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Greetings and welcome.
Winchester silver tip loads in a 38 special pistol delivers 218# at the muzzle. i would expect to see a yote die quicky if I shot it with a 38 special point blank.
So you can use 218 ft. lbs. as a good number.
22 LR ammo produces about 100 ft. lbs. at the muzzle. I would expect a coyote to die if i shot it in the head with a 22 rifle point blank.
So 100 pounds at the cranium is a good number.
The way I look at rifle killing power at extreme long range, is by looking at pistol killing power at normal pistol range.
Like I have killed deer, with my GI .45. a good 'ol 45 makes about 375-400# at the muzzle. and at 30 yards in my experience a 45 will pile up a whitetail every time.
So I hunt deer now days with my AR .223, with my short barrel, anbd my loads, I'm still hitting at 400 yards with the same energy that my 45 killed those deer with at 30.
good enough for me. (And proven effective: read the post in this forum "dont underestimate your ar .223")
Sure I have used mathmatical tables in my eager youth, but it would never fail that someone would ask my "expert opinion" on this stuff at a gun show, or out whereever and I would never have my calculator handy to do the math for them, regarding there game and load.
So hence my "pistol dialog".... it evolved like this:
a guy see's me at the local gunshow and runs me down to ask about a new rifle for a new kind of game he has never hunted what to get?
I ask what range hunting? a 1000 yards gas/power line cut? or a .8 yard visibility rhodedendrum thicket?
So let's say guy says well where I hunt I can see 300 yards across a bottom...
Let's say the game is wild boar. So I say to guy, well if you were to have to defend yourself, at pointblank range, from a charging wild boar, what is the LEAST powerful pistol you would feel comfortable with?
Lest's say guy says, wow man, I would hope to at least have a .357 magnum.
Then I say okay, well a .357 at point blank produces around 550 # at the muzzle.
So if you think it takes minimum .357 mag energy to quickly stop a boar,when it's your rear on the line choose a rifle round that has that much energy, at the max range you would shoot a boar- when it's the boars rear on the line to make a quick & ethical clean kill.
get a rifle round that has at least 550 # left at 300 yards.
That has been my standard that has evolved over the years for the whole debate of "what is needed to kill what at how far"
No, it's not sexy, absurdly scientific, etc, but it is practical & logical. and it helps guys, laymen figure out the stuff for themselves.
And when the pressure is more than you can bear, and your there with your wallet quivering, motuh watering over a firearm at the gun show, it is a quick "kill-power formula- at range method" that just works, without a calculator & PHD.
So you asked about Coyote? If I or my wife were being charged by a highly motivated, highly ticked off coyote at point blank, I would hope to have a minimum of a 22 Magnum pistol....
Well, an average 22 mag load out of a 6 inch ruger single six revolver would be spitting out 150 +/- ft. lbs. of energy.
So, by my unsexy logic here, my 16" ar-15, spitting out Sierra 55 grain blitzkings @ 3000 fps still has 150 ft. lbs. of energy at 700 yards. So that is my max range, for MINIMUM "killing power."
Waht the 22 mag pistol will do point balnk is equal to what my AR & my loads will do at 700.
Can I put the bullet in the vital zone at 700 yards? Can I read the wind that well? Can i get the coyote to stand still long enough to range him, read the wind, measure for up or down shooting angle, and adjsut my scope for all those varibles and shoot before he moves? That is a whole other topic.
You wanted to know about required kinetic energy on coyote at range. I have given you a handy "pistol/rifle comaprison tool" to use as a rough approximation. but know this,
99% of the time, the shooter is the limiting factor, not the cartridge or it's power at range. If YOU, the driver of the weapon, can not put the bullet in the vitals, then allbets are off, even it your shooting at bumble bee's with .50 cals.
The best words of wisdom i was even given in shooting was
"amatuers study ballistics, experts study wind" in reagrds to shootng rifles.
i have taken quite a long time to try to give you a useable tool to answeryour questions, ad enable to help you answer these types of questions for the rest of your shooting life.
I hope I havw made up for you being possibly "rubbed the wrong way" on this forum. This is the nicest, most kind and helpful out doors froum on hte net. We hope you can participate and enjoy it!
gdc One of the things that this theory fails to consider is energy transfer, The .22 magnum pistol at point blank range will offer full expansion and energy transfer to the coyote, however the .223 depending on bullet construction and remaining velocity may fail to expand having a far less devastating effect on the animal