Difference between revisions of "Extreme Spread"
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− | + | {| class="wikitable" | |
− | + | | [[File:Bullseye.jpg|50px]] This page is a draft and needs review! | |
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= Experimental Summary = | = Experimental Summary = | ||
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| Assumptions | | Assumptions | ||
| | | | ||
− | * Ideally the shots would | + | * Ideally the shots would have a circular pattern (i.e. the shots would have the Rayleigh Distribution). |
− | ** <math> | + | ** <math>h \sim \mathcal{N}(\bar{h},\sigma_h^2), v \sim \mathcal{N}(\bar{v},\sigma_v^2)</math> |
** Horizontal and vertical dispersion are independent. | ** Horizontal and vertical dispersion are independent. | ||
** <math>\sigma_h = \sigma_v</math> (realistically <math>\sigma_h \approx \sigma_v</math>) | ** <math>\sigma_h = \sigma_v</math> (realistically <math>\sigma_h \approx \sigma_v</math>) | ||
** <math>\rho = 0</math> | ** <math>\rho = 0</math> | ||
− | ** <math>PDF_{r_i}(r) = \frac{r}{\ | + | ** <math>PDF_{r_i}(r) = \frac{r}{\Re^2}e^{-r^2/2\Re^2}</math> |
− | :: '''Note:''' It is not necessary to | + | :: '''Note:''' It is not necessary to calculate the COI, nor the constant <math>\Re</math>, to calculate the Extreme Spread. |
* No Fliers | * No Fliers | ||
|- | |- | ||
| Data transformation | | Data transformation | ||
− | | Identify two holes, <math>i, j</math> which are the farthest apart. | + | | Identify two holes, <math>i, j</math> which are the farthest apart and measure <math>ES</math>. |
+ | <math>ES = \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}</math> | ||
|- | |- | ||
| Experimental Measure | | Experimental Measure | ||
− | | <math>ES | + | | <math>ES</math> |
|} | |} | ||
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== Assumptions == | == Assumptions == | ||
− | None are needed to make measurement. However | + | None are needed to make measurement. However some points are worth considering. |
+ | |||
+ | * The same ES measurement could result from a vertical group to a round group. If the shooting process can vary that much then the ES measurement won't give any indication of the change. | ||
+ | |||
+ | :: If the shot patterns aren't "fairly" round, then using the measurement makes little sense. For instance if muzzle velocity variations are severe, then the vertical range will dominate the ES measurement. Muzzle velocity variations would correlate better with vertical range than with ES. | ||
+ | |||
+ | * Making assumptions about the dispersion will enable theoretical predictions about the ES measurement. It must be realized that the theoretical solution, assuming the Rayleigh distribution and using Monte Carlo simulation, isn't some arbitrary goal, it is the best case scenario. | ||
== Data transformation == | == Data transformation == | ||
− | The data transformation for a human has simple requirements, just the ability to locate the holes which are the furthest apart. If the target has a ragged hole it can be a bit tricky, but the edges of the hole should have enough curvature to make shot location possible. | + | The data transformation for a human has simple requirements, just the ability to locate the holes which are the furthest apart and measure the distance between them. If the target has a ragged hole it can be a bit tricky, but the edges of the hole should have enough curvature to make shot location possible. |
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If measuring on the range, then the center of the hole is difficult to locate. Typically a vernier caliper (cheap is fine!) would be used to measure the distance from the outside edges of the holes, then the bullet caliber subtracted to get a c-t-c measurement. | If measuring on the range, then the center of the hole is difficult to locate. Typically a vernier caliper (cheap is fine!) would be used to measure the distance from the outside edges of the holes, then the bullet caliber subtracted to get a c-t-c measurement. | ||
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If using a computer then the center location would be a matter programming. For example a mouse might be used simply to point out the holes, or to drop a dot at the center of the hole, or to drag a circle over the hole. The computer would then make the c-t-c measurement. | If using a computer then the center location would be a matter programming. For example a mouse might be used simply to point out the holes, or to drop a dot at the center of the hole, or to drag a circle over the hole. The computer would then make the c-t-c measurement. | ||
− | == | + | == Experimental Measure == |
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− | + | No calculation needs to be done to get the measurement. The single physical measurement is the data sought for the target. | |
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= See Also = | = See Also = | ||
− | [[Dispersion | + | [[Projectile Dispersion Classifications]] - A discussion of the different cases for projectile dispersion |
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Latest revision as of 18:42, 9 January 2024
This page is a draft and needs review! |
Contents
Experimental Summary
Given |
All of the (h,v) positions do not need to be known so a ragged hole will suffice. |
Assumptions |
|
Data transformation | Identify two holes, \(i, j\) which are the farthest apart and measure \(ES\).
\(ES = \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}\) |
Experimental Measure | \(ES\) |
Given
The requirements for this test are very basic. Just a target with \(n\) shots, and some measuring device. Assuming an Extreme spread of under 6 inches then a vernier caliper is used. A measurement is possible to a few thousandths of an inch which is vastly more precision than is usually required. From longer distance a ruler, or perhaps a tape measure.
Assumptions
None are needed to make measurement. However some points are worth considering.
- The same ES measurement could result from a vertical group to a round group. If the shooting process can vary that much then the ES measurement won't give any indication of the change.
- If the shot patterns aren't "fairly" round, then using the measurement makes little sense. For instance if muzzle velocity variations are severe, then the vertical range will dominate the ES measurement. Muzzle velocity variations would correlate better with vertical range than with ES.
- Making assumptions about the dispersion will enable theoretical predictions about the ES measurement. It must be realized that the theoretical solution, assuming the Rayleigh distribution and using Monte Carlo simulation, isn't some arbitrary goal, it is the best case scenario.
Data transformation
The data transformation for a human has simple requirements, just the ability to locate the holes which are the furthest apart and measure the distance between them. If the target has a ragged hole it can be a bit tricky, but the edges of the hole should have enough curvature to make shot location possible.
If measuring on the range, then the center of the hole is difficult to locate. Typically a vernier caliper (cheap is fine!) would be used to measure the distance from the outside edges of the holes, then the bullet caliber subtracted to get a c-t-c measurement.
If using a computer then the center location would be a matter programming. For example a mouse might be used simply to point out the holes, or to drop a dot at the center of the hole, or to drag a circle over the hole. The computer would then make the c-t-c measurement.
Experimental Measure
No calculation needs to be done to get the measurement. The single physical measurement is the data sought for the target.
See Also
Projectile Dispersion Classifications - A discussion of the different cases for projectile dispersion