Calculating Miller Stability

[cody g]

<< Mentor Note:Thread moved from the Homework forums because it isn't really about homework >>

Preface
With my limited understanding of physics, I am unaware of what section of the forums this question would fall into. I am not doing this for school(though possibly it might help with that in the future), however, it is work that I am doing from home, so I put it here. I apologize for any inconvenience this may cause, and feel free to move this thread or ask me to move it to a more appropriate location.

Goal
My goal is to convert said equation(s) into excel format, given known variables of velocity in feet per second(measured with chronograph), altitude in feet above sea level, temperature in degrees Fahrenheit, twist rate in inches per turn, bullet diameter in inches, bullet length in inches, bullet mass in grains, and barometric pressure in in/Hg
All units above are known to be in standard measurement for the equation, other than barometric pressure, temperature, for which a conversion may be needed for all I know.
In the process of completing this integration into excel format, I hope to come to better understand the equation not just in terms of creating a variable to use in a spin drift calculation, but truly understanding the equation, why it is the way it is, and the accuracy I can expect out of it.

As far as the practical application, I have developed calculators in excel format for wind drift, spin drift, hold on moving targets, and bullet drop. I am also working on a calculator for compensating for the Coriolis Effect, however I have not researched that enough at this moment to feel right asking questions about it... though so far it has been the most exciting to research. I plan on compiling these calculators into one master calculator that, in environmental conditions that muzzle velocity and ballistic coefficient has been tested in, given relevant information, the calculator will simply give you an adjustment for your optic to match your point of aim to your point of impact.

As far as the why? I view shooting as an art and science, at a certain performance level everything goes into it from your mind and body, to the care which you took in selecting components for your rifle, and the care taken in it's assembly and maintenance, to the same care taken with your optic(though I do not assemble my own) and your ammunition. I see a well placed shot as the proof of mental clarity, attention to detail, responsible action, skill and knowledge.

1. Homework Statement
solve for "s", incorporating corrections for velocity and air density

Homework Equations

I don't have the equation for how to get air density from the environmental conditions, as far as I know. I have f(a)= e^(3.518x(10^-5)+h), but I don't know how that can be used with the other equation(s), essentially where to plug it in or what I am missing if I am missing anything.

The Attempt at a Solution

I know how to balance the equation to have it solve for "s", but I do not know how to implement the corrections, as I recall from school almost 8 years ago, if f(a)=1, and f(c)= a+2, then I plug in 1 for a and get f(c)=3... or something like that. here though, I think it might possibly be that simple but the format is confusing me.

Sources/reference material
PDF file on article regarding the comparison of various models for calculating stability factors
http://www.jbmballistics.com/ballistics/bibliography/articles/miller_stability_2.pdf
Calculator that does exactly what I am trying to do
http://www.jbmballistics.com/cgi-bin/jbmstab-5.1.cgi

The next step
I currently use the calculator above to get my stability factor, then use that and time in flight to calculate spin drift at the target range, however I do not know if this accounts for loss in angular velocity due to drag, after I find that out, which should come with understanding the above equations, I may choose to make a more accurate method of calculating spin drift, by adjusting for that loss in angular velocity of the bullet per yard at every range up to the target range, then add the drift of every yard line together to form the total drift at target range. I am thinking the equations for remaining velocity and time in flight could possibly come in handy but I will cross that bridge when I come to it.

My end results I plan on posting here, as I am sure it would be of use to someone trying to do the same thing I am doing, and because if anyone wants to check my work for errors and finds any, that would be of great benefit to me.

 

[Dr. Courtney]

Preface
With my limited understanding of physics, I am unaware of what section of the forums this question would fall into. I am not doing this for school(though possibly it might help with that in the future), however, it is work that I am doing from home, so I put it here. I apologize for any inconvenience this may cause, and feel free to move this thread or ask me to move it to a more appropriate location.

Goal
My goal is to convert said equation(s) into excel format, given known variables of velocity in feet per second(measured with chronograph), altitude in feet above sea level, temperature in degrees Fahrenheit, twist rate in inches per turn, bullet diameter in inches, bullet length in inches, bullet mass in grains, and barometric pressure in in/Hg
All units above are known to be in standard measurement for the equation, other than barometric pressure, temperature, for which a conversion may be needed for all I know.
In the process of completing this integration into excel format, I hope to come to better understand the equation not just in terms of creating a variable to use in a spin drift calculation, but truly understanding the equation, why it is the way it is, and the accuracy I can expect out of it.

As far as the practical application, I have developed calculators in excel format for wind drift, spin drift, hold on moving targets, and bullet drop. I am also working on a calculator for compensating for the Coriolis Effect, however I have not researched that enough at this moment to feel right asking questions about it... though so far it has been the most exciting to research. I plan on compiling these calculators into one master calculator that, in environmental conditions that muzzle velocity and ballistic coefficient has been tested in, given relevant information, the calculator will simply give you an adjustment for your optic to match your point of aim to your point of impact.

As far as the why? I view shooting as an art and science, at a certain performance level everything goes into it from your mind and body, to the care which you took in selecting components for your rifle, and the care taken in it's assembly and maintenance, to the same care taken with your optic(though I do not assemble my own) and your ammunition. I see a well placed shot as the proof of mental clarity, attention to detail, responsible action, skill and knowledge.

1. Homework Statement
solve for "s", incorporating corrections for velocity and air density

Homework Equations

View attachment 227267
I don't have the equation for how to get air density from the environmental conditions, as far as I know. I have f(a)= e^(3.518x(10^-5)+h), but I don't know how that can be used with the other equation(s), essentially where to plug it in or what I am missing if I am missing anything.

The Attempt at a Solution

I know how to balance the equation to have it solve for "s", but I do not know how to implement the corrections, as I recall from school almost 8 years ago, if f(a)=1, and f(c)= a+2, then I plug in 1 for a and get f(c)=3... or something like that. here though, I think it might possibly be that simple but the format is confusing me.

Sources/reference material
PDF file on article regarding the comparison of various models for calculating stability factors
http://www.jbmballistics.com/ballistics/bibliography/articles/miller_stability_2.pdf
Calculator that does exactly what I am trying to do
http://www.jbmballistics.com/cgi-bin/jbmstab-5.1.cgi

The next step
I currently use the calculator above to get my stability factor, then use that and time in flight to calculate spin drift at the target range, however I do not know if this accounts for loss in angular velocity due to drag, after I find that out, which should come with understanding the above equations, I may choose to make a more accurate method of calculating spin drift, by adjusting for that loss in angular velocity of the bullet per yard at every range up to the target range, then add the drift of every yard line together to form the total drift at target range. I am thinking the equations for remaining velocity and time in flight could possibly come in handy but I will cross that bridge when I come to it.

My end results I plan on posting here, as I am sure it would be of use to someone trying to do the same thing I am doing, and because if anyone wants to check my work for errors and finds any, that would be of great benefit to me.

Hi. I helped Don Miller with the testing of his original twist rate formula and also helped him modify the formula to apply to plastic tipped bullets and later to open tipped match bullets. We co-authored two articles on bullet stability that appeared in Precision Shooting in 2012, shortly before Don passed away. Send me a PM and we'll work out how to get you a copy of the stability calculator spreadsheet, which applies the same formulas as the JBM site for computing stability. I would note that using an actual barometric pressure (as measured with something like a Kestrel weather meter) is far preferable to computing pressures from altitudes.

Once you have the stability, the formula for spin drift is from Bryan Litz and explained in more detail here:

http://forum.accurateshooter.com/threads/spin-drift-calculation.3862266/

The Litz formula for spin drift (which JBM also uses) is empirical - an engineer determined it works well through experimental testing. It is not based on rigorous theoretical results (neither are the stability formulas). It is known that stability tends to increase as a bullet flies downrange, but the Litz formula uses the stability at the muzzle. The constants in his spin drift formula account for that, but they may give varying results for bullets whose spin slows at different rates. But changing it puts you in the realm of developing new formulas and computational methods that have not been tested rather than using established and tested results. Experiments that reliably test tweaks in computing spin drift are difficult, because you need to exclude other confounding factors (wind, Coriolis, etc.)