Quick comparision to Lapuas radar measurements and Lapua's QuickTarget

Started by admin, February 15, 2011, 09:01:48 AM

admin

Lapua has radar measurements for many of its bullets. From this their specific drag functions has been calculated. I downloaded the free Lapua QuickTarget ballistic calculator from www.lapua.com and made a quick comparision of its output for the Lapua GB478 Scenar 6,8 gram (105 gr) 6mm NormaBR bullet. Later, after I have sorted out things with Pejsa's calculations (did he use US Army Standard Metro or ICAO conditions plus 78% humidity?) I will do a more elaborate calculation. I think the results are pretty good. The question is how well the QuickTarget calculations match the exact trajectory? Ideally one wants to compare calculations with the actual path properties too!

mman

Would it be a problem to to add possibility to use lapua dopler radar measurement data in bfx? At least data files can be downloaded free.

admin

#2
No, it is not a problem, but an awful lot of work. BfX needs these functions as a set of power laws - the basis of Pejsa method. For power laws many physics equations can be integrated mathematically.

mman

#3
Quote from: admin on May 08, 2011, 09:41:12 PM
No, it is not a problem, but an awful lot of work. BfX needs these functions as a set of power laws - the basis of Pejsa method. For power laws many physics equations can be integrated mathematically.

How about multi BCs? Is that awful lot of work too? Bryan litz offers multi bcs and some times using them leads to better results. There also several cases when single bc is simply not enough. Couple good examples are most air rifle pellets and 22 lr bullets. That is first hand experience when I have tried to fit those to drag functions. My guess is that there is some degree of dynamical unstability involved. For short distances path fits fine but for longer distances drop tends to grow more than traditional A, RA4 or G1 drag curves would estimate. That's where you would have to correct the effect with multi BCs. Another case is ELR shooting where bullet slows down to transonic velocities..

IMHO multi bc input is programmed wrong in ballistic programs which even offer the possibility to use this feature. Program should be done so that BC would be interpolated between given bc values. Linear interpolation is very good default but in best case scenario advanced user could choose polynomial interpolation degree. Another thing is that multi bc boundaries should be tied to mach number and not to the velocity like it's done in QTU.

admin

This would be a relatively minor thing to do, compared with other adventures in mind. it is also easy with excel yourself. Just create a table where you supply a specific bc for a specific velocity range.

However, a bc is directly related to the drag function: deacceleration=drag/bc*(other factors). Hence the concept of multiple bc is the same as using multiple drag functions for different velocity ranges - which is in fact a new drag function. The current receipe for max accuracy is for most situations: use G7 and Litz BC. The Lapua data are not validated, much is unknown about them. With BfX it is also easy to fit your own BC

The quest for maximum accuracy, however, I pursue by providing 6dof, later. 6dof will introduce yaw depending drag, amongst others.

admin

... it is not completely true what I said that one should parametrize drag functions with power laws in order to get Pejsa's approach working - drag functions are parametrized with a series of constants  - cd(v)= c_i v_(i-1) < v =< v_i and power = 0

I will run a test. In princple I have a full runge kuta based trajectory simulator implemented - however I am not convinced that it would help sporting shooters, it would help non-friends is countries like Afghanistan.

mman

Quote from: admin on May 12, 2011, 09:09:08 AM
however I am not convinced that it would help sporting shooters, it would help non-friends is countries like Afghanistan.

Like I said before there is many applications for this but I don't think that afgan snipers can make use any of them.

ThunderDownUnder

#7
Quote from: admin on May 10, 2011, 02:08:04 PM
This would be a relatively minor thing to do, compared with other adventures in mind. it is also easy with excel yourself. Just create a table where you supply a specific bc for a specific velocity range.

However, a bc is directly related to the drag function: deacceleration=drag/bc*(other factors). Hence the concept of multiple bc is the same as using multiple drag functions for different velocity ranges - which is in fact a new drag function. The current receipe for max accuracy is for most situations: use G7 and Litz BC. The Lapua data are not validated, much is unknown about them. With BfX it is also easy to fit your own BC

The quest for maximum accuracy, however, I pursue by providing 6dof, later. 6dof will introduce yaw depending drag, amongst others.

Robert, 6DOF may be more work than you need to give yourself for accurate ballistic analysis. It would appear that only bullet manufacturers would have the aerodynamic data to use with 6dof programs. I have just re-read Litz's article on ballistic programs and he puts forward the argument that for small arms use then 3dof is best suited to the task. I compare the results I get using your current BfX function with Bryan's 3dof program and the results are almost exactly the same for all his G7 data. Not being very good at maths myself,  I'm assuming your BfX functions are already using 3dof?

I quote part of Bryan's article below and would like your opinion on 3dof compared to what you would like to add to BfX with 6dof, if you could be so kind as to give it. Link http://www.appliedballisticsllc.com/howprogramswork.html

"If I were to write a ballistics program for small arms that's intended to surpass the existing available packages, I would use a point mass solver (3-DOF numeric solver) for the following reasons:

1. Modern computers, even field deployable devices like palm pilots and cell phones have fast enough processors these days to solve a numerical solution in a reasonable amount of run time.

2. The program does not require you to store large tables (S, T and V functions) like the Siacci method.

3. You can make use of multiple standards (G1, G7, etc) depending on whichever one is best suited to the bullet you're modeling.  (Siacci also has this feature).

4. If you have access to a 6-DOF simulation, you can investigate trends like gyroscopic drift as a function of flight time for certain classes of projectiles, and then apply the trends as corrections to the point mass solution (Ref article: Extending Max Effective Range of Small Arms on this website).  Applying the 6-DOF corrections won't significantly affect computer run time.

I would avoid the Pejsa solution because of the difficulty of modeling bullet drag.  Since the Pejsa method does not make use of any standard projectile drag curves, it's up to the user to describe the drag of his own bullets.  This requires establishing obscure coefficients and exponents for each bullet for several velocity bands.  Large compromises are made when the projectile slows to transonic speeds and the drag curve is approximated with linear segments.  The complexity of Mach dependant projectile drag belongs in the solution method, it should not be up to the shooter to figure out."

Ian

admin

Quote from: ThunderDownUnder on May 30, 2011, 01:09:00 AM
Robert, 6DOF may be more work than you need to give yourself for accurate ballistic analysis.

Completely true, BfX is already good enough. Never the less - this is physics and programming fun for me! 6DOF is however the easy part - I do have already 3dof implemented and used to check BfX

Quote from: ThunderDownUnder on May 30, 2011, 01:09:00 AM
It would appear that only bullet manufacturers would have the aerodynamic data to use with 6dof programs.

Yes, there are hard to obtain things like the skin friction coeficient. But we need only two - for copper plated and moly coated bullets.

Quote from: ThunderDownUnder on May 30, 2011, 01:09:00 AM
I compare the results I get using your current BfX function with Bryan's 3dof program and the results are almost exactly the same for all his G7 data. Not being very good at maths myself,  I'm assuming your BfX functions are already using 3dof?

No, not 3DOF. I use the Pejsa method that mathematically integrates, assuming small elevations (<15 degrees) the equations of motion. Required is a partametrization of the drag function in the form of d=a*m^b where a and b are constants depending on a specific velocity region. I have such parametrizations for many dragfunctions. If one sets b=0 then the drag function is parametrized as a large collection of constants - indeed the drag table itseff. Hence the Pejsa method can use in principle any drag table (without the parametrizations that speed up the calculations). I am planning to try this out and modify the interface to bfx a bit so that the drag function parameter points to a drag table.

Quote from: ThunderDownUnder on May 30, 2011, 01:09:00 AM
"If I were to write a ballistics program for small arms that's intended to surpass the existing available packages, I would use a point mass solver (3-DOF numeric solver) for the following reasons:
1. ...
2. ...
3. You can make use of multiple standards (G1, G7, etc) depending on whichever one is best suited to the bullet you're modeling.  (Siacci also has this feature).

4. If you have access to a 6-DOF simulation, you can investigate trends like gyroscopic drift as a function of flight time for certain classes of projectiles, and then apply the trends as corrections to the point mass solution (Ref article: Extending Max Effective Range of Small Arms on this website).  Applying the 6-DOF corrections won't significantly affect computer run time.

Well as said, BfX uses the Pejsa method and works fine with many functions, certainly G1 and G7. What you can do, as Brian did for the gyroscopic drift, is to parametize the effects of the spinning projectile and add them to the 3dof or in many cases equivalenty, bfx values. Parametrization means determining parameters of a mathematical function that effectively calculates the drift. Another example is the parametrization of the maximum range of a bullet that I published some where else on this forum. This parametrization depends only on the ballistic coeficient and muzzle velocity and is accurate (compared to 3dof) within 10%. Known for the Pejsa and Siacci methods are also other parametrizations as the large angle corrections.

Quote from: ThunderDownUnder on May 30, 2011, 01:09:00 AM
I would avoid the Pejsa solution because of the difficulty of modeling bullet drag.  Since the Pejsa method does not make use of any standard projectile drag curves, it's up to the user to describe the drag of his own bullets.  This requires establishing obscure coefficients and exponents for each bullet for several velocity bands.  Large compromises are made when the projectile slows to transonic speeds and the drag curve is approximated with linear segments.  The complexity of Mach dependant projectile drag belongs in the solution method, it should not be up to the shooter to figure out."
There is, within its assumptions of a point mass projectile and small elevations, nothing wrong with the Pejsa method. It gives the same answers as a numerical calculation (simulation) of the equations of motion. The only odd thing about a strict Pejsa implementation is his drag function, which is the default one in BfX and should be used with the G1 ballistic coefficient. However I also allowed other drag functions in BfX for those wo whould like to use other functions. It also allows a comparision - the bonus of using Excel. I did this inn the gettingstarted workbook that cross evaluates the use of various drag functions. I concluded there that for many sport shooters it does not matter which drag function one uses. Furthermore, Pejsa was an able man - his drag function does make a lot of sense.

By the way I have obtained such "obscure coeficients ...." - they are not obscure for me and the BfX user does not have to worry about them - I did.

In conclusion: a 6DOF is a bit of a physics and programming challenge. There is a part of me that wants to simulate the aerodynamics of the bullet itself. This is the final challenge - drag functions would be the outcome of these calculations.

ThunderDownUnder

Robert, thank you for such an excellent reply! It has enabled me to get a better understanding of just what you have put into creating the BfX functions.

I guess this means that one day I will be using your next generation BfX that will use data from 6dof simulations. Its a rare thing that a competitive shooter like yourself will make such a contribution back into the sport. I think the target shooting community has really benefited from your interest in ballistics and your ability to make it accessible thru your skills as a physicist and programmer. I look forward to the next generation 6dof, BfX functions, should you decide to go ahead with it!

Ian

admin

Quote from: mman on May 09, 2011, 03:04:19 PM
Quote from: admin on May 08, 2011, 09:41:12 PM
No, it is not a problem, but an awful lot of work. BfX needs these functions as a set of power laws - the basis of Pejsa method. For power laws many physics equations can be integrated mathematically.

How about multi BCs? Is that awful lot of work too? Bryan litz offers multi bcs and some times using them leads to better results. There also several cases when single bc is simply not enough. Couple good examples are most air rifle pellets and 22 lr bullets. That is first hand experience when I have tried to fit those to drag functions. My guess is that there is some degree of dynamical unstability involved. For short distances path fits fine but for longer distances drop tends to grow more than traditional A, RA4 or G1 drag curves would estimate. That's where you would have to correct the effect with multi BCs. Another case is ELR shooting where bullet slows down to transonic velocities..

IMHO multi bc input is programmed wrong in ballistic programs which even offer the possibility to use this feature. Program should be done so that BC would be interpolated between given bc values. Linear interpolation is very good default but in best case scenario advanced user could choose polynomial interpolation degree. Another thing is that multi bc boundaries should be tied to mach number and not to the velocity like it's done in QTU.

Well BfX supports custom drag functions now. Mman show me what you would like to do with air rifle drag functions!

mman

Quote from: admin on August 29, 2011, 12:39:39 PM
Quote from: mman on May 09, 2011, 03:04:19 PM
Quote from: admin on May 08, 2011, 09:41:12 PM
No, it is not a problem, but an awful lot of work. BfX needs these functions as a set of power laws - the basis of Pejsa method. For power laws many physics equations can be integrated mathematically.

How about multi BCs? Is that awful lot of work too? Bryan litz offers multi bcs and some times using them leads to better results. There also several cases when single bc is simply not enough. Couple good examples are most air rifle pellets and 22 lr bullets. That is first hand experience when I have tried to fit those to drag functions. My guess is that there is some degree of dynamical unstability involved. For short distances path fits fine but for longer distances drop tends to grow more than traditional A, RA4 or G1 drag curves would estimate. That's where you would have to correct the effect with multi BCs. Another case is ELR shooting where bullet slows down to transonic velocities..

IMHO multi bc input is programmed wrong in ballistic programs which even offer the possibility to use this feature. Program should be done so that BC would be interpolated between given bc values. Linear interpolation is very good default but in best case scenario advanced user could choose polynomial interpolation degree. Another thing is that multi bc boundaries should be tied to mach number and not to the velocity like it's done in QTU.

Well BfX supports custom drag functions now. Mman show me what you would like to do with air rifle drag functions!

I just got new air arms 0.22 cal PCP rifle. I'm still searching most accurate pellet for this gun. When this is done I'll measure velocities for few different ranges and then I'll fit them on drag coefficient curve (if this feature is available on bfx) or with multi bcs. I'm going to place CED M2 chrono in plastic pipe which blocks all external light and use IR leds as a light source when measuring velocities. I'll also consider extending distance between sensors.  I think this changes improve measuring accuracy.

Is there something else you would like to hear about my plans with those drag functions?

admin

mman, I missed this.

any progress?

mman

Quote from: admin on February 27, 2012, 09:22:23 PM
mman, I missed this.

any progress?

Yes...

Most accurate pellet for my gun is 1 g. JSB exact. It shoots pretty good.

CED is modified and works well. I'm shooting inside 25 m long warehouse with rimfire and PCP. External lights do not affect velocity measurements. There is still no way to calibrate this setup but I already know that absolute velocities are at least 1 % accurate. How do I know...From comparisons to other chronos and drop tests.

I have also measured drag of this bullet but I don't have any data at the moment.