Caliber Choice for Long Range

[rsterne]

I just received a PM asking some very good questions about why I chose flat-nosed designs for my BBTs rather than round-nose or spitzer.... and a follow up question about my opinion regarding .308 vs. .45 caliber for long range shooting with an airgun.... Here is my response....

Flat nose vs. round nose or spitzer.... I think this is a case of what your brain tells you (logic) not matching what actually happens in fluid dynamics.... All of the available "bullet design" programs I have run across, and those that calculate the BC, are based on the work of Robert McCoy who worked at the Aberdeen Proving Grounds and wrote several ballistics programs (in C++ I think), including McDrag and McGyro.... McDrag calculates the Cd (drag coefficient) and then compares that to the G1 drag model, to get the BC (G1) at all velocities from Mach 0.5 to Mach 5 in Mach 0.1 increments, with some extra calculations thrown in between Mach 0.8 and 1.0 where things change in a hurry.... McGyro calculates the gyroscopic stability over the same range, using the same bullet dimensions.... The required dimensions for each program are caliber, overall length, nose length, meplat diameter, nose radius (if not tangent), and base diameter and boattail length, if used.... This program is used on two websites, JBM, and Geoff Kolby's, and is also used by Lila in his drag/twist calculations.... JBM have it available for download (in C++ ? ) which I couldn't use, but I printed it out and then used all the equations and wrote my own Excel spreadsheet which faithfully duplicates all the calculations, and I used that to refine my Bob's Boattail designs.... I have both the original version, and a truncated version for airgun use that stops at Mach 1.5.... To get a feel for how this program works, try out Geoff Kolbe's site.... and JBM's Drag/Twist program....

http://www.geoffrey-kolbe.com/drag.htm

http://www.geoffrey-kolbe.com/barrel_twist.htm

http://www.jbmballistics.com/cgi-bin/jbmdrag-5.1.cgi

JBM's calculator artificially limits the Meplat diameter to 0.35 calibers (35%), that limit is NOT in McCoy's original program.... If you play with the calculators and change Meplat size, and concentrate on the high subsonic range, you will find that a bullet with a moderate Meplat actually has less drag than either a round nose or a spitzer.... In addition, there is no doubt that Meplats hit harder on game instead of just punching through, and they alloy the use of a Hollow Point without any drag penalty (only a slight reduction in BC because of the loss of mass).... Since MOST guys are not JUST paper punchers, and want the best possible performance on game, using a moderate Meplat makes sense, if it comes at no drag penalty, or actually with a slight drag reduction.... It is counterintuitive, but based on the best (only) ballistics programs we have access to, seemed to be the way to go.... 

One thing I found by playing around with the spreadsheet using McCoy's math, is that in the high Subsonic range (specifically Mach 0.85-0.95) and particularly right around Mach 0.9 (1000 fps) there is a slight reduction in drag available if you have the angle between the Ogive and the direction of flight around 20 deg.... I have never seen this published before, I believe it to be "original work" to come to this conclusion.... This means that shorter bullets, with shorter nose radius Ogives, need larger Meplats.... while longer, heavier bullets need smaller Mepats, to achieve minimum drag in that velocity range.... Below Mach 0.85, the Meplat size seems to make little difference.... but above Mach 0.95, and certainly above Mach 1 where a shockwave forms around the nose of the bullet then the Meplat needs to be smaller.... In fact at Mach 3 and above, the optimum seems to be a Meplat of only about 5% of the caliber (0.015" on a .30 cal).... which is likely why all the best long range bullets seem to have a tiny HP tip.... We get so used to looking at those shapes, and the hype about their incredibly low drag.... that our brains become nearly hardwired into thinking that spitzers must then LOGICALLY be best for airgun use as well.... McCoy's math certainly doesn't indicate that, and in comparisions to test data from the Aberdeen Proving Grounds, his McDrag program is supposed to be within 3% Supersonic (over Mach 1.2), 11% Transonic (Mach 0.8-1.2) and 6% Subsonic (below Mach 0.8 ).... The limitations of his program are clearly spelled out on the Kolbe Drag Calculator page.... Here is an example of the output of my spreadsheet using the McDrag math, for my 200 gr. .308 cal "Whiteout" bullet that won the EBR 200 yd. Big Bore in 2015....



That bullet was designed to take advantage of the extra power available from Helium, which they have since banned at the EBR.... Regarding the choice of .308 vs. .45 cal, I think that for airgun use, smaller is better, and here is why.... If you look at a cylinder of lead, the Sectional Density is proportional to the length.... The same thing applies to any given shape of bullet.... To get a higher SD, you need more length.... Consider this photo of a collection of bullet of nearly identical SD....



Note that the length is virtually unchanged from .22 cal to .45 cal.... I think it is pretty obvious which bullets have the lowest Form Factor (drag), it would have to be the smaller ones, right?.... You can calculate the Ballistics Coefficient of any bullet from the simple equation....

BC = SD / FF

where SD = Sectional Density (bigger is better) and FF = Form Factor (lower is better, the G1 model has an FF of 1.000).... Therefore, for bullets of the same SD, the lower the FF (drag) the higher the BC.... In the photo above, you would expect (other than for detail changes between designs) that the smaller calibers would have the higher BC.... OK, but larger calibers have higher SD's, doesn't that make up for it?.... Not in airguns, and here is why....

We have limited pressure available to accelerate our bullet.... We want to end up with a certain velocity range, and we can't realistically use barrels that are many feet long.... This puts an UPPER LIMIT ON SECTIONAL DENSITY that is related to pressure times barrel length.... Here is a graph showing that, if we want to reach about 950 fps....



Each line represents a different barrel length, so if, for example you select a 36" barrel and 3000 psi, the maximum SD you can drive to 950 fps is about 0.250.... In fact you will find these SD numbers are higher than you are likely to actually GET to 950 fps, you should consider them a "lofty goal".... What would these bullets look like in .308 can and .458 cal?.... Well, an SD of 0.250 in .308 cal would weigh 166 gr.... and in .458 cal it would weigh 367 gr.... I don't have any BBTs designed at those specific weights, but let's drop the SD down just a bit and compare a 334 gr. in .457 (SD = 0.227) to a 154 gr. in .308 (SD = 0.232).... and throw in a .257 cal of 112 gr. (SD = 0.242) for good measure.... Here are NOE's drawings, and their calculated BCs....





Just visually, there is little question in my mind which bullet would have the best BC, and the best long range performance.... how about you?.... In an airgun, operating at 3000 psi with a 36" barrel, all three would end up getting about the same velocity.... THAT is why it is my opinion that smaller calibers are better for long range airgun use.... Now are there limits, YES.... Eventually at constant SD a small caliber bullet gets so long and skinny you can't make a barrel with a fast enough twist to stabilize it.... For the three bullets above, the optimum twist rate is 7" for the .257 cal, 11" for the .308 cal, but only 30" for the .458 cal.... A .172 cal bullet with an SD of 0.250 would have to weigh 52 gr., and need about a 4" twist rate.... but the BC would likely be over 0.40.... Alternately, if you have Helium available, you can reach the same velocity with a higher SD, which is why my "Whiteout" bullet was 200 gr., with an SD of 0.301.... You would need 3600 psi with a 36" barrel to even consider such a bullet shooting with air.... more likely about 4000 psi with that barrel....

As you increase the pressure (or barrel length), then you can increase the usable SD.... This is why people are having success with larger caliber PCPs, they require that combination of pressure and barrel length to allow them to use long, heavy bullets (with low FF's) in larger calibers.... and such guns are becoming more available.... Also, barrels with high enough twist rates to utilize such high SDs in the smaller calibers are harder to source.... That doesn't change the fact that ballistics favour the smaller calibers for airguns.... simply because of the limited power we have available.... There can be arguments made for why any individual caliber is "best".... but each argument will start with a premise regarding the combination of barrel length and pressure you choose to use.... Ultimately, that ends up back at the SD, which is the factor that governs the velocity you can reach with any given barrel length and pressure combination.... and the fact that for any given SD.... smaller calibers will tend to have a lower FF.... and hence a higher BC.... plus use less air and produce less recoil to obtain those results.... Again, practical limits, such as sourcing barrels and bullets will put a limit on your choices, however....

Bob

[rkr]

What about the efficiency drop when we go towards small calibers? In pellet guns  .177 usually gets less fpe per fill than .22.

[MJP]

Don't know about sizes and sd or what not, we have a measured bc for the 20mm bt round 0.702 and it does fly pretty good for 170 gram chunk of lead.
Its not just about the caliber, you just need to make the bigger bullets well bigger and longer.

And what comes to distance and caliber choices, ask Carl what he thinks about the best caliber?

I'm with going bigger, but you need the gun that has the guts to deliver the velocity.
Easier to see what you hit when there's a big impact don't you think?
And no offense to anyone just my point of view.

Marko

[triggertreat]

So Bob are you saying that a .357 flat nose bullet would be better than a diablo and also that a .357 is better than a .457 for say hog hunting at 50 yards?  Thanks!

[MJP]

Any bullet is better than a diablo!
Diablos have a terrible ballistics no matter what size.

Marko

[rsterne]

It is true that larger calibers tend to have better efficiency, but not by much.... From the same powerplant, they generally produce more total FPE because the larger caliber bullet has a greater area for the pressure to push on.... so although you get less velocity, you get more FPE.... because the barrel volume is larger.... Barrel volume and pressure are the major things that affect FPE....

That huge barrel volume of the 20mm (0.80" bore x 43" long) is the major reason for the huge FPE numbers.... At 300 bar, the theoretically maximum possible FPE is about 7800 FPE, but because of the mass of the gas, and many other factors, getting half that on air would be a HUGE accomplishment.... A 170 gr. bullet at 3100 FPE works out to about 730 fps.... The bullet has an SD of 0.585, which with a BC of 0.702 gives it a form factor of 0.83, about right for a boattail.... However impressive the energy is that bullet retains downrange, trajectory is much more influenced by velocity than BC, even at extreme range.... Using the chart in your thread in Reply #326, your drop at 1000 M will be 95.88 Mils (a Mil at 1000 M. is 1 M), so that is 3775".... The 112 gr. .257 cal bullet I show above, with a BC of just 0.396, at 900 fps, will only drop 2917" at 1100 yds. (slightly more than 1000 M).... Let's say the BC is way overestimated, and it's only 0.300.... Starting at 900 fps, it will still only drop 3126".... roughly 54 feet less than your 20 mm at 1100 yds..... Long range shooting requires BOTH velocity (for flat trajectory) and a high BC (for minimum wind drift).... The point of my post was that for any given combination of barrel length and pressure.... which governs the SD you can drive at a given velocity.... a smaller caliber bullet will have a higher BC for that SD.... and will require less air, and make less recoil doing it....

Carl loves large calibers because they kick up more dirt, which allows him to find the target easier at extreme ranges.... I won't argue the merit of that assessment....

Hunting is a totally different game than shooting at targets, it is mostly a game of delivering the appropriate ENERGY for the size of your quarry at the intended range.... Obviously, a .45 cal can deliver more energy than a .35 cal, from the same barrel length and pressure.... How much you NEED for your chosen game depends on what it is.... For a Ground Squirrel, or a Prairie Dog.... or even a Coyote.... I doubt you need the power of a .45, even a .35 cal.... Something in the .25 - .30 cal range might be a better choice.... For an angry big Hog.... MO POWER can't be argued with....

Bob

[triggertreat]

Thanks Bob!  Some of the hogs I've seen on the trail cams are pushing 300lbs plus, but don't really want them for table fair.  I prefer the smaller ones.  Just trying to learn more about big bores and their ammo and always appreciate your insight.

[kamora187]

Very impressive work Bob!

[rkr]

I was more trying to figure out if there's a practical minimum caliber where the air as a propellant medium starts to get strangled. We now have .172 build for bullets and people are talking about even smaller calibers, is there a point where air is no longer practical for powering up small bullets? Casting those tiny bullets is then another thing but I guess we don't have to cover that in this discussion.

[MJP]

Nice comparison Bob, and while bringing the 20mm up to the conversation as a reference for a bullet shape I was meaning to point out that a equally shaped bullet in bigger caliber would be beneficial over the smaller ones.

Something like 400-500gr out of a .457 at 900fps would be my choice.

Marko

[rsterne]

I agree 100%, Marko.... IF you have the power to push it.... Your bullet scaled down to .457 would be 489 gr.... the SD would be 0.334.... It would take about 4000 psi in a 36" barrel to hit 900 fps and develop 880 FPE.... A great combination.... but what a monster....

Bob

[MJP]

Yes that it is Bob, and not too fun to shoot all day long. But no pain no gain right.

Anyway, we have the platform to do it infact you guys have it even easier. You just need to have Doug to make you a texan valve like Carl has.

This year there will be more truly high powerd pcp out I'm sure of that. Not by the big brand names but from the small shops around the globe. We have the valves to deliver very high flow with minimal hammer strike, all it takes is to build the frame around one of those valves.

Marko

[Gippeto]

This year there will be more truly high powerd pcp out I'm sure of that. Not by the big brand names but from the small shops around the globe. We have the valves to deliver very high flow with minimal hammer strike, all it takes is to build the frame around one of those valves.

Marko

Totally agree with you Marko.

Very nice treatise on the subject Bob.

Al

[rsterne]

rkr, you asked about the practical "minimum caliber", and considering that the air molecules themselves are pretty tiny, I don't think the physics of the airflow are the limiting factor.... You mention the difficulty of making very long tiny bullets, and THAT certainly offers a practical, and perhaps limiting, challenge.... If we look at trying to get the same SD as the three bullets in my first post (say about 0.24) in .172 cal, what would that look like?.... Well, it would be about 50 gr., and carrying the BBT idea to it's extreme conclusion, you would have something like this....

      (image obtained using the Kolbe Drag-Twist Calculator)

That calculator gives a subsonic BC (G1) of about 0.43.... but specifies a twist rate of 3.5".... The bullet is just over 1" long, so that is one revolution in less than 3.5 bullet lengths.... At 970 fps, it would be turning 200,000 RPM....  ....This, in itself, probably makes this an impractical combination for a bullet in a PCP with a 36" barrel at 3000 psi (our original criteria for the other 3 bullets).... If we shortened the barrel to 24", which would drop the maximum SD to about 0.17 (to get 950 fps).... that would drop the weight down to 35 gr.... and the bullet would look similar to the 112 gr. .257 cal drawing in the first post.... certainly a lot easier to cast.... It would still need a twist rate of about 5", which would require a custom barrel.... but it starts getting back into the realm of the possible....

Extrapolating this idea, there is, indeed, a minimum PRACTICAL caliber for PCPs, depending on the product of barrel length and pressure.... For instance, with Marko's 20 mm Monster, there would be little point in trying to build a .308 cal on that platform.... The gun, with it's 43" barrel running 300 bar, should be capable of pushing a bullet with an SD of 0.40 at about 950 fps on air (let's forget about Helium for now).... That would be a bullet weight of 266 gr. in .308 cal. (never heard of one).... or 394 gr. in .375 cal. (heavier than even the heaviest .375 H&H Magnum bullets)... but "only" 585 gr. in .457 cal.... You can "almost" get bullets that heavy in .457 cal.... If you jump up to .50 cal, then a bullet with an SD of 0.40 would weigh 728 gr.... NOW we're talking, you can get excellent long range bullets in that caliber for the .50 BMG.... even cast ones.... So for a gun like Marko's, a PRACTICAL minimum caliber might be .50 cal.... and with the ability to get much higher velocities and therefore a flatter trajectory, it should be much better for long range work.... I know it's jacketed, but for example a 750 gr. Barnes TAC-X Boattail has a BC (G1) of 0.766, and at 950 fps the drop at 1100 yards would be "only" 2384" (55 Mils).... compared to the 3775" (96 Mils) of the 20 mm bullet.... So, as you can see, the same idea holds true, smaller is better.... but with the proviso that there is, indeed, a PRACTICAL lower caliber limit that depends on barrel length and pressure....

Bob

PS. Marko.... Please realize I'm not picking on you, but it is helpful to have a gun so far "out of the norm" to use as an example.... to show that the same principles still apply, even in extreme cases.... I am still in complete AWE of your accomplishments.... 

[MJP]

No worries there Bob,
But that .50 cal info gives me some ideas... 

Marko

[rsterne]

I thought it might.... 

Thinking about the idea of a minimum PRACTICAL caliber, I wondered how I could best convey that information.... Well, it relates to the maximum SD you can use to have any expectation of hitting 950 fps on air, which is in the chart I presented in the first post.... That, of course, is dictated by barrel length and pressure.... I have done quite a bit of looking at bullet designs, and VERY few are more than 4 calibers long (like my 112 gr. .257 cal in the first post).... If we make that assumption, and allow for flat-based bullets (which are a bit heavier than a boattail of the same length), we can calculate the approximate weight of a bullet that is 4 cals. long and then the SD of that bullet.... and they both relate to the caliber, like this....



Bullet weight is in red (left axis), and the SD is in blue (right axis).... The upper chart is for .177 to .357 cal, and the lower one for .357 cal to .80 cal (20 mm).... You can use these, in conjunction with the SD chart in the first post (shown below for convenience)....



We will assume you want the heaviest bullet you can have any hope of driving at 950 fps, to get the best possible combination of flat trajectory and BC (from the heavy SD), so you use the SD chart first.... Let's say you have a PCP with a 30" barrel running 4000 psi.... The maximum SD you should consider would be about 0.28.... So, you look at the right axis on the upper chart, find 0.28, and the slide to the left to the blue SD line (there just happens to be a dot there).... Go straight down to the X-axis (caliber), and it says 0.250".... Any bullet of a caliber smaller than that, you would expect to be greater than 4 calibers long.... which is going to be hard to stabilize (requiring a very fast twist), and more difficult to cast.... This puts an effective lower limit on the caliber for that combination of barrel length and pressure.... If you look at where the red (weight) line crosses the vertical line at .250 caliber, you will see that the weight is about 125 gr.... indeed a VERY heavy bullet for that caliber.... Therefore, for a PCP with a 30" barrel running 4000 psi, I would recommend that you look only at .257 cal and above.... 

You can do the same thing with any other combination of barrel length and pressure.... First find the maximum SD (for 950 fps), and then use the other chart to find the minimum practical caliber for that SD.... Interestingly, if you decide that you want some other SD (either lower or higher than recommended as a maximum on the first chart).... you can still use the other charts to determine the minimum bore size and bullet weight at that caliber.... Pretty neat way of looking at it, I think.... 

Bob

[Taso1000]

This is a slight tangent and question on the max velocity and rotation speed that cast lead bullets can handle.  What I am getting at there must be a point where the velocity and rotational forces are too great for lead to handle. 

I don't remember the details so I'm going to generalize.  So please excuse me.  I remember reading that if you shot a powder burner bullet (copper jacketed) too fast and in too fast a twist it would disintegrate from the rotational stresses.  I also remember reading that firing lead bullets too fast the lead would be stripped away by the lands because the lead didn't have the strength to stay together.

The only speed limit I remember is that the powder would melt the lead bullet base at a certain power level. 

I know you can make lead harder but then it may be harder to engrave rifling thus reducing velocity or allowing blow by.

Has anyone confirmed a velocity and rpm limit for cast lead bullets? 

Thanks,

Taso

[rsterne]

No idea.... but it would depend on the relationship between RPM and caliber.... 200,000 RPM on a .50 cal would have twice the centrifugal force at the surface of the bullet than on a .25 cal.... However, the force increases by the square of the RPM, so at 100,000 RPM the force would only be 1/4 as great....

Since for bullets of identical shape and proportions, the twist rate in inches required for stability is proportional to the caliber.... if the .50 cal bullet needed a 20" twist, then a scaled down .25 cal bullet would need a 10" twist.... Since we are generally aiming at about 950 fps, regardless of caliber, then the smaller bullet would be spinning twice as fast (4 times the force) but it has only half the radius (1/2 the force).... so the net centrifugal force at the surface of the bullet would be twice as great for the smaller caliber....

This means that smaller calibers are more likely to have a problem with coming apart if driven at high velocity in a fast twist barrel than their larger counterparts.... The point at which that would occur (combination of fast twist and high velocity) is something beyond my ability to calculate, however.... I can give you an example of what DOES work however.... My Hayabusa .257 shoots a 100 gr. bullet at about 950 fps, and it has a 7" twist.... The bullet is therefore spinning at nearly 100,000 rpm.... and I can tell you for a fact that they do NOT come apart.... Nor did the .308 cal 200 gr. "Whiteout" that was used in the 2015 EBR, even at 1050 fps in a 8" twist.... That is 94,500 RPM with a 20% larger bullet than my Hayabusa, so the equivalent of 103,500 RPM in the .257 cal.... To get the equivalent force in a .224 cal would require 110,800 RPM (about a 6.5" twist at 1000 fps).... and in a .172 cal it is the equivalent of 126,500 rpm (about a 5.7" twist at 1000 fps).... If I had to guess, lead bullets of less than 4 calibers in length will not require a twist rate fast enough to make them come apart in flight at airgun velocities....

Leading should be more related to the forward velocity than the rotation.... The distance travelled by a point on the bullet as it travels down the bore, even in a fast twist barrel, is not hugely greater than the barrel length.... In a 6" twist, in a 24" barrel, the bullet would rotate 4 times.... If the barrel is a .22 cal (that might need that fast a twist for a long bullet), the circumference is 0.69" times 4 = 2.76".... Think about drawing a triangle that is 24" long and 2.76" high and then measuring the hypotenuse.... It would only be 24.16", so that would be the distance travelled by a point on the circumference of the bullet.... If the muzzle velocity was 950 fps.... the speed of the lead relative to the metal of the bore would be (24.16 / 24) x 950 = 956 fps.... a difference not worth mentioning....

Think about it this way.... The only bullets I have heard of coming apart are .224 cal pills driven at over 4000 fps.... from something like a 7" twist.... They are rotating at 400,000 RPM, which is 16 times the centrifugal force you get at 1000 fps and 100,000 RPM in an airgun.... They have a thin copper jacket, which has been scored by the rifling, with weak spots just looking for a force big enough to rip the jacket from the core.... Is it any wonder it happens?.... I don't know what the velocity limit is for lead.... either before it melts and leads the barrel.... or comes apart from spinning too fast.... but my gut feel is that airguns staying under 1000 fps aren't going to run into significant problems.... although the faster you shoot a lead bullet, the more often you have to clean your barrel, I'm told....

Bob

[Taso1000]

Thank you Mr. Sterne!  There was mention in the .17 HMaiR thread of shooting bullets at 1300 fps or faster.  So I thought my question was more appropriate in this thread than that one.

I've been interested in a .17 caliber bullet shooter for a long time but have not had the time or means to get the project going.  I've just bugged you a couple times for your recommendations so I appreciate your explanations immensely.

Thank you!

Taso

[Tofazfou]

Thank you Mr. Sterne!  There was mention in the .17 HMaiR thread of shooting bullets at 1300 fps or faster.  So I thought my question was more appropriate in this thread than that one.

I've been interested in a .17 caliber bullet shooter for a long time but have not had the time or means to get the project going.  I've just bugged you a couple times for your recommendations so I appreciate your explanations immensely.

Thank you!

Taso

1300 FPS?  WOW thats fast.  I bet I could if I had some Helium......lol.  But i have seen 1030 fps and 1020 fps often.