Changing My Thinking About Slugs

[rsterne]

One very cool thing about airguns is that I never stop learning something new, or at least a new way of looking at something!.... There have been a few things happening lately that have changed my thinking about airgun slugs and the velocity we shoot them at.... Here are the "new" developments....

It turns out that the G1 drag model we have been using to calculate the Ballistics Coefficient of our slugs is not a very good fit to the drag curve of the slugs.... This first showed up as higher than expected BC's for our slugs when they were shot at higher velocities.... Manufacturers were claiming high BC(G1) values for their slugs, to the point of being hard to believe.... When tested at 800-900 fps, we got much lower values than claimed.... Then articles started showing up claiming that the faster slugs were shot, the higher the BC(G1) was.... If the drag model being used to calculate the BC (in this case the G1 model) is a poor match, then BC values change with velocity, whereas they should remain constant.... This was a warning flag that something was wrong.... When we started investigating the actual drag of slugs, by shooting them over a LabRadar chronograph, we quickly found out that the drag in the low Transonic region, between Mach 0.8-0.9, was lower than the G1 model.... This was the reason that as the velocity was increased, the calculated BC(G1) increased, because the slugs were being compared to a drag model where the drag was increasing faster than it was with our slugs....

Miles Morris, UK ballistician, calculated what the drag should be doing for our typical slugs (a tangent ogive with meplat design), and confirmed that what we were seeing in fact had a base in theory.... He called this new drag model SLG0, and while it is a work in progress, it gives more constant BC's than does the G1 drag model.... However, it is only available in one Ballistics Calculator, the "MERO" developed by another UK chap, George Conway.... We have found that the RA4 Ballistics Model, which was intended for the .22LR rimfire bullet, is not a bad match for our slugs, and far better than the G1 model.... Slug manufacturers would be doing a great service to their customers if they quoted the BC(RA4) instead of, or at least in addition to, the BC(G1).... Unfortunately the "quoted BC" using the RA4 model is lower than by using the (flawed) G1 model, so they can't brag as much!....

Those who have followed my writings over the years will remember that I have proposed that there is an "optimum" velocity to shoot pellets at to minimize the wind drift.... It turns out that is about 900 fps, plus or minus a bit, depending on the range you are shooting.... Since the G1 and GA drag models have similar drag curves, then the same thing should apply to slugs, optimum velocity for minimum wind drift should be similar to pellets.... Well, it looks like I got that wrong, because our slugs do NOT follow the G1 drag curve.... Follow this thread as I add to it, and you will see why....

Bob

[mr007s]

Interested and following along.

[splitbeing]

Exciting news! Following with interest in discoveries...

[Baco]

following 

[JuryRigger]

Watching with great interest! 
Jesse

[Motorhead]

Curiosity has me following as well   

[Ronfiveo]

This is all Greek to me, but I am here to learn. Following.

Ron

[rsterne]

OK, I hope you are with me so far.... Here is a chart showing what the BCs would be for a slug that matched the RA4 Drag Model perfectly, and using that model had a BC of 0.22.... That is the black line on this chart....



The red line represents the BC's you would calculate, for the same slug, if you used the G1 Drag Model.... Instead of being a straight, horizontal line, it shows pretty good consistency below 800 fps, but the faster you drive the slug above that, the higher the BC is.... NOTE, this does not mean it has less drag, only that the BC's above 800 fps using the G1 model are faulty, if the slug drag follows the RA4 proflie.... The other two lines are for the G7 (boattail) model, and Miles' SLG1 model, which he has developed for my "Bob's Boattails".... Both the G1 and SLG1 models agree pretty closely with the RA4, and you could use any of the three with this slug with minimum error.... However, the G1 model simply does not work well for this slug above 800 fps....

I am following this post with another dealing with why this is important in determining the optimum velocity to shoot a slug at for minimum wind drift....

Bob

[rsterne]

OK, so here is the meat and potatoes of this thread.... Since the drag of any projectile rises quickly in the Transonic region (Mach 0.8-1.2), and the wind drift of a projectile is proportional to the "Lag Time", which is the DIFFERENCE in flight time between in a vacuum and in the real world, the worse the drag is, the faster the projectile slows down, and the more it drifts.... This results in an "Optimum Velocity" for any projectile, to minimize the wind drift.... These curves take this general form....



However, the specific shape of the curve depends on the SHAPE of the drag curve of the projectile.... If we use the G1 profile to predict the optimum velocity, and that is a poor match, we get the wrong answer for the optimum velocity.... Here is the curve of wind drift for the projectile in the previous post, predicted using the G1 drag profile....



These curves are part of the "MERO" Ballistics Calculator developed by George Conway, and available for most platforms at:  https://gpc.fotosoft.co.uk/

Note that the optimum velocity to minimize wind drift (using G1) is only 850 fps over a distance of 300 yards!.... Now let's see what happens if we use the RA4 drag model....



Note that the optimum velocity for minimum wind drift is now 1000 fps, instead of 850 fps.... If we use the wrong drag model, we get the wrong results.... Here are two more charts, for the SLG1 and G7 drag models....





These two drag models also predict an optimum velocity of close to 1000 fps.... The eagle-eyed among you will have noticed that the value of the BC used for each chart changes with the drag model chosen.... If you look at the chart in the previous post, the BC values for 1000 fps change as you change drag models, and MERO selects the correct value for the other drag models at the velocity you are looking at, in this case 1000 fps....

So, all the articles I have written previously, where I talk about 900-950 fps as being the optimum velocity to minimize wind drift are in error! (for slugs).... That is true for pellets, which largely follow the GA drag model pretty closely, but our slugs do NOT follow the G1 model very well, so the RA4 (or the G7 or SLG1) is a far better choice.... Now which one you choose will give you a completely different NUMBER for the BC, but as long as you use the same drag model to calculate your BC as you do to use it in your Ballistics Calculator, you will be fine....

OK, so I have changed my mind, for slugs, I now would prefer to shoot that at around 1000 fps (assuming they are accurate at that speed).... Does that make a difference in how I design them or choose them?....

You bet it does!.... Stay tuned!....

Bob

[Motorhead]

THOSE OF US WHO HAVE THE POWER / MIENS TO SHOOT SLUGS at +/- the 1000 fps range have seen that they can do it & quite well.
Great to read up on some data that supports those who really are / have done it because it works 

Nice bit of work with support from other ballistics experts .. kudos !!!

[rsterne]

Those of you who have been following my articles will remember that there is a way to calculate the absolute maximum FPE that a PCP can produce.... You take the bore area (sq.in) times the pressure (psi), and multiply by the barrel length (in feet), and you end up with the total FPE that can be produced.... However, that number includes all the energy lost to friction, etc., plus the biggest loss of all, which is the energy required to accelerate the mass of air that in turn accelerates the projectile.... I came up with a "lofty goal" of 50% of that for a maximum power shot, a number which is seldom achieved in practice.... My own guns usually fall about 10% short of that goal for a full power shot (ie 45% of maximum), and in fact by the time I detune to a level where it isn't wasting huge quantities of air on every shot, 40% of the theoretical maximum is pretty typical, for the way I shoot them....

So, since we can calculate the maximum possible, if we take 40% of that as the likely result, we can get a pretty good idea of how much FPE one of my "high power" PCPs is likely to produce.... If we work the FPE equation backwards, instead of calculating the FPE based on weight and velocity, we can pick a velocity, and knowing the likely maximum FPE, we can come up with the heaviest slug I am likely to be able to drive at that velocity, knowing the barrel length and pressure.... I built a spreadsheet to do this for me, where I can input the velocity desired, the pressure, and my 40% typical efficiency factor, and it will spit out the maximum slug weight.... That can then be converted to the Sectional Density of the slug, and that number will be a constant, regardless of calibre.... Here is the first chart giving maximum slug weight, for .224 through .308 cal.... using 1000 fps, 28" barrel, and 40% efficiency....



Here is the next chart, showing the how slug weight varies with the SD.... Similar lines can be drawn for any calibre.... I chose .224 through .308 as they are the most likely I would use for a long range, maximum power PCP....



And here is the conclusion, a single chart showing maximum SD vs pressure, again for 1000 fps, a 28" barrel, and 40% efficiency....



Note that the calibre is no longer important.... It is the SD that matters, and there is a maximum SD depending on the pressure.... Notice the dot at 3600 psi, at an SD of 0.17.... that is my new "design point".... While this may seem a rather conservative SD, it is about the heaviest slug I will be able to drive at 1000 fps using a reasonable pressure (3600 psi) and barrel length (28").... This will influence my choice of calibre....

Since I will be limited by an SD of just 0.17, the larger calibres are a poor choice, unless you want to run more pressure or a longer barrel.... This doesn't mean you can't use a 7mm of .308, just that you will have to accept less than 1000 fps, or as Scott Hull did on his contest winning rifle, a longer barrel (he uses a 48", at only 2800 psi).... Scott shoots a 106 gr. 7mm BBT (SD = 0.188) at 1055 fps, for 260 FPE, which incidentally is 37% of the theoretical maximum FPE.... When I put all those numbers in my spreadsheet, it confirms that 106 gr. weight, by the way!....

My choices for calibre are now limited (personally) to .257 cal and smaller to reach 1000 fps using 3600 psi and a 28-30" barrel.... Stay tuned and I will tell you what the slugs will look like, depending on the calibre I choose....

Bob

[rsterne]

OK, so down to the nitty-gritty of how this new thinking results in a range of calibres I find best for the job at hand.... a long range slug gun....

If you look at the first chart in the last post above, and determine the maximum slug weight for each calibre, you will find the following for 3600 psi (using a 28" barrel at 40% efficiency).... These all have an SD of 0.170.... They will all be close to the same length overall (because they all have the same SD).... However, their shapes will be vastly different....

.308 cal - 113 gr.



.284 cal.... 96 gr.



.257 cal.... 80 gr.



.243 cal.... 70 gr.



.224 cal.... 60 gr.



.183 cal.... 40 gr.



I added this calibre because I have a barrel coming for this, with a 5.9" twist rate!.... Any guesses as to which slug will have the best BC?.... Remember, they all have the same SD....

Bob

[splitbeing]

What is .257?

[rsterne]

.257 cal is a powderburner calibre (as are all the others mentioned), just a few thou larger than a .25 cal airgun.... The advantage of using PB barrels is that they are built to tight standards, whereas airgun barrels are all over the place in diameter.... The barrel I usually use for my .257's is a 14" twist TJ's, originally made for a 25-20 Winchester....

Bob

[rkr]

Good thread Bob, thanks! Some comments, 250bar/3600psi is rather high pressure and you may need two tanks at the range if you shoot well over 100 shots with .257. I dug out my Chairgun and some old labradar data and it seems that the old G1 BC number I calculated earlier is the same when calculated with RA4 model, should that be the case? I also did some wind drift estimation at 100M using 257420BBT bullet which is the range I typically shoot at and the difference in drift from 920fps to 1000 fps is only 1mm so really not worth pursuing, below 920fps it starts to increase fast. That then means that for 100M paper punching it is not necessary to chase that 1000 fps but find the best accuracy in the 920-1000 fps range. I then went to check the drift at 200M (which I seldom shoot) and there I can see 7mm difference from 920 to 1000 fps. I think that for most shooters that 1000 fps goal is a bit too much, 3000 psi fills and 920-950 fps speed would give in practice the same results unless you regularly shoot at 300M. Another aspect worth consideration is the actual BC, the higher it is the smaller the difference. For people shooting low BC commercial slugs (0.1 and less BC) that 1000 fps would be better but those slugs are light so they could also use lower starting pressure.

[Waldo1]

"Any guesses as to which slug will have the best BC?.... Remember, they all have the same SD.... "

Robert, if OAL and SD are all practically identical, then my SWAG would be the .183 slug. I'm looking at the L/D ratio for the projectiles. How wrong am I?

[rsterne]

Yes, the .183 cal should have the best BC of those shown.... The "slenderness ratio" (L/d) has a large influence on the form drag, although an inverse effect on the surface drag (which is less important).... Providing the long slender slug does not yaw excessively, it should have a better BC....

rkr, I had a lengthy response written but lost it.... Bear with me as I rewrite it.... 

Bob

[rsterne]

rkr, you are correct that 3600 psi is high, but with 300 bar/4500 psi bottles readily available, it is within reach, even with a regulated PCP.... If you are tethered to, or filling from, an 88CF SCBA bottle that starts out at 4500 psi, you will have 900 psi of "headroom" (pressure available), times the 550 CI internal volume, which even allowing for the VanDerWaals correction should give you about 30,000 std. CI of air available.... An 80 gr. slug at 1000 fps is almost 180 FPE, so at 1.0 FPE/CI efficiency that should give you about 160 shots or so.... Calibres smaller than .257 will of course get more shots (with less recoil as well)....

If you scroll up to Reply #7 and look at the chart, the RA4 and G1 BC's are the same at just over 900 fps, so if you checked your BC at that speed, they would have been the same.... The BC(G1) is lower than the BC(RA4) below that velocity, and higher above that....

You are of course correct that shooting at the most accurate velocity for your slug is of paramount importance.... By selecting a slug with a low enough SD that I can push it at 1000 fps without having to tune the gun as an "Air Hog" gives me the ability to do so, it is always easy to tune it slower if that is more accurate.... It may well be that shooting a heavier slug slower could produce better results.... Shooting at 950 fps only increases the drift about 8%, which could be made up by using an "equally slippery shaped" heavier slug at a lower velocity.... However, the lighter one, shot at 1000 fps, will have a flatter trajectory than the heavier one at 950.... Sighted at 100 yards, a shot at 300 yards will impact about 10" higher using the higher MV....

The change in my thought process just gives me more options.... Previously I was designing and selecting slugs with the idea in mind of shooting them at 900-950 fps.... Now that we are finding that their drag is less at 1000 fps than we thought, I am encouraged to work on lighter slugs as part of my "inventory" of possibilities, which affects both gun and slug design....

Bob

[cosmic]

.284 proven long range..

[Motorhead]

The reining RMAC LEADER in Big Bore / Long range shoots 7mm / .284

Really sad the folks or whomever who do there Match Reports ( RMAC ) seem to not give credit where CREDIT is due .. because rifle doing this work is not a production unit, or is the shooter sponsored by an affiliated manufacturer.