Predictive tests in water

[Ghost Dog]

Although they don't directly answer your questions, you might find these links interesting and somewhat relevant...

https://brassfetcher.com/Wounding%20...Expansion.html

https://www.ballisticstudies.com/Kno...57+Magnum.html

"As a general guide to performance, the .357 can produce quite spectacular kills at impact velocities of 2000fps and faster using hollow point projectiles.

At impact velocities of 2000 to 1600fps, game hit with a fast expanding hollow point tend to react in a drunken manner, often attempting to run but not generally making too much ground before succumbing quickly to blood loss.

Between 1600 and 1300fps, dead runs may be longer but wounding is still somewhat disproportionate to caliber. Again, bullet weights must be matched to the job at hand. If the bullet is too heavy, it may not meet enough resistance to render a wide wound at low velocities. If the bullet is too light, it may not have enough energy to render a deep and broad wound on larger bodied animals.

At impact velocities of 1200fps and below, bullet expansion may be fully evident, yet wounding can be narrow (proportionate to the expanded caliber of the bullet) and blood trails poor. At these velocities and in the absence of any major hydraulic force, the .357 is reliant on mechanical wounding, the size of the wound being directly proportionate to the diameter of the expanded bullet."

Thank you very very much for this!

[DocGKR]

I have never been impressed with ΔE15/EKE or P[I], as they are pretty inaccurate as a measure of wounding effects in living tissue.

[the Schwartz]

I wish I knew how to figure E15/EKE from published data, is it a fairly easy formula to apply if you know bullet weight and velocity, as well as penetration and expansion?

Yes, it is fairly easy, so long as one has the ability to rearrange algebraically any of the five existing bullet penetration equations to solve for instantaneous projectile velocity; the only parameters that one needs to have available is the projectile's expanded diameter, mass, and impact velocity.

Rearranged correctly, any of the five bullet penetration equations can also be manipulated to solve for deceleration history (ΔV/ΔT), ballistic limit (V₅₀), residual velocity (V_R), instantaneous kinetic energy with respect to projectile position (F = ΔE/Δx) which is also known as the ''Work-Energy theorem'', and other relevant terminal ballistic performance metrics such as time with respect to projectile position (ΔT/Δx).

Each of the five existing bullet penetration equations will require a unique solution for these functions since they differ (mathematically) from one another.

[Ghost Dog]

I have never been impressed with ΔE15/EKE or P[I], as they are pretty inaccurate as a measure of wounding effects in living tissue.

Thank you for re-joining this thread. I appreciate your time.

I'm aware that #1 is adequate penetration for the expected situations or job description
#2 Expansion
I thought this gave you the amount of Tissue physically Crushed based on Dr Martin Fackler, but maybe I am wrong in figuring out Wound Volume ...is that only by high speed camera so it's not just r2 x penetration distance?

Given that having far greater priority to anything that doesn't penetrate deeply enough, wouldn't higher EKE be desired as long as adequate penetration? Obviously, Sub 11" penetration & Incapacitation Index shallow BS isn't good.

It seems to me that anything of at least 115 gr, or 125 gr at over 1300 fps , and better at 1450 fps seemed to work exceptional well from all reports I have ever heard ie 9bple, 125 gr Magnum/Sig why do you think this so? Isn't the initial wound the first few inches a bit wider in those velocity bullets Given Pen and Exp, doesn't it seem something closer to 475+ ft lbs seem to do more than 350 ft lbs or is it all just physical crush in your opinion? And the reports from the hunter that claims to have killed 8k+ animals on .357 in the 1300-1600 fps range seems to say there is a bit extra there, and certainly in the 1600-2100 fps from lever guns....Dick Fairburn says he trained with Dr. Fackler some and he is big on a .357 levergun for home/ranch defense with 125 gr xtp. He is also a big fan of .40/.45 over 9mm. Perhaps isn't the higher physiological sensation bad guys recognizing that they have been shot more likely to have a psychological reaction? I read your comments about .357 sig Loud bang and Flash perhaps having some psychological effect.

I believe you were originally a fan of .45...and I believe you liked HST, you've acknowledge .40 is really good if you are dealing in and around vehicles a lot (I assume Gold Dot would be the desired one for that, though I have lurked LE here saying everyone was very happy with 180 HST performance), and I believe you are now set on 147 HST is that so and if so from all barrel lengths? What are you carry choices and in which calibers? Always prefer the heavier for caliber? I don't know if you are still working LE part time or deputy etc or just carrying in a civilian context?

How often did Duty Caliber size JHPs under penetration and stop short of reaching vital organs in real world data you got? What about 115 gr was this or major bone deflection more of an issue with lighter for caliber 115 vs 124+p or 147 which penetrated straight line better? What about .32/380 FMJ vs JHP real world can you touch on that a bit more, how often did under penetration or major bone deflection changing path happen in this mouse caliber vs .38 & larger...I have read everything on here and other forums you have put out like .38 over .380... Thoughts on so many on here liking .32 H&R Magnum?

Final question for now, did you or anyone ever get to Read whatever study the Secret Service supposedly did? The 115+p+ Ranger they selected was a pretty shallow penetrator, & then they went to better .357 Sig.

Thank you very much,

[Ghost Dog]

Yes, it is fairly easy, so long as one has the ability to rearrange algebraically any of the five existing bullet penetration equations to solve for instantaneous projectile velocity; the only parameters that one needs to have available is the projectile's expanded diameter, mass, and impact velocity.

Rearranged correctly, any of the five bullet penetration equations can also be manipulated to solve for deceleration history (ΔV/ΔT), ballistic limit (V₅₀), residual velocity (V_R), instantaneous kinetic energy with respect to projectile position (F = ΔE/Δx) which is also known as the ''Work-Energy theorem'', and other relevant terminal ballistic performance metrics such as time with respect to projectile position (ΔT/Δx).

Each of the five existing bullet penetration equations will require a unique solution for these functions since they differ (mathematically) from one another.

Thank you

Where is the easiest or free place to learn these formulas? Or are they in your book? Being able to figure out EKE from like Vista or Hornady's published data is of interest to me

[Glock17JHP]

Suggest reading DocGKR's "sticky"" titled: "Basic Wound Ballistic Terminal Performance Facts"...

[the Schwartz]

Thank you

Where is the easiest or free place to learn these formulas? Or are they in your book? Being able to figure out EKE from like Vista or Hornady's published data is of interest to me

All five bullet penetration equations are available—some at no cost—while others will require a purchase.

1.) A Mathematical Model for Assessing Weapons Effects From Gelatin Penetration by Spheres (AD-770352); Sturdivan, LM; Edgewood Arsenal, SAREA-BL-BS, Aberdeen Proving Ground, MD, 21010, September, (1973)

Available here as a PDF: https://apps.dtic.mil/sti/tr/pdf/AD0770352.pdf

This particular bullet penetration model is a Resal's form equation. Algebraic manipulation may prove challenging to those unaccustomed to the form.

2.) A Mathematical-Physical Model of Wound Ballistics; Peters, CE; J Trauma (China), 6(2), Supplement: 303 - 318; (1990) University of Tennessee Space Institute, Tullahoma, TN, 37388

Peters' model is a Poncelet form equation. It also can be used to represent the temporary cavity using ''disc-energy trading'' by the integration of volumes using the method of disks in calculus. This mathematical method represents the temporary cavity as a series of disks with each separate disc diameter closely approximating the temporary cavity at a given penetration depth.

I cannot locate a link online for the PDF. I do have a copy of the technical paper if you'd like.

3.) Bullet Penetration: Modeling the Dynamics and the Incapacitation Resulting from Wound Trauma, MacPherson, D; 1995 and 2005

MacPherson's WTI model is also a Poncelet form.

Available here: https://www.amazon.com/Bullet-Penetr.../dp/0964357712

4. & 5.) Quantitative Ammunition Selection; Schwartz, C; (2012, 2014)

The Q-model is a Poncelet form. The mTHOR equation is a modified power law derived of a 1950's armor penetration equation.

Available at Barnes & Noble, Books-A-Million, Amazon, etc.

Once you decide upon an approach, you can use any of these models to investigate anything from deceleration (ΔV/ΔT), ballistic limit (V₅₀), residual velocity (V_R), instantaneous kinetic energy with respect to projectile position (F = ΔE/Δx) and even ΔE₁₅ (EKE). Any exploration of the mathematical incapacitation models discussed here—

https://pistol-forum.com/showthread....=1#post1566571

—will require the use of the correct respective 'a', 'b', and 'n', coefficients. The coefficients for the first two mathematical incapacitation models (Dziemian, 1961; Sperrazza & Kokinakis, 1965) are widely available. The coefficients for the Sturdivan mathematical incapacitation model remain classified so I cannot release them.

=====

Finally, using the approach described by Alekseevskii (1966) and Tate (1967) which assumes a steady-state flow stress field in a gelatin target ahead of the projectile and setting 'm' as the slope of the intact yield strength/pressure curve (where m = ¾) of the target material, solution of the transcendental equation for 'a' is—

[1 + (ρ_TU² ÷ Y_T) · √(K_T - ρ_Ta²U²)] = Y_T · [1 + (ρ_Ta²U² ÷ 2G_T) · √(K_T - ρ_TU²)]

a = √[(2√3G_T) ÷ (2σ_yT + ½mρ_TU²)]

—where 'a' must then be utilized in the computation of R_T —

R_T = (7 ÷ 3) · LN(a) · σ_yT

σ_yT = yield strength of the gelatin target material (350 kPa)

U = √(ρ_T ÷ ρ_P)

At any point along a bullet's path of travel, once the instantaneous velocity of the bullet is computed using any of the five bullet penetration equations above, the diameter of the penetration cavity, Ø_CAVITY, produced by the passage of the projectile through the target is—

Ø_CAVITY = Ø_PROJECTILE · √[(½ρ_PV² ÷ R_T) · ((V - U) ÷ U)]

[the Schwartz]

An interesting application of AT (Alekseevskii-Tate) hydrodynamic model is that the diameter of a projectile's temporary cavity in 10% ordnance gelatin can be predicted using the approach described below by Alekseevskii (1966) and Tate (1967) which assumes a steady-state flow stress field in a gelatin target ahead of the projectile and setting 'm' as the slope of the intact yield strength/pressure curve (where m = ¾) of the target material, solution of the transcendental equation for 'a' is—

[1 + (ρ_TU² ÷ Y_T) · √(K_T - ρ_Ta²U²)] = Y_T · [1 + (ρ_Ta²U² ÷ 2G_T) · √(K_T - ρ_TU²)]

a = √[(2√3G_T) ÷ (2σ_yT + ½mρ_TU²)]

—where 'a' must then be utilized in the computation of R_T —

R_T = (7 ÷ 3) · LN(a) · σ_yT

σ_yT = yield strength of the gelatin target material (350 kPa)

U = √(ρ_T ÷ ρ_P)

At any point along a bullet's path of travel, once the instantaneous velocity of the bullet is computed using any of the five bullet penetration equations above, the diameter of the penetration cavity, Ø_CAVITY, produced by the passage of the projectile through the target is—

Ø_CAVITY = Ø_PROJECTILE · √[(½ρ_PV² ÷ R_T) · ((V - U) ÷ U)]

For example, several years ago we conducted tests where 45 ACP 230-grain FMJ bullets were fired into calibrated 10% ordnance gelatin under high frame rate videography.

In this still image taken from a video in which a 0.451'' 230-grain FMJ was fired at 648 fps into 10% ordnance gelatin—



—the diameter of the temporary cavity was determined to be 1.65 ± 0.05 inches.

Using the equation above, predicted diameter of the temporary cavity was 1.75 inches.