When you use completely unrealistic values in published work, that is ok. When I point out your errors and show where real life examples are superior in areas you conveniently ignore, that is cheating.

The example I used, and the one that you are whining about, is the first 175gr spitser bullet on the list in Ballistic Explorer (Speer Mag Tip #1641) and, as you pointed out, even your absolute best case example still lost by a huge margin. I thought if I let you dig a bit you would keep going into a nice deep hole.

When you conveniently forget about your technical mistakes and go off at a tangent, that is ok but when I show additional reasons that point out where your logic circuits are not working, that is veering off and creating confusion.

Seeing that you have closed the discussion, a summary is in order.

1. You have made several technical errors in your published work and posts.
2. You are adamant that more Ke does not increase the wound channel volume.
3. You become confused and then you cannot count properly.
4. You are fond of "proving" your point of view with irrelevant examples
5. You resort to name calling and physical threats when proven wrong.
6. You switch position and back again thinking no one will notice.
7. When proven wrong, you just ignore the fact and pick up on some other detail.
8. You repeat errors as if repetition will make them right.
9. By omission you admit to little practical hunting experience.

Need I go on?

So, all together now, to the tune of Glory Halleluja:

How the hell can we belieeeeeve you..............

PS. How come you have not yet figured out how to post stuff yourself? <--------- Rhetorical question, no answer required.

Posting for Chris Bekker

Posting for Chris Bekker:

Gerard,

I am not going to waste my time to respond to your bullshit summary. Gerard I don't want to be ugly with you in public, I had my say and that is it. If I start to attack you now in similar fashion, I will lower myself to your level. I will rather illustrate and summarise with one more example as to your style of reasoning and I am quoting you ... "Your SF 1.19 is woefully inadequate for general hunting to 500m and you will experience many failures through bullets that tumble and turn. You just havn't shot that many yet." I will not be ugly, I shall merely analyze the key elements for the readers as it will be like water off a duck's back for you:

1. You decided that the SF of 1.19 is WOEFULLY inadequate. None of the bullets I have shot so far have tumbled. When a bullet stays head-on in a wet pack you are safe. It has also been proven on Kudu, but you know better, despite the results to the contrary!

2. Then you go on to stretch it to 500 meters. I suppose you do not know that the decay in spin velocity is hardly measurable even at 500 yards. Bullet drop and incorrect range estimation actually dwarfs the aspect of spin stabilization. Despite me telling you emphatically it is one of my bushveld cartridges, you stretch it out to 500 yards.

3. Then you go on to say I WILL experience many failures through bullets that tumble and turn. Your are adamant about that. The fact is none have tumbled and turned - all I got was straight line penetration. Check carefully, you say I WILL experience MANY failures ...

4. Then you state that I have not shot that many. Very presumptions of you to say the least. You must surely believe that you have psychic abilities. Where do we draw the line 25 or 50 or 100? Then another beaut is ... "By omission you admit to little practical hunting experience" Statements like these will get you nowhere. You must be thinking if you print things like this you can elevate yourself and belittle other people ... you are sadly mistaken.

If you have any further personal issues to settle with me you can call me to arrange a meeting. In fact I am available for the duration of the Aim Show (4 th - 6th March). You can call me on 082-469-9380. The best for you may just be to forget about me and enjoy your hunting.

Take care
Chris

quote:

Originally posted by mehulkamdar:

Hey, who is the big guy and who is the paleface in that photo, and whose kill is it supposed to represent? What cartridge, bullet, range, muzzle velocity, autopsy reports, recovered bullet?

RIP,
I was wondering about that as well. Looking at Chris' post above, the expanded bullet above that is probably supposed to be proof that the Barnes X bullets he has recovered did not tumble. I thought Barnes X bullets were solid copper and here Chris proves me wrong again. Did I mention his propensity for proving his points with irrelevant examples?

(For the record, I do not have an issue with X bullets, only with the facts as (mis)represented here.)

Chris,

Your points in order:

1. If you are of the opinion that I decided that SF 1.19 is inadequate, I regret to inform you that I did not. People who are a lot smarter than I am decided this a long time ago. Hint: That is why that right hand column in WinGyro carries the heading SF 1.5.
2. If you knew anything about the subject, you would have realised that the SF requirement reduces as distance increases. That was the context of my remark and in fact favours your SF 1.19 at longer ranges. I did not accuse you of shooting animals at 500 yards/meters/yards at all but interestingly, the bullet you use is better suited to it than close range shooting. You should try the 140gr X for close range. You will be amazed.
3. You will experience many failures when you start shooting animals. Failure in the context of our discussion is a bullet that tumbles. If you have done as many wetpack/hunting comparisons as you claim, you must know that bullets are far more prone to tumbling in animals than in the ideal, 90 degree impact on wetpack. How many 175gr X bullets have you recovered from kudu? One, two, ten?
4. I get this feeling that there is smokescreen here. Post me a picture of you and a kudu shot with a 175gr X bullet. This picture must be posted within 24 hours and be acompanied by sworn testimonials of those who witnessed the shot and the fact that you loaded the ammunition yourself. We need to see receipts for the bullets and certifeid copies of the hunting licence.

See, I can also dish out demands for proof like you do.

I have no personal issues with you Chris. I warned you more than a year ago that I will not tolerate technical errors when you mention our products in print. Get your facts straight when you write technical articles involving my products or get used to my reaction when you dont.

quote:

Originally posted by Gerard:
RIP,
I was wondering about that as well. Looking at Chris' post above, the expanded bullet above that is probably supposed to be proof that the Barnes X bullets he has recovered did not tumble. I thought Barnes X bullets were solid copper and here Chris proves me wrong again. Did I mention his propensity for proving his points with irrelevant examples?

(For the record, I do not have an issue with X bullets, only with the facts as (mis)represented here.)

Not tyring to enter this fight but he never said the picture was of an X bullet.

quote:

the 380 gr .375 Rhino bullet opens up to 27 mm and cuts a huge hole through the hart with its 4 sharp petals and is also more effective than a soft that mushrooms in a ball like appearance with smooth edges. See the attached picture of a retrieved 400 gr .416 Rhino bullet.

The picture of the expanded bullet was posted two minutes before the post referring to bullets tumbling/not tumbling. All the discussions around non tumbling were using X bullets as the example. It did not occur to me that the picture posted at 23:15 today, would refer to a post made 46 hours earlier. I have always had difficulty herding cats.

Posting for Chris Bekker:

Neverflinch,

Thanks buddy for being so levelheaded. Pardon Gerard for not being able to recognize a Rhino bullet that I referred to in my previous post that Mehul published a little bit too late. Nevertheless, it is there now in all its glory. The important thing that you have noticed was, and it stands as a monument for Gerard, and that is his bizarre reasoning pattern making up a whole story about a Barnes-X. That is the nature of the beast.

RIP,

The big man is Katte Katzke, a PH that takes Americans to the Zim Valley.
Katte is a friend of mine and the President of the Big Bore Ass. in SA.
The 'paleface' in the picture is Jack Krieger who hunts every year with Katte.
Katte uses 430 gr Rhino Solid shank bullets @ 2,220 fps in his 416 Rigby.
According to him it is the best bullet that he used so far on buffalo.

Best regards
Chris

Posting for Chris Bekker:

Buffalo hunters with their trophies in 7 days - these are clients of Katte Katzke. Anyone interested can contact me (Cell no. 082-469-9380 in RSA) and I will put them in touch with the BIG MAN for the time of your life - the best hunting ground in the world with a true professional buffalo hunter - you could not wish for better.

Posting for Chris Bekker:

Gerard,

My name is Pieter de Klerk. I am a PH and have been working as a PH for about 12 years. This can be confirmed with one of the biggest one man safari operators in South Africa by the name of Jan Swart of African Safaris. I have hunted extensively for a living primarily with a 416 Rigby, 300 Win Mag and a 7 mm Mauser. I worked with Peter Lawrence, another ex Rhodesian PH, in a joint venture as Serolo Safaris. I have hunted elephant, buffalo, rhino, hippo, leopard and many antelope species on offer throughout SA, Zimbabwe, Tanzania and Botswana. I am widely known as a Barnes-X man.

Chris Bekker is a good friend of mine and he has hunted with me before. I can vouch for it that he is an avid hunter and no attempt from you to deny that has any substance. I am not an internet junkie, have no computer and doing a post to you through his PC. He asked me to state my experience with Barnes-X in particular the 175-gr bullet in the 7 mm Mauser, which you claim will tumble in game. The controversy that you create can only be a figment of your imagination.

Just to give you some background on 2 winter seasons; I have shot 58 kudu bulls on Gert Roux's farm and 2 neighboring farms in Thabazimbi and another 46 kudus in Graaf Reinette in a culling operation. These were all shot with Barnes-X bullets with my 7 mm Mauser and 300 Win Mag. I think my experience is extensive enough (I hope you will accept it) to comment that the 175 gr bullet does not tumble and straight line penetration is what you can expect. I have never had one tumble on me. I will attend the Aim Show with Chris Bekker and you can call him if you want to see the pictures - I will bring my albums along to validate all of the above. It seems you have to oppose everything Chris says, just because you have an action against him. If you are man enough to meat with us, I will make all the telephone numbers available to you if you want to check my credentials.
Stop behaving like a know-all.
Pieter de Klerk

Hi Pieter,
Thank you for taking the time to shed light on the subject for us. I do not need to check your credentials, I accept your word in good faith as with anyone else.

My interest lies in only one area and that is the technical correctness of the discussion. It is of course entirely possible that your rifle will stabilise a 175gr monometal bullet and, to that end, I will send you a little device I have designed, with which you can accurately measure the rate of twist of your 7x57 barrel. It takes but a couple of minutes to do and would probably be of interest to you as well. Further to the discussion, if you have any good pictures of recovered 175gr bullets, I would be most interested to see them. The actual expansion of the bullet is of lesser interest, it is the shank I would like to examine. Alternatively, I can arrange for someone to meet with you in the Gauteng area or elsewhere, and take pictures to mail to me electronically, if all you have are recovered bullets.

Please call me on 084 338 3006 and let me have your postal address, the twist checker will be on its way on the first business day.

We have not yet decided on whether we will be at the show, we are in the middle of building operations and we are expecting machinery to arrive within the next several weeks. We would love to be there and, if at all possible, will make the effort.

It is regrettable that you feel that I am a "know all". You should ask Chris to point out the myriad of errors he has made in his technical journalism and then perhaps check for yourself that I have only addressed him when his errors involve my products. If that makes me a "know all", there is little I can do about it.

If I spread the word in print that you are a one legged pirate and can't shoot straight to save your life, would you take me to task? I bet you would.

In case Chris did not show you this, here is what I said earlier in this discussion: "I have no personal issues with you Chris. I warned you more than a year ago that I will not tolerate technical errors when you mention our products in print. Get your facts straight when you write technical articles involving my products or get used to my reaction when you dont."

Chris goes out of his way to find any small reason to put a negative slant on my opinions ever since I pointed out a slew of technical errors in an article he wrote a couple of years ago. On this forum, many participants have called him some pretty insulting things, yet he barely responds to them. All his "research" and complicated explanations seem to address mostly the disproving of facts I raise when he is technically challenged. You may conclude yourself who is having a problem with whom.

Chris,
So you have never said that you have always had linear penetration with a 175gr X bullet in wetpack as well as kudu? This is why I say you are fond of "proving" a point with irrelevant examples. Read back over the posts and then tell me what the relevance of that Rhino picture and the story about it has in the discussion. Bizzarre reasoning? Well at least I have not yet multiplied rotational force by forward force or as another poster has said of your writing: "......makes up equations to prove whatever pre-conceived notion he has. I find it amazing that he spent enough time to write as much different falacious crap as he did."

Posting on behalf of Pieter de Klerk

Gerard,

Firstly, I would like to consolidate Chris' 5 basic points, that I cannot find fault with:

1) Chris proved to us that high-SD bullets will out penetrate low-SD bullets in any given cartridge, due to the fact that increased velocity cannot make up the lost momentum value. However, when the same momentum value is reached (in another cartridge) penetration is equal, but then only is solids that can withstand extreme velocities.

2) Chris' penetration test was most interesting and he demonstrated the interplay between momentum and cross sectional area and proved that it is a valuable yardstick for the non scientist to judge a bullet's penetration ability (Mo/Xsa). Equally interesting, he showed that SD x Velocity = Mo/Xsa. (again this pre-supposes that the bullet will not lose weight on impact)

3) Chris highlighted the fact that high velocity is self destructive on Softs and really more suitable for Monolithics. That is why a higher SD at moderate impact velocities works so much better when we shoot Softs that loose a substantial percentage of their mass.

4) Chris highlighted that the apparent bigger volume cavity created by higher energy is useless as a killing mechanism, as living flesh reacts differently than homogenous target media. Target behaviour is a key factor and cannot be ignored.

5) Chris highlighted the importance of the size of the 'hole' in the killing mechanism. His contention is that it is far more important than the shallow temporary cavity created by higher energy bullets, be they Softs that shatter or non-expanding solids, and hence his reference to the Rhino bullet that intrigues you so much.

Given the above, I have to agree with him that high-SD bullets (higher mass causes higher momentum) are superior to low-SD bullets. Beyond SD we must look at bullet behaviour in the target media, and in this case our application is live animals.

Secondly, I do not want a saga about the 175 gr Barnes-X bullet. I know what works and what not - I am a PH and I earn my bread and butter with hunting. Chris pointed out to you that none of his bullets tumbled so far, and that stabilization is not an issue at range (rotational velocity is the same at practical hunting ranges). I also confirmed that my experience was the same, but you want to send me a measuring instrument so I can measure the twist rate, which I already know (1-in-8.66"). Then in addition, you want to examine a retrieved bullet and offer a prognosis as to its stabilization potential. Gerard, this sounds like Rasputin behaviour to me.

This is my last post as there is really nothing to debate further.
Pieter de Klerk

Pieter,
SD X V does not equal Mo/XSA

SD is a "figure of merit" that has no reality in a units based equation.

SD is based on a square bullet.

SD = W/d^2

W = M under standard gravitation, numerically, but you still can't get around the square bullet. Read my tag line below and you might pick up a clue.

I have to say that Gerard seems to have won this dogfight, and he should let his dog go to sleep under the porch.

quote:

Originally posted by RIP:

SD is based on a square bullet.

?????????????? I'm assuming SD = sectional density. Why is SD based on a square bullet??

-Bob F.

quote:

Originally posted by BFaucett:

quote:

Originally posted by RIP:

SD is based on a square bullet.

?????????????? I'm assuming SD = sectional density. Why is SD based on a square bullet??

-Bob F.

Gee Bob, I know you are an intelligent man. You just never thought about it.

Look at the formula for sectional density, it is the only one ever, and it is just a FOM, figure of merit:

SD = W/d^2
where
SD = sectional density
W = weight of bullet in pounds = weight of bullet in grains divided by 7000
d = diameter of bullet in caliber or inches

If SD were based on the true cross-sectional area of the bullet, then SD = W/(pi)(d/2)^2 ...

So the actual SD's listed for ages are just shorthand easy ways to express a number that is proportional to reality, but has no real units.

It is based on imaginary square bullets.

You don't read my posts very often do you? We have been hammering on this for a long time.

SD is useful, but you gotta be aware that it is not reality based in units for inclusion in equations unless you put in a factor of pi/4 or 4/pi to correct. If you fudge a reality based formula with an SD number, then you gotta un-fudge it.

Time honored SD listings are 3.1416/4 = 78.54% of what a "reality based" SD using round cross-section bullets would be.

The true definition of sectional density is BASED ON SQUARE BULLETS. IT IS PROPORTIONAL TO REALITY, BUT IT AIN'T REAL.

Do the math.

RIP,
Not my nature to let it go when the logic is so badly flawed and the reply is so pointed. I have said before that Chris has got someone helping him because one man cannot be that wrong on his own, now I am wondering......

Pieter,
And you have the nerve to call me a know all.

Your points in order:
1. Please share this proof with us as we have not seen it. The very test that Chris did with the cut down X bullet proves that lighter and faster bullet behaviour can be compared with slower and heavier bullets. All the X bullets in his test expanded to almost identical shapes, despite a wide variation in speed. Solids are not required for such a comparison. We have proven several times over in this discussion that Sd has very little to do with penetration. I suggest you read it otherwise we will be rehashing the whole thing again.

2. Mo/XSA is indeed an exellent yardstick with which to estimate terminal performance. On page 2 of this thread HenryC470 first posted that SD x Velocity = Mo/Xsa. Did Chris tell you he came up with the idea? At any rate, therein lies the crux of the matter. Sd on it's own is a croc. Take velocity out of the equation and you are left with Sd = Sd and we all know that; and it proves nothing.

3. No argument from me on that one. As you have found with X bullets, an expanding mono will outperform a bullet that contains lead every time.

4. As a PH, is it then your firm opinion that a 300 win mag with a 165gr X bullet at 3100fps will kill less effectively than a 30-06 with a 200gr X bullet at 2480fps? My opinion is that both will shoot to the vitals on a going away shot on an eland, but that the 300 will allow a wider margin of error. Additionally, the 200gr bullet is much more likely to tumble and curve and may not even expand.

5. Again as a PH, are you saying that when two X bullets of equal momentum, but one having more energy, strikes, they will kill equally well? They will penetrate to similar depths and the higher energy bullet will cause a larger temporary cavity which will undoubtably add to the permanent cavity, but it will be less effective because it is lighter and faster?

Regarding the 175gr X bullet, I see your position is one of not wanting to be confused with facts. I have measured the twist rate of more barrels than you can shake a stick at. The one fact that is absolutely clear is this: Only hammer forged barrels get close to the stated twist rate every time. All other barrels had better be measured to be sure what they are.

If your barrel is one turn in 8" it will give the good results with a 175gr X bullet that you describe. If it is one in 7.5", it will be even better. If it is one in 8.66", expect trouble from time to time. I offered you the opportunity to check it and be sure but if you prefer to suppose it is 8.66", so be it.

"examine a retrieved bullet and offer a prognosis as to its stabilization potential" Sounds like something Chris could have come up with. I deal in facts and examining a retrieved bullet under a microscope tells me a lot about what happened in the terminal phase. Specifically I can prove if it has tumbled or not. I do not thumb suck opinions when I can examine, find the facts and be sure.

Your attitude raises the questions in my mind: Why so defensive? Might I be proven right if all the facts regarding your success with the 175gr X bullets are examined? I do not doubt that you have had success. After all, only a fool would continue using something that keeps on failing. Do you have any recovered X bullets to examine? We will probably never know.

I completely forgot to do this yesterday. Here is a picture I was asked to post on behalf of a hunting buddy in Gauteng.

HO HO! That HV looks like a boat propeller on a banded copper drive shaft!

Please do tell what caliber, weight, impact medium, and estimated impact velocity???

It is a 450gr .458" fired from a 460 Weatherby loaded down to 2500 fps. Impact is 2500 fps as it was fired into the water catch tank at the police forensics lab in Port Elizabeth. Impact angle on the water is approximately 30 degrees.

Here is another one. 95gr .264" at 1900fps into water saturated florists foam. I should have posted this last week on behalf of another aquaintance of mine.

Posting on behalf of Pieter de Klerk

Gerard,

I was not going to answer you again, and I will refrain to answer previously discussed differences relating to Chris, but don't get 'clever' with me when you lack experience in particular bullets that I use extensively.

Just imagine a PH sending bullets to a "doctor" to be examined with a microscope - holy shit! Why on earth must I send you a bullet when I know I am getting straight-line penetration and that after 12 years of using these bullets daily with success - both the 175 grainer (7 mm) and the 200 grainer (.308). You must be out of your scull to think I would play games like this with you. What is more, having told you about my past experience and the various culling operations I have been involved in, you still want to inspect my bullets? Then you pose the question ... "Might I be proven right if all the facts regarding your success with the 175gr X bullets are examined?" Sorry pal, you don't believe a word I say and I would not have voodoo thrown at me. In any event, how can I have confidence in you after you were so dishonest with the trajectory comparisons? Which is worse, dishonesty or technical errors?

But you have just gone another step further when you used the following statement in defense of one of your arguments by saying ... " Additionally, the 200gr bullet is much more likely to tumble and curve and may not even expand." I am completely astounded how you are clutching at straw. Despite all my achievements with these Barnes-X bullets you make statements like this to me, and you claim to be so technically correct? You should actually write this type of crap to the Barnes company and see if they take you seriously? It would really be funny when these bullets "tumble and make curves" when you shoot them, but go straight when I shoot them. If that is not enough, you hint that the bullet MAY not even expand at 2,480 fps. I just noticed the operative word ... MAY ... you do not know, right, you are speculating, you are hoping ... and I thought you were only dealing in facts. They open up around 1,850 fps depending on caliber - ask Randy Brooks of Barnes. Go shoot them in a wetpack at 2,000 fps and then talk to me, just be honest, because I know the answer.

Please don't twist my words when you say ... "As you have found with X bullets, an expanding mono will outperform a bullet that contains lead every time." This is not true, the 380-gr Rhino Soft, puts buffalo down far more quickly and reliably than any other bullet up to .375 caliber. No light weight bullet (low-SD) in any super fast cartridge known to me can beat Rhino's 380 grainer at 2,220 fps. High energy cavitation won't do it for you on buffalo, you need a big hole through the hart. Ask Dr. Kevin Robertson, alias Doctari, if you doubt my word - he is up to about 800 buffalo by now. Gerard I am sorry, but I have to correct you on this, before it becomes gospel. Personally, I use 400 grainers in a 416 Rigby for backing-up my clients - with high-SD bullets (.330) - I like more weight behind a given frontal area, so Mo/Xsa can do its work when I have to anchor a runaway buffalo from a client. More weight behind a given frontal area is what SD is all about.

Don't get mad at me, even if you think I used a heavy hand. We can't make scrambled eggs, if we don't brake the eggs.
Pieter de Klerk

RIP,

Okay. I get your point. I just forgot about the (pi)(r)^2 calculation of area. Sometimes something that should be obvious, isn't.

My guess is that back in the "good old days" (before electronic calculators, etc.) the d^2 was just used for convenience and ease of (manual) calculation.

-Bob F.

Pieter,

Making an omelette here.

How about getting off your high horse and thinking just a little bit. I am not questioning your successes and I do not doubt that you get linear penetration with the 175gr X bullets. I am saying that your rifle does not have a one in 8.66" twist rate. It is 8" or tighter and you are too disbelieving of my field of expertise to slow down and think about what I am asking. You ask that I give you credit for having 12 years of experience in hunting. I ask that you give me credit for 40 years worth of hunting and 12 years worth of making the most advanced bullets currently available. Am I arrogant in saying this? If you think so I ask: Why is there suddenly a rush to manufacture some sort of drive band or grooved bullet by all and sundry? Because it works and we proved it first. Look at the Rhino solids, Barnes TSX, Groove bullets, North Fork and a at least five other manufacturers in Europe. Are they trying to copy a concept that does not work? Pretty stupid of them then.

If you believe that the very important link between twist rate and bullet length is voodoo, never take a plane to the USA. It might just fly off the end of the earth and then you are in big trouble.

Fortunately the dishonesty with the trajectories are all in Chris' mind. He accused me of comparing my 120gr boat tail bullet with a round nose flat base bullet. I quoted him the bullet I used and it is a Speer spitser flat base. He tried to save his argument and used the best BC bullet he could find and still lost the debate by a wide margin. So when I prove him wrong and he keeps digging after that, it makes me dishonest. I am amazed that you fall for the he is dishing out to you.

Will an X bullet expand at 2480fps? Of course it will but as it flies away from the rifle it slows down, I trust you have noticed this phenomenon. It will eventually reach a speed where it may not expand. (Whoops! There is that word "may" again!) At 250 metres it is way below 1800fps and we could place bets on its expansion at that point. Our HP bullets are dicey at that speed and they are softer than X bullets. Get the context or should I spell it out more clearly? (Chris, I know you are lurking in the background. Note that I said HP above and not HV. The HP is the smooth bullet and the HV is the one with the drive bands and expand at even lower speeds.)

"the 380-gr Rhino Soft, puts buffalo down far more quickly and reliably than any other bullet up to .375 caliber"

I can give you several quotes from PHs who have used a wider variety of bullets and they say otherwise. The question here is, have you used our GS softs or solids or say North Fork bullets in any calibre on game at all? If not, then what qualifies you to make that sweeping statement. Your field of experience does not include all the available bullets. You are saying that your Toyota Land Cruiser is the most powerful 4x4 you have ever driven. But have you driven a Touareg or Cayenne?

So you like the idea of putting Mo/XSA to work for you. Here is a wake up: The Mo part consists of weight and speed. You are just too timid to try a new idea I think.

quote:

Originally posted by RIP:

quote:

Originally posted by BFaucett:

quote:

Originally posted by RIP:

SD is based on a square bullet.

?????????????? I'm assuming SD = sectional density. Why is SD based on a square bullet??

-Bob F.

Gee Bob, I know you are an intelligent man. You just never thought about it.

Look at the formula for sectional density, it is the only one ever, and it is just a FOM, figure of merit:

SD = W/d^2
where
SD = sectional density
W = weight of bullet in pounds = weight of bullet in grains divided by 7000
d = diameter of bullet in caliber or inches

If SD were based on the true cross-sectional area of the bullet, then SD = W/(pi)(d/2)^2 ...

So the actual SD's listed for ages are just shorthand easy ways to express a number that is proportional to reality, but has no real units.

It is based on imaginary square bullets.

You don't read my posts very often do you? We have been hammering on this for a long time.

SD is useful, but you gotta be aware that it is not reality based in units for inclusion in equations unless you put in a factor of pi/4 or 4/pi to correct. If you fudge a reality based formula with an SD number, then you gotta un-fudge it.

Time honored SD listings are 3.1416/4 = 78.54% of what a "reality based" SD using round cross-section bullets would be.

The true definition of sectional density is BASED ON SQUARE BULLETS. IT IS PROPORTIONAL TO REALITY, BUT IT AIN'T REAL.

Do the math.

W/d^2 ...........................W/(pi)(d/2)^2

7mm 120gr .213 .................... .271 ....
7mm 139gr .247 ...116%............. .314 ..116%
7mm 175gr .310 ...146%............. .395 ..147%

30..165gr .247 .................... .316 ....
30..220gr .331 ...134%............. .422 ..134%

375 270gr .274 .................... .349 ....
375 300gr .305 ...111% ............ .388 ..111%

416 350gr .289 .................... .368 ....
416 400gr .330 ...114% ........... .420 ..114%

458 350gr .238 ................... .303 ......
458 400gr .272 ...114% ........... .347 ..115%
458 500gr .341 ...143% ........... .434 ..143%

Hummmmmmmmmm??

BigRx

BigRx,

You are a genius!!!!!!

Bullets that were nowhere on the Sd scale, now have respectable Sd values. This will surely make them penetrate better!

Bekker and Pieter, how come you guys did not see this? Some of those correctly calculated Sd values are so good, those bullets will kill if you just show them to a buffalo.

Bullet / Speed / Momentum / Mo/XSA / Penetration / Energy/ E-Index
175 --- 2,200 ---- 55.00 ----- 682 ------ 57.76 ---- 1,881 --- 100
142 --- 2,712 ---- 55.00 ----- 682 ------ 57.76 ---- 2,320 --- 123
108 --- 3,565 ---- 55.00 ----- 682 ------ 57.76 ---- 3,049 --- 162

Posting for Chris Bekker

RIP,

I am glad you can see some use for SD. I have already commented on the fact that certain writers used the simplified equation of D x D for area when it comes to SD and XSA, when in fact it would be more precise if Pi*R^2 were used - no argument about that. However it does not change its correlation to penetration depth - just the factor will differ between Mo/Xsa and P (Penetration) - the formula is self explanatory:

SD x Velocity = Mo/Xsa
Mass/Area x Velocity = Mass x Velocity/Area
(M/Pi *R^2) x V = MV/Pi *R^2
MV/A = MV/A
Mo/Area = Mo/Area

The example I published before was as follows:

SD -- / --Velocity / Mo/XSA
.310 -- x -- 2,200 = 682
.252 -- x -- 2,712 = 682
.191 -- x -- 3,565 = 682


Mass / Velocity / Mo / Mo/XSA
175 ---- 2,200 ---- 55.0 --- 682
142 ---- 2,712 ---- 55.0 --- 682
108 ---- 3,565 ---- 55.0 --- 682

The final answer would simply change to 868 in all cases, and the factor would become 868/57.76 = 15.0 instead of the previous 11.8. The underlying logic stays the same as well as the correlation. As I have said before, the lost momentum, by using low-SD bullets, cannot be made up by increased velocity in a given cartridge - in this case a 7 x 57 mm. I can load the 175 grainer to over 2,500 fps, but I only load it to 2,390 fps, as you can see in the article that I wrote - that gives a Mo/Xsa value of 741 and this cannot be achieved with lighter bullets, as the top end for the 110 gr Impala bullet is around 2,870 fps, giving a Mo/Xsa value of only 559 - that gives the High-SD bullet a lead of 33%. It is then fair to say that a higher-SD bullet, in any given cartridge, will out perform a low-SD bullet. Quite simple and nobody can wish this away, not even the Queen in England.
My best regards.
Chris

Posting for Pieter de Klerk

Tabular trajectory data at Std.ICAO Atmosphere
-------------------------------------------------------------------------------------
Gun / Ammunition : .300 Win Mag.
Bullet : .308, 200, BAR 'X' S 30845
Bullet weight : 200 grains or 12.96 Grams
Muzzle velocity : 2480 fps
Crosswind speed : 10 Mph
Ballistic Coefficient(s) (G1):
C1=0.540@V>0 fps;

The 200 gr Barnes-X bullet loaded to 2,480 fps MV: (per Quickload program)

At 250 yds it is doing 2,098 fps
At 350 yds it is doing 1,955 fps
At 400 yds it is doing 1,885 fps
At 450 yds it is doing 1,818 fps

Not sure how you got to a figure "way below 1,800 fps at 250 yds" - who is bullshitting?
I very seldom if ever shoot further than 350 yds - bullet is still performing at 1,955 fps
and I have the hard evidence for that. Just another correction - I have been hunting since
the age of 10 and I am now 45 years old - 35 years, but 12 years as a PH.
But before you get carried away, my load in my 300 Win Mag is actually 2,700 fps,
since I use it as a long-range gun and that puts the velocity at 2,003 fps at 450 yds

Pieter de Klerk

Bekker,
Admit it. You're mind was warped by the Bwana Saeed Index, the BS Index, which relied heavily on the sectional density.

Laddie, you must give it up. It was only a parlor game and is not to be taken too seriously.

I am sorry I have misled you so.

I am glad that everyone is now admitting that the sectional density, SD = W/d^2, is based on imaginary square bullets.

And no, SD x V does not equal Mo/XSA. How many times does this have to be explained?

Cheers!

quote:

Originally posted by mehulkamdar:
Bullet / Speed / Momentum / Mo/XSA / Penetration / Energy/ E-Index
175 --- 2,200 ---- 55.00 ----- 682 ------ 57.76 ---- 1,881 --- 100
142 --- 2,712 ---- 55.00 ----- 682 ------ 57.76 ---- 2,320 --- 123
108 --- 3,565 ---- 55.00 ----- 682 ------ 57.76 ---- 3,049 --- 162

Posting for Chris Bekker

RIP,

I am glad you can see some use for SD. I have already commented on the fact that certain writers used the simplified equation of D x D for area ...
Chris

Chris,
You are bullshitting again, and you just go on and on, spewing bull shit!

The DxD form of sectional density is the only form there is, flawed as it is.

Quit bull shitting, get a real job, and do something useful with your life!!!

Posting for Chris Bekker

RIP,

Perhaps we should make a few changes:

1) We should cancel the word SD and simply talk about 'more weight behind a given frontal area'. If we find that it works better than bullets with 'less weight behind the frontal diameter', the we should not coin a phrase, but rather see it as coincidental. Aren't we lucky not to shoot lead balls anymore.
2) We should not attempt to calculate the value in (1) because it may get confusing.
3) Even Momentum in the British system differ from the metric system - Momentum is Mass x Velocity, not Weight x Velocity. By using bullet weight (i.e., pounds) instead of bullet mass (i.e., grams or pounds-mass or slugs), you get a simplified and slightly erroneous measure of momentum. It differs only by a constant (acceleration due to gravity). We should really question why America refuses to go to the metric system, and that the 'uninformed' US hunters and the British derivatives perpetuate an archaic system. Fuck it man I am also guilty, dammit!
4) This makes the value of Mo as suspect as SD, as both are flawed - ever so slightly, or may be if you prefer, too serious to actually use these terms in good company.
5) Using 2 terms in the same formula, that are slightly flawed, surely makes a bigger flaw, and so we should steer clear from that - not being scientific enough.
6) That leaves us with the energy formula - its scientifically correct.
7) As energy is not a good predictor of bullet performance (sorry to say), we should positively reject it too and insist that it does not get published on ammo boxes.
8)That leaves the hunter pretty much with his intuition and/or hard earned experience.
9) When we buy bullets we should also be weary of the term BC, because it is based on a flawed SD value divided by a form factor (i) for one and BC values do not stay the same over the entire velocity band - shit we are getting deeper into trouble the further we go. So if SD is a croc then BC is a croc by logical deductive reasoning.
10) Where do we stand now? I am fucked if I know. Perhaps you can develop an all-embracing index for us that would hold true under all circumstances. It should not be a guideline, because it may not be perfect; we need something technically correct across the ambit of lead bullets to copper bullets no matter the velocity.

Best regards
Chris Bekker

quote:

Originally posted by Gerard:

1. Please share this proof with us as we have not seen it. The very test that Chris did with the cut down X bullet proves that lighter and faster bullet behaviour can be compared with slower and heavier bullets. All the X bullets in his test expanded to almost identical shapes, despite a wide variation in speed.
2. Mo/XSA is indeed an exellent yardstick with which to estimate terminal performance.

Sd on it's own is a croc.

3. No argument from me on that one. As you have found with X bullets, an expanding mono will outperform a bullet that contains lead every time.

Sorry Gerald, but I ask you to re-read your very first sentence following: "1."
"proves" highlighted is not CORRECT.

"All the X bullets in his test expanded to almost identical shapes, despite a wide variation in speed." THE ONLY THING WE KNOW HERE IS A STATIC RECOVERED BULLET IS THE SAME!

UNTIL SOMETHING is in this formula that tells us how much frontal area occurs when; it is all estimation.

Number 2 is an estimation until you factor time and frontal areas in.

Sectional density is as fair an estimation to use as some others stated.

AND.....If one looks at the percentages the "numbers" increased from the lightest bullet listed in my chart to the heaviest regardless of caliber, you WILL FIND THEM (percents)THE SAME WHETHER WE USE SQUARE BULLETS OR ROUND! Seems a piece of (pi) is not needed unless the bigger numbers make you happy!
But you already knew this RIP,.... as you mentioned "proportional" more than once!
So S.D is no more a croc than most this blather of estimation andestimation over these pages!

Item #3 may be true sometimes and then it may not as well. A little dog may beat a big dog once in a while; but atomic weights are a tough fight for the lesser.

I ask again if we are going to compare expanding bullets with anything besides an "educated opinion" that SOMEONE in all these pages spit out a formula with ALL THE PIECES! We will never hit the moon the way we are going.............

BigRx

Chris,
More Bekker BS??? SD is not a crock, it is a FOM. Mass and Weight are close enough over most of the earth's surface to be considered standard gravitation, and this issue shouldn't muddy the water ... unless you are from another planet, or lost in outer space.

The only all inclusive is:

BAM! = MV/(pi)x(r^2)

BigRX,
Regarding soft points, I can only run away screaming "INTRACTABLE!" However, BAM! can be a guide if the bullets are not too soft.

Posting for Pieter de Klerk

Gerard,

I love your quotation ... "So you like the idea of putting Mo/XSA to work for you. Here is a wake up: The Mo part consists of weight and speed. You are just too timid to try a new idea I think." That is correct Gerard, I think most of us understand that, but the way I mix the recipe is to add more weight and less speed for a better result, especially if we come to big game at short range such as hunting buffalo. I have a feeling that is why the 378 Weatherby Magnum has not overtaken the 375 H&H despite its ability to drive a 300 grain Barnes Solid at 2,965 fps using 114 grains of Reloader 22. More momentum and more energy ... what is wrong ... there are other considerations such as shootability, high recoil, high pressure and throat erosion to mention but a few. John Taylor said the 375 H&H is already over-penetrative on buffalo in herd situations and preferred the 404 Jeffery. That is still applicable today when we talk Solids. Luckily today we have controlled expansion bullets in the 375 H&H that change the scenario. If you have hunted buffalo before, you will know that more often than not you are going to be confronted with a herd situation. Thanks for your wake-up call, but it is no good to be wide awake and your eyes are cluttered with yellow gum.

Gerard then you make another statement ... "Fortunately the dishonesty with the trajectories are all in Chris' mind. He accused me of comparing my 120gr boat tail bullet with a round nose flat base bullet. I quoted him the bullet I used and it is a Speer Spitzer flat base." I have gone back and checked and would like to make a few observations regarding your 7-mm bullet comparison:

1) Why compare a HV-Spitzer BT bullet with a Spitzer Flat Base?
2) Why did you not pick Sierra's SPBT bullet with a BC of .524, as that would be more equitable?
3) Chris used a Nosler Partition with a BC of .519 to check you - it is not the highest BC bullet as you claimed.

Here are some BC values for you:
Sierra SPBT with a BC = .524
Barnes-X with a BC = .521
Nos. Part. with a BC = .519
Sierra Grandslam with a BC = .457
Speer Magtip with a BC = .378
Hornady RN with a BC = .285
Magic bullet with a BC = .228 (imaginary bullet)

4) You say Chris accused you of using a RN Flat Base ... let us see if this is in fact true. I looked in the QuickLoad database and used Speer's Magtip with a BC of .378 and it turns out that the result is still more favourable than what you dished up - see the figures below! I could not find a Speer Spitzer FB Bullet, but Speer's Magtip is a Semi-Spitzer and therefore should have a worse BC than a Spitzer version. Exploring the database further, I noticed that the bullet with the worst BC is actually the Hornady RN with a BC of .285 and will model its results to get a check point. Since I do not know for sure which bullet you used, I will refer to it as the MAGIC bullet for comparative purposes:

Who---- Bullet -- Cartridge --- Mass - Path @ 100 - Path @ 300 -- Wind Drift @ 200
Gerard - Magic -- 7 x 57 mm - 175 gr -- +4.38" ------ -18.54 --------- 12.45"
Pieter -- Magtip -- 7 x 57 mm - 175 gr -- +3.80" ------ -13.40 --------- 6.8"
Pieter -- Hdy RN - 7 x 57 mm - 175 gr -- +4.10" ------ -15.10 --------- 9.5"
Chris -- Nos Part - 7 x 57 mm - 175 gr -- +3.60" ------ -11.70 --------- 5.1"

It turns out that the 'Magic bullet' is even far worse than the Hornady RN bullet (BC=.285) with the lowest BC in the database. I could not model the figures you obtained, but the BC seems to be in the region of .228 which should more likely represent a flat-faced cylinder. Based on the above I am compelled to conclude that you were in fact dishonest. Based on your past responses to me about wanting to be technically correct, I do not take it as an inadvertent mistake, but that you willfully skewed the results to deceive the readers, as you had to be victorious at all costs, even if you have to cheat and put the blame on Chris.

Then your reference to the 'corrected' calculation of SD on the more respectable values...

# Mass on its own means nothing
# Velocity on its own means nothing
# Momentum on its own means nothing
# Cross sectional area on it own means nothing
# Sectional density on its own means nothing
# Combined it begins to make some sense and yes then it can kill

One way of lowering a bullet's SD is to make it of aluminum, another way is to cut it in half. To optimize we should go back to shooting round balls, perhaps aluminum balls, because that way we will get the lowest SD and the lowest BC. My Bushmen tracker also has no understanding of SD, even though his arrow has a respectable BC, but the bow gives a low velocity. The momentum though is not very respectable. The frontal area is small and sharp and it does not expand. One day I will measure and calculate his value of Mo/Xsa and may just be surprised ... Doctari is doing an article next month for Man Magnum about the 380-gr Rhino bullet on buffalo .... So you don't have to call him, you can read about it - may be he has not seen or used enough bullets either? Perhaps Doctari will tell us the effect of this large expanding bullet (terminal Xsa) with just the right amount of momentum behind it.

The art of hunting has nothing to do with ballistics!
Pieter de Klerk

Posting for Chris Bekker

RIP,

When it suites you, you will point out when something is not technically correct, but when it does not, you will rationalize that it is immaterial. I am beginning to see some pragmatism that I actually like. RIP we must be consistent in our criticism, and that is why I pointed the conundrum out to you, even if it was a bit facetious of me. I just wanted to show that this path is riddled with technical problems. I divide people in two categories - simplifiers and complicators and tend to think of myself as a simplifier and thus I have not worried too much about those apparent square bullets that became such a big issue - so the same goes for weight and mass.

Since 1865 scientist have been breaking their heads to find solutions for armor piercing problems and devised an array of formulae in an attempt to correctly (technically correct) formulate the dynamic behaviour of penetration. This may be an eye opener to see the amount of work that was done in the past. As can be expected none of these formulae are the same, but surely has some similarities. In does strike me that our formulas (yours and mine) are fairly crude in comparison with these as well as those of Poncelet that was published by Alf a while back. You may wish to review these formula for correctness or where it could possibly assist us in finding better solutions as the penetration issue.

Basics Formulaes:

VL = (K)(C)TtDd/[Ww COSa(Ob)]

K.E.=(0.5)(W/g)V2

Work = FL = (W/g)AL

Work=Sum of all FL=KTT=KT2

K(T/D)2=(0.5)(W/D3)V2
or
T/D=[(0.5/K)(W/D3)]0.5V
1. Fairbairn (English, Circa 1865)
T/D=(0.0007692)[(W/D3)V2]0.5

2. Tressider (English, early 1870's)

T/D=(0.00003798)(W/D3)0.5V1.5=(0.00003798)[(W/D3)V2]0.75/(W/D3)0.25

3. Krupp wrought iron (German, early 1870's)

T/D=(0.00004643)[(W/D3)V2]0.75
4. Gavre (French, 1870's)
T/D=(0.00002887)D0.42857[(W/D3)V2]0.71429
5. Krupp KS vs uncapped AP projectiles (German, Circa 1895)
T/D=(0.00006659)[(W/D3)V2]0.5
6. Davis harveyized nickel-steel vs uncapped AP projectiles (U.S., Circa 1895)
T/D=(0.00003466)D0.3333[(W/D3)V2]0.6667
7. Davis harveyized nickel-steel vs capped AP projectiles (U.S., Circa 1900)
T/D=(0.00002887)D0.25[(W/D3)V2]0.625
8. De Marre nickel-steel (French, Circa 1890)
T/D=(0.00005021)D0.07144[(W/D3)(V/C)2Cos3(Ob)]0.71429
9. Krupp all-purpose armor penetration (German, 1930's)
T/D=(0.30386)D0.25[(W/D3)(V/C)2]0.625
Best regards
Chris Bekker

Pieter,
With the exception of one item, all your points have been covered to distraction in this thread. Do us the courtesy of reading it off the top otherwise we will be rehashing the whole thing again.

By way of example:

1. You nitpick about exact BC values and whether a bullet was a semi-spitser or a spitser when it does not change the outcome of the comparison being made. In the comparison I made, even if you plug in the highest possible BC for a 7mm bullet which is 0.689, it still loses by a wide margin. We are using two different ballistic programs and you expect identical results? Get real. Now if you want to argue about a bullet losing to another by a wide margin or a very wide margin, go ahead and argue on your own.

2. You say: " Then your reference to the 'corrected' calculation of SD on the more respectable values... "

The point you make about parameters in isolation was made on the second page of this thread. In addition to that, did you not notice the row of jumping grins at the bottom of that post? That means I made an effort at inserting some humour.

I see you also degenerate into the irrelevant with aluminium balls just like Chris did as well. You guys obviously hang out together frequently. Your parting shot: " The art of hunting has nothing to do with ballistics!" Prompts me to ask again,as I did higher up on this page

"4. As a PH, is it then your firm opinion that a 300 win mag with a 165gr X bullet at 3100fps will kill less effectively than a 30-06 with a 200gr X bullet at 2480fps?

5. Again as a PH, are you saying that when two X bullets of equal momentum, but one having more energy, strikes, they will kill equally well? They will penetrate to similar depths and the higher energy bullet will cause a larger temporary cavity which will undoubtably add to the permanent cavity, but it will be less effective because it is lighter and faster?"

For the sake of clarity on your position I would really like to know If you believe that the very important link between twist rate and bullet length is voodoo?

Chris,
You dishonest,cheating,two faced manipulator of half truths and slanted arguments. You have cheated again!

You say to RIP that:

" I can load the 175 grainer to over 2,500 fps, but I only load it to 2,390 fps, as you can see in the article that I wrote - that gives a Mo/Xsa value of 741 and this cannot be achieved with lighter bullets, as the top end for the 110 gr Impala bullet is around 2,870 fps, giving a Mo/Xsa value of only 559"

I run a 130gr HV to 2950 fps in several 7x57s. You deliberately use a bullet much lighter and slower than any realistic example to make your argument look good.

Cheater!

And watch your language. My father used to say that swearing is always a sign of an inadequate vocabulary or a bad upbringing or both.

BigRx,
I hear what you say but can you imagine having a discussion around all the parameters with members of the flat earth society hanging around? Look at Chris' posts and then check out the very serious statement: ".... tend to think of myself as a simplifier ...."

I have not asked yet but I am sure some of them still use hydrostatic shock as a term of reference.

Pieter,
I forgot. I must admit that I have made detail errors in some of my posts. I forgot to adjust the barometric pressure to sea level in some examples and in another, the humidity and temperature was set to that of Cradock in June. Resetting them did not change any outcomes, so I left it alone. Your mention of the 375H&H vs. the 378 Weatherby is valid. Shootability is important and extra recoil does not add to that. Wouldn't it be useful to elevate Mo/XSA values by increasing the speed without going to lighter bullets and without increasing pressure and recoil?

At the front end of this discussion I made the statement that Mo/XSA is a better indicator of the likely penetration of a bullet than Sd. Do you and Chris disagree with this?

Chris Bekker the "simplifier" is truly the definition of oxymoron. Too funny ... ho ho ... hee hee ... visualize Chris Becker doing Michael Jackson moon walk ... gut hurts from laughing ... gasp ,,, wheeze ... drool ... roflmao ...

Posting for Chris Bekker:

Rip,

Here is the full text - the summary of the formulae that I have given may not be of great help without the text - I thought to make it simpler for you (being a simplifier). Enjoy. Construct a RIP (Rest In Peace) Index for us with the aid of the collectice work that was done over the last 140 years but do not confine yourself be creative and add some of your own experience.

Best regards
Chris bekker
Major Historical Naval Armor Penetration Formulae
I. INTRODUCTION
The following formulae give the thickness "T" of iron or steel armor penetrated with increasing striking velocity "V" at a given impact angle ("obliquity") "Ob" by naval gun projectiles of various diameters "D" and weights "W" in use at the time. The definition of "penetration" varies and usually is either the "Nose Through" or "Through Crack" Ballistic Limit (later called in the U.S. the "Army" Ballistic Limit) or the "Base Through" or "Complete Penetration" or "Perforation" Ballistic Limit (later U.S. terminology was "Navy" Ballistic Limit), though other definitions have been used less often. This is not always clear cut, since, for example, a shattered projectile in many pieces may pass through the plate, but exactly how many pieces will constitute a penetration by these definitions?

Definitions of various metallurgical, armor, and projectile terms can be found in my document "Table of metallurgical properties of naval armor and construction materials".

The original penetration formulae format used was, in its most general form:

VL = (K)(C)TtDd/[Ww COSa(Ob)]
where "K" was a constant and "C", if used, was a plate quality factor. Many formulae were for normal impact only or used a separate table/graph to handle oblique impact and had no COSa(Ob) term or sometimes C was combined with the COSa(Ob) term to give a C that varied with obliquity, also dropping the COSa(Ob) term. However, this format does not lend itself to separating the various terms for W, T, D, V, and Ob in an understandable way that explained why the exponents w, t, d, and a had the values that they had.

To fix this, the penetration formulae are usually given here in the re-arranged form of dimensionless, size-separated penetration in projectile diameters or "calibers" (T/D) on the left-hand side of the equal sign versus a function of all other factors (W, D, V, K, C, and Ob) on the right-hand side, since this makes the effects of each factor more obvious. Also, the units used here are English units of feet/second for V, inches for T and D, and pounds for W. By merely changing the Numerical Constant (= K-(1/t)) found at the beginning of the right-hand side of each formula to the proper value, these formulae can be used in their existing form for any units desired (usually using metric units of metres/second, centimeters, and kilograms).

Impact obliquity Ob is measured here in degrees such that a right-angles impact on the plate (along the "normal" line to the plate surface at that point) has a value of zero and a tangential impact that just skims the plate before glancing off has an obliquity near 90o. The angle is that of the projectile's direction of motion vector to the plate's normal line, not the direction that the projectile's nose itself is pointing, since the projectile will usually have some yaw (tilt in some sideways direction), though not much if the projectile and gun are designed properly. A yaw can be in any direction and can actually be corkscrewing around the direction of motion vector after a plate impact that wobbles a spinning projectile (most projectiles used spin stabilization, except for cannon balls (round shot) fired by early smooth-bore cannon or modern fin-stabilized super-high-velocity sabotted armor-piercing projectiles (APFSDS) used in post-WWII tank cannons). A small yaw (up to circa 10o) can be merged with the impact obliquity by assuming that it is a shift of the obliquity in the yaw direction by half of the magnitude of the yaw angle from the direction of motion vector. No matter how fixed the other factors are, firing ship motion, target motion, and target design will always make the obliquity of impact very unreliable in any scenario.

As long as the penetration process is slow compared to the speed of sound in the iron/steel armor and projectile (which is on the order of 16,000 feet/second), the entire kinetic energy of the projectile gets involved with the penetration from beginning to end. Kinetic energy has the formula

K.E.=(0.5)(W/g)V2
where "g" is the acceleration of gravity (32.2 feet/sq.second) when using English pounds, but which is set to 1.00 (ignored) when using metric kilograms, since kilograms already have had this division done ("newtons," not kilograms, are the metric equivalent of English pounds). An alternative form of energy called "Work" is defined as

Work = FL = (W/g)AL
where "F" is the current force of resistance due to the plate's mass and metallurgical properties over a small thickness slice of length "L" and "A" is the deceleration (in feet/sq.second in English units) that the projectile undergoes due to that force. Summing the values of Work for each individual slice L until the total plate thickness T is reached gives the total Work needed to punch through the plate, which will just equal the projectile's available kinetic energy when the projectile is striking the plate at its Navy Ballistic Limit at near normal obliquity (at high obliquity, the projectile is being deflected as well a decelerated and can switch from high-speed ricochet to high-speed penetration without ever slowing to a stop in the middle).

As mentioned above, if the factors of the penetration are changing rapidly, such as the fracture of the projectile and/or plate as the impact shock moves through them, then the value of W being used to calculate Work in a given length L may not be the total projectile weight and thus the predicted penetration as V, W, D, and Ob vary may not follow a "total-kinetic-energy" rule. In the penetration formulae this results in a smaller exponent for the W/D3 term than the value of one-half of the exponent for the velocity term, which is true for cases where total kinetic energy determines penetration (see below). For example, when dealing with shock-induced failure of the hard face of a face-hardened armor plate (Gruson, Compound, Harvey, and Krupp KC plates introduced in the 1860's to 1890's) the exponent of the weight term in my penetration formula is only 0.2, even though the exponent for the velocity term is 1.21 (6.05 times as large). The reason is that only the metal volume of the front end of the projectile is "informed" by the impact shock wave that the projectile has hit the plate before the plate's face layer caves in and thus only this front volume gets involved in the face penetration, where most of the energy is absorbed, with the rest of the projectile only involved in pushing through the soft back layer afterwards (without the soft back layer, the weight exponent would probably be near zero, once the projectile reached a minimum weight - always less than the weight of all real projectiles).

The projectiles assumed in these tests are usually between 1 and 3.5 calibers long (ignoring the projectile's windscreen, if any), made out of iron or steel, weigh from 0.148 (cannon balls) to 0.67 (most U.S. WWII naval APC projectiles) times the cube of their diameters (D in inches and W in pounds), have tapered noses that were usually, though not always, either pointed or elliptical in shape, and were consistent for the most part from round to round in their resistance to impact damage under a given set of conditions.

"W/D3" stays the same for a fixed projectile design of any D.
In the following formulae, except for the Tressider Wrought Iron Penetration Formula, the entire projectile weight is always used without modification to form the projectile's total kinetic energy that is used in determining penetration. To eliminate any confusing effects of projectile size (absolute scale) on its weight when calculating the size-free T/D value, W/D3 replaces W/g everywhere in the formulae, creating a scale-free or "normalized" kinetic energy (actually, energy density) function "[(W/D3)V2]" that is raised as a unit to a power "k" that is between 0.5 and 1.0, mostly very close to the middle of this range. Any scale effects will be given by a separate explicit multiplier term in the formula involved.

What does this value of "k" mean?
If k = 1.0, then the penetration is directly proportional to the Work or kinetic energy available to do the penetrating, which means that each thin armor layer L is resisting by a force F roughly equal for all L layers that sum to the total plate thickness T, but that each L is separated of any other L, much like when one is swimming in water (each volume of water in a swimming pool is the same as any other volume and how big the swimming pool is usually does not matter to how much effort it takes to swim a given distance down the length of the pool). Only when the projectile reaches a given armor slice L need it use up energy to penetrate that slice; ideally, not before and not after. Here, if you quadruple the available energy by doubling the striking velocity, to a first approximation you also quadruple the thickness of armor penetrated.

If k = 0.5, then the penetration increases slowly where the relationship between penetration achieved and striking velocity is linear - double the striking velocity and you double the penetration. This implies that the thicker plates are more difficult to penetrate than the thinner plates to a far higher degree than merely the ratio of thicknesses would imply. In fact, this value of "k" is true when the entire volume of plate material in front of the projectile is resisting the penetration from the first instant; that is, the material at the back of the plate is involved in the plate's resistance to the penetration of the material at the front of the plate! This occurs under conditions where the plate material is being pushed out the plate back and the material at the plate back is resisting that motion in addition to the resistance from the armor material at the front and middle of the plate - this punching-out is either as a cylindrical or conical plug sheared around the edge of the hole and pushed straight back like a cork from a bottle or as full-plate-thickness triangular flaps or teeth called "petals" in a ring around the forming hole that are being torn open at the center of the impact site and bent outward in all directions around the edge of the hole. If we make the simple assumption that all of the plate material is resisting equally, then adding up the Work required to penetrate the plate of thickness T gives

Work=Sum of all FL=KTT=KT2
where the sum of all L is T and, as defined, the resistance force F is the sum of the equal forces of resistance of each slice L acting over the entire penetration time instead of only when the projectile reaches that particular slice, which means that the resistance force F is the entire plate thickness (sum of all thicknesses L) times a constant "K" giving the resistance of each slice L. Changing T to T/D to match the normalized kinetic energy format and equating this to the projectile's available normalized kinetic energy gives

K(T/D)2=(0.5)(W/D3)V2


or


T/D=[(0.5/K)(W/D3)]0.5V
as required. For hard materials, this rule may apply for all plate thicknesses, but for ductile, homogeneous armors, it only applies when the plate is rather thin, less than 0.5 calibers at even the most extreme case.

In real life, neither of these two extremes is usually true, though the linear case is much more nearly approximated for some plate types and/or ranges of thickness, so that the formulae approximations used over the years tended to split the difference when trying to apply a single-exponent "k" power law to all plates. However, only when the plate always fails in exactly the same way no matter how thick it is will this kind of formula be accurate over more than a narrow range of plate thicknesses. Even face-hardened armor, which approximates this single failure mode (always breaking of the face followed by tearing out of the back) better than any other armor type, has a more complex formula that modifies this simple picture, though my face-hardened formulae set is indeed based at bottom on a single-exponent power rule. Homogeneous, ductile armor drastically changes its modes of resistance as plate thickness increases from very thin, trampoline-like sheet metal plates that "dish" (dent) over a wide area ("k" is actually greater than 1.0 here, reducing resistance per unit thickness as thickness increases, because the thicker plates in this range of very low thicknesses are more rigid and absorb less energy per unit volume of armor than the thinnest plates do, which are more flexible and can stretch more before tearing), through medium-thickness petalling plates that fold back in an area ringing the hole ("k" near 0.5), through thick plates that must be bored through like a nail through a thick wood board ("k" near 1.0), petalling only in a narrow thickness region at the plate back.

Hollow, sharply-pointed windscreens (also called "windshields" or "ballistic caps") and Hoods (thin, soft, soldered-on, form-fitting nose coverings introduced after WWI in many new uncapped, base-fuzed Common projectiles so that the now-universally-used windscreens could have their attachment screw threads cut into them instead of into the projectiles' hard, brittle noses) had only minimal effects except on very thin plate impacts, while thick armor-piercing caps ("AP caps," for short, looking much like very thick Hoods, but later AP caps were usually very highly hardened), when used, had major effects under some conditions, especially when reducing or even entirely preventing projectile nose damage against face-hardened armor.

Oblique impact was ignored by most of the earlier of these formulae because the projectiles were not very well designed for handling the sideways forces caused by such impacts and had considerable variation in penetration ability from test to test due to projectile deformation and breakage in various unpredictable ways. This problem remained true when attacking face-hardened armor using some of the weaker projectile designs even through the end of WWII, but by then it had mostly been solved by improved projectile designs and metallurgical expertise.

Oblique impact is rather complex. Below the projectile's "biting" angle (the highest obliquity where nose-first penetration occurs at the Navy Ballistic Limit with this projectile against all thicknesses of the plate type under test), for a given plate type thickness does not significantly affect the percentage increase in striking velocity required to penetrate at a given angle compared to penetrating the same plate at normal (a single multiplier for a given obliquity gives good results for all plate thicknesses where projectile damage is not changing things). The projectile's nose immediately digs into the plate and inhibits ricochet. However, projectiles that impact plates at above their biting angle will have their noses pushed strongly away from the plate, so they will rotate in the direction parallel to the plate face and try to push through the plate sideways, which causes a considerable increase in the required energy to penetrate due to the larger hole needed and the loss of concentrated impact force on the plate at the point of initial impact as the nose skids sideways on the plate surface. Above the biting angle, increasing plate thickness drastically increases the required energy to penetrate until any sideways penetrations are essentially impossible for thick plates. When this occurs for a thick plate, it is necessary to increase the striking velocity even more to the point where a nose-first penetration can be obtained at the Navy Ballistic Limit (similar to below the biting angle, but requiring much more energy to accomplish), but to do this requires that the projectile dig into the plate so deeply on the initial impact that the nose is caught by the mound of armor material pushed up in front of it (no mound can form with face-hardened armor, but the nose can dig into the hard material at the far side of the hole after punching out a plug) and held until the glancing rotation of the projectile ceases when the base hits the plate's surface. The very large increase in striking velocity needed at high obliquity for complete penetration is essentially impossible above about 75-80o even for thin plates when pointed projectiles are used, though brittle plates can have plugs of armor punched out of them by the impact that can cause severe damage by themselves (especially a problem with face-hardened armor).

At high obliquity, interestingly enough, projectile damage that breaks a projectile (not just bends it, which is always bad) can help penetration, since the ricochet of the nose does not pull the entire projectile away with it and at least some of the lower body of the projectile can sometimes penetrate through the tear made in the plate by the nose before it bounced off. This is especially a problem with face-hardened armor, where a high-obliquity impact can punch out a large plug of armor, resulting in a large elongated hole, even when the projectile itself has no possibility of penetration unless it snaps apart and its lower body can pass through the hole it just made. Unfortunately for the target of such an impact, face-hardened armor is designed to cause such projectile damage on purpose and will thus enhance rather than reduce the damage to the ship compared to the use of ductile, homogeneous armor under such highly oblique impact conditions (as if the punched-out plug of face-hardened armor flying around wasn't bad enough!).

II. WROUGHT IRON ARMOR
A. Fairbairn (English, Circa 1865)
T/D=(0.0007692)[(W/D3)V2]0.5
Linear increase of T with increasing V nearly correct for thin plates at normal obliquity and/or with projectiles that suffer progressive damage that gradually reduces penetration ability as plate thickness increases (solid wrought-iron round shot, for example).

B. Tressider (English, early 1870's)
T/D=(0.00003798)(W/D3)0.5V1.5=(0.00003798)[(W/D3)V2]0.75/(W/D3)0.25
Increase of T with V is close to average value for medium-thickness plates (0.25-0.75 caliber) at low obliquity with a non-deforming projectile. Note that the power of the weight density function is only one-third the power of the velocity, not one-half as a true total kinetic energy function would require, meaning that increasing the projectile's weight has less effect on its penetration than all other armor penetration formulae given here require. While in agreement with my data on penetrating hard, brittle armor, such as face-hardened armor, though much less extreme (see introduction, above), this reduced dependency on projectile weight is not evident in any of my data for penetrating homogeneous, ductile armor with tapered-nose (pointed or rounded) projectiles - flat-nose projectiles punching out armor plugs may also show this reduced dependence on weight under some conditions, especially against thin plates. Perhaps the plates were acting in a brittle manner due to poor quality control (dirt and other impurities in the metal and improper crystal structures that could not move or deform freely), forming cracks at or just after initial impact, prior to the entire projectile getting involved in the impact, or perhaps many of the tests were done with flat-nosed projectiles against thin plates. Lack of a scaling term implies that these effects were for all plate thicknesses against all size projectiles more-or-less identically.

C. Krupp wrought iron (German, early 1870's)
T/D=(0.00004643)[(W/D3)V2]0.75
Similar to Tressider Formula, but total kinetic energy is used.

E. Gavre (French, 1870's)
T/D=(0.00002887)D0.42857[(W/D3)V2]0.71429
Similar to the De Marre Wrought Iron Formula in II.D., above, but the rate of increase in penetration with kinetic energy is slightly less (more in line with later results) and the scaling term is of the same form, but considerably higher (in line with some of my face-hardened armor results), which possibly indicates an extreme plate quality drop with increasing thickness at the French Gavre Naval Proving Ground (N.P.G.) at the time.

III. FACE-HARDENED ARMOR
A. Krupp KS vs uncapped AP projectiles (German, Circa 1895)
T/D=(0.00006659)[(W/D3)V2]0.5
First attempt to describe the penetration into the new deep-faced (35%) Krupp Cemented armor's effects on armor-piercing projectile penetration (KC was introduced by Krupp in 1894). Linear with increasing striking velocity, indicating that projectile damage was progressively worse as plate thickness increased, countering the higher increase rate due to the kinetic energy rise with striking velocity. Used total kinetic energy, which is at odds with my data and with my concept of the theory of face layer penetration due to shock effects. Use of uncapped projectiles caused the test-to-test variation to be considerable, though less than with thin-faced Harveyized armor (introduced in 1891) since the deep face would more thoroughly and consistently destroy the projectile body after the hard surface shattered its nose.

B. Davis harveyized nickel-steel vs uncapped AP projectiles (U.S., Circa 1895)
T/D=(0.00003466)D0.3333[(W/D3)V2]0.6667
First attempt to describe face hardened armor penetration as a separate phenomenon from homogeneous armor penetration. Harveyized mild steel and Nickel-steel armors (developed by the U.S. Harvey Steel Company in 1890-91) had a thin "Harveyized" (also called "case hardened", "cemented", or "carburized") super-hard face layer of only about 1" (2.54cm) thickness with the remainder of the plate remaining slightly hardened, ductile, homogeneous steel. The slightly lower increase in penetration with striking velocity compared to the De Marre Nickel-Steel Formula and huge "Dd" scaling term indicate that these plates were causing less and less damage as their thickness increased, due to the thin constant face layer becoming less and less effective as either projectiles got larger or striking velocity increased against thicker plates. Even with the thin face, plate failure had to be by punching the hard face pieces through the back of the plate, so the use of total kinetic energy is at odds with my understanding of face-hardened armor penetration. The data must have been very scattered from test to test due to the rather low projectile quality against shock, giving widely variable shatter damage effects (a statistical average with a wide range) due to the lack of a deep hardened face behind the cemented layer to consistently pulverize the now nose-less projectile body as it tries to push through the plate.

C. Davis harveyized nickel-steel vs capped AP projectiles (U.S., Circa 1900)
T/D=(0.00002887)D0.25[(W/D3)V2]0.625
Similar to the Davis Harveyized Nickel-Steel Vs Uncapped AP Projectiles Formula, but the scaling term is somewhat smaller and the increase in the penetration with striking velocity (V-exponent=(2)(0.625)=1.25) is almost exactly the same as my own face-hardened armor penetration formula's V-exponent of 1.21, though the use of total kinetic energy by using an exponent of 0.625 for the W/D3 term instead of my formula's much smaller exponent of 0.2 is at odds with my data. However, the thin face would, as described in III.A. and III.B., above, cause less consistent projectile nose and body damage with or without the AP cap, especially with the poor impact shock resistance of these projectiles, and this makes the test results more scattered and hard to define without a good grasp of the theory, which they did not have, either.

IV. "UNIVERSAL" FORMULAE
A. De Marre nickel-steel (French, Circa 1890)
T/D=(0.00005021)D0.07144[(W/D3)(V/C)2Cos3(Ob)]0.71429
The variable "C" is the "De Marre Coefficient" that compares the test results for the given plate to the striking velocity required to barely completely penetrate, using the Navy Ballistic Limit definition, under the same conditions an identical Nickel-steel plate of average French 1890 quality. For example, later Chromium-Nickel-steel armors such as STS had normal-obliquity "C"-values of circa 1.2-1.25. The obliquity range Ob was usually restricted to 30o. As usually used later for other homogeneous armors, the "Cos3(Ob)" term was dropped altogether and "C" was used to define the velocity ratio alone. This formula became the "standard" used for many years from which most others were developed. If the value of "C" is properly chosen, this formula works amazingly well for impacts at a fixed low obliquity using a single constant value for "C" when non-deforming pointed projectiles are used against all kinds of homogeneous ductile iron and steel plates from about 0.1 to 0.75 caliber thick - above 0.75 caliber, the exponent for the kinetic energy term increases from 0.71429 to nearly 1.0, while below 0.1 the exponent increases actually to a value higher than 1.0 (see introduction, above). The formula was also applied to face-hardened armor penetration, but value for "C" was restricted to a narrow range of plate thicknesses, requiring a table of "C" values. Note that it has a very small, but significant, scaling term of the "Dd" form that matches homogeneous armor test results reasonably well, which is being caused by the cracking of the armor that occurs with even the best ductile homogeneous iron and steel.

B. Krupp all-purpose armor penetration (German, 1930's)
T/D=(0.30386)D0.25[(W/D3)(V/C)2]0.625
Note that this is almost exactly the same as the U.S. Davis Harveyized Nickel-Steel Vs Capped AP Projectile Formula, with the addition of the coefficient "C" that acts exactly the same as the De Marre Coefficient of the De Marre Nickel-Steel Formula (even the same letter "C" was used). The value of "C" varied from a minimum of 525 for most Armor-Piercing, Capped (APC) projectiles penetrating unbroken through mild steel (post-WWI German "Ste. 42" shipbuilding steel, I assume), through 655-694 for average APC projectiles penetrating unbroken through German Krupp post-1930 "Wotan Harte" (Hardened 'Wotan' armor steel) (Wh) homogeneous (horizontal and thin vertical) armor, to a maximum of 804 for the weakest APC projectiles penetrating unbroken through KC n/A (the last, post-1930 form of Krupp's own "Krupp Cemented" armor, called "New Type"), though the specific projectile used modifies this value considerably in most cases, sometimes, but not always, compensating for the large scaling term that does not apply to most forms of homogeneous, ductile armor and for the use of total kinetic energy for the face-hardened armor computations. See the table at the end of this entry for typical "C" values. This formula is for normal obliquity only; oblique impact was handled by a special formula/data table set produced for each projectile separately - Krupp's KC n/A armor oblique angle data set included both a Navy Ballistic Limit (bare penetration entirely through the plate usually by a broken projectile when using Krupp's APC projectile designs) and an estimated "Effective" (i.e., intact) Ballistic Limit where reliable post-impact APC projectile base fuze and filler "as-designed" functioning could be assumed after the projectile had passed through the plate (these two ballistic limits were much closer together at normal than at oblique impact or for thinner armor at any obliquity, with older Krupp - and most other - APC projectile designs having considerably inferior performance when either bare penetration or, more obviously, effective penetration was computed).

TABLE OF "C" VALUES FOR THE KRUPP 1930'S ALL-PURPOSE PENETRATION FORMULA USED IN GERMAN NAVY'S "G.KDOS. 100"
APC PROJECTILE DATA "C" VALUE USED
Identification Diameter
in. Weight
lb. Wh
intact KC n/A
broken KC n/A
intact
GERMAN L/3.7 (NURNBERG, Z Cl.) 5.91 100.3 690 739 780
GERMAN L/4.6 (Experimental)* 5.91 110.2 688** 618** 627
FRENCH (LA GALISSONIERE) 6.00 119.0 694 714 781
BRITISH (LEANDER)*** 6.00 112.0 685 739 780
GERMAN L/4.4 (HIPPER) 8.00 269.0 660 637 650
FRENCH (ALGERIE) 8.00 255.7 660 638 652
FRENCH (COLBERT) 8.00 271.2 660 633 650
BRITISH (EXETER)**** 8.00 249.1 648 628 640
GERMAN L/3.7 (LUTZOW) 11.14 661.4 668 762 804
GERMAN L/4.4 (SCHARNHORST) 11.14 727.5 665 680 704
FRENCH (OCEAN) 12.00 952.4 666 677 685
FRENCH (DUNKERQUE) 12.99 1212.5 659 678 687
FRENCH (LORRAINE) 13.39 1221.3 664 676 685
GERMAN L/4.4 (BISMARCK) 14.96 1763.7 658 676 685
BRITISH (HOOD) 15.00 1929.0 663 678 689
BRITISH (NELSON) 16.00 2050.3 655 674 687


German data on foreign guns was not always correct, as the projectile weights given above show when compared to actual data in modern sources, such as the various battleship books by Dulin and Garzke.

The value for "C" always assumed a German-type APC projectile with various improvements added.

* This projectile was an elongated, slightly improved Krupp L/4.4 (4.4 calibers long; latest design) APC projectile design. It may never have been actually used by any German ship. It is found in the document "G.KDos. 144," a booklet of German naval gun penetration tables in 1944, most of which duplicate "G.KDos. 100."

** This data not given in "G.KDos. 144." Estimated from similar Krupp 8" L/4.4 APC projectile data.

*** No British naval 6" APC projectile existed in WWII. Actual projectile type was an uncapped, base-fuzed Common, Pointed, Ballistically Capped (CPBC) design, whose capability against KC n/A armor would be much worse than any design given here, but against Wh at low obliquity, it would probably have a lower, better "C" of perhaps circa 650 due to no AP cap. Penetration ability degrades as Wh plate thickness went above circa half-caliber (i.e., half the projectile's diameter in thickness) even at right-angles. Oblique impact penetration loss against Wh armor over half-caliber was very rapid at obliquity over 45o.

**** No British naval 8" APC projectile existed in WWII. Actual projectile type was a hard-capped Semi-Armor Piercing, Capped (SAPC) design (i.e., base-fuzed Common with an AP Cap), whose capability against any armor would be somewhat worse than most APC projectiles at oblique impact or against plates over circa half-caliber, being perhaps roughly the values given above at right-angles for plates up to half-caliber and then degrading slowly to circa 780 for Wh plates of 1.25 caliber or greater, but more rapidly to circa 800 for KC plates of caliber or greater. Oblique impact penetration loss was very rapid for all plates over circa half-caliber, especially at obliquity over 45o.
C. Thompson "F-Formula" all-purpose armor penetration (U.S., 1930)
T/D=(1728.04)(W/D3)[(V/F)Cos(Ob)]2
Developed by Dr. L.T.E. Thompson at the U.S. Naval Proving Ground (N.P.G.), Dahlgren, Virginia, from a theoretical application of the basic laws of physics through the "Theory of Similitude", where calculations would be made and the final units adjusted to agree with the three major Newtonian Physics Conservation Laws (Energy, Linear Momentum, and Angular Momentum). The F-Formula purposely had no form of scaling term and used total kinetic energy. The coefficient "F" was used as a measure of the required armor penetration energy and originally absorbed the effects of all factors including obliquity - the "Cos(Ob)" term was later added to reduce the range of "F" values if only impact obliquity was changed. The formula was usually used in its reverse form

VL=(0.024056)[(T/D)/(W/D3)]0.5[F/Cos(Ob)]=(0.024056)(D)(T/W)0.5[F/Cos(Ob)]
for the U.S. Navy Ballistic Limit, given as "NBL" or "VL" here. Also, the "F" values calculated from using the formula with known armor plate thicknesses, projectile diameters, impact obliquities, and striking velocities were usually compared directly to each other during analytical work, ignoring the striking velocities altogether. The values for "F" used for comparing all U.S. Navy Ballistic Limits were calculated using an empirical formula for all armor-piercing projectiles derived in 1930 by Dr. Thompson from test results of U.S. Navy Bureau of Ordnance Class "B" homogeneous Chromium-Nickel-steel armor and the similar Bureau of Construction and Repair (Bureau of Ships in WWII) "Special Treatment Steel" (STS) armor and construction material hit by the standard U.S. WWI 260-lb. 8" (20.3cm) Mark 11 Mod 1 soft-capped AP projectile (the first of the "Midvale Unbreakable" designs) at 0-75o obliquity (plotted in BuOrd Ordnance Sketch #78841):

FSTD=(6)[(T/D)-0.45][Ob2+2000]+40000
where, as previously mentioned, impact obliquity "Ob" is in degrees with zero meaning a right-angles impact on the plate face. The actual striking velocities in tests were compared in U.S. N.P.G. documents during and just after WWII with the "standard" VL calculated by inserting FSTD into the F-Formula by a velocity-ratio technique termed the "% NBL" where the term "NBL" always meant the FSTD-derived, theoretical Navy Ballistic Limit value and "VL" always was the actual Navy Ballistic Limit value obtained from the tests.

For example, if a plate was tested at some obliquity with some projectile that gave an FSTD-calculated NBL of, say, 2000 feet/second but used actual test striking velocities of, say, 1950 and 2150 feet/second and this lead to an estimated 2100 feet/second value for the plate's VL, then the test impacts would be reported to have been at (1950/2000)(100)=97.5%NBL and (2150/2000)(100)=107.5%NBL and the estimated VL=(2100/2000)(100)=105%NBL, slightly better than the FSTD-based NBL value, perhaps due to a more accurate analytical result, to better armor, to an inferior projectile design, or to using the FSTD formula for face-hardened armor, for which it was not designed, but for which it was used anyway at the U.S. N.P.G. to give a standard starting point for comparative purposes. Unfortunately, as mentioned above several times, when physical processes occur so rapidly that the entire projectile and/or impacted plate region are not contributing to the penetration process during at least part of the time due to the speed of sound limit in the metals, the simplified application of the concept of Similitude used in the Thompson F-Formula will give incorrect results (see Introduction).

However, if the values of "F" are not restricted to any pre-conceived formula (FSTD is not used), comparison of test-derived "F" values can be quite enlightening because of the simplicity of the plain Thompson F-Formula (only the Numerical Constant 1728.04 has a fixed value and it only exists because of the use of mixed units, such as feet instead of inches when measuring the striking velocity, and so forth). In such a study, the effects of scaling, projectile design, projectile weight changes, and varying methods of plate failure due to composition, toughness, hardness, thickness, and so forth, are all reflected in the values of "F" generated from test results and these "F" values can be used to derive the true laws governing these factors, if one has a open mind and does not try to use pre-conceived ideas to try to force "square pegs into round holes" as was done over and over again in the study of armor and its laws of application. During and after WWII, until the U.S. Navy's armor program was shut down in 1955 and transferred to the U.S. Army, Dr. Allen V. Hershey lead the U.S. N.P.G. armor analysis effort and the tables of "F" values were the center of the formulae and test data sets developed by his department.



Author:
Nathan Okun

Sources:
Nathan Okun "Table of metallurgical properties of naval armor and construction materials"
"Basis and guidance for the choice of the optimum fighting range and projectile type" OKM, 1940

Posting for Pieter de Klerk:

Gerard,

Your ballistic program is fucked-up and you should throw it in the trashcan. Claiming that a program can differ so widely is the biggest crap I have ever heard. But what is more is that a Speer Spitzer bullet can have a BC of only .228 - it really takes the cake. The Speer company should give you a Grammy Award for a bullet they don't have. Somehow this MAGIC bullet found its way into your program - that is even more brilliant! I would like to know the name of this program and if it behaves so erratic with trajectory data then surely all your other calculations must be suspect, unless it only works out HV-bullets correctly but victimize all other bullets. You should buy me a present for pointing this out to you, before you getting into real trouble. Nevertheless, I will re-open the case of dishonesty and grant you an appeal hearing if you come forward with this Magic program for me to examine as a PH.

Gerard you just don't seem to get the point - I think you are just too stubborn to admit that even with your HV bullet, at such high velocity as you claim, you still cannot make up the lost momentum. Let us take the max values then:

Bullet Mass / Velocity / Momentum
175 gr --------- 2,525 ----- 63.1 -----
130 gr --------- 2,950 ----- 54.8 -----

This proves that Chris is not cheating, but you atre the one that refuses to admit. How many times did Chris tell you this? But you continually accuse him of using irrelevant examples, but the fact is you are guilty of that. All your resposes prove that. It is of no use to make slanderous statements against my friend, you just show us your real colours. He actually warned me of your devious style, but nevertheless I engaged in talks with you in the hope that you may see the light, but I have come to believe that it is in vain.

O yes, then you go off at a tangent about a new topic - hydrostatic shock ? Chris mentioned to me that it is your style to drift off to other topics and you have just proven him right! What is hydrostatic shock - is it linked to high velocity? We PH's do not know what this is - is it some kind of a Tsunami shock wave that we should watch out for when we cross riverines when in hot pursuit of buffalo? I think a buffalo hiding in swampy reeds is more of a real danger. That is when I am glad I have got 400 grainers with me - constructed in such a way that I put all that mass behind a .416 for an SD of .330.

That's it.
Pieter de Klerk

Well, I guess there's only one way left to settle all of this!



-Bob F.

quote:

Originally posted by BFaucett:
Well, I guess there's only one way left to settle all of this!



-Bob F.

Excellent. Pieter can be Chris's second, and I shall perform as second for Gerard.


Chris continues to baffle with his BS and a few dazzling rays from the works of our ancestors.

All very entertaining.

Now back to the field of honor ... sunup tomorrow.