❓ Is there is an "ideal" caliber for achieving maximum BC in typical airguns?

I will do slugs first, although most of this applies to pellets as well....

Rule #1....

For a given "shape", in theory the "Form Factor", which is how the drag coefficient of your projectile compares to the drag of a "standard projectile" at the same velocity, should be the same, regardless of caliber.... However, the Sectional Density (for identical shapes and materials) varies in proportion to the caliber.... This is because of the "square-cube" rule, so for a given projectile, the base area increases by the square of the caliber, but the mass increases by the cube of it.... SD = Mass / Area, so since BC = SD / FF this means that for a given shape, the BC increases in proportion to the caliber....

Rule #2.... (Not critical to the discussion, but provided so that you can understand better)....

The total energy (FPE) that can be achieved by a PCP is proportional to the Bore Area ("A" in sq.in.) times the Average Pressure ("P" in psi), times the barrel length ("L" in ft.).... That total energy is divided into the FPE of the projectile, the FPE of the air mass that accelerates it, and other losses.... The very best PCPs, running wide open full power, with bore area porting and a large plenum, and dwell sufficient that maximum pressure is being applied all the way to the muzzle, barely achieve 50% of the theoretical.... anything you do to decrease the power, lowers that percentage.... These include a smaller plenum, smaller porting, and of course reducing the dwell to get more shots and efficiency.... As a "lofty goal" I use FPE = A x P x L/24 with L in inches.... Dividing by 24 accounts for using inches instead of feet, and the 50% reduction from the theoretical maximum.... If you are dealing with smaller ports, you can correct the area you use by multiplying the smallest port diameter by the caliber, and then by PI/4, and use that instead of the bore area for "A"....

Rule #3....

While Sectional Density is a good thing to maintain velocity and energy downrange (beneficial to BC), the exact opposite occurs INSIDE the barrel.... A projectile with a high SD is more difficult to accelerate.... This means that to achieve a given velocity, and hence a given FPE for the weight, you need a more powerful "engine", ie one capable of a higher FPE (see Rule #2).... For a PCP that meets my "lofty goal", you can calculate the maximum SD that can achieve a velocity of 950 fps if you know the pressure and barrel length.... This chart shows that relationship....



Now remember, these are based on a PCP that can achieve my "lofty goal", and not many can (my best guns run about 45% instead of 50%).... A useful way to use this chart is to use the coloured line for your barrel length and find the operating pressure on the horizontal axis, and where those lines cross, consider that the maximum practical SD for your gun.... As an example, if you have a 24" barrel operating at 3000 psi, the maximum SD you could hope to push at 950 fps would be an SD = 0.17, and more likely you might get that to about 900 fps.... To make this easier to use, so that you don't have to calculate the SD, you can use the charts below.... They assume a 24" barrel, but in fact you will probably need a bit more than that, depending on how closely you approach that 50%....



The lower chart is an expanded version of the bottom corner of the upper one, to make it easier to read.... Again, remember that these should be considered maximum weights, unless you want to shoot below 900 fps....

Rule #4....

This combines all the above.... Since for a given shape, the SD and hence the BC increases with caliber.... and the maximum SD depends on barrel length and pressure (for which there are practical limits).... if you look at how bullet shapes change as you increase the caliber for a given SD, you will notice that larger caliber slugs tend to be short and fat.... while smaller caliber slugs can be relatively longer and more slender.... This means that for a given combination of barrel length and pressure, for constant SD, smaller calibers should have a better Form Factor, and hence a better BC.... NOTE THIS IS THE EXACT OPPOSITE OF RULE #1....  .... This is in stark contrast to conventional wisdom that larger calibers have less wind drift.... In fact, when you approach the limits of practical PCPs, the reverse is true.... Smaller calibers should have better BC's.... Here is an interesting photo comparing different caliber slugs with an SD = 0.17.... Calibers (L to R) are .224, .243, .257, .308, .357 and .457....



You will notice two things about these slugs.... First of all, they are all about the same length.... In fact, if they were cylinders, they would all be exactly the same length, regardless of caliber.... Secondly, it is pretty obvious that the bigger calibers are not as slender a shape as the smaller ones.... These slugs were not selected to be "optimum", they were just some I had around that were all the same SD....

CONCLUSIONS....

Now does this mean that everyone should scrap their Big Bores and go smaller and smaller?.... No, of course not, because your choice of caliber will most be affected by the amount of energy you need to deliver to the target.... However, when your quarry is a paper target, and all that makes a difference is your ability to hit the center of it, don't dismiss the advantages of going smaller.... You will use less air, get less noise and recoil, use less lead, and not have to give up BC, in fact you may see a decrease in wind drift.... The negatives have more to do with the long narrow slugs.... They have to be of higher quality, and spun much faster to be accurate, and getting a barrel with a fast enough twist can be problematic.... The combination of a long (for caliber) slug, and that faster (required) twist rate can make the slug more susceptable to "aerodynamic jump", which makes the bullet move up or down in a crosswind.... You will have to be even more aware of what the wind is doing, and how it affects your slender, fast spinning slugs.... You ultimate caliber choice will be determined by a combination of all these considerations....

Bob

Great information there about complicated and expensive rifles, Bob, and a lot to digest. However,

For those of us who shoot lowly multi-pump rifles with diabolo pellets, how can we achieve the best BC for the buck, as it were? Very few pumpers can shoot harder than 800 fps even in .177 unless they have been significantly modified. We can, OTOH, "tune" our rifles by varying the number of pumps according to the projectile and/or situation. What should our optimum caliber/weight/velocity be?

Bob, 😊

you did it again! Phenomenal posts of yours! Wow, you have so much to teach us.
THANK YOU for taking the time and effort to do this.

This is so complicated, yet so totally interesting!


Definitely goes into my archives with so many other posts of yours — to read them over again and again. In one reading I'm just scratching the surface of understanding this complicated ballistic maze. There are just so many interrelating factors to understand. 👍🏼

Matthias

Miles, it is interesting to see the trend in the heavy JSB Monster and Beast pellets.... They used to have a cylindrical mid-body, with a short flare.... The "Redesigned" versions of the Monster, in several calibers, have a long, tapered skirt that starts right behind the waist.... The new pellets are more accurate, and have a better BC, than their short-flare predecessors....

I am curious about the length at which you see a significant problem with Dynamic Instability of slugs?.... There are very few PB bullets that are 5 or more calibers long, but lots that are 4 calibers long.... Yes, they require a faster twist rate, of course, but in every case, we are talking about bullets intended to be driven Supersonic, and remain there for most, if not all of their trajectory.... Since we are dealing with low-Transonic and Subsonic only with airguns (eg. up to maybe Mach 0.95), where the CP is further aft than when Supersonic, what difference does that make?.... Are 4 caliber long slugs OK, or should they be shorter than 3 calibers?.... Even shorter?.... I am hoping you can put a number on the length in calibers above which dynamic instability will likely cause and increase in BC for airgun use?.... This would put a lower limit on caliber, for a given barrel length and pressure (and hence SD).... and indeed give Matthias the answer he is seeking.... 

Bob

Maximizing the BC usually involves trade offs that can be detrimental to the intended use.

I try to figure what’s the minimum BC that will do the job and start with that. The “job” for me usually involves acceptable accuracy at a given target distance.

For most conditions, the minimum acceptable GA or G1 BC for me is about equal to yards/2000. Higher BC is always better, until you factor in the trade offs, which are considerable for high BC airgun projectiles.

To add, .177 pellets tend to loose accuracy around 70-80M so it's not a good idea to shoot 100M/100Y with .177. I don't know the science behind it but it has been extensively tested a couple times by 100M BR shooters.

I've been following since Matthias first posted.  I don't mean to de-rail the thread, but have a question concerning slug design also.

Has there been any study or evidence that a dish based slug deforms slightly to form a "pellet type skirt" that aids in stabilization?  I'm just wondering if shorter/lighter slugs with a "skirt" perform better than flat based as far as accuracy goes.

I just wanted to say thank you 
for this very educational thread — and all the effort and time many of you are giving me and thousands of others on the forums.


The BC numbers in and of themselves are already gems — done with the best that amateur money can buy, calculated with the best formulas and mathematical understanding.

And so much else in this thread and countless others. 😊

With you around, this can be a good year!! 😄

Matthias 



PS: 
Would you have a BC for the .30cal Hades as well? 😉

As for pellets, longer pellets usually have much longer flares at the back, meaning the airflow tends to see much more of the flare. It is this which will cause an increase in the drag coefficient and thus a reduction in BC. Unless the speeds are approaching sound speed, the pellet head, assuming a rounded shape, definitely not a pointed or wadcutter shape, contributes relatively little to the overall pellet drag.

Very interesting.

I remember a way back Gregor was advocating the use of 1 in 32" twist rare for .22 JSB Monster redesigned pellets which are longer and heavier than the typical .22 pellet.

I wonder if any tests have been.done with even heaviér pellets and smooth bore?