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Sectional density and foot pounds of energy

Discussion in 'Caliber Corner' started by ABNAK, Sep 12, 2012.

  1. ABNAK


    Apr 22, 2005
    Ballistics is as much an interesting hobby as it is a serious consideration for carry ammo. Been thinking of something lately and decided to crunch the numbers.

    Sectional density has a direct impact on penetration with bullets of the same type (i.e. Nosler, Sierra, HST, whatever). Going up or down in caliber with the same or close SD *should*, in theory, give similar penetration.

    Let's say one wanted to mimic the ballistics of the .357 Magnum or 357Sig with the 125gr JHP at 1400-1450fps but in another caliber. I only used .40 as an example here.

    The sectional density of .357 magnum 125gr SJHP's is 0.140, with the 125gr 357Sig at 0.142. Pretty close, so let's use 0.140 for a nice round number. This bullet moving at 1400fps will yield ~ 543ft/lbs of energy, 1450fps is ~ 583ft/lbs.

    The closest .40 bullet in sectional density is the 155gr at 0.138, the 150gr coming in at 0.134. You'd have to kick the 155gr out at 1250fps to get ~ 537ft/lbs of energy; the 150gr would need to hit 1300fps for the 150gr to achieve ~ 562ft/lbs.

    As you can see, the 357Sig can easily reach the velocites to get well over 500ft/lbs of energy (same for the .357 Magnum). However, good luck finding .40 caliber 150/155gr loads getting the necessary velocities to rival the energy of the 357 loads with close sectional densities.

    The focus of this mental exercise is energy (based on velocity/weight) and penetration (based on SD). Once again I assume the same type/brand of general.

    For those who may wonder, the 135gr .40 bullet has a lower SD (0.121) than the 115gr 9mm (0.13). So while you can achieve the velocities and corresponding energy out of the 135gr'ers you will come up well short of the penetration of the 125gr 357 loads because of a sub-optimal SD.
    Last edited: Sep 12, 2012
  2. Bigpoppie50


    Oct 2, 2010
    Great observations, although I find stuff like this(Phiysics & Ballistics) interesting and have been studying it for a while.

  3. fortyofforty


    Jul 9, 2005
    Thanks. I also find such discussions quite interesting, yet of little value in predicting real-world results.
  4. SCmasterblaster

    SCmasterblaster Millennium Member

    Sep 24, 1999
    Hartford, Vermont
    = 0.5 x bullet mass x velocity squared. Bullet mass is kind of complicated. One has to convert the bullet weight in grains to bullet pounds (divide by 225113). The mass = the bullet weight (in pounds) with the acceleration of gravity (32.159 ft/sec squared) divided out. So (knowing that there are 7000 grains in a pound) a 200-grain bullet is divided by (2x7000x32.159) to get a mass of 0.000888. Multiply this funny number by the square of, let's say, 800 FPS and you get just over 284 foot-pounds of energy. So my 9mm carry load is a 115gr bullet at 1400 FPS. The KE of this load is 115 divided by 450226 times 1400 squared (196000) = 500 foot-pounds (!)
  5. M 7

    M 7

    May 22, 2012
    Y'know, rather than chase after all of those figures which will not tell you how far a bullet will penetrate or how much tissue it'll damage along the way, there are bullet penetration models that'll give you a reasonable prediction of those things (the title mentioned in my sig-line- hint, hint :whistling:) without all that heavy-lifting. :cool:
  6. ABNAK


    Apr 22, 2005

    What got me thinking was how do I find (as an example) a .40 round with the "wallop" of the vaunted 125gr .357 Magnum round with approximately the same penetration in the same bullet brand. First instinct says "Oh, it must be the 135gr Nosler or Sierra load at 1300+fps." Not so much, which is why the light .40 load is a relatively "shallow" penetrator.

    If you go on up in caliber, such as .45ACP, you'll find significantly higher sectional densities such as in the 230gr loading but no where near the velocity and subsequent energy dump in target.

    I used the 357Sig/Magnum as the control and figured the .40 midweights were the closest sectional densities and went from there. Unfortunately, in order to get to the necessary velocity/energy equivalents you'd be looking for unicorn loads (or ones handloaded at home to over-the-top pressures).

    For instance, if you jump to .45ACP, the 200gr JHP has a SD of 0.140, the same as our 357 "control" round. But it takes a velocity of 1100fps to get a muzzle energy of ~ 537ft/lbs. Try getting that out of a .45 at consistently safe pressure levels and in a handgun suitable for CCW (think Glock 19/23/32 as the biggest).

    Bottom line? Sectional density favors smaller caliber rounds if you want 500+ft/lbs of energy. Otherwise, with larger calibers you have to load to potentially unsafe pressures to get there (if you even can without blowing up the gun).
  7. M 7

    M 7

    May 22, 2012
    Oh, OK. I thought that you were looking for a way to figure out if one particular arrangement penetrates more than another as opposed to generally theorizing about ballistics.

    One point- Sectional density favors no caliber large or small. It is simply the mass of the bullet in grains divided by 7000 (a conversion to pounds) which is the divided by the square of the bore diameter in inches-

    SecDen = (m/7000)(D^2)

    - sectional density being expressed in psi.
    Last edited: Sep 13, 2012
  8. fredj338


    Dec 22, 2004
    You observations are correct, as long as the bullets are of identical construction. With new mono metal designs & binded bullets, SD is getting trickier to measure. As the bullet expandsm, it's SD changes along it's path. SO you can start out w/ a high SD bullet that is "soft" & it will expand sooner & larger & changing it's SD or penetration potential. Basically though, yes, the higher the SD the better the penetration. Sometimes a lto of expansion is not a good thing.
  9. M 7

    M 7

    May 22, 2012
    How's that? :dunno:SD has nothing to do with the construction of the bullet, just its weight and cross-sectional bore area.

    SD is nothing more than a mass per unit area ratio. If you know 'em both (bullet weight and the cross-sectional area of the bore) you know SD, right?
  10. SDGlock23

    SDGlock23 Glockoholic

    There are 155gr .40's that will get the 1250+, mainly Underwoods for loaded ammo. Reloading will do it as well, but that doesn't count as much since most don't handload. Actually you can get 165gr .40's that fast too and then you have higher SD than the 124/125gr 9mm/.357.

    I know SD is an important aspect, but mainly so for penetration and in this case, probably hard barriers. Sure the 135gr .40/10mm has poor sectional density and wouldn't penetrate like the 125gr 9mm, but it's not exactly going to bounce off someone and it will do a good bit of damage to the intended target. Not to mention, weight is weight and the .40 has more and more bullet mass.
    Last edited: Sep 16, 2012
  11. bac1023


    Sep 26, 2004
    Great info and observations