Range Report Question on stability derived from 6 dof modell

[tobias]

Hello,

I don't understand how one can calculate the gyroscopic stability factor from the 6 dof modell. I understand how it is derived from the linearized theory, but the 6 dof modell can only be solved numerical, so how can you define a stability factor at all?
Is here someone doing 6 dof calculations and can help me?

 

[BobinNC]

Re: Question on stability derived from 6 dof modell

This is the extent of my knowledge of 6 DOF...

"6 DOF modelling needs such elaborate input, knowledge of the employed projectiles and long calculation time on computers that it is impractical for non-professional ballisticians and field use where calculations generally have to be done on the fly on PDAs with relatively modest computing power. 6 DOF is generally used by military organizations that study the ballistic behavior of a limited number of (intended) military issue projectiles."

I use this resource for my stability calculations:
JBM Ballistics - Miller Stability Calculator

 

[Country]

Re: Question on stability derived from 6 dof modell

I make my own bullets so I have to use JBM point mass program to model them as I have no factory BC information like store bought bullets have .
I would love a 6 DOF model to play around with but they are very expensive. I have the 6 DOF calculations in a spread sheet that I got from a German guy but it is an incomplete model with no input interface . I am too dumb to do anything more with it.

 

[tobias]

Re: Question on stability derived from 6 dof modell

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: BobinNC</div><div class="ubbcode-body">I use this resource for my stability calculations:
JBM Ballistics - Miller Stability Calculator
</div></div>

JBM uses the Miller formula. This formula is a simplification of the formula derived from the linearized theory and has nothing to do with 6 dof calculation. Anyway, thanks for your answer!

 

[tobias]

Re: Question on stability derived from 6 dof modell

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Country</div><div class="ubbcode-body">I would love a 6 DOF model to play around with but they are very expensive. I have the 6 DOF calculations in a spread sheet that I got from a German guy but it is an incomplete model with no input interface .
</div></div>

I don't want to do own calculations, I just need to know HOW it is done, otherwise I can't sleep at night...
McCoy for example shows figures of the stability factor versus range based on 6 dof calculations. How is the factor defined? In the linearized theory you get e-functions as solutions of yawing and pitching and the amplitudes should decrease to get a stable bullet. With this condition you can naturally define the stability factor. But in the 6 dof modell there are no e-functions, everything is solved numerical.

 

[Greg Langelius *]

Re: Question on stability derived from 6 dof modell

I once had your brand of insomnia.

After some educational catch-up, I got my teeth securely sunken into the problem. I learned a lot, especially about developing an intuitive grasp of which factors mattered, how, and why.

At the end of the day, I finally recognized that all I was doing was reinventing the wheel, and that all of the info I thought I needed was superfluous.

The basic data values the manufacturers provide for their products are more than adequate to determine a valid choice and those critical factors for employing the projectiles. The how and why are beyond our capacity to change anyway, unless we were planning to make our own. The manufacturers do a better job at that, and it's a lot more affordable, too.

I won't tell you what to do; but I will say that sleeping better has more to do with how much you can bite off, and how much you can chew.

The best approach to this sort of question is to recognize one's own limitations, to quit coming up with things you need to do besides shooting, and to get out there and shoot. It's the stuff you learn at the range that has the real value, the rest just pampers one's ego.

Greg

 

[Lindy]

Re: Question on stability derived from 6 dof modell

Like Greg, I used to worry a lot about things like that.

Then I started listing the limitations of the models I was using. Here's a partial list:

Sources of Ballistic Program Inaccuracies

Shooting taught me a lot more about shooting than computer models did.

To paraphrase an old Jewish saying, too soon old, too late wise.

 

[tobias]

Re: Question on stability derived from 6 dof modell

This isn't for my ego and I know that this knowledge won't improve my shooting skills. I know that it's better to spend a day at the range and not in front of a computer doing calculations. That's not the point. I'm an elementary particle physicist and I'm just curious. I have to understand things, I have to know how formulas are derived, then I can understand the possibilities of a theory and of its limits.

Besides, actually I can sleep at night. When my little boy allows it....

 

[Greg Langelius *]

Re: Question on stability derived from 6 dof modell

Knowing about the physicist part would have probably engendered a different response; and in any case, my comments were not intended as admonition. Really, I was just trying to provide some guidance through the shallows before you reach the deeper water.

I agree that as an intellectual exercise, one can get all the satisfaction one seeks from the deriving proportional relationships interent in ballistics and projectile stability. It just left <span style="font-style: italic">me</span> with so little in the way of useful avenues once the exercise was concluded.

But I'm also getting on in years, and my prejudice is toward expending my remaining time in <span style="font-style: italic">doing</span>, rather than in calculating. One gains the insight that one does not have forever to get the benefits from one's preferred pursuits. One of my few smaller regrets is in how much I've expended doing the latter, when I could have been doing the former.

Greg

 

[JByrd]

Re: Question on stability derived from 6 dof modell

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Greg Langelius *</div><div class="ubbcode-body">I once had your brand of insomnia.

After some educational catch-up, I got my teeth securely sunken into the problem. I learned a lot, especially about developing an intuitive grasp of which factors mattered, how, and why.

At the end of the day, I finally recognized that all I was doing was reinventing the wheel, and that all of the info I thought I needed was superfluous.

The basic data values the manufacturers provide for their products are more than adequate to determine a valid choice and those critical factors for employing the projectiles. The how and why are beyond our capacity to change anyway, unless we were planning to make our own. The manufacturers do a better job at that, and it's a lot more affordable, too.

I won't tell you what to do; but I will say that sleeping better has more to do with how much you can bite off, and how much you can chew.

The best approach to this sort of question is to recognize one's own limitations, to quit coming up with things you need to do besides shooting, and to get out there and shoot. It's the stuff you learn at the range that has the real value, the rest just pampers one's ego.

Greg </div></div>
what he said^^^^^^^^doesnt matter what your calculations are if you can't read wind/ mirage

 

[JByrd]

Re: Question on stability derived from 6 dof modell

When you walk around lookinng at the leaves in the tops of trees and the grass blowing and run mil calculations in your head then you might be onto some practical calculatory guesssmatical equatiions that will put the hole a little closer to the center. Put that brain to work at the range/reloading bench

 

[Emouse]

Re: Question on stability derived from 6 dof modell

I will assume you have read McCoy's book "Modern Exterior Ballistics"?? If that hasn't stisfied your mathematical urges then perhaps a direct discussion with Brian Litz would assist.

Brian is approachable and can be found on this forum.

If all else fails,...sleeping tablets will work followed by a day expending vast amounts of ammunition.

 

[gstaylorg]

Re: Question on stability derived from 6 dof modell

Tob,
Sorry I can't help you with your question, wwwaaaaaayyyy beyond my comprehension of ballistics. However as a scientist myself, I completely understand your position. It's not a "shooting" issue, per se, or one that can be solved by more time at the range. You want an answer to the question; it's like an itch that can't be scratched by anything other than the answer to the question. I'm the same way. Hopefully someone here can step up with the info you're looking for. Good luck.

 

[tobias]

Re: Question on stability derived from 6 dof modell

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: procovert45</div><div class="ubbcode-body">When you walk around lookinng at the leaves in the tops of trees and the grass blowing and run mil calculations in your head then you might be onto some practical calculatory guesssmatical equatiions that will put the hole a little closer to the center. Put that brain to work at the range/reloading bench </div></div>

I have a question about 6 dof calculations and you tell me to look at the leaves and read the wind. Are you kidding me?

@gstaylorg: Thank you!

 

[tobias]

Re: Question on stability derived from 6 dof modell

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Emouse</div><div class="ubbcode-body">I will assume you have read McCoy's book "Modern Exterior Ballistics"?? If that hasn't stisfied your mathematical urges then perhaps a direct discussion with Brian Litz would assist.
</div></div>

The book is fantastic! But McCoy doesn't explain how you can calculate the factor using the 6 dof model.
Thanks for the tip. I try to contact Mr. Litz.

 

[Country]

Re: Question on stability derived from 6 dof modell

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">I don't want to do own calculations, I just need to know HOW it is done, otherwise I can't sleep at night...
McCoy for example shows figures of the stability factor versus range based on 6 dof calculations. How is the factor defined? In the linearized theory you get e-functions as solutions of yawing and pitching and the amplitudes should decrease to get a stable bullet. With this condition you can naturally define the stability factor. But in the 6 dof modell there are no e-functions, everything is solved numerical </div></div>





Sorry mate I am an ex soldier not a an ex rocket scientist .

 

[Eaglet]

Re: Question on stability derived from 6 dof modell

Tob, I can't help you either... Well... see Changes below!

<span style="color: #3333FF">LB3.0 Desk Top Edition, calculates it using McCoy's method.</span>

I'm posting this info for those that need to get some of that information and don't have to know how to calculate it but will actually use it.

I, as some folks would know, love ballistic applications and my very favorite is Load Base 3.0


Here's some examples of calculations from Mach 0.1 to Mach 5.0 in increments of Mach 0.1

Using the default values. (FF)on the forth screen shot stands for Form Factor.

THIS SCREEN IS VERY USEFUL AS WELL! AGAIN JUST USING DEFAULT VALUES.

 

[Eaglet]

Re: Question on stability derived from 6 dof modell

I made changes in my former post in reference to McCoy's method. please check it again. Thanks.

 

[BryanLitz]

Re: Question on stability derived from 6 dof modell

The equation for gyroscopic stability of spin stabilized projectiles can be found on page 230 of McCoy's book; equation 10.85. It's also given here but without the derivation provided in McCoy:
http://www.nennstiel-ruprecht.de/bullfly/gyrocond.htm

This equation can be solved for any point in a bullets trajectory provided one knows the pitching moment coefficient; Cma at any given Mach number. There are other variables in the equation that are not easy to find/calculate like the axial and transverse moments of intertia (Ix and Iy). Also the spin rate (p) of the bullet and it's forward velocity are decaying as the bullet flies so you would have to know their values if you wanted to calculate Sg for an entire trajectory.

The equation itself doesn't have to be solved numerically if you know the instantaneous values of all the variables involved. However if you do have a 6-DOF model and all the required aero and mass properties data to model a particular bullet, then you can run the model (numerically) and the Sg can be calculated for all points in the trajectory. It's the increase in the Cma term near the speed of sound which primarily reduces Cma at long range, however it's usually poor dynamic stability that will actually cause the bullet to tumble at transonic speed.

JBM hosts two methods for calculating Sg; on is the Miller formula, he also hosts the McGyro method under the 'drag and twist' link;
http://www.jbmballistics.com/cgi-bin/jbmdrag-5.1.cgi

McGyro is more accurate estimate, but it's not a direct calculation of Sg and it requires more detailed bullet inputs.

Hope this satisfies your question.

Take care,
-Bryan

 

[tobias]

Re: Question on stability derived from 6 dof modell

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Bryan Litz</div><div class="ubbcode-body">
The equation itself doesn't have to be solved numerically if you know the instantaneous values of all the variables involved. However if you do have a 6-DOF model and all the required aero and mass properties data to model a particular bullet, then you can run the model (numerically) and the Sg can be calculated for all points in the trajectory.</div></div>

That's the point. For me it is very irritating to speak of 6 dof calculation when in fact you use a formula derived from the linearized theory (meaning you also have the limitations of the linearized theory for Sg, e.g. small-yaw flight). My mistake was, that I always referred to the nonlinearized differential equations when I hear of 6 dof calculations.
Thus Sg versus range (figure 9.6 for example) is more or less determined by e^(-2 K s) in eq. 10.78 (and the dependence of Cma on Mach number), which means Sg increases roughly exponentially.

Thank you very much, Mr. Litz! I can go to bed now...


Thanks also to Eaglet. I appreciate your efforts.