You can shoot elephants behind the forelegs with an AK47 ( 7,65x39 ), also the .303 is used by poachers. But that is not ethical hunting. You can shoot like Bell with the 7x57, 173 gr at 2350 f/s if you are experienced like Bell to find the right spot for a side brain shot just in front of the earhole. That is the weakest point of an ele`s skull. You should use like Bell a ladder to achieve the right angle and have a gunbearer with your big double for backup.
But being honest, today for sportive ele hunting we want a cartridge which guarantees, using a head shot, a one shot kill under most circumstances, even on a charging animal. That means, the bullet has to penetrate and exit the head from all possible angles. For frontal shots sometimes a massive part of the trunk is also to penetrate. If an elephant is wounded and will disappear, you need also high penetration for the backup shot.
To achieve this properties, you should look for a modern FMJ bullet with a sectional density of .3 to .35, launched with a muzzle velocity around 2350 to 2400 f/s and use it on a distance around 20 m for a head shot. If you hit the brain, the caliber may be 9,3 mm, .375 and .416. If you go up to .458 or .510, you have a margin and a few inches miss will nevertheless bring down or kill the animal. The respective cartridges are hot loads of 9,3x64 and .375 H&H, the .416 Rigby and RemMag, .458 improved as Lott, Watts or Ackley, .460 and .500 A-square. There are many other cartridges giving the figures mentioned above, but also many which have myths around them and their use may end in fatal situations because of a lack in penetration. But reports on such events are normally not for the public. Already a 535 gr .510 bullet at 2350 f/s travelling diagonally from ear to eye is sticking in the ele´s head and not exiting. You have to use a rifle from this caliber group which you can handle without flinching. The diameter or surface area of the wound channel is only the second parameter to look at. If you want a bigger one, you have to go up with the caliber, e.g. 500 A-Square. But here we are coming to an end soon, because the older caliber in the .600 and .700 range have not sufficient penetration and the modern cartridges in this group, .577 Tyrannosaur or .584 Nyati give problems with handling and recoil to most of the hunters. The matter is different for smaller game, but as mentioned above, here we are discussing the hunt of dangerous game with the highest possible performance.
The dead elephant supplies meat for the locals ----->
--to follow and shoot a single ele bull in most cases is without any
problems, even to shoot a bull out of a group is not dangerous, after the
shot the other animals disappear. But to shoot a bull close to a herd or
a cow in a herd can cause charges from the other cows and the hunter should
be aware of that.
--a brain shot at a distance around 20 yards is easier than a heart/lung shot at more than 50 yards.
--no discussion on shot placement, you can read about it everywhere. But penetration is often neglected and can vary a lot depending on the bullets path inside the animal. Not the caliber, not bullet mass, not kinetic energy counts, but look for a cartridge with the most penetration you can handle.
--very often the elephant is only stunned. A final heart/lung shot is obliged, preferredly with a good soft point.
--a very personal opinion: when fighting a charging elephant, it is better to release four shots from a quick bolt action than to reload a double with shaking knees and fingers.
If your team did
a good tracking,
it may happen
that you encounter
How to stop charging elephants:
--A charging ele is the least dangerous game compared to buffalo or lion. In most cases you don´t need a big gun. It depends of course on the distance where the charge started and the character of the terrain. But in many (most?) cases you will make the ele to turn off by producing a lot of noise. You can do it with shouting or metallic noise from punching a knife against the barrel. Next measure is a shot in the air above the ele´s head. The caliber is any you like. Once I had only my camera at hand when a bull started a charge. I tried to give room by walking backwards, but fell down on my back. My PH shot in the air, the bull stopped immediatly making a skid mark and veered round. Even some steps sideways are not wrong, because an ele has a very bad eye sight and no directional smelling when running. All this measures are advisable, because to kill an ele in self defence will often cause a strong investigation by the governmental or National Park authorities. But if that all doesn´t help, you have to apply a frontal head shot. In this stirred up situation a brain shot is doubtful and missing it often occurs. You have to rely on a "knock down" effect hitting the head. My experience is that for at least stunning the elephant a .458 Lott and more is a good recommendation.
Nowadays hunting tuskless elecows to improve the genetic pool is very popular, but told to be the the most dangerous hunting exercise.
--When hunting tuskless ele cows in a big herd, you may apply a "hit
and run" technique. Approach the ele for about 20 yards, shoot and hit the
brain, the ele falls down and the hunters must run away because now other
members of the herd may start a charge. In a save distance you observe the
scene and when the herd moves on, you can go to the laying animal, prepared
for a final shot. This period can take several minutes, so I was able to
observe the phenomenon of the animal being still alive after minutes. But
in most cases they were stone dead.
--The ele is not waking up or standing up after 20 minutes, but as I observed several times it is still breathing and/or moving extremities for minutes. Taylor reported the same up to 30 minutes. I don´t know what physically has happened in the ele´s head. With a bad head shot normally an ele is stunned only for seconds, just touching the ground and up again. But enough time for preparing a second, hopefully final shot.
An elephant is very susceptible for head shots missing the brain but knocking it down. That is the reason, why also calibers of high energy but poor penetration (where the bullet may not reach the brain) are satisfactorily used for head shots. The experienced hunter knows, that he has to run to the animal and give as early as possible the final shot into the neck or lung/heart. Sometimes the ele is up again and disappears. The time span a knocked ele is down can be from a few seconds to 20 minutes (still alive!). If the shot placement and the penetration is very poor, the elephant only shakes its head. A real miss of about an inch above the brain into the honeycomb structure is not lethal to an ele bull, because this structure is filled with air and there is only a relatively poor energy dissipation. The situation is dramatically changed with ele cows. Their honeycombs are filled with liquid and a shot into it causes a pressure wave immediately killing the animal, sometimes brain tissue is pressed out of the trunk.
A test report with images showing the bullet placement and how many shots were needed.