Ok, I can never get this correct. When shooting at a target downhill, will the bullet rise or drop more in comparison to a level shot? Same questions for an uphill shot? Thanks

Both shorten the actual distance the bullet travels. There are formula's for finding the actual distance and several of the new rangefinders on the market are set up to take care of that problem.

Both shorten the actual distance the bullet travels. There are formula's for finding the actual distance and several of the new rangefinders on the market are set up to take care of that problem.

Ok, say my gun is zeroed at 225 yds and I am shooting 225yds on an uphill angle and my particular load at that distance is typically on the way down. Because the distance the bullet actually travels is shorter then on level ground, my bullet would land high of zero?

Yup - doesn't sound logical, but (depending on the acutal angle) you should always hold lower when shooting uphill or downhill.

Check this out for the math:

http://en.wikipedia.org/wiki/Rifleman%27s_rule

jonas

Thanks. I will take my engineering calculator to the field with me on opening day. HAHA!

In actual field use, it means little until the angle gets notably steep. I think it starts to get noticeable at about a 30* up or down angle, IIRC. Even then, the trajectory difference is probably less than the shooter's wobble.

In actual field use, it means little until the angle gets notably steep. I think it starts to get noticeable at about a 30* up or down angle, IIRC. Even then, the trajectory difference is probably less than the shooter's wobble.


That all depends on the angle, the bullets BC, the velocity, and the distance as to whether are not it makes a major difference or not. Past 600 yards or so, only adjusting for horizontal distance will allow for errors as this does not allow for time of flight...

I live in the Rockies, and cannot think of many places where I'd be taking shots beyond 600 yards at more than 30* angles -- or would choose to. As 90+% of all game is taken inside 200 yards, I think my point is valid.

But even in situations such as you describe, the shooter's wobble also covers more ground as range lengthens, so I may still be right.

An often misunderstood topic. If you point a muzzle straight up in the air, if it were not for the rotation of the earth, on a windless day a bullet would go straight up and straight down. Anything within range that was bore-sighted would be hit. No bullet drop off the bore line would occur. Note that in the straight up example, bullet transit time has no effect on the result.

Firing off the horizontal, maximum bullet drop off the bore line occurs because gravity is now perpendicular to the bore axis. In the straight up shot it was merely opposing the direction of the bullet's travel, limiting maximum bullet altitude, but being applied, albeit negatively, along the bullet's path, it did not pull the bullet out of line with the bore.

Every other angle gets results between these two extremes. Just as a long range shot has the bullet falling farther per yard (pulling more m.o.a. off the bore line per yard of forward travel), so it will be that at long range elevated shots, the hold change will grow in m.o.a.

For example, for the 175 grain Sierra Match king fired at at 2600 fps, by the time it gets to 200 yards the drop difference between horizontal and 30° elevation is 1.5" or about 0.72 moa. As Rocky said, just becoming detectable. At 600 yards the difference is 16.9" or about 2.7 moa. Bigger than a shooter's wobble if he is slinged up in prone position, and for some, in sitting position. Most people won't be able to hold offhand that tightly, and it would still be under their wobble.

Rocky, when I shoot at game at long range I do not have wobble, if I do then I do not shoot.. I prefer to shoot prone and from a bi-pod with Jamison rea bags beneath the stock for steadyness
Uncle Nick, You are spot on....

That's refreshing, jwp. The usual internet claim goes something like, "I always shoot 'em right in the eye at 700 yards. I just hold right on 'em with my 317 Loudenboomer Ultra Magnum. I just stand up and whang 'em."

I almost never shoot any game beyond 200 yards (varmints excluded), so it's not an issue for me. But the few times I did shoot at steep angles, I just held a little bit low. Always worked.

The JBM trajectory calculators can calculate the trajectory at any angle. Put your angle into the LOS Angle box.

http://www.eskimo.com/~jbm/calculations/calculations.html

Bye
Jack

Distance from horizontal, whether up or down, regardless of the cartridge or bullet, is always the same. It makes no difference if you shooting a .47-70 Gov't, or a .50 BMG.

Shooters must know the sighted-in distance, and the rise and fall along the path for any distance that might be attempted.

Steep angle shots aren't the norm, but do happen, but not by accident. If hunting where shots of 30, 45, or 60 degrees could happen, then be prepared. For shots 100 yards or less, distance change isn't relevant for big game.

At 30 deg, distance decreases about 15 percent; so at 100 yards, distance is about 85. At 45 deg, distance decreases about 30 percent; so at 100 yards, distance is about 70. At 60 deg, distance decreases about 50 percent; so at 100 yards distance is about 50. Taking distance to 500 yards, 30 degs is about 425; 45 degs is about 350, and 60 degs, is about 250.

The JBM trajectory calculators. . .

Glad to see the server is back up. Was down for awhile.

Distance from horizontal, whether up or down, regardless of the cartridge or bullet, is always the same. It makes no difference if you shooting a .47-70 Gov't, or a .50 BMG.

Shooters must know the sighted-in distance, and the rise and fall along the path for any distance that might be attempted.

Steep angle shots aren't the norm, but do happen, but not by accident. If hunting where shots of 30, 45, or 60 degrees could happen, then be prepared. For shots 100 yards or less, distance change isn't relevant for big game.

At 30 deg, distance decreases about 15 percent; so at 100 yards, distance is about 85. At 45 deg, distance decreases about 30 percent; so at 100 yards, distance is about 70. At 60 deg, distance decreases about 50 percent; so at 100 yards distance is about 50. Taking distance to 500 yards, 30 degs is about 425; 45 degs is about 350, and 60 degs, is about 250.


Let's examine your 30 degree example above and for the example we will use a 308 Win shooting a 175 SMK at 2600 FPS

The horizontal drop at 425 yards with a 100 yard zero is 41.1 inches now the acctual drop at 500 yards when shooting at a 30 degree angle is 52.3 inches that is a difference of 11.2 inches.
As the example clearly shows it is not enough to simply caulculate the horizontal distance to the target as it does not take into account all of the parameters affecting bullet drop. This is the reason that dedicated Long Range Hunters carry a pocket computer inorder to input all realitive data and conditions at the time of the shot...

The above infor was calculated on the Nitghforce Exbal (Perry Systems) balistics targeting ccomputer soft ware... The data was figured at Sea level, temperature of 59 degrees and 78% relative humidity..

What if your target was 500 yards away on a 40° slope. Not 500 in the horizontal, thus making the distance less, but an actual 500 yards. It would still shoot higher than the horizontal true 500 yard shot?

A quick read of the Sierra #4 manual, because it's getting late, shows that the distance they use is the slant distance, not the horizontal distance. It does shoot higher when you're shooting uphill or downhill when you use the slant distance.

Bye
Jack

What if your target was 500 yards away on a 40° slope. Not 500 in the horizontal. . .

All the information I gave at 600 yards and that which appears in the compensating tables are for actual range, not horizontal range. Horizontal range is only mentioned because dividing it by the actual range results in a fraction proportional to the change in bullet drop off the bore line.

For example, I shoot the 600 yard 30 caliber match load I described in my earlier post. If fired it 600 yards from a horizontal bore, the drop is 126.4 inches. If I elevate the bore 30°, and shoot at a 600 yard distant target, the horizontal travel is 519.6 yards.

126.4 inches × 519.6 yards ÷ 600 = 109.5 inches.

That is the drop difference I gave earlier for that elevation angle.

Figuring the horizontal distance for the above calculation is really an extra step. I got it by multiplying 600 times the cosine of 30°. You can skip a step and just multiply the horizontal bullet drop by the cosine of the elevation angle directly:

126.4" × cos(30°) = 126.4" × 0.8660 = 109.5"

If the shot angle elevation was 55°, then the drop would be:

126.4" × cos(55°) = 126.4" × 0.5736 = 72.5"

And so on and so forth.

This is a good read on the subject;

Orignaly posted here.

http://precisionlongrangehunter.com/eve/forums/a/tpc/f/8321005821/m/4981022132


It would seem that I have made some errors in the way I have instructed up/downhill shooting correction. I would like to post this to get everyone headed down the right track. I have forever instructed that to correct for up/downhill shooting with a cosine indicator you take the lazered yardage and multiple by the cosine. This number would be the distance that the bullet is affected by the force of gravity. After determining this distance you simply look on your chart at the corrected distance and dial the dope for the corrected distance. This is the correct way to “triangle” the shot if you were shooting a lazer. For the rifleman this method does not take into account that the bullet, while only being affected by gravity over the corrected distance still has a longer time of flight to be affected by. IF YOU USE THE ABOVE METHOD YOU WILL BE LOW EVERYTIME, if you are setup correctly (more on that later).
The second method I have tried is to lazer a yardage find your drop and multiply the drop by the cosine. While this method will work better that applying it to yardage it is still off as much as 4 or 5 moa at ranges inside of 1000 yards. The odd thing about this method is that most of the time it to will make you shoot low but not as much as applying to the yardage. However with some calibers and some angle ranges it will make you shoot high.
Now then how all this came before me, I was talking to Jeff Huber (of Nightforce fame) about their new angle indicator and mount. The NF mount reads in degrees, when I questioned why you would want it setup like that the debate was on. On my side I had the fact that I had been using my method of correction for along time and had taken game at some extended distances using it. On the other side is Jeff & Perry (Perry is the developer of the Exbal program) with a pile of computer and formula knowledge. First some facts about how I roll with respect to LRH, I use the pocket PC when ever possible but like to know and teach how to manually figure drops etc for times when a PC is not working or available. As with most issues concerning LRH the more distant, the steeper, the slower the bullet the more compounded the problem. I based most of my knowledge and experience from shots with a 260 Remington and a 338 Edge at slight angles of around .90 or less. Most of these shots were under 1300 yards. With those kind of ballistics and slight angles even given the long distances, applying the cosine either way or using the PC all got results good enough to hit moa sized targets. The core of the problem is that there is no way to apply the cosine in the field and factor in the additional time of flight. The only way to get correct dope is to enter everything into the PC or have a chart with drop values for different angles (the Exbal program has this function under the Excell button) The problem with another chart is it probably won’t match the conditions your shooting in at that moment.
I ran numerous charts in various calibers and angles to check my theory and then ran some field testing to confirm my findings. I shot the 260, a 308 Winchester 20” barrel, and a 338 Allen Mag. I shot distances from 300-1300 yards and angles from 0-45 degrees downhill. I shot every shot with cosine corrected yardage first, then cosine corrected dope next, and lastly pocket PC dope. Here is what I found in the field:
• The cosine corrected yardage method impacted low on every shot over 400 yards, however the cosine corrected dope worked well .90 and above at all distances, not perfect but well.
• The 308 was helpless the only way to get good hits past 400 with any real amount of angle was to use the ACI and the pocket PC.
• The Allen as you would expect was the most forgiving but still needed PC input to make solid hits past 800 yards if the angle was more than .90. If the angle was less than .90 even out to 1300 yards I could still make good hits.

In the end the solution is fairly simple always use the PC at angles over .90 (cos), distances over 600, have the printed angle sheet for your best guess on hunting conditions for when the PC doesn't work and shoot something with as much ballistic advantage as you can. As always do everything you need to make the shot the best you can or pass on it.
Also I will post a picture of the new NF angle indicator and mount that prompted all this very soon, the mount is the nicest base mount I have seen.

Shawn Carlock
Defensive Edge Inc.
gunsmith@defensiveedge.net

All the information I gave at 600 yards and that which appears in the compensating tables are for actual range, not horizontal range. Horizontal range is only mentioned because dividing it by the actual range results in a fraction proportional to the change in bullet drop off the bore line.

For example, I shoot the 600 yard 30 caliber match load I described in my earlier post. If fired it 600 yards from a horizontal bore, the drop is 126.4 inches. If I elevate the bore 30°, and shoot at a 600 yard distant target, the horizontal travel is 519.6 yards.

126.4 inches × 519.6 yards ÷ 600 = 109.5 inches.

That is the drop difference I gave earlier for that elevation angle.

Figuring the horizontal distance for the above calculation is really an extra step. I got it by multiplying 600 times the cosine of 30°. You can skip a step and just multiply the horizontal bullet drop by the cosine of the elevation angle directly:

126.4" × cos(30°) = 126.4" × 0.8660 = 109.5"

If the shot angle elevation was 55°, then the drop would be:

126.4" × cos(55°) = 126.4" × 0.5736 = 72.5"

And so on and so forth.

Sorry, but that question was a little bait. I wanted clarification for arguements sake.

The cosine was what I was searching for. I knew it was cosine, but I wanted to know how the "horizontal" arguement derived it. I believe that the cosine give the factor that either uphill/downhill trajectory thrusts into the equation. In other words; uphill/downhill gravity acts upon the bullet at cosine times coeffecient of gravity. Not that you are shooting equivelant to XXX time cosine yards.

After all you you are shooting 600 yards, not 519. The bullet will be in the air the amount of Time for a 600 yard shot, not a 519 yard shot. Drop equals time of flight(600/fps) x the coeffecient of gravity. Drop uphill/downhill equals Time x coeffecient of gravity x cosine.

Now, the cosine gives you the EQUIVELANT distance that the bullet drop will be related to. Now, I realize all this means squat, you can multiply yards time cosine and get "horizontal" and it'll put you on target. But, it is how gravity acts either up/down hill upon speeding objects, not because you are shooting at 519 yards, because the bullet is in the air for 600 yards.

You and others may be saying the same thing, but it seems to me you are saying that you are "shooting 519 yards" not that the bullet will drop the "equivelant of a 519 yard shot".

Hpdrifter,

I think you've got it. I haven't yet had time to read jwp475's link, but yes, the cosine is multiplied by the drop for that same target distance on the horizontal to get a correction. Multiplying the target distance by the cosine and looking up the drop for the resulting shorter range can't work because bullet drop with distance is non-linear. Non-linear, by definition, means non-proportional (over the range, in this case). It is why the drop error introduced by angling up 30° is almost four times as many minutes of angle at 600 yards as it is at 200 yards. The error angle would be constant if it we were describing a linear function.

Multiplying the 600 yard drop by the cosine of the elevation angle, you get a new drop for 600 yards at the angle. That is comparing two bullets with about the same time of flight. Tiny bits of further correction accuracy require several things. One is that the vector force of gravity acting on the bullet be added to the drag function of the bullet over the range. In other words, actual time of flight uphill will be a little greater than horizontal, and downhill at the same angle will be a little shorter than horizontal. It is not a significant difference in practical terms, but bears mention only in the name of being complete and to say not to worry about it if you find yourself analyzing the problem.

Another source of error that impedes exact results is the nearly 100 year old G1 ballistic coefficients supplied by most bullet makers and used by most software are not derived from the best drag function fit to modern bullet shapes. With the Sierra MatchKing in my earlier example, either the G5 or G7 BRL functions come closer to matching its actual drag function. Manufacturers don't make B.C.'s for these functions available for other drag functions because you can't rank bullet performance by ballistic coefficient unless you use a common drag function for them all, no matter how inappropriate it may be to the actual shape of the bullet. That is why the G1 numbers are, for match bullets, provided at different numbers between different velocity boundaries; it is an attempt to compensate for using an inadequately fit drag function. I have found the G1 approximations usually result in excessive drop for match bullets, even with the incremental velocity corrections. Come-ups figured by ballistic software have always turned out too great for me, though, since I am using iron sights in service rifle matches, I have not analyzed how much of that is due to my vision?

I will also point out that the calculation for change in drop is applied to the bore line angle. The bore line is already angled up over the line of sight for whatever range your sights are zeroed to. Thus the angle you are correcting for based on the sights will be very slightly low. The angle of the line of sight plus the angle of bore line elevation above the line of sight (the angle of departure) is what the cosine solution works for. The difference is small, however. If you sight in at 200 yards with a scope that is 1.5" above the bore axis, you are looking at something on the order of a twentieth of a degree. Even at 600 yard zero, with the .30-06 example I gave, the angle of departure is only a third of a degree. At 1000 yard zero it is just under three quarters of a degree. At that point you can begin to see the effect, but only a little. I only mention it to be concise about the angles we're discussing.

Robert Rinker's book, Understanding Firearm Ballistics, p. 247, 3rd ed., Mulburry House, Pub. 1999, has a good illustration of sight angle correction. It also explains the terms involved on p 248.

The post is the link copied and cross posted

Ah! I didn't look at the signature. So, I have read it (now, including the signature). :)