Most efficient cartridge?

Hmmm.
Maybe depends more on quarry - 19gns of Viht N120 sending a 50gns Vmax trundling along at north of 3100 fps - brilliant for foxes; same charge with a 55gns Sierra is very “efficient” for Roe and prior to the minimum calibre introduction saw off quite a few stags…
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What's the most efficient rifle cartridge? Powder charge vs bullet weight? Or does it really depend on caliber?
By your standards it must be CB cap that uses no powder, so it's infinitely efficient.

You must first set some conditions, like deliver X amount of energy at Y distance. Or X amount of muzzle velocity with bullet that weighs Y. And even then answer is "it doesn't matter" for most usage scenarios.
 
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Many classic cartridges used in the UK are American designs based on the .30/06 which is overlong compared to contemporary German cartridges of similar calibre and performance. This was because American powders at the time of the .30/06 were not as good as German powders. Thus the 7mm Mauser and 8mm Mauser in a 57mm case surpassed in performance what the Americans had to use a 63mm case to do with their .30/06.

Thus with modern powders .257 Roberts (a 57mm case does 95% of what a .25/06 needs a 63mm case to do.

 
The most efficient cartridge is the one that
A. Your local RFD has plenty of ammo and in good selections
B. The rifle you like and fits you, is available in that
C. It’s a cartridge you shoot well recoil wise
D. It’s a cartridge which suits the species you target
E. It’s a cartridge which doesn’t need a 26” barrel if you are planning to use a moderator
 
Many classic cartridges used in the UK are American designs based on the .30/06 which is overlong compared to contemporary German cartridges of similar calibre and performance. This was because American powders at the time of the .30/06 were not as good as German powders. Thus the 7mm Mauser and 8mm Mauser in a 57mm case surpassed in performance what the Americans had to use a 63mm case to do with their .30/06.

Thus with modern powders .257 Roberts (a 57mm case does 95% of what a .25/06 needs a 63mm case to do.

I did a rather deep research into these German flake powders as they were showing up in all the older rounds that I had de labbed from deceased local hunters to me.These were Wehrmacht powders recycled from 8x57IS 1940-45 dated ammo. It appears that the nitro mix was rolled out to a 2mm thickness then square cut x 0.45mm this finished powder came from many varied locations to avoid any critical bomb damage to their supplies (shadow factories) it was then transported to mixing stations where they created the final energy requirements for ack ack shells, rifle, aircraft machine guns or 20mm cannon & infantry machine guns.
 
The most efficient cartridge is the one that
A. Your local RFD has plenty of ammo and in good selections
B. The rifle you like and fits you, is available in that
C. It’s a cartridge you shoot well recoil wise
D. It’s a cartridge which suits the species you target
E. It’s a cartridge which doesn’t need a 26” barrel if you are planning to use a moderator
Just to add to your excellent points F. What you can reload yourself within points B-E
 
Dr Geoff Kolbe in his book plotted powder againt muzzle energy, that illustrates the concept nicely, now we have a lot of new wonder cartridges but I doubt the results will have changed
 
Are the super duper accurate modern cartridges more efficient than the older stuff?

Yes, but only insofar as they generally employ higher pressures. Modern powders and increased pressures have also produced smaller capacity cases for a given level of performance and calibre, and cartridge efficiency is closely linked to the case capacity capacity to bore ratio. @enfieldspares points this out re the 30-06 which was less efficient than competing designs among early 20th century military cartridges and loadings.
 
Dr Geoff Kolbe in his book plotted powder againt muzzle energy, that illustrates the concept nicely, now we have a lot of new wonder cartridges but I doubt the results will have changed

The classic measure of efficiency is ft/lb ME per 1.0gn propellant. On that basis, the better .22 rimfires are vastly more efficient than large centrefires. However, the job to be done intrudes into theoretical efficiency and horses for courses applies. That is, the standard .22 Long Rifle loading producing ca. 100ft/lb from less than 2gn powder is a p*ss poor deer cartridge, 1,000 yard F-Class cartridge, and all it'll do to the typical Cape buffalo, elephant or rhino is p*ss it off and get you killed.
 
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