Rifle Cartridge Efficiency Formula

[375rifleman]

I was just wondering if there's a formula for rifle cartridge efficiency taking the Ballistic Coefficient of the Bullet, the Sectional Density of the Bullet, the Bullet Weight, the Velocity of the Bullet, the Taylor Index of the Bullet, the Powder Charge of the Cartridge, and the Recoil of the Cartridge ? If there is a formula please let me know if not could someone please make one or explain why or why not one of the parameters could or couldn't be used. Thanks

 

[MagnumManiac]

I was just wondering if there's a formula for rifle cartridge efficiency taking the Ballistic Coefficient of the Bullet, the Sectional Density of the Bullet, the Bullet Weight, the Velocity of the Bullet, the Taylor Index of the Bullet, the Powder Charge of the Cartridge, and the Recoil of the Cartridge ? If there is a formula please let me know if not could someone please make one or explain why or why not one of the parameters could or couldn't be used. Thanks

The reason why not is far simpler than the reason you can take all of those parameters into consideration for one formula.
One, BC is an external ballistics parameter, two, SD is a terminal ballistics parameter which doesn't use the BC of a bullet, or in other words, it's construction and shape or it's velocity to come to a figure of any significance, 3, velocity alone means little, 4 weight alone also means little, 5, the powder charge means little, 6, the recoil is just a fact of life and 7, Taylors Knockout index is also flawed because it bases it's figures on weight and bullet diameter to knockout an elephant from any angle, there are many cartridges that will kill far better than what the Taylor index would suggest.

I really don't know what you are looking to discover, but there are already in place many DIFFERENT formula's out there that calculate myriad aspects of ballistics, of which there are 3 distinct different aspects of ballistics, 1, internal ballistics, from cartridge ignition to bullet exit, 2 external ballistics, bullet flight, and 3, terminal ballistics, from bullet impact in a medium to bullet stop and what that bullet does.

Hope this answers some questions for you, if not, good luck finding an answer, if you do find a formula, please let us know. I would be interested in reading it.

Cheers.
gun)

 

[Mikecr]

It's probably possible to define a combination that is neutral across the board.
That is, best at nothing AND worst at nothing.

In other words -factory rifle/factory chamber.

 

[davkrat]

It would be easier to first define what you want to do. Elk at 1000 or prairie dogs at 400? Then narrow it down to some cartridges you're interested in without pushing the limits. Get a load manual or look at Nosler or Hodgdon online data and figure out how fast your cartridges can reasonably be expected to launch a high weigh/BC for caliber bullet and see how it compares to your goal.

Either that or just go buy a 7mm Rem Mag for the stuff bigger than a coyote and a .243 for everything smaller and be happy the rest of your life.

 

[jrsolocam]

What is the least amount of energy required to make x amount of energy at x distance. That would be efficiency. A loaded cartridge has potential energy and a bullet in flight has kinetic energy. PE is determined by the charge weight, specific heat of the powder, and bullet mass. When fired the pe loses most of the energy through heat and recoil, with the balance sending the bullet off. That's when BC comes into play. Norma's new manual talks about it a little bit. Someone here smarter than me could derive a formula that would solve this...

 

[davkrat]

There isn't anything to solve. It's like trying to draw a smiley face on a spinning tire. You'll just keep going round and round in circles. Personally I looked at overbore (whatever that is) charts and decided to ditch my .270 and go to a 7mag. If my brother didn't already shoot one I would have stayed with the .270. With the new high BC .277 bullets I would have been very happy too.

There's a reason the .270, .30-06, 7mm Rem Mag and .300 Win Mag have been so popular for so long. They are efficient enough to launch bullets heavy enough to kill at substantial ranges any North American big game without destroying your shoulder or being hard to load for. In the end it all comes down to what your chosen bullet, load, rifle and most importantly YOU the shooter are capable of. Knowing and sticking to those limitations is up to you.

 

[mitch260]

SD is a terminal ballistics parameter which doesn't use the BC of a bullet, or in other words, it's construction and shape or it's velocity to come to a figure of any significance,

SD and BC are directly related and are important to external ballistics solutions. Ballistic Coefficient is a function of Sectional Density and Form Factor.

A cartridge's efficiency is a matter of Internal Ballistics.

 

[mitch260]

Quick Loads is an Internal Ballistics software and calculates Ballistic Efficiency based off its predictions. I do not know what their equation is.

 

[jrsolocam]

DAVKRAT, there is something to solve. Converting potential energy into kinetic energy. Its basic physics. Now the solution may mean anything, or not be relevant, but that is a different story...

 

[Truc]

Read somewhere that the 35 Whelen, 358 Winchester and probably the 350 Rem Mag were the most efficient cartridges.

 

[davkrat]

Yes but you have to solve for a specific end result. Some of the OP's perameters are extremely subjective. How much recoil is too much? How much energy is unethically not enough, just right or meat ruining too much? How much throat eroding barrel eating over-boredness is too much? Do you want to punch paper, kill one pound rodents or 600 lbs elk? I'm sure there is a model that can be made that would assign negative scores to perameters like recoil but I still say the end number won't mean squat until you know what it is you want the rifle to do.

Lets say you have three cutting instruments: a butter knife, a carving knife and an axe. Which of those three is best for the three tasks of splitting a muffin and spreading butter on it, carving up a turkey or chopping wood. If your some sort of masicist maybe chopping wood with a butter knife is fun. Chopping a muffin with an axe would be fun for the splat factor alone.

There are good categories of paper punchers. There are good categories of varmint rifles. There are good categories of deer rifles. There are good categories of elk rifles. There are good categories of dangerous game rifles. On and on and on. I am a complete math nerd in the sense I love pouring over data and comparing loads, comparing energy levels but in the end you have to realize we are just splitting hairs. Just pick one and go shoot!

 

[jrsolocam]

I agree with what you are saying from a practical point of view. What I had said was from a technical point of view that one can calculate the relative "efficiency" from a cartridges pe comparing it to down range kinetic energy.

I also said the output may not be relevant or material in the real world...

 

[JaseinMT]

With a single bullet, in a specific caliber, in guns that are similar, one can simply look at powder charges and velocity, and get relative efficiency comparisons. Short, fat cartridges shooting fat bullets at the maximum pressure allowed in the platform are the most efficient. Small capacity and large bore size equals high efficiency. So a 40s&w is a very efficient cartridge.

 

[MagnumManiac]

SD and BC are directly related and are important to external ballistics solutions. Ballistic Coefficient is a function of Sectional Density and Form Factor.

A cartridge's efficiency is a matter of Internal Ballistics.

Yes you are correct, but when discussing the 2, BC is referred to as external ballistics and SD is referenced as a way to summise if a bullet will penetrate, which is terminal ballistics.
I stand by my statement.

Cheers.
gun)