Shooting close range with a long range firearm?

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Is there some kind of recipe for these kind of shots? I realize practice and trial will give me some answers, but I am a bit perplexed.
Saturday I set up on coyotes, shot two, one standing at 300 yards, the next at a run at 350.
Yesterday I stood in my same footprints in the snow and started calling. A coyote got to about 20 feet before I even seen him, he paused, looked behind him and I put the crosshairs right on his pumpkin.
Clean miss.
Ended up getting him at about 100 yards, took me that long to digest my miss and regain composure.
Looking back, I realized I should have aimed low, but is there an equation on just how low?
The gun is a Ruger M77, 220 swift. 14x scope (dialed for 4x at the time), zeroed for 200 yards. My scope is as close to bore as possible, about 1.5" from crosshairs to bore center.
My .204 would not have missed at that range, slightly different setup though.
I understand that this is something I need to get behind the gun and practice at that range, but any attempts at finding any actual math for these ranges is coming up blank.
I was tempted to leave out the part about the headshot in an attempt to bypass being judged, but it is out there now. Not what I normally do, but it has never failed me inside of 200 on a standing coyote. My thought was saving the hide because of the caliber/range combination, but logic failed me.
Any links or advice on these shots would be appreciated, new gun to me, and a new learning curve. I shoot a silly amount of coyotes, but not at that range, advice will help for jumping bunnies too, close target, long gun.
Thanks!
 
I am not sure what bullet you are shooting but a swift sighted in a 200 yards will be about -1.5 inches at the muzzle, .8 inches high at 100 yards, -5.4 inches at 300 yards and -17 inches at 400 yards. It would seem to me that it was maybe the shooter not the gun.
 
If the crosshairs of your scope are 1.5" above the bore, the lowest you could possibly be is 1.5". If you're zeroed at 200 yards, anything from 0-225 would be a hit if your crosshairs were on it when you pulled the trigger. If anything you should have aimed an inch high at point blank range.
 
So it looks like it was me. Not terribly surprised, it was a lot of brown in my scope, and a sudden shot.
I thought there might be more to it. Time to bring a second gun..
 
I know that a lot of old timers sight in at 25 yards when they first mount the scope. with the scope 1 1/2 " above the bore they are very close at 200 yes depending on the calibre. Shooting at 25 you should be within 1/2" of your point of aim. 25 yes or thereabouts would be the first time the bullet crosses the line of sight. At 5 or 10 yds you may have to aim 1-11/2 low.
Check it out for yourself if you can focus the scope that close.

Neil
 
At 20ft you should aim high, not low, as the bullet hasn't had a chance to cross the line of sight or the peak of it's arc.

Let's say you're zero'd for 100 yards. The bullet will remain below line of sight until it reaches the highest point of it's arc (zero range of 100 yards) before it starts it's downward arc after passing the zero range. To determine exactly how much you'd need to measure from the center of the bore to the center of your scope to know just how low the bullet will be at point blank range.

Rough example with crosshairs 2.5" above the bore, 100 yard zero, placing crosshairs on the yotes eye:
-5 yards the bullet will hit 2.5" low
-50 yards 1.5" low
-100 yards bang on
-150 yards 1.5" low
-200 yards 2.5" low




This is much more evident when shooting your crossbow as the scope is so much higher than the rail and your Excalibur is likely the easiest and cheapest way to practice close shots. Assuming the crosshairs are 3.5" above the rail, at 5 yards the bolt will hit the target roughly 3" low meaning you need to aim 3" high to hit bang on at such a close range.

Using 20 yard pin and aiming dead on:
-5 yards the bolt will be 3" low
-10 yards 1.5" low
-20 yards bang on
-30 yards 1.5" low
 
Neilm said:
I know that a lot of old timers sight in at 25 yards when they first mount the scope. with the scope 1 1/2 " above the bore they are very close at 200 yes depending on the calibre. Shooting at 25 you should be within 1/2" of your point of aim. 25 yes or thereabouts would be the first time the bullet crosses the line of sight. At 5 or 10 yds you may have to aim 1-11/2 low.
Check it out for yourself if you can focus the scope that close.

Neil
Click to expand...

With the scope 1.5" above the bore, aiming 1.5" low at 5 yards would put the bullet 3" lower than where you wanted the bullet to hit. Aiming 1.5" high would result in the bullet hitting exactly where you wanted it to go at such a close range.
 
The above is correct... You should have aimed high not low... The amount depends on how high your sightline is above the bore, generally 1.5" - 2"... Also always start with your scope at its lowest power setting... If one gets in close, it will be a quick shot... If they are 2-400 yards out you will have the time to dial it up.
 
Thanks for the tips guys.
A bit of a typo on my part, I knew I should be aiming high opposed to low, but got excited when I was typing.. Keyboard fever.
Still trying to apply math to this situation, so I have taken it upon myself to chart it out by benching my gun (a couple) and putting holes in paper. That started when I put a paper target at 15 yards and shooting, I was surprised to see my POI 3.5" below my line, and I assure you, my scope is not 3.5" above my bore.
This gun shoots small groups at 100 yards, so I have been left wondering what is going on.
My shot felt good, coyotes don't shake me up the way they once did, but I still haven't ruled out coyote fever, or the fact I had my scope zoomed for a target I was anticipating farther away.
When I am done with these tests, I will give specific numbers when my shooting is done, if anyone is interested. 3 Calibers with very slight differences in bore/crosshair variances, all in the 4000 FPS range.
 
I know when I have missed more coyotes under 50 yds than coyotes much further out. The best I can figure, my 4 x 12 scope takes up all the coyote on 4 x when they are that close and I guess I don't take the time to place the crosshairs on a spot, instead I just take the shot thinking easy shot. I probably rush it or yank the trigger or both but definitely have missed more close ones than ones that are 100 yds out.
 
He was so close, and I was not ready for that, couldn't tell a nostril from a testical. Noted above to keep the scope on a low zoom, easier to turn it up when needed than turn it down.
One reason I like my 6500, even with a 16x zoom, I can still back it off to 2.5x.
 
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