changed directly, the content of these tabs is also likely to change to more closely match the Current Form.
Each tab generally reflects the same basic data but in different forms. When the Apply button is clicked, the main focus of the tab is used to calculate the Current Form. Thus the Direct tab will apply the group size, the Rating tab the rating, while the Round and Comprehensive tabs use the numerically generated score. It will be seen that Round scores are not always the best measure of archer's form - Rating or Archer Skill Level (ASL) are better for most purposes.
A small complication to the archer's form is the so-called Range Squared Law. It has been observed that good archers tended to perform poorer at longer ranges than anticipated by a simple "Range Linear Law". So a simple range squared model is used to allow for this small effect.
The Range Squared Law correction is set up in Preferences where the group dispersion at a range of 100 meters can be defined. This is the group size for perfectly fired shots i.e. with perfect archer's form, and defines the smallest group that can be achieved.
The cause of the observed dispersion is highly debatable. Air movement and the aerodynamic complexity of a bending, spinning and vibrating arrow, are generally accepted as probable causes. As the modelling of the archer's equipment and environment is improved, answers should emerge.
The following diagram illustrates the factors that complicate grouping:
Group size changes over ranges with complicating factors. The horizontal scale is significantly exaggerated.
The ideal grouping model would have the group size increasing with range, but typically it is more complicated. The "Square Law" shows how the group size increases at a greater rate than ideal - largely due to air movement.
The Fishtailing or Porpoising shows lateral movement caused by aerodynamic "lift" on the arrow. If the fishtailing is repeatable the result is offset grouping with a periodic nature but with the actual group size close to the ideal. The archer could theoretically compensate for this in aiming, however it is simpler to tune the system to eliminate the action.
If Fishtailing or Porpoising is not repeatable due to the arrow striking the bow or poor archer form, then the Fishtailing Envelope applies and the group sizes will be larger than ideal from the start, then reduce as the fishtailing oscillation is dampened.
The sport of archery tends to use round scores as a measure of an archer's ability. However, a score is but a sample in a process with a significant random component. An archer with constant form from one day to the next will, more likely than not, produce significantly different scores. The average of many rounds is required to express the archer's true form, so many in fact that that it may be impossible without the archer's form changing during the process.
Because FlyingSticks uses a statistical model that reflects this reality to determine the placement of each shot in a group, each grouping for a round will be different. This results in the score ± spread figure, which is calculated as two standard deviations (or 95% confidence) of the (~500) sample rounds. When scores are evaluated in parametric plots with Precision enabled, up to 20,000 sample can be taken.