I'm afraid I must disagree with this statement, within the MPBR of the cartridge you are shooting, you hold more or less exactly where you want to hit. However I do understand what I think you are saying..........on a hard uphill shot one would be holding closer to the brisket than on the level, and on a hard downhill shot one would hold closer to the spine. It isn't really holding high or low but center on the animal as it appears to you. Shoot for the center of the "basket ball" regardless of presentation...........
How accurate do you strive to be?
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I'm afraid I must disagree with this statement, within the MPBR of the cartridge you are shooting, you hold more or less exactly where you want to hit. However I do understand what I think you are saying..........on a hard uphill shot one would be holding closer to the brisket than on the level, and on a hard downhill shot one would hold closer to the spine. It isn't really holding high or low but center on the animal as it appears to you. Shoot for the center of the "basket ball" regardless of presentation...........
pete dobinson
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There is less arc in the bullet path shooting uphill or downhill.
That just is not true............there is exactly the same arc as any other shot over the same horizontal distance.
pete dobinson
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If you were to shoot exactly 90 degrees straight up, there would be no arc. It would go straight up till gravity takes over then drop straight down . Same thing if you were able to shoot straight down. Shoot an arrow straight up, it will go till gravity takes over and drops straight down. Shoot an arrow over a flat plane, it will have arc. At least thats the way I see it. Put me straight if I'm wrong.
You are absolutely correct Pete, however straight up and straight down have no horizontal component, hence the bullet has no arc as such. Technically speaking the up and down shots do have a arc, as far as the mathematical formula goes, but it is expressed as zero, because the horizontal distance is also expressed as zero. If you have a rifle sighted in for 200 mtrs and you take a shot that is 1000 mtrs down and 200 mtrs out your bullet will strike exactly where your crosshair is when the trigger breaks, same goes for uphill. Even though your time of flight is affected by the distance the gravitational pull is still only equal to the 200 mtr horizontal distance. It's just pure physics of external ballistics.
If you were to vice a rifle perfectly horizontal on a dead flat plain, like the salt flats and you were able to fire the rifle and drop a bullet from the exact muzzle height at precisely the same time, both bullets would hit the ground at the same time. The forward momentum of the bullet does not in any way change the gravitational effect upon that bullet, therefore neither does an uphill or downhill angle.......the only relevant distance over which gravity affects the bullet is the horizontal component of it's flight.
Gravity is a constant and does not change with altitude nor velocity. The only variable in the experiment of the horizontal rifle to the dropped bullet, is how far the fired bullet will travel before touching down. This is dependent on several factors such as velocity, ballistic coefficient of the projectile, air density and humidity. All of these factors affect the arc of the bullet, but the gravitational effect is constant.
I was absolutely amazed at how flat my bullets flew from my 300 Wby when shooting at my Marco Polo and the 2 ibex I shot in the Pamirs at over 17,000 feet ASL. Air density is at about 40% of sea level and 50% of any sheep hunting I had done previous, so my sight in gave an increase in my MPBR of nearly 150 mtrs, giving me a 500 mtr MPBR. We confirmed this by shooting at camp using a range finder..........camp was at 15,500 feet ASL !!!!!
I just reread your post, and you are correct in what you say........the uphill and downhill bullet flight will have a shallower arc over it's flight at that angle, but it will strike at the same point of aim as the horizontal component of the right angle triangle............gravitationally speaking. The biggest problem in uphill and downhill shooting is gauging the horizontal distance...........
If you were to vice a rifle perfectly horizontal on a dead flat plain, like the salt flats and you were able to fire the rifle and drop a bullet from the exact muzzle height at precisely the same time, both bullets would hit the ground at the same time. The forward momentum of the bullet does not in any way change the gravitational effect upon that bullet, therefore neither does an uphill or downhill angle.......the only relevant distance over which gravity affects the bullet is the horizontal component of it's flight.
Gravity is a constant and does not change with altitude nor velocity. The only variable in the experiment of the horizontal rifle to the dropped bullet, is how far the fired bullet will travel before touching down. This is dependent on several factors such as velocity, ballistic coefficient of the projectile, air density and humidity. All of these factors affect the arc of the bullet, but the gravitational effect is constant.
I was absolutely amazed at how flat my bullets flew from my 300 Wby when shooting at my Marco Polo and the 2 ibex I shot in the Pamirs at over 17,000 feet ASL. Air density is at about 40% of sea level and 50% of any sheep hunting I had done previous, so my sight in gave an increase in my MPBR of nearly 150 mtrs, giving me a 500 mtr MPBR. We confirmed this by shooting at camp using a range finder..........camp was at 15,500 feet ASL !!!!!
I just reread your post, and you are correct in what you say........the uphill and downhill bullet flight will have a shallower arc over it's flight at that angle, but it will strike at the same point of aim as the horizontal component of the right angle triangle............gravitationally speaking. The biggest problem in uphill and downhill shooting is gauging the horizontal distance...........
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Hmm. Great post, but I think I'm going to go out on a limb and disagree with the bolded part.
As you alluded to, gravity doesn't care that the bullet is in motion. But NEITHER does it care how far it travels (horizontally or otherwise) All gravity knows, is force and TIME.
A bullet with a longer flight time will spend more time being enacted upon by gravity (exponentially, btw). As such, in your 1000 down, 200 out example, the bullet would be exposed to the effects of gravity for at least 5 times the time, and closer to 10 if you factor in the deceleration down range. This increased exposure to gravity would pull the bullet lower at such extreme downward angles and ranges.
To take the analogy further, imagine a canyon 200 yards across, but 50 miles deep. If you aimed the rifle just one degree out from vertically straight down, it would still be pointing at the opposite canyon wall several miles down. However, when fired, the bullet would never make it to the other side, because the flight time would be so long, that it would expend whatever horizontal energy it had into deceleration from drag, and gravity would have ample time to take the bullet's parabolic arc and smooth it into a practically vertical fall, not allowing it to ever come into contact with the canyon wall that's only 200 yards away horizontally.
A ridiculous example, but if time of flight is an important factor in the extremes, then it's still SOME factor in the ordinary.
Or maybe I'm out to lunch
pete dobinson
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c-fbmi, Thanks for your post.
Cameron SS
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Hmm. Great post, but I think I'm going to go out on a limb and disagree with the bolded part.
As you alluded to, gravity doesn't care that the bullet is in motion. But NEITHER does it care how far it travels (horizontally or otherwise) All gravity knows, is force and TIME.
A bullet with a longer flight time will spend more time being enacted upon by gravity (exponentially, btw). As such, in your 1000 down, 200 out example, the bullet would be exposed to the effects of gravity for at least 5 times the time, and closer to 10 if you factor in the deceleration down range. This increased exposure to gravity would pull the bullet lower at such extreme downward angles and ranges.
To take the analogy further, imagine a canyon 200 yards across, but 50 miles deep. If you aimed the rifle just one degree out from vertically straight down, it would still be pointing at the opposite canyon wall several miles down. However, when fired, the bullet would never make it to the other side, because the flight time would be so long, that it would expend whatever horizontal energy it had into deceleration from drag, and gravity would have ample time to take the bullet's parabolic arc and smooth it into a practically vertical fall, not allowing it to ever come into contact with the canyon wall that's only 200 yards away horizontally.
A ridiculous example, but if time of flight is an important factor in the extremes, then it's still SOME factor in the ordinary.
Or maybe I'm out to lunch
I also disagreed with CFBMIs assertion that " If you have a rifle sighted in for 200 mtrs and you take a shot that is 1000 mtrs down and 200 mtrs out your bullet will strike exactly where your crosshair is when the trigger breaks". There is a reason why there is a market for elevation angle indicators, and I can tell you from experience that shots fired uphill and down hill, will both fall short of the point of aim if not corrected for. The more extreme the angle, the further short the shot will be.
I think your method of expressing it in terms of time of flight is good, but a more simpler method is to just consider the difference between horizontal distance to target and actual distance to target.
200m horizontal distance with a 45degree up angle, or down for that matter, using Pythagorean theorem, yields an actual distance travelled of 283 meters. So obviously if you take a shot at 283 meters, zeroed for 200, the shot will fall short.
Using this same formula, the extreme example of 200 meters out, 1000 meters down, gives me an actual distance to target of 1020 meters. So if you are zeroed for 200 taking a shot at 1020, yeah, you are going to fall a little short.
Cameron SS
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The last paragraph there leads to believe I may not have fully understood the distinction you are trying to make.
You are absolutely correct about the dropped bullet vs horizontally fired bullet hitting the ground at the same TIME, but that is because both bullets start the experiment at a velocity of zero, have the same vertical distance to the ground to travel, and gravity affects them the same as it accelerates them from a vertical speed of zero until they hit the ground. When a bullet is fired horizontally, the only force pulling it down is gravity.
If you were to point your rifle straight down, and drop a bullet from the same height at the same time, will they hit the ground at the same time? No, because now your have the explosive energy of the cartridge as another variable driving the bullet down, in addition to gravity. Likewise if you dropped a bullet at the same time you fired a bullet straight up, would they strike the ground at the same time? obviously not. Therefore your conclusion, which I underlined, that angle does not affect the gravitational affect inaccurate, because it is incomplete. Yes the gravitational effect on both bullets are the same, but gravity isn't the only factor acting on a bullet fired at an angle.
Now if we changed the parameters of what we were talking about slightly, which is to say a muzzle to target distance of 200 at 0 degrees from horizontal vs a muzzle to target distance of 200m at a 20 degree angle (which would be less than 200 horizontal meters), then I think the point of impact would in fact be very close to the point of aim, and the only minor variance would be a result of scope height offset and resulting offset angle. I think that might have been what you meant in your last paragraph.
Punching the first case into a ballistics calculator...(2600fps, 168gr, BC of 0.5, sight height 1.5, zeroed at 100yd). Shooting level, at 200yds the POI is 4.4" below POA. Shooting at 45 degrees, at 283yd the POI is about 6.5" below POA. So while your shot will fall a little bit short, it's not too far off from what you'd get by considering just the horizontal distance. Shooting 283yd at level the POI is 14" below POA, so if you adjusted for a 283yd level shot and then shot at 45 degrees you'd hit 10" over your POA.
Shooting 200yd out and 1000yd down is 78.6 degrees and a more extreme case. In this case, your POI is 55.5" below POA, so clearly time in flight is a factor and you can't just consider horizontal distance. But shooting 1020yds at a level target your POI is 439" below POA so as you can see the angle plays a huge factor.
If you take the ballistics parameters from my previous post, zero for 200yd level then shoot at a target 200yd away uphill/downhill at a 20 degree angle, you'll hit 0.7" above your POA. At 30 degrees you'll hit 1.5" above your POA. At 40 degrees you'll hit 2.7" above your POA.
The horizontal distance is a factor, but so is time in flight.
Cameron SS
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Would love to take a look at the calculator you are using.
pete dobinson
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So to us hunter's that are mathematically challenged, what does this all mean? MPBR will be extended shooting uphill or downhill me thinks.
Now that I read your posts, I must admit there is a flaw in what I have learned theoretically. Of course time of flight allows gravity to act upon an object for a longer time therefore it must drop more....period. I was actually thinking about this after I typed it last night and pondered that flaw in the theory. There is another factor that is not being considered though in sharp downhill long range shooting.........that is the positive effect of gravity on retained velocity. I do not know the mathematics to express this but I do know for a fact it exists and the drop over 1000 mtrs at 78 Deg downhill is not 55". I watched my sheep hunting buddy make this shot, it was actually between 7-800 mtrs downhill with about 150-200 mtrs horizontal component. I was spotting on the scope while he shot. He was shooting my 7 mag with 160 Parts at 3000 fps sighted dead on at 300 mtrs. We had a long discussion about the range and it's effect on the bullet and disagreed as to where to hold. He decided to hold about 6-12 inches over the ram that was bedded out on a little finger and that is exactly where the bullet went. The ram got up and bailed over the edge of the finger and disappeared out of sight, only to return to his bed a couple minutes later, totally confused. My buddy then took my advise and held right on the upper shoulder of the ram and killed it stone dead on the next shot. We were prone and basically benchrested on a ledge so sighting and holding was not an issue. I can say for a fact that the bullet was striking more or less exactly where the cross hair was and the range was definitely approaching the 1/2 mile mark of bullet flight but with only a 150-200 mtr horizontal distance. Again, I do not know how to express this mathematically but I know what I saw and in my mind it follows perfect logic........uphill I'm sketchy about as the opposite principal must exist but I have never taken or witnessed an uphill shot that far or that steep.
Cameron SS
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Yes, depending on the angle, your MPBR will be extended, possibly by as much as 100% if shooting at 60 degrees.
I have been racking my brain trying to wrap my head around the totality of the math problem before us. In the end I stopped trying to reinvent the wheel, and googled it.
One thing I can say for certain is the more I read on this subject, the less I actually grasp it.
Found five sources that articulated the math problem five different ways, but in the end they all agreed. If shooting at angles without corrections, your shots will land HIGH. The rule of thumb is when correcting for angle, hold low. So your buddy that held high on his first shot would have made the problem worse.
With respect, not much can be learned from your one shot, unless we can run the numbers on exact range and exact angle. There is a lot of difference between 700m and 800m. From what I just read, again with all due respect, if he did a dead hold for a 800 meter distance to target shot, and hit it, he got lucky.
http://www.exteriorballistics.com/ebexplained/5th/33.cfm
http://thearmsguide.com/wp-content/uploads/2013/11/uphilldownhill.jpg
http://www.rifleshootermag.com/network-topics/tips-tactics-network/hitting-a-high-or-low-angle-shot/
In a previous post, I used Pythagoras to show how horizontal distance to target actually results in a longer shot than anticipated, resulting in shots landing low. While technically true, this is an utterly useless statement. In fact, it is the exact opposite of the correct way to articulate the problem. Unless you are using a map to estimate horizontal distance, no one estimates distance on a strictly horizontal basis. Apparently though, the actual horizontal distance is what you need to know. This is impossible to estimate reliably because it usually means estimating a distance in the air over your target, if looking down, or estimating a distance to some point underground, if looking up.
Several references talk about finding the actual horizontal distance by measuring line of sight to distance, and applying a formula based on the angle to find the actual horizontal distance.
If you look at the image at the arms guide link, you can see in the horizontal shot, a vertical blank line labelled "bullet drop at level range," or DROP. When shooting horizontal, drop is measured vertically. When shooting up at an angle, you are essentially rotating the entire Line of Sight/Line of Departure equation, meaning your 'drop' is also affected by the angle. Its important to remember, that even when shooting up or down, we are still imagining our DROP as a vertical line.
In the elevated shot shown in that image, you can see the yellow line labelled 'bullet drop at slant angle', you can see that the actual distance of drop is the same as for horizontal, however it is being indicated at a different point in the bullets flight path, a point where the bullet is still above the line of sight, and results in the bullet actually impacted above the sight line.
At the end of the day, as several references have said. It is not important to understand WHY it works, you only need to know HOW it works, and how to apply the correct formula.
I know how good charts for this formula, and look forward to a chance to put in use, apply the formula, hit my target, and still end up scratching my head about why that worked.
This has been an educational experience.
As you have stated it is all very complex mathematically. I also agree that the one case stated with the estimated distances is not enough data to hang one's hat on, however I have made many moderate uphill and downhill shots on game and have always had good success just roughly calculating the horizontal component. I believe that within normal hunting ranges, say 500 mtrs and less and angles of not more than 45*, this method works every time.
I took my Altai Argali at a lazer ranged distance of 462 mtrs uphill at about a 45* angle. Altitude was not crazy, about 8000 ft ASL. We glassed him for a long time as he was bedded and not presenting a viable shot. I decided to wait him out while my entourage voted to spook him out, which I over ruled with threats of gun butting if anyone spooked him up. I have hunted enough sheep to know that they only lay in one position for 45-60 minutes before they get up and look around and then change position and lay down again. During this time we kicked around the horizontal distance it would be to him, using Pythagoras Theroum we estimated the actual distance to be about 300 mtrs horizontal. My 300 Wby happened to be sighted at exactly this distance, so when he stood up I called a heart shot and held exactly on where I guessed the heart to be and touched off. I was again prone and we had arranged gear so that I was benchrested over packs and stuff and was able to hold rock solid......I hit the top of the heart.
Of course everything but the actual distance to the ram was guesstimated but such is the luxury of shooting fast and flat cartridges when hunting, they make up for small and sometimes larger errors in guesstimation.
Having done most of my hunting prior to the advent of accurate range finding equipment and turreted scopes and range finders that calculate angles for you, it was incumbent upon one's self to learn how to do this with some degree of consistency and I found that high velocity and high BCs were two of my dearest friends in overcoming the human error factor when estimating distance and angle. I still believe this today and I still believe in the horizontal distance theory within normal hunting ranges. My lifetime of shooting and hunting experiences support this, even if I can't do the math to prove it to others.
I took my Altai Argali at a lazer ranged distance of 462 mtrs uphill at about a 45* angle. Altitude was not crazy, about 8000 ft ASL. We glassed him for a long time as he was bedded and not presenting a viable shot. I decided to wait him out while my entourage voted to spook him out, which I over ruled with threats of gun butting if anyone spooked him up. I have hunted enough sheep to know that they only lay in one position for 45-60 minutes before they get up and look around and then change position and lay down again. During this time we kicked around the horizontal distance it would be to him, using Pythagoras Theroum we estimated the actual distance to be about 300 mtrs horizontal. My 300 Wby happened to be sighted at exactly this distance, so when he stood up I called a heart shot and held exactly on where I guessed the heart to be and touched off. I was again prone and we had arranged gear so that I was benchrested over packs and stuff and was able to hold rock solid......I hit the top of the heart.
Of course everything but the actual distance to the ram was guesstimated but such is the luxury of shooting fast and flat cartridges when hunting, they make up for small and sometimes larger errors in guesstimation.
Having done most of my hunting prior to the advent of accurate range finding equipment and turreted scopes and range finders that calculate angles for you, it was incumbent upon one's self to learn how to do this with some degree of consistency and I found that high velocity and high BCs were two of my dearest friends in overcoming the human error factor when estimating distance and angle. I still believe this today and I still believe in the horizontal distance theory within normal hunting ranges. My lifetime of shooting and hunting experiences support this, even if I can't do the math to prove it to others.
Cant a target and shoot at the bulls eye see what side of the bull you're shots land. Cant it the opposite and see where they land. It is because you are shooting at an aspect of the bull your shots will land further away on the bull if you are shooting center of bull. Your shot goes where it is aimed but does not land center. This is why you need to aim lower on target when shooting uphill or down.
Like an old hunter said......."Shoot for the center of the basketball regardless of presentation" This refers to the vital zone of most critters as being the size of a basketball laying between the shoulders in the bottom 2/3 of the chest. I bear this in mind every time I squeeze the trigger on an animal.
I just used the "advanced" calculator on the Hornady website. http://m.hornady.com/ballistics-resource/ballistics-calculator
