Physics of a bullet in flight

[neviander]

I found this thread and thought I'd share.

http://www.physicsforums.com/showthread.php?t=10591

My initial question was how a bullet with similar ballistics, but significantly different weights (a 140 grain .270 Winchester bullet traveling at 2,916 ft/s with 2,644 ft·lbf and a 300 grain .50 Beowulf bullet traveling at 1,870 ft/s with 2,330 ft·lbf) really truly differed.

The article is way over my head, but I figured some of you more educated gun nuts might enjoy

 

[56hawk]

Well, if two bullets have the same energy they have the same ability to do work, or I suppose damage in this case. The effect on the target is going to depend a lot more on the bullet design and construction though.

Did you have a more specific question?

 

[brickeyee]

Terminal ballistics in living things is not as simple as energy and momentum calculations.

 

[rcmodel]

In simple terms, the bullet with the better Ballistic Coefficient (Mass, Dia, and Drag) will fly further, faster, with a lot less drop, and more remaining energy.

With a 100 yard zero:
The 270 with a bullet having a SD of .339 drops approximately 5' feet at 500 yards and has 910 ft/lb remaining energy.

The .50 with a SD of maybe .200 and starting out a lot slower would drop about 22' feet, and would have about half as much remaining energy as the .270.

rc

 

[neviander]

A different way to phrase the question would be, if the .270 has the same amount of energy as the .50 (at whatever distance) how much faster does the .270 slow down, once it hits something? Or, how much more stuff does it take to stop the .50? The .50 Beowulf was designed for penetration, with that heavy of a bullet, it makes sense, but when you look at the numbers it seems strange.

 

[Voltia]

Why do people have to create terms like ballistic coefficient? It's one step away from "knock down power factor." Derived terms are derived, might as well use the engineering formulas, since that is what they are there to do.

Try saying "coefficient of drag," it makes you sound like an actual engineer.

 

[Skribs]

The term ballistic coefficient has been around for a long time, I remember reading a memoir written by snipers in Vietnam that used that term. I don't think the OP made it up.

 

[rcmodel]

Why do people have to create terms like ballistic coefficient?

Who wants to sound like an actual engineer?
All of them I knew at work were kinda "different" if you know what I mean!

Ballistic Coefficient is an old term that has been in use almost since artillery and small arms were invented. Ever hear of the Ingall's Tables??

Anyway, Drag is but one factor used in arriving at the BC of a projectile in flight.
While not a mathematician, I think the CF is a constant, while the BC changes with velocity of the projectile for one thing.

At any rate, Ballistic Coefficient of the projectile is still used in calculating artillery & small arms fire today.

But Coefficient of Friction isn't

rc

 

[MachIVshooter]

My initial question was how a bullet with similar ballistics, but significantly different weights (a 140 grain .270 Winchester bullet traveling at 2,916 ft/s with 2,644 ft·lbf and a 300 grain .50 Beowulf bullet traveling at 1,870 ft/s with 2,330 ft·lbf) really truly differed.

As has been pointed out, the more aerodynamic spitzer of the .270 starts out at a higher velocity and retains it better over distance than a large, blunt pill like that of the .50 Beowulf

Another difference in the terminal performance between these two is directly a result of the velocity; The .270 (or any other high velocity rifle round) produces wounds far larger than the bullet diameter, while slower rounds (under ~2,000 FPS) do not create that kind of permanent crush cavity, and significant trauma is only evident in the tissue directly contacted by the bullet.

Penetration? All else being equal, lighter, faster bullets penetrate hard barriers better, but in live tissue, the heavier and slower bullet carries with it greater momentum, thus tend to penetrate flesh better. This is why dangerous game rifles are usually chabered in large bore cartridges. Close-in, a big, blunt .458" bullet will do much better against the thick-skinned, densly-built and very large species. But for a 400 yard shot on an 800 pound bull elk, the poor trajectory and rapid deceleration of these big bullets makes them a rather poor choice as compared to the common big game rounds like .270 Win, .30-06, 7mm mag, etc. That's not to say a .458 win mag won't kill an elk cleanly at 400+ yards, but it would be rather silly to tolerate the recoil and have an 8 foot hold-over.

Let's compare

7mm Rem Mag, 160 Gr. Accubond, 200 yard zero:

Velocity/ Energy:
Muzzle: 3,000 FPS/3,213 FPE
500 yards: 2,317 FPS/1,908 FPE

Max height above line of sight: 1.4"
Drop at 500 yards: 34.5"

Free recoil energy (7.5 lb rifle): 27 ft/lbs

.458 Win Mag, 500 gr. Banded solid RN, 200 yard zero:

Velocity/ Energy:
Muzzle: 2,100 FPS/4,945 FPE
500 yards: 1,233 FPS/1,686 FPE

Max height above line of sight: 4.1"
Drop at 500 yards: 96.4"

Free recoil energy (7.5 lb rifle): 72 ft/lbs

 

[browningguy]

Why do people have to create terms like ballistic coefficient?

So in your brand of engineering you don't use any derived terms/formulas? Having had an electrical engineering degree for 30 years, and currently managing a lrge group of PhD Mechanical and Structural engineers I can say that we use derived formulas all the time, particularly when trying to understand votex indced vibrations and the associated fatigue in tubular structures.

But in any case, BC is more accurate than Cd for this particular application. Cd alone does not account for the flight of a bullet, while the various BC's that can be calculated and measured do. As already pointed out in the case of calulating BC the Cd is only part of the equation.

 

[brickeyee]

Ballistic coefficient was invented so that a different projectiles could be compared to a 'standard projectile' that had very detailed measurements available.

It is time consuming and expensive (less so now with radar for tracking projectiles) to measure the performance of every bullet to determine drag effects.

The use of a BC allows other similar bullets to use the measured data.

 

[Loosedhorse]

really truly differed.

To my mind, the two bullets you mention vary chiefly in their mechanism of wounding (termnal balistics). Heavy projectiles have more momentum than lighter projectiles of the same energy. Therefore the heavy projectile may have more straight-line-penetration (permanent cavity) wounding, and the lighter one more tissue-overstretch (temporary cavity) and fragmentation wounding. The type of wounding will also depend on bullet design and materials.

Also, faster bullets get to the target faster, and so have less time to be deflected by wind and gravity. Many shooters therefore prefer faster bullets for longer range shots.

I am sure there are other perpsectives. Thanks for the physics link.

 

[neviander]

You guys are awesome. Thank you for the intelligent feedback. This changes my opinion of the .50 beowulf. I really thought it held something over and above the established rifle rounds, but I guess not. I guess I'm still saving up for either an M1A, or an LR-308.

 

[jbm]

Why do people have to create terms like ballistic coefficient? It's one step away from "knock down power factor." Derived terms are derived, might as well use the engineering formulas, since that is what they are there to do.

Try saying "coefficient of drag," it makes you sound like an actual engineer.

Because it's not the same thing as the drag coefficient. You can read this article to show the relationship between Cd, Kd (older nomenclature for the drag coefficient), G and the BC:

CD and KD

The bottom line is that the a drag curve was developed for a standard bullet and this curve defined a "G" function (also not the same as the Drag Coefficient). The BC was then used to modify the drag function for bullets of the same general shape as the standard bullet but of different size, weight, etc.

For what it's worth, I agree with you, but until bullet manufacturers can afford radar testing for all their bullets and start providing CD versus mach number (like Lapua does for some bullets), we're stuck with the BC and drag function convention.

Brad

 

[MachIVshooter]

This changes my opinion of the .50 beowulf. I really thought it held something over and above the established rifle rounds, but I guess not.

Well, if you wanted a semi-auto with a big bore thumper of a cartridge for bear protection or something, the .50 Beowulf and .450 Bushmaster do have a use. For big game hunting in general? Not so much. They're equal to moderate .45-70 loads. Like I said before, they'd certainly take an animal at range, but with their rainbow trajectory, you'd have to know your ballistics tables backwards and forwards, and range the animal effectively. With a 7mm mag or similar, being off by 30 yards at 400 isn't a big deal. But with the .50 Beowulf or the .450 Bushmaster, being off by the same 30 yards at 400 could be a wounding shot or a clean miss:

7mm Rem Mag, 160 gr. Nosler Accubond, 3,000 FPS MV, 200 yard zero

Bullet drop from 400 yards to 425 yards: 3.7"

.450 Bushmaster, 250 gr. Hornady FTX, 2,200 FPS MV, 200 yard zero

Bullet drop from 400 yards to 425 yards: 12.2"

.50 Beowulf, 325 gr. Speer JHP, 2,010 FPS MV, 200 yard zero

Bullet drop from 400 yards to 425 yards: 17.6"