Ballistics Coefficients Changing with Velocity

[rsterne]

In another thread I mentioned that I had done some testing of pellets at various velocities to determine the Ballistics Coefficient.... What I found was quite interesting as it was NOT a constant but in fact a curve with a definite peak.... The peak was at a higher velocity with heavier pellets.... Here is a graph of the trends I found....



Those results are smoothed to show the trends, and should not be relied on to predict the BC at a given velocity.... I did not have a powerful enough gun to propel the 25.2 gr. Monsters fast enough to see their dropoff.... The BCs were calculated by measuring the velocity at the muzzle and 25 yards and then using the BC Calculator in ChairGun.... I used the JSB Exact series of pellets as they are designed to have a high BC and there was a good range of weights available.... Once I realized that there was a big drop in the BC at the higher velocities I did more testing at much shorter range, just 5 yards....



Note how low the BCs get when the velocity approaches the speed of sound.... At 600 fps I measured a BC of 0.035 for the 13.4 gr Exact RS but at 1100 fps it had dropped to only 0.010.... It lost over 11% of its energy in just 5 yards.... With the 18.1 gr. Exact Heavy I measured the BC at 0.040 at 800 fps and at 1000 fps it was down to 0.020.... If you are looking for an explanation of what is happening, then check out what happens to the Ceofficient of Drag in the transonic region (which starts at Mach 0.85 - 950 fps)....



After these experiments I concluded that there is no point in pushing a pellet past about 950 fps.... It takes a lot of energy to accelerate it that last bit.... and then it turns around and loses all that extra energy in the first few yards.... In addition, once you start pushing over about 1050 fps then you can be dealing with locallized shock waves which can initiate tumbling or other loss of accuracy.... If you need more power, once you hit 950 fps go to a heavier pellet....

Bob

[S.S.Tupperware]

Interesting... I was thinkin a 950 plus 22 would be good, but...

[ltpro]

Great post!Whats funny to me is that I just got into airguns 7 days ago and I already had come to the very same conclusion!Thanks for the work in getting this done you may save a lot of people tons of trouble.

[RedFeather]

Are these diabolo, waisted pellets?  What are you shooting them out of?  Do you think that, at the higher velocities, they are over-stabilized? 

[rsterne]

JSB Exact Series (diablo, waisted).... Shot from a PCP (24" Crosman barrel) with variable power.... The gun will produce sub MOA groups with 18.1 gr. JSB Exact Heavies at 25 yards when shot at 950 fps (36 FPE).... My twist calculator (Miller Rule) indicates a stability factor of about 1.5 with these pellets at subsonic velocities.... so that would indicate they are not over-stabilized.... in fact near optimum....

Here is the raw data for the 18.1 gr. JSB Heavies.... MV and BC (over 25 yards)

566 fps : BC = 0.030
710 fps : BC = 0.036
819 fps : BC = 0.040
899 fps : BC = 0.032
967 fps : BC = 0.027
1004 fps : BC = 0.022

Bob

[Jay]

Bob just want to say I have enjoyed reading(really guess studying) the work you do with AGs, it is fantastic Brother having you around to drop these golden nuggets of knowledge(and formatting so its seeable/understandable) for us so we can find the gold mine in the use of our guns. THANK's for your work.
 P.S. Hope you don't mind that I save most of your work to my files.

[rsterne]

Anyone is absolutely welcome to save any of my posts.... I do them to share my results with the airgun community.... When I started back into airguns 4 years ago when I retired I was frustrated by the lack of detailed information available.... Now, when I do an experiment or project I try and document it and share it.... Glad it helps....

Bob

[Snaab9-2]

Excellent post, and very interesting!  Really appreciate the information. 

I look forward to any additional chonro work you do on this in the future!

[rsterne]

I can't test every possible combination, guys!.... JSB Exacts seem to work well in most of my guns in one weight or other.... that's why I tested them.... Anyone with a Chrony, some time, and some pellets can get in on the act.... You need to set up your Chrony at two measured ranges from the muzzle and fire 5-shot groups and record the average velocity.... I used 1 yard and 25 yards for most of my testing.... When you get into the area where the BC is really tanking then to get better data you really need to shorten up the range.... You could use as little as 5 yards or as much as 10 yards.... The problem is that the pellet loses so much velocity in the first 5 yards when it starts out near the speed of sound.... that if you measure it at 25 yards you are only getting an "average" and the calculated BC will be higher than it really is....

When you think about what is happening when you shoot at near sonic velocities.... it's pretty complex.... The BC starts out low and then increases.... If you shoot at really long range then it peaks and starts to fall again.... The actual trajectory will be more curved on the ends and flatter in the middle than the "average" value would indicate.... Some of the best FT shooters in Canada have remarked to me that they have observed this and previously didn't have an explanation until they saw my data....

Incidently, I tried an RWS 11.9 gr. Hobby that was just supersonic (1131 fps) just out of curiousity.... In just 5 yards, it lost 96 fps and the energy dropped from 33.8 FPE to 28.3 FPE... a loss of 16.3%.... The BC was a feeble 0.007....

Bob

[Snaab9-2]

Well, even if you cannot test ever pellet.... still a good (excellent) post. 

[rsterne]

Here are some Ballistics Coefficient measurements I did a couple of years ago.... The "Non-PAL" numbers are using a gun that shoots under 500 fps with "normal weight" pellet as required by Canadian law to not be classified as a Firearm and require a "Possession and Acquisition License".... They were done with Crosman pumpers (1389 / 2289).... The "PAL" numbers were done using a Diana 34 in .177 and a Crosman based PCP with regulator in .22 cal.... 5 shot groups were fired to collect the muzzle velocity and the velocity at 25 yards and then the BCs calculated using ChairGun....









You will note that in general terms, wadcutter (flat nosed) pellets performed poorer at the higher velocities (ie the BC dropped).... while round nosed pellets had a better BC at the higher velocities than they did at under 500 fps.... Most pointed pellets were also not quite as good at the higher speeds with the notable exception of Predators.... The numbers in bold in the second set of data indicated that the BC improved at the higher velocities.... Note that there aren't that many pellets that did that.... This is not a comprehensive study of each type of pellet as there are only two velocity data points.... It clearly shows, however, that the BC of pellets is affected by the velocity....

Bob

[ltpro]

Thanks again for your work , very informative layout.

[Daysailer]

Bob, very good post!
Thanks for the charts and data at the two different velocities !!!  Great Stuff!

Solid data and science really help prove, or not, so many of the myths and "common knowledge" that gets passed around in many sports.

I have enjoyed you lessons on BC on this post and the other these last few days.
One question, maybe very much off track, keeps popping into my head.
My other pastimes are racing sailboats and flying RC sailplanes (gliders).
When self teaching the aerodynamics and hydrodynamics to design and build
the planes and the centerboards and rudders for my boats, there is a number
in the aero and hydo-dynamic world that may be the equalivent of  BC, ...
...but I am not sure.

Are "Reynolds Numbers" used in BC calculations ?
They are a function of speed, form drag, viscosity of the fluid, and length of the  object.
When reading your other post, I wondered if assuming the form drag would behave
the same in .177 vs .22 (for the same shape) would account for some of the BC
differences at different velocities.  Given the same fluid (air); speed, viscosity, humidity,
pressure...etc, a larger cross section will have to have a higher drag.

In the airplane world,  a 50k Reynolds Number might apply to a wing at 100 mph.
The same wing at 500 mph will have a RN in the millions, when calculating lift/drag ratios.    
(not actual #'s in my example.  Just foggy memories from years ago)
In water, a boats rudder might have the same 50k RN at 3mph.  Viscosity really affects this number.  

I also remember how the factor of RN affected my gliders preformance.
When practicing and tweaking trim, the gliders flew much better in winter temps
and humidity, than they did in summer temps and dryer air.  One way the RN
factor was explained to me was that the thickness (# of air molecules for a given volume)
of the air improved the lift of the wings noticably.  Drag would have also
been increased, but at the slower speeds was not as big a part of the RN calculation.

I wonder if the top FT and BR guys find the same issues with their accuracy in different air conditions ?

If you are a trained engineer, please forgive my layman's explaination.
Just trying to put outside experience into practice in my airgunning.


One of my scratch designed/built gliders placed in the top 10 at a Nationals in the '80's. My sailboat preformance in the last 15 years.....much better)

[rsterne]

I too spent much of my life doing R/C yachts and sailplanes.... in fact my business for 30 years was R/C racing yachts.... My designs have won a World Championships in 1980 and many US National Championships over the years.... I had a website which I tried to take down when I retired but couldn't contact the webmaster so it's still around if you want to take a look....

http://www.myrc.org/bobsterne.htm

Anyway, I'm VERY familiar with Reynolds Numbers....  but I never though of doing a calculation to see if there was something going on with pellets.... The critical Rn is 50,000 where all sorts of weird things change.... Sooooooooooo.... let's see where that happens with pellets.... Here is a calculator that will take into account all the possible atmospheric variables....

http://aero.stanford.edu/StdAtm.html

It turns out that a pellet only 0.0158 ft. long (0.190") moving at 500 fps has a Reynolds Number of just over 50,000 (at sea level).... What that means, in practical terms for airgunners, is that most pellets will be moving fast enough to be above the critical Rn.... However, there are still signiifcant changes in how air flows past an object up to a Rn of about 400,000.... A pellet that is 0.75" long travelling at 1000 fps would have a Rn of about 400,000.... Therefore, significant changes in the flow around almost all pellets will exist at different velocities.... just not critical ones....

Bob

 

[Daysailer]

Thanks for the Rn info for airgunning...I had a feeling you knew about them.

[Snaab9-2]

Wow, excellent post.  Thank you so much for the information.

Based on your information, I think I will try the JSB exacts (15.7 grain) as it looks like they may help me during my long range shooting (I do a lot of 50-70 yard stuff and have been shooting Premier Domed).  Intersting how much better they are at high FPE (.037 vs .028) but it is actually slightly worse (.020 vs .022) at low velocities.  I think overall though for my shooting, based on your data, they will be better.  I would expect them to be at least as accurate as the Premiers but only one way to find out!

I am not sure they will have such a good BC in my 22-23 FPE Disco but should be fairly close.  I may also try the 18.0 grain JSBs and Kodiak's... though fear shooting a pellet too slow at those ranges as it will be harder to compensate.

Thanks again!

[rsterne]

My Disco loved the 15.9 gr. JSB Exacts.... shot them at a whisker over 800 and they were the most accurate pellet in that rifle....

Bob

[Snaab9-2]

I cannot wait to try them!  I also cannot wait to get a chrono to play with... maybe for Christmas.

[JonnyReb]

  Love the sharing of your impressive knowledge Bob and glad you chose this forum to educate. For the first time you've really got me thinking about the science behind the simple numbers i pull off a chrony and the science behind some of the best ammo available for our respective guns. Your posts are often simply brilliant.

  Knew there was another reason i loved JSB's so much

[rsterne]

Thanks for the kind words.... I love to learn and love to share....

Bob