Connecticut Custom Airguns
  • Welcome!
  • Hector's Airgun Blog
  • Products and Products Blog
    • One-Off's
    • The "Héctors Special'" scope by Sightron
    • K1050i FT
    • The Hex Louver or "Secret Sunshade"
    • Pellet Path Calculator >
      • Questions, Answers and Comments on P-P Calc
      • Privacy Policy for PP-Calc
    • The Nautilus SideWheel
    • The X-10 TiltMeter
  • Zimmer-Silhouetten
    • Results 2017-2018
    • Results 2016-2017
    • Results 2015-2016
    • Results 2014-2015
    • Results 2013-2014
  • References and Links
  • Contact us
  • Store

Hector's Airgun Blog

Where we discuss, CIVIILY,  anything airgun.

Return Home

Just what the H---k is the "Ballistic Coefficient"?

6/23/2014

0 Comments

 
There is a ton of misconceptions about what REALLY is the B.C. (acronym of Ballistic Coefficient) of a projectile.
Probably, the most noxious one is the one that equates a high B.C. to a "good" projectile and a low B.C. to a "bad" projectile.
B.C. is NOT a measure of the "design qualities" of a projectile.

So. . . . ¿What is BC?

First and foremost, BC is a SCALE FACTOR.

To explain this we need to go back almost two hundred years, to the heroic days when small, field worthy artillery pieces were truly coming into their own. When smokeless powder first became a commercial and military reality, and when the value of a soldier's life was less than the value of the musket he carried.
So, imagine yourself living from the 1840's to the late 1880's:
The US has just doubled its territory by waging war on México.
Crimea has just been lost by the Russians to a Western European bloc
Germany has just annexed all the Alsace Lorraine
The French have just invented the "75" and Captain Dreyfus is spending some time in "Devil's Island" because it is easier for the "Establishment" to send an innocent person to his death in a tropical island than to accept that the ring of spies is so well entrenched in the government circles as to make it a "Reason of Sate". 
Russia is trying to assert its role in the "modern world" and the Czar decides to support the Army because supporting the Navy, with no warm water sea port is senseless. There is a peculiar alliance being established between France (the 3rd Republic) and Russia (an Imperial Autocratic State).

Out of England (THE Maritime Power of its day), comes a young chap by the name Francis Bashforth; developing on the (by then 200 years old) ideas by Benjamin Robins, he creates in the late 1860's an electromechanical chronograph that is capable of measuring velocities of projectiles to much greater precision than the ballistic pendula of the day. Consider that to measure ACCURATELY, a ballistic pendulum has to have a mass at least 200 times greater than the projectile it tries to measure. Now consider the size of ballistic pendula for artillery ogives.
Bashforth measures and creates tables for all his measurements, and then comes up with a flash of brilliance:
¿What if ALL the effort was devoted to a "standard" projectile, could he then prove that all other projectiles would have a SIMILAR behaviour? 

Similarity, in the mathematical context, is the capacity to change one thing into another using a scale factor.

And so, he proposes the Ballistic Coefficient; a SCALE factor that can tell technicians how a given projectile will behave BASED on a LOT of firings of a STANDARD projectile.

Being a good Yorkshireman, and VERY British, Bashforth uses a Standard Projectile (S.P.) of 1.00" Caliber, with a 1.5" tangent Ogive, weighing (¿What else?) 1 lb. And this becomes the B.C. = 1.00

Now, let's come to the present and analyze this a little: ¿What on earth can be MORE DIS-SIMILAR than a flat base, 1.5 calibers tangent ogive, parallel sides projectile, weighing all of 7,000 grains in 1.00" Cal. AND an 8.44 grains, diabolo shaped (waisted) pellet with an ogive barely 1.25 calibers in cal. 0.177"?

Caliber of the S.P. is more than 5½ times the caliber of the projectile we are interested in. 
Mass of S.P. is more than 800 (eight HUNDRED) times the mass of the projectile of interest.

There is NOTHING of the S.P. that barely resembles our pellets. How can we HOPE to use a simple SCALE factor?

Well, we can't.

And neither can do many others interested in the exterior ballistics.

Going back to the late 18th Century, the Russian Mayevski, then the Italian Siacci and then the American Ingalls, conducted a LARGE number of tests. At the same time, Krupp was conducting their own experiments and by 1875-1890 all nations had a pretty well informed knowledge of what exterior ballistics truly meant, as far as field artillery pieces were concerned. Just in time for the Balkan Wars, and then World War I.
Picture
Little Circles are results from Russian and English experiments, "+" signs are results by Dutch experimenters, little triangles are results by Krupp
Let's get this chart clear. The chart illustrates how the DRAG changes with speed. It is NOT a B.C. change chart, but it is close in an inverse sort of way.

Now, please consider: IF drag changes like this for every speed along the pellet's projectile, then the B.C. that is trying to scale a whole trajectory is much more dependent on how closely the projectile of interest is to the S.P.

It was the Russian, the Italian and the American, the ones that first proposed a DIFFERENT way to look at things: ¿Why not develop a mathematical model that, taking into account the physical characteristics of the projectiles will give us firing solutions?

Ah! that sounded GREAT!, let's call it Drag Function and then we can PREDICT what things will behave like as long as we know how those physical characteristics relate to the external ballistics.
At first it seemed that a "form factor" could be established that related the B.C. to the sectional density (the weight of the projectile -in lbs.- divided by the square of the caliber), BUT then the form factor became something to be qualitatively assigned. Tables were prepared where by graphical observations, shooters could ascertain which form factor they could use for their bullets.

REAL problem is that reality is a little too rich in details and too complicated to actually be able to do this with any really good precision. Few functions are linear, and since the old days, the exterior ballistics solutions have been, in reality, approximations by velocity regions. One set of equations, constants and coefficients apply from 0 to about 850 fps, another from 850 to about 1,100, another from 1,100 to about 1,400, then another between 1,400 and 2,200, and another between 2,200 and 5,000 fps.

Even at present, military applications use one Drag Function and commercial applications use another.

In the market there are several programs and types of software that use the drag coefficients. BUT they all have the same caveat: Use only by sections and make sure that YOUR case is not close to the boundaries of the sections. A few really good and conscientious manufacturers publish the B.C.'s for their bullets by MV regions.

In more recent times, with the advent of cheap and relatively reliable and precise chronographs, it has become easy to determine the "deceleration" (loss of velocity) of ANY projectile, and there have been some rather interesting approaches to solving the firing solutions. 

Among the more imaginative is Pejsa's "Velocity Retention Factor", and similar approaches whereupon some of the modern airgun pellet ballistics programs work.
Picture
Do note how pellets deform upon firing.
Another aspect about shooting pellets as opposed to bullets, is that our pellets deform upon firing.
The BEST mathematical model taken from the dimensions of the newly produced pellet will NOT be true once you fire that pellet through ANY barrel.

Modern pellets and modern barrels do this less dramatically than those made only a few decades ago. Compare the above picture to this one:
Picture
An older pellet being fired from an older barrel in an older experiment. Note how extreme the deformation is.
And, I think it is obvious, but I will say it again: EACH pellet/barrel combination will do this in a slightly different manner.
So, there is NO way to use a "table" B.C. for your pellet calculations, if you want them to be precise.

One of the peculiar differences between airgun shooters and powder burners is that, for them, some differences are "small" or "inconsequential". For airgunners where the targets are measured in fractions of an inch, there is no really inconsequential difference. 
Especially for FT shooters. 
A 40 Troyers target (a measure of relative difficulty) is a ½" target at 20 yards. The pellet occupies 0.177" of that, so the real wiggle room is about 0.32" If you consider that the pellet needs to be LESS than one caliber off to any side from center, you realize how accurate FT shooters and gear have to be.
And that is not the hardest target in an FT course, Match Directors can place these ½" targets all the way out to 30 yards! for a 60 Troyer shot.
Picture
Anyway, coming back to B.C.:

It seems to be one of those things that you are bad with it, and even worse without it.

For years I used Pejsa's approach and tried to calculate and keep good records of Velocity Retention Coefficients for all pellets in all my rifles. And then we went to Norway to shoot at the FT World's Matches and  I got faced with wind drift.

This is the OTHER side of B.C.: ONCE YOU HAVE A TRUE B.C. then wind DOES become a scientific calculation.

Not only that, Wind drift is proportional to normal velocity (velocity vector measured perpendicular to the trajectory plane). So, if you could have the B.C. for YOUR pellet, shot from YOUR rifle, at the place you ARE shooting, then wind drift is really more a matter of learning how to "guesstimate" this normal wind velocity.

BUT. . .  chicken and egg situation! How can I find the B.C. of my pellets shot at places as dis-similar as Norway (coastal location), Germany (mountain location), Texas (lowland, dry location), or Baton Rouge (humid, coastal location). ¿Should I take my two, matched, Chronos and do all my testing all over again?
¿At EVERY venue?

Well, enter a different point of view and a recently modern mathematical approach called "Fuzzy Logic", where one quantity can have not only A value, but a RANGE of values. Then you go on the next "test case" and check that range of values against the new one, and by discarding those values that are OUTSIDE BOTH ranges, you have a narrower range. Then you take a THIRD test case and come up with a different range of values, when you compare all three and come up with the value that meets all three test cases, then you have your solution.

This is how P-P Calc works.

And that is why I came back to the B.C. method. By using a zero range and THREE more ranges and POI's, the software calculates the B.C. by sections of the pellet path, it will give you a weighted average and use that for the calculations, but more importantly, it will calculate the wind drift.

While discussing the error in B.C.'s  vs. the Wind Normal Velocity reading error with a very good shooter, Scott Hull, he came up with this example:
Picture
As you can see, an error of 0.006 in the B.C. (six thousandths, from 0.021 to 0.015) will move your POI as much as an error of 1 mph in reading the wind.

As much as we dislike the idea, we cannot fault our pellets for having such a low B.C. (just to illustrate, some modern 0.50" cal bullets have B.C.'s GREATER than 1.00)
The low B.C. is what makes the use of our pellet rifles relatively safe in urban environments and at close distances.
The low B.C. of our pellets is what gives us the same challenge shooting out to 55 yards as the H.P shooters get shooting at 600 yards.
The low B.C. of our pellets is what makes our sport unique.

In conclusion:
Pellet shooters CAN use the B.C. concept, but they need to be careful to apply it by sections.
"Fiddling" with the B.C. is not too smart unless you REALLY know your rifle/pellet combination well. You may arrive at a scale factor (the B.C.) that has nothing to do with reality.
P-P Calc will allow you to MEASURE the B.C. from YOUR rifle/pellet combination at EVERY venue. You can then store that venue for future reference.

Hope this has been informative and I hope to see you at some FT Match soon!







HM
0 Comments

The 2014 GOB, Tennessee, GP Shoot, our experiences

6/11/2014

2 Comments

 
The GOB Ft Club is one of those Institutions without which you simply could not imagine Field Target being what it is in the US of A.

It started off many years ago and it has survived the first "passing of the baton" in the long relay race that creating a sport needs.

Roz Sumpter, some years ago, decided to retire to Tennessee, and in the process, he got a good chunk of heaven in stewardship. He planted trees, cut paths, created a small pond, then built a house.
And he started cutting lanes into the forest at the back of his house, the "White Course" was born.
Then some more lanes over at the creek at the bottom of the small valley (wherefrom: "Roz's Hollow") and this is what makes the "Red Course".

I started going to the GOB's shoot in 2009, when I discovered that PCP's don't fly well. Then in 2010, though I improved my scores, I had other problems and decided that PCP's were not reliable enough to shoot under all conditions. For 2011, I had had a good run all season with a Full Power D-54 in 0.20" cal. and decided to compete with that. Alas! the spring guide broke on the second lane of the first day and I ended up competing with a gun that I had only carried as a "Demo" (to get other shooter's feedback on the idea of a short stroked, 12 ft-lbs 0.177" cal. D-54). No dope, no trajectory, no IDEA what the gun was doing! LOL! I ended up placing in 4th place. But we learned from that experience.
For 2012, I had a good trajectory established and I felt confident about taking the rig (a WFTF D-54 with a HorusVision 4-16X50 scope) to the GOB's shoot. I did not count, however, on Rod Bradley showing up with a Whiscombe and putting all the rest of the spring shooting roster to shame; so, I ended up in third place. It was also the year when Roz announced that it would be the last event, as he was being pulled by other interests.

2013 was the year of our accident, so we did not go to too many GP shoots and we missed the "Tennessee Two Step", that while not shot completely at the GOB's club, it still took the place of the Tennessee GP event in the AAFTA roster. It is important to mention that the TN Two Step was sort of a "transitional" event, because it allowed Robert Ray, the current Match Director at the GOB's GP Shoot to get "the ropes"; and boy, has he done well!

For 2014, Robert prepared a very typical GOB's match. A VERY hard match (34-36 Troyers).
When the top shooters in all PCP disciplines drop more than 10% of the possible points, you know it was a hard match.

And, like some of the best stories, we start at the end: I placed second.

Now, let's backtrack to the beginning and see how it all happened!

We are in the process of getting ready to go to the World's Matches that will take place in New Zealand, first days of September. One of the main problems for us has been the ridiculous laws that govern airguns in Australia. ¿Why Australia, if we're going to New Zealand?, well, because after New Zealand, and given that we are already halfway around the globe, we are taking up the chance of visiting the Australian side of the family. Who knows when we will have the chance of being in that region of the world again.

So, we are going to Australia and my research showed that we can not even be guaranteed to bring back our scopes, should we make the mistake of taking them to Australia. Let alone the rifles!

We found a place to store our piston guns in Auckland, but they charge per day per case, and storing two cases was almost as expensive as paying a high end courier service to bring the guns back home (more than what the guns are worth, BTW). Of course, the New Zealand Postal Service does not want to transport anything that resembles a firearm, AND, peculiarly, their constitutional mandate does NOT include the concept of transporting "ALL lawful goods". SO, the New Zealand laws did not help either. SO . . . the ONLY way to make the whole thing economically feasible was to be able to place TWO COMPLETE SHOOTING SYSTEMS in a single case.

Many years ago, I had been given a largeish rifle case that had been dedicated to a Blaser hunting rifle. It was made for takedown guns, and it was solidly built. The dimensions complied with airlines max. added dimensions (62" adding length, width and height), and it had combination locks.

After MANY hours of thinking how would be the best way to get two complete systems in there, I procured the material, laid out the geometry and started cutting, this is the result:
Picture
The case as it started.
Picture
At the bottom, there is a foam layer, then we added another, THICK layer of hard foam with the cutouts for the stocks and the scopes. Notice how the scopes remain what in essence is the TOP of the case, when the case is carried or is laid down on its edge.
Picture
Then we added a protective layer of hard foam. Note that the scopes use the ENTIRE height of the case, whereas stocks (and later, actions) use only half of the height.
Picture
Now, come the actions. As commented above they use only the bottom section of one half of the height. The only thing missing are the scope wheels. ¿Or is it?
Picture
The scope wheels have been added, located where there is the least interference between the scope's turrets and the rest of the parts. Again, I repeat: We are now complete, or ¿Are we?
The truth is that we are NOT complete!

What can you think we are missing?

I'll give you three seconds to guess.

.

.

.

The PELLETS!

Yes, I forgot the pellets!

At the time I did not realize it. I went and picked Verónika from her office and we drove to LaGuardia airport in NYC.
We checked in the bags and when the Port Authority Police arrived (common procedure in LGA), they ask: What do these rifles shoot?

And I go: "Pellets, officer, like these. . . .  Oh . . . . s.....t!" and then I realize that we do not have ONE pellet to shoot!

I was on the fence about going home and trying for another flight, or doing something else, like calling some friends and asking them to overnight some pellets to us in TN, when Verónika suggests calling Pyramyd Air and ordering some to be overnighted to Pulaski.

So, we dial the call center number and when the phone is answered, there is a familiar voice at the other end, the conversation went something like this:

HM.- "Tyler?"
TP.- "Hector??"
HM.- "What are you doing answering the phone there?
TP.- "Well, this is what I do, it's my job (chuckle)"
HM.- "Wow, am I glad to hear your voice!"
TP.- "Why?, what has happened?"
HM.- "Well, I am ashamed to admit it, but we're going to Tennessee and I forgot our pellets at home. Is there anyway Pyramyd Air can overnight us a couple of tins?"
TP.- "What pellets do you shoot?"
HM.- "AA 8.44's 4.52's"
TP.- I have a tin, the company is out and backordered on those, but I have a tin and I will be departing to TN in a few hours, I will take them for you.
HM- "Wow!, thanks you're a lifesaver!"
TP.- "See you tomorrow at the range!"
HM.- "Yes! thanks a bunch!"

And so we were able to get a tin of pellets for both of us.

That still left the issue of the lubricant pending, but in the end, we at least had pellets to shoot!

Our flight was delayed and then delayed again. I would have had time to go home, pick the pellets and return, but there was no way of knowing that, so we stuck to the plan. We arrived in Pulaski at 01:00 AM of Friday, and after sleeping a few hours, I went to the range, where I met Tyler. What a Relief to see his smiling face there!

We horsed around a little and then the second part of the quest started, did anyone had any T-9?

We had looked for the T-9 lubricant in the shops around town and all the way to Nashville, no luck.

Suddenly I ask Mike V. and he says: I do not use T-9, but I use Krytech in my spring guns. Want to try some?

So, Mike was kind enough to lend me a little KryTech and I hand-lubed some pellets and tested them. Rain was pouring down like the skies had opened, so I had some time on my hands till the range would be useful again.

One by one the test pellets were lubed and when the rain stopped, I had the chance of testing the pellets and the lubricant.

Not quite what I would have liked, but at least we had SOMETHING to shoot! LOL!

My deepest appreciation to Tyler and Mike for their unflinching support!

We counted the pellets, sorted them into small zip-locs so that we would not shoot too many at the sight-in/warm-up sessions and we got ready to shoot the GOB's courses.

As usual with all FT matches, the day starts with a good sight-in and warm-up session:
Picture
The "downhill" sight-in range.
Picture
Some of our top shooters, all shooting Steyr rifles, from top: Ken Hughes Peter Brooks (2013 PCP Team USA) Neil Youngren (2013 PCP Team USA)
Picture
From top: Leo Duran, with his Whiscombe, David Alsup shooting a Steyr, then Peter Nylen shooting a TM-1000 and Doug Vinson with his "Bling-Thing Special", the brightest FT Rifle I have ever seen.
Picture
A closeup of Leo Duran and his fine form, plus a good look at his Whiscombe. Leo uses a Bushnell 8-32X40 on his Whiscombe, but that scope may be replaced later by a March.
Picture
And, of course, my MUCH-better-than-me half. Veronika Ruf.
After the shooters meeting, the squads were assigned and off we went to the Red Course.
Picture
Veronika was squadded the first day with Sandra Rutterford.
Picture
From left to right: Charles Garvey (sitting), Ron Robinson (kneeling), Mike Vredenburg (shooting with harness), Steve Vines (sitting on the ground), Peter Nylen (Standing), Robert Ray (scoring), and Leo Duran (contemplating the immortality of the crab).
Picture
Roz Sumpter enjoying the shooting.
The first day was a little bit frustrating because even having re-calculated the trajectory and even knowing that the lubricant was not the usual one. I did find that the POI from the Sight-in range was not the same as down in the lanes.
I lost quite a few targets to hits in the lip of the KZ, and I kept adjusting the POI little by little.
After a while I got in a good streak of hits and I was able to post a respectable 36.
In a course that was designed for Open and Hunter PCP's shooting a flatter trajectory, with less wind deflection from stable and supported positions, with borrowed pellets, I was not completely unhappy.

Veronika posted a 35, and so she was not unhappy either.

Of course, after a day of shooting at the GOB's, ¿what is on the order of the day?

A dinner at Legends!
Picture
Left to right: Tyler Patner, Leo Duran, Ron Robinson, Roz Sumpter, Tara, Harold Rushton, Steve Vines, ??, Robert Ray, Mike Vredenburg, Veronika Ruf, Bob Dye
The second day saw us shooting the White course.
Picture
Where Leo and I exchanged places a number of times. Veronika was having problems finding her POI and she even wiped the lubricant off some of the pellets to see if that was the problem, she did stage a comeback, but it was not as good as we would have liked.
In the end, we placed 2nd and 3rd and, considering that the option was to not shoot at all, I think we are grateful we had the chance and that we have the good friends and comrades that are willing to go out of their way to help a fellow shooter.
Picture
Now that I know that there is a street in Pulaski in my honor, I will go back even more gladly! LOL!
We cannot stress enough our thanks to Tyler and Mike, without them we could not have shot AT ALL!

BIG thanks go to Robert Ray, David Slade, Steve Vines, Pat (FireMarshall), Roz Sumpter, Cliff Smith and each and everyone of you that made the shoot possible. As I said, it IS an Institution of American FT.

I will keep on going, hoping one day to break the Jinx that the GOB's range has on me!

;-)





H Medina
2 Comments

    Hector Medina

    2012 US National WFTF Spring Piston Champion
    2012 WFTF Spring Piston Grand Prix Winner
    2013 World's WFTF Spring Piston 7th place
    2014 Texas State WFTF Piston Champion
    2014 World's WFTF Spring Piston 5th place.
    2015 Maine State Champion WFTF Piston
    2015 Massachusetts State Champion WFTF Piston
    2015 New York State Champion WFTF Piston
    2015 US National WFTF Piston 2nd Place
    2016 Canadian WFTF Piston Champion
    2016 Pyramyd Air Cup WFTF Piston 1st Place
    2017 US Nationals Open Piston 3rd Place
    2018 WFTC's Member of Team USA Champion Springers
    2018 WFTC's 4th place Veteran Springer
    2020 Puerto Rico GP Piston First Place
    2020 NC State Championships 1st Place Piston
    2022 Maryland State Champion WFTF 
    2022 WFTC's Italy Member of TEAM USA 2nd place Springers
    2022 WFTC's Italy
    2nd Place Veteran Springers

    Archives

    August 2022
    May 2022
    April 2022
    February 2022
    August 2021
    July 2021
    June 2021
    May 2021
    April 2021
    March 2021
    February 2021
    October 2020
    September 2020
    August 2020
    July 2020
    June 2020
    May 2020
    April 2020
    March 2020
    February 2020
    January 2020
    December 2019
    November 2019
    September 2019
    August 2019
    July 2019
    May 2019
    April 2019
    January 2019
    December 2018
    November 2018
    October 2018
    September 2018
    August 2018
    June 2018
    May 2018
    April 2018
    March 2018
    February 2018
    January 2018
    December 2017
    November 2017
    October 2017
    September 2017
    March 2017
    December 2016
    October 2016
    September 2016
    July 2016
    June 2016
    March 2016
    January 2016
    December 2015
    November 2015
    October 2015
    September 2015
    August 2015
    June 2015
    May 2015
    April 2015
    March 2015
    February 2015
    January 2015
    December 2014
    November 2014
    October 2014
    August 2014
    July 2014
    June 2014
    May 2014
    March 2014
    February 2014
    December 2013
    November 2013
    October 2013
    September 2013

    Categories

    All
    Events
    Gear
    Hunting
    Tests

    RSS Feed

Proudly powered by Weebly