Pistol Caliber Effectiveness from a Medical Point of View

[OldMarksman]

Posted by Frank Ettin:

How much tissue is crushed/cut/damaged is a function of the diameter of the bullet and the penetration of the bullet.

How deeply the bullet will penetrate is a function of velocity and mass.... (momentum) and the sectional density of the bullet (the ratio of cross sectional area to mass).

Keep in mind that energy is also a function of mass and velocity (velocity squared).

I think that to complete the analysis, one may also have to at least consider the shape of the ogive. It is my impression, though i do not know this, that a bullet such as the old .38 158 grain LRN bullet can push its way though flesh and leave a narrower permanent wound channel than would a wadcutter or Keith semi-wadcutter bullet. Whether there are any analogous, meaningful comparisons among different kinds of JHP bullets after that have expanded, I do not know.

Of course, a lot of this discussion has centered on the emergence of new bullet technology. New bonded JHP bullets better retain their integrity and therefore penetrate more deeply.

One should not take special Agent Urey Patrick's statement that kinetic energy does not wound out of context. He goes on to say, correctly (as it applies to most handgun calibers) "the much-discussed "shock" of bullet impact is a fable...". Those statements ran counter to the deep seated faith of many people afflicted with magnumitis.

What he was telling us is true. It is that bullets have to hit and destroy something directly-- and not that energy does not play an inmortant role in that, and most certainly not that the conservation of momentum has anything to do with it.

In Post #229, Sharkbite put it quite well this way:

There is NOTHING else with handgun rounds. No hydro static shock at the low impact velocities. No magic "knockdown power".

There is the damage done by the bullet impacting and destroying whatever structures it impacts...period

In Post #224, I listed some processes related to the use and conversion of energy and some that illustrate the conservation of momentum. Perhaps these will help.

The slowing or stopping of a object in motion by applying either friction braking or regenerative braking relates to the conservation of energy. Slowing an object in motion by deploying an aerodynamic deceleration device involves the conservation of momentum.

One will see no reference to the conservation of momentum in technical discussions of cutting, grinding, forging, plowing, jack-hammering, etc. Those processes are highly analogous to creating a wound with a bullet.

There does exist a rather retailed report by someone who has been able to correlate, with reasonable accuracy, penetration in ballistic gel with penetration in with penetration by identical bullets in water, using, among other factors, momentum calculations. his objective was to save cost, and he would not represent his correlative relationships as causal ones.

 

[mavracer]

In terms of medical examination after an individual has been shot it doesn't matter what caliber was used. The damage is either fatal, critical, or superficial.

The problem with analizing wounds from the emergency room table is it gives you damn little insite on what happened immediatly after the shooting.

Ever had somebody walk in with a wound that ended up being fatal or had somebody come in totally non respondent that survived?

one may also have to at least consider the shape of the ogive. It is my impression, though i do not know this, that a bullet such as the old .38 158 grain LRN bullet can push its way though flesh and leave a narrower permanent wound channel than would a wadcutter or Keith semi-wadcutter bullet.

Shape of the bullet can not cheat the laws of physics the LRN will leave a narrower permanent wound channel and cause less damage along the way but it will also penatrate deeper hence conservation of momentum.

and not that energy does not play an inmortant role in that, and most certainly not that the conservation of momentum has anything to do with it.

Then stop jacking around and prove it's energy and explain how a 240gr 44 Special going 750 fps and has only 300 ft.lbs of energy will leave a larger permanent crush cavity greater volume than a 124gr 9mm going 1200 fps that produces 400 ft.lbs. in any controlled medium?

shape of the bullet can not cheat the laws of physics the LRN will leave a narrower permanent wound channel and cause less damage along the way but it will also penatrate deeper hence conservation of momentum.

 

[OldMarksman]

What Matters....

...if one intends to rely upon a physiological stop, is what the bullets damage inside the body.

That depends upon three things:

1. Penetration and the volume of the permanent wound channel;
2. "shot placement"; and
3. the number of hits.

For the first, the defender need not understand one whit about how the wound may be created. No discussion of kinetic energy or any other physical property makes any practical difference at all, whatever the underlying facts are.

For the second and third, however, the physics do matter to the shooter, whether he or she understands the subject or not.

"Shot placement" in a real defensive encounter involves a lot more than marksmanship. It is likely that the defender will have to engage a fast-moving target at lose range, and to stop it very, very quickly. It is almost chain that the defender will not be able to pick and choose the entry points and angles to hit those important internal parts of the the target, much less aim to hit them.

No, the defender will have to rely in large part on probabilities. That's because, since "Holes in the right places are better than holes in the wrong places", and since the defender cannot really choose the right places in the event, that's one reason why "more holes are better than fewer holes". There are, of course, other advantages to having "more holes".

Because the time available to put a sufficient number of holes in a close target that is moving very fast is very limited indeed, it matters a great deal for the defender to be able to shoot rapidly--much more rapidly than most of those who practice at the square range may realize.

That means that the defender's handgun would best not move very much between shots.

There are two ways to reduce that movement:

• Increase the mass of the firearm; given the same recoil momentum (mass times velocity), more mass will mean slower movement; and/or
• Reduce the momentum (the product of the mass and velocity of the ejecta) to start with.

That means that if we can choose a load that generates less momentum without sacrificing penetration and wound channel volume, we will be better off.

Some time back, the Personal Defense Network had a guest author pose the question about when a .380 might be a better carry piece than a compact 9mm-- Anathema, according to the inventional wisdom!

His answer was that the really compact 9mm carry pistols often recoil so much that controlled rapid fire becomes virtually impossible, and that even with the limitations of the terminal ballistics of the .380, the latter may well be preferable.

My solution is to carry a heavier pistol.

 

[JohnKSa]

So if you choose to believe 12" is a magic number and is the very definition of sufficient that's fine good luck with that.

It's interesting how you play this. Because it doesn't fit your arguments, you attack the 12" penetration minimum in spite of the fact that it is universally accepted and can be supported by basic human anatomy and the realities of gunfights.

But you maintain that wound volume differences amongst the service pistols--differences that have not been demonstrated to have a practically significant effect on incapacitation times/failures--MUST have a practically significant effect because that fits your premise.

Then you try to support your contention about terminal effect with a fundamentally flawed characterization of the physics of moving objects and when the error is pointed out, you pretend it has no effect on your arguments.

In the one case, the evidence doesn't agree with your premise so you reject the evidence. In the second case there isn't any evidence to support your premise but you cling to it anyway. In the third case, when it turns out your understanding of basic physics is incorrect you still don't re-evaluate your position which you claimed was based on physics.

In other words, although you hold your position regardless of the evidence or lack thereof, and although your position is based on a flawed understanding of the science involved, you refuse to drop the pretense that your arguments are based on evidence and science.

 

[dirtd0g]

Ever had somebody walk in with a wound that ended up being fatal or had somebody come in totally non respondent that survived?

Yes and yes.

 

[mavracer]

It's interesting how you play this. Because it doesn't fit your arguments, you attack the 12" penetration minimum in spite of the fact that it is universally accepted and can be supported by basic human anatomy and the realities of gunfights.

I'm not attacking the 12" minimum, I'm attacking the 12" sufficient and the idea the more isn't an advantage

But you maintain that wound volume differences amongst the service pistols--differences that have not been demonstrated to have a practically significant effect on incapacitation times/failures--MUST have a practically significant effect because that fits your premise.

And again this same evidence shows that there really isn't a significant difference between a 380 and a 9mm but you keep holding that there is because 12" is a magic #

Then you try to support your contention about terminal effect with a fundamentally flawed characterization of the physics of moving objects and when the error is pointed out

If my contention is wrong
"Then stop jacking around and prove it's energy and explain how a 240gr 44 Special going 750 fps and has only 300 ft.lbs. of energy will leave a larger permanent crush cavity greater volume than a 124gr 9mm going 1200 fps that produces 400 ft.lbs. in any controlled medium?"

In the one case, the evidence doesn't agree with your premise so you reject the evidence. In the second case there isn't any evidence to support your premise but you cling to it anyway. In the third case, when it turns out your understanding of basic physics is incorrect you still don't re-evaluate your position which you claimed was based on physics.

In other words, although you hold your position regardless of the evidence or lack thereof, and although your position is based on a flawed understanding of the science involved, you refuse to drop the pretense that your arguments are based on evidence and science.

 

[OldMarksman]

Posted by mavracer:

And again this same evidence shows that there really isn't a significant difference between a 380 and a 9mm...

Several 9mm premium loads meet FBI standards. Do you know of any .380 loads that have been shown to meet them?

"Then stop jacking around and prove it's energy and explain how a 240gr 44 Special going 750 fps and has only 300 ft.lbs. of energy will leave a larger permanent crush cavity greater volume than a 124gr 9mm going 1200 fps that produces 400 ft.lbs. in any controlled medium?"

There are two parts to that.

First, proof that "it's energy" is inherent in the basic concepts of physics.

Relevant points are covered in the descriptions set forth in Posts #224 and #241.

Do you agree that the action of a bullet penetrating flesh and bone are in large part rather analogous to that of a pile being driven into the ground by a pile driver, if you ignore the increase in the drag imparted by the friction as the pile goes deeper into the ground? Do you contend that the pile driver works on the principle of the conservation of momentum? Do you believe that any educated person would say so?

Regarding the .44 vs the 9mm example: if your contention is true, and if and only if the test media were identical, the answer to your question is obviously contained in Post #217:

The behavior of the bullet as it enters the body will depend not only upon its initial kinetic (mass and the square of the velocity), but also upon sectional density, the shape of the ogive, and effect of the construction of the bullet on the way the projectile expands and deforms as it enters and travels through the target.

You obviously did not read or comprehend that.

What, pray, would ever lead you to believe that wound channels result from the conservation of momentum?

Can you show that with equations, using example values? Unlike energy equations that pertain to inelastic collisions, momentum equations are extremely simple, as they involve only four variables.

 

[mavracer]

Do you contend that the pile driver works on the principle of the conservation of momentum?

ROTFLMAO
The fact that you think it doesn't and have an engineering degree is priceless.

I'd suggest you look up inelastic collisions "Inelastic collisions may not conserve kinetic energy, but they do obey conservation of momentum"
again and understand that while I agree that friction and sound pressure waves are a small part of wounding. The FBI in HWFE totally discounts the effects of temporary wound channel that would come from transfer from kinetic energy.

Here's pretty compelling evidence that at the upper end of service calibers (357 magnum,10mm) that the effects shouldn't be totally discounted if/when combined with adequate penetration.
9mm won't do that

 

[JohnKSa]

I'm not attacking the 12" minimum, I'm attacking the 12" sufficient and the idea the more isn't an advantage.

No, specifically you have been trying to discount the 12" minimum specification in an attempt to prove that there's no practical/significant difference between the .380 and the 9mm.

And again this same evidence shows that there really isn't a significant difference between a 380 and a 9mm but you keep holding that there is because 12" is a magic #

As demonstrated by the very next statement you posted...

If my contention is wrong.

The contention that momentum is the same as work is most definitely wrong. Which means that your understanding of the basic physics of moving objects is flawed.

"Then stop jacking around and prove it's energy and explain how a 240gr 44 Special going 750 fps and has only 300 ft.lbs. of energy will leave a larger permanent crush cavity greater volume than a 124gr 9mm going 1200 fps that produces 400 ft.lbs. in any controlled medium?"

It has already been explained, but because your understanding of the basic concepts is flawed, you either didn't understand the explanation or rejected it.

"Rather, it is caused by the diameter of the expanded bullet, by the speed which the bullet expands, by the configuration of the expanded bullet, by the extent to which the bullet holds together as it penetrates, and by how far it penetrates."​

In other words, there's more than just energy (or momentum) involved in wound volume size. There are a number of factors involved, including energy. Your question, which varies virtually every possible factor at once is creative but not productive.

The fact that you think it doesn't and have an engineering degree is priceless.

I have to say that your confidence is impressive. It's worth pointing out that confidence is not the same thing as competence and that a lack of competence on a topic often results in false confidence.

http://www.vulcanhammer.info/drivability/efficnt.php

"Every since the simple ENR formula with its emphasis on the rated striking energy of a pile driving system, the common concept amongst pile drivers and others involved with driven piles has been simply that "Energy drives piles.""​

http://www.assakkaf.com/courses/ence420/lectures/chapter19.pdf

http://www.fhwa.dot.gov/publications/research/infrastructure/geotechnical/05159/chapter3.cfm

"During impact, the kinetic energy of the falling ram is transferred to the pile, causing the pile to penetrate the ground."​

"Inelastic collisions may not conserve kinetic energy, but they do obey conservation of momentum"

You are correct about conservation of momentum and energy, but your comment isn't particularly relevant to the topic. You think it is relevant only because you don't understand the topic.

 

[OldMarksman]

Posted by mavracer:

I'd suggest you look up inelastic collisions.

I have been quite knowledgeable of the subject since the early 1960s.

"Inelastic collisions may not conserve kinetic energy, but they do obey conservation of momentum"

Very true indeed.

That does not mean that the effects of cutting, drilling, bending, crushing, abrading, forming, scraping, lifting, compressing, or similar actions can be described with equations that describe the conservatiion of momentum. It simply means that, since kinetic energy is converted into other forms of energy, kinetic energy is not conserved. Total energy is conserved, but that and the fact that kinetic energy is not conserved take us beyond a simple discussion of mass and velocity, and therefore well beyond a discussion of momentum.

The FBI in HWFE totally discounts the effects of temporary wound channel that would come from transfer from kinetic energy.

Temporary wound channel yes, but not permanent wounding.

If you really do believe that the action of a pile driver can be described by equations that take into account only the mass and velocities of objects before a collision and the resultant velocity of those objects after a colliion, velocity being a vector, I have to conclude that your level of understanding of physics is insufficient to enable you to carry on an intelligent conversation on the subject.

Of course, I may be wrong, and you may simply be trying to be deliberately obtuse. That would not be helpful.

 

[mavracer]

No, specifically you have been trying to discount the 12" minimum specification in an attempt to prove that there's no practical/significant difference between the .380 and the 9mm.

It's your data/information/reports that you are using that say there isn't a significant difference between service calibers that shows there isn't a significant difference between the 9mm and 380.
I just want to know why you believe one and not the other?

The contention that momentum is the same as work is most definitely wrong.

As I said earlier I'm very sorry I used work in the same context that OldMarksman did, my mistake

"Every since the simple ENR formula with its emphasis on the rated striking energy of a pile driving system, the common concept amongst pile drivers and others involved with driven piles has been simply that "Energy drives piles.""

Do you actually read the stuff you reference the the ENR formula is outdated and wrong. emphasis mine.

•The EN Formula, as with Sanders, assumed that the penetration of the pile was linearly proportional to the rated striking energy of the hammer, be it drop or steam operated. This was important to Wellington, and he touted it as a major advantage over Trautwine's cube root of the stroke (and thus the energy.) Unfortunately Wellington's insistence of this overlooks the fact that, for the same energy, the impulse of the impact decreases with a longer stroke and a lighter ram, which changes the character of the blow. (This issue appears again and again in pile driving, as can be seen here.) It's intersting to note that the Gates Formula, the formula currently favoured by the FHWA, uses the square root of the energy.

It would seem that even with pile drivers the light and fast crowd overestimate the meaningfulness of energy figures.

Rather, it is caused by the diameter of the expanded bullet, by the speed which the bullet expands, by the configuration of the expanded bullet, by the extent to which the bullet holds together as it penetrates, and by how far it penetrates

While how much the bullet expands and the rate will affect the diameter of the wound as it opens faster/more penetration will be less it only has so much momentum

That does not mean that the effects of cutting, drilling, bending, crushing, abrading, forming, scraping, lifting, compressing, or similar actions can be described with equations that describe the conservatiion of momentum.

It does mean that the energy changing form does not and can not cheat the laws of inertia.
And it means you really can't do this

That means that if we can choose a load that generates less momentum without sacrificing penetration and wound channel volume, we will be better off.

 

[A pause for the COZ]

Keep it going guys!!! I am on my 3rd bag of popcorn.
You guys left me behind long ago, but I am still picking up a thing or three.

 

[JohnKSa]

I just want to know why you believe one and not the other?

I've answered that and explained my answer in posts 207 and 237 and possibly others on this thread.

As I said earlier I'm very sorry I used work in the same context that OldMarksman did, my mistake.

"Work" in the context of physics always has the same definition. The idea that a person with a proper understanding of elementary physics would use a different definition of work in that context is laughable.

Do you actually read the stuff you reference the the ENR formula is outdated and wrong.

I'll give you points for motivation and again for confidence but none at all for understanding what you read and quoted in your last post.

You are absolutely correct that the ENR formula is somewhat simplistic and no longer as commonly used as it once was. Your conclusion that this fact somehow supports your position is without basis in reality.

 

[OldMarksman]

Posted by mavracer:

[...that the effects of cutting, drilling, bending, crushing, abrading, forming, scraping, lifting, compressing, or similar actions can(not) be described with equations that describe the conservation of momentum...] means hat the energy changing form does not and can not cheat the laws of inertia.

It really does not mean that at all, but it is true nonetheless that the laws of inertial apply. It is obvious. And it contributes nothing to the discussion.

And it means you really can't... choose a load that generates less momentum without sacrificing penetration and wound channel volume, [and thus] we will be better off.

Yes, you most certainly can. That''s because (1) penetration and creation of the a wound channel (or any other kind of removal or deformation of any material) essentially do involve cutting, drilling, crushing, abrading, scraping, and compressing, which involve the application of force over distance, which involve work, which is defined as the change in energy; (2) increasing velocity adds more in the way of energy than it adds momentum; and (3) since recoil, which makes rapid controlled shooting more difficult, is purely a function of momentum, we are better off with less of it.

Capisce?

 

[mavracer]

penetration and creation of the a wound channel ............force over distance, which involve work, which is defined as the change in energy.........increasing velocity adds more in the way of energy than it adds momentum

You keep stating that but in real world tests, it just doesn't fly.
Wonder why??

Should have stayed bowed out

 

[OldMarksman]

Posted by mavracer:

You keep stating that but in real world tests, it just doesn't fly.

Sure it does. Every time. Lets go over it one more time.

First, let's take "penetration and creation of a wound channel ............force over distance, which involve work, which is defined as the change in energy".

The creation of a permanent wound channel, and any other kind of removal or permanent deformation of any material, involves a material failure, whether brittle or ductile or a combination thereof. That involves exceeding the maximum strength properties--tensile, shear, or compressive, or some combination thereof.

Anyone who has ever worked in a materials lab, machine shop, hammer room, saw room, sheet metal stamping shop, whatever--is well aware that any such process, which starts with the application of kinetic energy, creates heat--thermal energy, which is converted from kinetic energy. It's very basic, and it is undeniable.

When it comes to the action of a non-exclusive high velocity projectile, the process occurs very rapidly indeed. If you ever get the opportunity, observe a test of armor plate against a kinetic energy projectile, and go up and touch the target immediately after a shot.

ENERGY! Material failure is not described by the simple measurement of mass and velocity after a collision.

Now let's go to "increasing velocity adds more in the way of energy than it adds momentum". For that we can stay in our eleventh grade physics classroom. Kinetic energy is proportional to the sure of the velocity, and momentum, to the velocity itself. QED.

I'm afraid that you continue to demonstrate either an abundant level of misunderstanding of the physical world, or an obtuse tendency to argue for the sake of argument, or both. You are not impressing knowledgeable people in a positive way.

But once again, whether energy constitutes the bigger component than momentum doesn't matter to a shooter.

What is important, if one intends to rely upon a physiological stop, is what the bullets damage inside the body.

That depends upon three things:

1. Penetration and the volume of the permanent wound channel;
2. "shot placement"; and
   the number of hits.
3. the number of hits.

For the first, the defender need not understand one whit about how the wound may be created. No discussion of kinetic energy or any other physical property makes any practical difference at all, whatever the underlying facts are.

Anyone with the most rudimentary understanding will understand the the second and third depend in large part upon the rapidity of controlled fire, and that less recoil better.

I suggest that a D in high school physics would be adequate to equip one to relate recoil with momentum

 

[mavracer]

Did you even get a D in physics lol here is a quote from my old physics 101 book about the first law of motion.
"This law holds no matter how complicated the force is between particles."

The creation of a permanent wound channel, and any other kind of removal or permanent deformation of any material, involves a material failure, whether brittle or ductile or a combination thereof. That involves exceeding the maximum strength properties--tensile, shear, or compressive, or some combination thereof.

And they can not break the laws of inertia, conservation of momentum. it can not move more material out of it's path than the momentum it contains.
now the fact that more energy means that more work can be done is fine more friction more heat and more pressure waves neither of which add any wounding value according to HWFE.

If you ever get the opportunity, observe a test of armor plate against a kinetic energy projectile, and go up and touch the target immediately after a shot.

Yep it's kinetic energy being converted to heat energy, but you aren't going to melt tissue with 400 ft.lb. of energy you can't even raise the temperature of 8oz of water 5 degrees.
And it still doesn't break the laws of inertia. all the momentum is transferred to the plate no more no less.


I'm wondering if Wellington that came up with the flawed equation for pile drivers was a ancestor of Roy Weatherby? LOL

 

[OldMarksman]

Posted by mavracer:

And they can not break the laws of inertia, conservation of momentum.

True, and completely irrelevant.

...now the fact that more energy means that more work can be done is fine more friction more heat and more pressure waves neither of which add any wounding value according to HWFE.

You have completely misunderstood that part of the report. What it said was, absent tissue destruction, energy per se does not wound, nor does"shock". That does not say a thing about how tissue is destroyed.

....you aren't going to melt tissue with 400 ft.lb. of energy.

Melt? Melt? Where on Earth did that come from?

What I said was that when materials fail because shear, tensile, and/or compession strength limits are exceeded, kinetic energy is converted to thermal energy.

What that means is that one cannot analyze the failure process by simply measuring velocities before and afterward--ie, by means of measuring momentum.

And it still doesn't break the laws of inertia.

There you go again--true but irrelevant.

all the momentum is transferred to the plate no more no less.

Only if it sticks in the plate. Capisce?

But one more time, what does it matter to you what causes the creation of a wound channel?

 

[mavracer]

True, and completely irrelevant.

You guys are amazing.
Universal laws of motion are irrelevant when it doesn't support your conclusion, The FBI's evaluation that more penetration is irrelevant when it doesn't support your conclusion and reports and evaluations of shootings are irrelevant when they don't support your conclusions.

Shees

Unfortunately for you anyone who reads HWFE will see a compelling argument that more is better, that the small increment between 380 and 9mm really isn't significantly different than what exists between 9mm and 40 S&W and that in thousands of gel tests penetration figures grow linearly as momentum goes up not exponentially as energy increases.

It's intersting to note that the Gates Formula, the formula currently favoured by the FHWA, uses the square root of the energy.

The hydrostatic shock theory has been around almost 70 years so, maybe in another 10 they'll realize that energy is a real poor predictor of external ballistic performance of handguns and stop publishing the figures.

Some of us already have.

 

[JohnKSa]

…anyone who reads HWFE will see a compelling argument that more is better, that the small increment between 380 and 9mm really isn't significantly different than what exists between 9mm and 40 S&W...

Actually they would see that there is no attempt to quantify the difference between the .380 and the 9mm or between the 9mm and the .40S&W. In fact, the .380 isn't mentioned at all in the paper and the .40S&W hadn't yet been invented at the time the paper was released.

They will also see that Urey makes the claim that a bullet MUST penetrate at least 12” (Urey’s emphasis). That would rule out the .380 when used with expanding ammo regardless of how much difference there is (or isn’t) between it and the 9mm by any other measures.

They will see that Urey believes “more is better” but is unable to quantify how much more is how much better and states that even the significance can’t be quantifed.

To the extent that he even tries to quantify the practical difference, he makes statements about how caliber might provide a “1% edge”, that it might make a difference in “10 out of a thousand” shootings (1%). This is a hint that he thinks it isn't a big edge and it would only rarely make a difference at all.

He also indicates that it would take examining a very large number of shootings (stating the results of 100 shootings wouldn’t be statistically significant) to even demonstrate that such an edge exists. To anyone with a basic understanding of statistics this would be synonymous with saying that the effect/edge is very small--in case they hadn't already picked up on his other hints.

Universal laws of motion are irrelevant when it doesn't support your conclusion…

Well, first of all, the universal laws of motion DO support the conclusion. But that doesn't mean they're relevant to any comment that could possibly be made. For example, parroting some basic physics rules, without understanding how they apply to this topic is going to guarantee that one's comments are sometimes irrelevant even if the rules themselves are quoted correctly.

It's intersting to note that the Gates Formula, the formula currently favoured by the FHWA, uses the square root of the energy.

This is an excellent example. The formulas you’re referring to as if they support your premise have nothing at all to do with the topic at hand. You seized on the incidental mention of the ENR formula in a cite from one of my posts and assumed that the formula itself was relevant. Unfortunately, since you don’t have any idea what the ENR formula (or the Gates formula) calculates or how it is used or what it means, your comments about it are both irrelevant and meaningless in the context of this discussion.