The Reverse Ballistics panel is for the entry of sight ranging data that can allow the calculation of launch speed, the bow's virtual mass, the bow's energy and the arrow's drag coefficient. The ultimate value is in providing greater accuracy in generating sight tapes.
The available data determines which parameters can be calibrated and to what accuracy.
The ballistics data is saved with other Sight and Tape data. The calibration is dependent on sight measurements, arrow parameters and available bow energy. So, if you change any of these, it is recommended you save the sight with a new "My Sight Name".
This panel requires careful and the best data that you can acquire. (Like most computing systems, garbage in garbage out).
There is absolutely no need for an archer to known about launch speed, virtual mass or an arrow's drag coefficient, but it does add something to the sport, besides allowing for more accurate sight tapes. If you fear becoming a confirmed archery nerd, please do not proceed!
Sometimes we need to make assumptions that may not always be true. One such assumption is that an arrow's drag coefficient is relatively constant in flight. Some fletching, such as feather and flu-flu, can change shape during flight. Arrows with high levels of vibration may also change during flight as the vibration is dampened.
The data table is like a small spreadsheet. Change any value and the effect will immediately ripple through on the panel and probably beyond, particularly when the bow's speed source and the arrow's drag coefficient source are set to Reverse Ballistics.
Columns may be individually enabled. Disabled columns appear dulled. Only enabled columns without errors (in red) are used.
Columns that have red text have been identified as containing errors. Fix the error or simply ignore the condition if you have sufficient other data.
A column need to be enabled to edit its content. The first field in a column (Range) is special. Deleting its content (followed by enter) will clear the entire column's data. A cleared column needs to be re-enabled to make the rest of the column visible again, but with defaults that will probably be in red.
Enter the range. Best to have a wide range of ranges:- 20, 50 and 90 meters or yards would be ideal for target shooters, or 20, 35 and 50 for hunters and even better with each of these ranges at two different arrow weights.
Enter arrow weight, ideally to ±2 grain precision or better. When using two different weights, best to ensure they are significantly different - 300 and 600 grains (e.g. could be a target arrow and a hunting/clout arrow). If this is not the case then the virtual mass calculation is likely to be less accurate. In this situation it is best to have a symmetrical data set of three ranges for each of two arrow masses.
Be careful not to go below the bow's minimum safe arrow mass. The field will be in read if this occurs.
Enter your estimated vertical group size for each range. It is assumed this estimate is reasonably close to your real group form.
The group size is used limit the amount of adjustment that can be applied to the data before rejection. See Practical Suggestions below.
This button (with a warning) will load the group height fields with you current performance as setup in the Groups panel.
In the main data table, three rows provide alternate data source for inputting the amount of drop an arrow experiences. Depending on what you have been able to measure, you should select the corresponding data type using the one of the radio buttons then enter the data. The other two rows will be calculated for you. Because these rows can be both manual entry and calculated, they are in green.
You may vary the data source for each data column. If you attempt to enter data into a row that has not been selected, the new data will not be accepted.
(and Row)This is the effective arrow drop over the range and is the preferred measurement. For short ranges it can be measures easily. The advantage of providing drop data is potentially improved accuracy as it is a more direct measurement.
(and Row)This is the height of the sight pin above the arrow center line when the pin is setup for the range. For sights well forward of the grip, this measurement is likely to require an assistant, whom needs to take great care, and an extended arrow. Alternatively, a board or string may be used.
In general, it is best to mark a reference point on the sight and measure that point, referring subsequent sight points to that point.
If the field appears in red, then the value is below the save minimum entered in Sight>Geometry [Minimum Pin to Arrow Axis (Dmin)] field.
(and Row)This is the measurement from the reference range mark on the range scale to the range select slide pointer.
Shows a the estimated launch speed of an arrow based on its column of data and the current arrow's selected drag coefficient (see Arrow>Aerodynamics). If Reverse Ballistics is selected, then the calculated values is used.
These speeds are used as a starting point for a more precise evaluation and assists in identifying an error in range or drop. These speeds should be the same (for the same arrow mass), so arrow drag and the launch speed are incrementally adjusted in searching for the best fit. The final launch speed result value is likely to be within a few percent of these initial estimated values.
This is the difference between the measured ballistic input data and the calculated best fit drop. Ideally the figure should be zero, but in practice there will be errors. If this error is small compared to the group size, then the result is considered acceptable. Indeed, because of the probable small number of shots used to determine the group size, one can validly nudge the data a little to get a better fit. See Practical Suggestions below.
For the technically minded, it is the sum of the squares of this row that is minimized for the optimal solution.
Checking this box allows FlyingSticks to nudge the drop data a little to achieve a better ballistic and aerodynamic fit. It assumes that you may have made a small error in estimating the center of your group positions. See Practical Suggestions below for justification and limits of this strategy.
This action only kicks in with three or more columns of same arrow mass data. Because of the extra computation required the response may be a little slower.
The default state is off and unlike many other options is not saved between FlyingSticks launches, although any adjusted data will be saved.
This action loads the ballistics table with theoretical data based on the current kit and archer's form. It sets up 3 ranges (30, 50 and 70 m) each with two different arrow masses, the first is the selected arrow mass (see Arrow>Assembly) and the second is 50% greater. The selected drag coefficient (see Arrow>Aerodynamics) is used for both arrows.
The bow's energy and virtual mass are drawn from current bow's dimensions (see Bow Speed - from Bow Dimensions in Bow>Speed).
Seeding provides a good starting point for getting a feel for sensible values for the data fields.
After the tabulated data is analyzed, the results are presented below the table. Sometimes liberties are taken and some data may be rejected to generate the most accurate result.
The process looks for the ideal data set - three sets of range data for each of two different arrow masses. If this cannot be found, expectations are reduced and virtual mass and drag coefficient calculations may be compromised. The best set is shown first. If your data does not fit with the calculator's ballistics and aerodynamic models, it will report the problem in the status area.
Once a solution is found, the best (i.e. the first) results are forwarded to the bow's speed selection options. If you have selected "Bow Speed - from Sight Reverse Ballistics" then the results can be immediately observed in the Target and Tape Windows.
The Recalculate button does just that - calculates a new set of results. Sometimes the recalculation results may change a little as it is an iterative process with different initial values. For most data entry, this is done automatically.
The arrow masses for the two best data sets.
This is the calculated launch speed. Its accuracy depends on the quality of the input data and should always be greater than the Average Speed Over Range for the same arrow mass.
At least two columns of good data with the same arrow mass are needed for the arrow's drag coefficient to be calculated. If there is insufficient good data the drag coefficient is set to that of the selected source in the Arrow>Aerodynamics panel. Should that source be the Reverse Ballistics option, then the Calculated value will be used.
Note that while the calculations perform best when the arrows of different masses have the same drag coefficients, it is not essential. This allows the use of two very different arrows for gathering the data.
The virtual mass can only be calculated if the ballistics data includes at least two different arrow masses.
This is the bow's calculated available energy to accelerate both the arrow AND virtual mass up to the launch speed.
The solution drop error standard deviation for the final fit for arrow mass data set. This is essentially a measure of the quality of the data. Smaller is better, zero is perfect. FlyingSticks tries to get this figure below ~5 mm (~⅕").
Low values become progressively more difficult to achieved with more data columns. This is usually due to errors in the group center location for each drop becoming more apparent as the calculator homes in on a solution.
To the right of the Drop Error SR field is a bracketed number e.g.(9). This is the number of iterations required to find the solution. Smaller is better and has a maximum value of 50. It can provide some insight to identifying data quality issues and initial drag coefficient value.
The old adage about computers "garbage in, garbage out" most definitely applies to reverse ballistics data.
The major issue is establishing the drop accurately at each range. The usual six arrows to measure the group size and center is simply insufficient for precision. The uncertainty in group center for just six arrows is about 40% of the archer's known form group size.
With the risk of getting even more confusing, one can say with 95% certainty the true group center is within a group oval that is 80% of the size of the perceived group oval. The 80% figure is reduced by the inverse of the square root of the number of arrows.
This is a diminishing return scenario as the following table illustrates:
| N | 1 | 2 | 3 | 4 | 6 | 12 | 18 | 36 | 72 | 144 |
| ±Error | 100% | 69% | 57% | 49% | 40% | 28% | 23% | 16% | 12% | 8% |
It assumes you already know the group size (i.e. your form) from previous work and then you loose N shots. The "±Error" row then gives the tolerance (as a percentage of the known group size height) of the true group center relative to the perceived group center of the N shots with 95% certainty.
A worked example might help. Suppose you just "know" your group height (G) at 50 m range is 200 mm (G = 200). You then do a drop test with just 6 shots (N = 6). The with 95% confidence the true group height center will be within ±0.40 x G mm or ±80 mm of the perceived group center of the 6 shots.
Thus for a six arrow test, you should feel reasonably free to adjust (nudge) the drop data up to say ±20% of group size to achieve a good fit.