Advanced Marksmanship Up HIll - Down HIll: Yes, once again!

[Killer Spade 13]

OK, I've read that when shooting up hill and down hill gravity affects the bullet drop equally.

However, the vectors of gravity, bullet velocity, etc. are a bit more complicated that that.

When shooting down hill, because of the forces of gravity, the speed of the bullet does not dissipate as quickly as it would when shooting up hill.

Is there a good mathematical table to predict the differences in drop associated with these differing values?

 

[Darkside-Six]

a 20 degree angle is a 20 degree angle. it's the same whether it's up or down. your time of flight may be .001 second different but not enough to make a noticeable difference. Figure out your angle, apply the proper cosine and that is it. no need to get any more technical then that.

 

[ShtrRdy]

As it turns out, gravity effects of shooting uphill versus downhill is minimal. The key difference is the distance the bullet travels over the horizontal distance. For example, if you're shooting at something that's 1000 yds away uphill at 45 degrees, this is essentially a 707 yd shot. The same goes for downhill - a 1000 yd distance at 45 degrees downhill is a 707 yd shot.

The caveat to this is when it comes to considering the effects of wind. The bullet is still actually travelling 1000 yds so you have to adjust for wind over the 1000 yd distance.

 

[flounderv2]

As it turns out, gravity effects of shooting uphill versus downhill is minimal. The key difference is the distance the bullet travels over the horizontal distance. For example, if you're shooting at something that's 1000 yds away uphill at 45 degrees, this is essentially a 707 yd shot. The same goes for downhill - a 1000 yd distance at 45 degrees downhill is a 707 yd shot.

The caveat to this is when it comes to considering the effects of wind. The bullet is still actually travelling 1000 yds so you have to adjust for wind over the 1000 yd distance.

I believe you are incorrect. Wind effect is not a component of distance but a component of time of flight. We just use distance as the base because thats how the ballistic calculators show it to us. The calc behind the scenes is based on time of flight. So when shooting an angle like previously mentioned, your wind should be based on the actual distance of 707 yards because thats how long it will take for the bullet to reach the target from a time perspective. i.e. Its the same reason we use the 707 as the distance because that is the amount of time that gravity has to act upon the bullet. Time is also the factor as to how the velocity of the bullet changes.

 

[ShtrRdy]

I'll attach a picture I found online that will help explain. The picture shows an actual distance of 100 yds instead of my example with 1000 yds. As you can see, the bullet will be covering a 100, (1000 in my example), yd distance in which wind can effect it.

 

[flounderv2]

Wind affects based on time of flight not distance... using random numbers here to prove a point. say your bullet takes 3 seconds to to cover 700 yards straight line and 5 seconds to cover 1000 straight line. You shoot the angular distance of 700 because that's the same amount of time the gravity can act on the bullet. Same thing with wind since the bullet will be there in 3 sec not 5. Gravity acts on the bullet for 3 sec not 5 which is why you dial for straight line distance and not the full angle distance.

 

[ShtrRdy]

Wind affects based on time of flight not distance... using random numbers here to prove a point. say your bullet takes 3 seconds to to cover 700 yards straight line and 5 seconds to cover 1000 straight line. You shoot the angular distance of 700 because that's the same amount of time the gravity can act on the bullet. Same thing with wind since the bullet will be there in 3 sec not 5. Gravity acts on the bullet for 3 sec not 5 which is why you dial for straight line distance and not the full angle distance.

I respectfully have to disagree with you. I thought the picture would help show that for an angled shot, the bullet is actually traveling 100 yds, (1000 in my example). That's the distance, (time of flight), the bullet will cover. That's the time over which the bullet can be effected by the wind.

As far as bullet drop due to gravity, we need to use cos(angle) times the true distance to see how far the drop will be. This is the horizontal component of the distance.

 

[flounderv2]

I don't think I'm explaining it well enough. I pinged ml - coder who programs the AB Kestrel to come here and try and help.

 

[goodgorilla]

Wind affects based on time of flight not distance... using random numbers here to prove a point. say your bullet takes 3 seconds to to cover 700 yards straight line and 5 seconds to cover 1000 straight line. You shoot the angular distance of 700 because that's the same amount of time the gravity can act on the bullet. Same thing with wind since the bullet will be there in 3 sec not 5. Gravity acts on the bullet for 3 sec not 5 which is why you dial for straight line distance and not the full angle distance.

I think I am missing the obvious. A 1000 yard bullet going down hill will have more flight time that a 1000 yard target on flat, and much more flight time than an uphill shot? Which would give each shot different wind corrections. How do you adjust your wind corrections for these situations? I'm having physics flashbacks now, I get the feeling that they are all the same flight times.

 

[flounderv2]

No. The flight time for up hill or down hill is the same as long as the angle is the same. But if you lrf an shot uphill it reads longer than the straight line distance.

 

[goodgorilla]

No. The flight time for up hill or down hill is the same as long as the angle is the same. But if you lrf an shot uphill it reads longer than the straight line distance.

I got it, I was trying to delete my old post, but I think it serves a purpose now. Just to make sure I got it right now, you always use the strait line distance for wind correction?

 

[M40_A1]

I don't think I'm explaining it well enough.

That's because you're going to have a tough row to hoe around here to convince us that a bullet adjusts its speed depending on what angle the barrel is when fired. 1000 yards distance is 1000 yards distance, and the time of flight will be (essentially) the same in any case, whether 45-degrees uphill, horizontal, or 45-degrees downhill.

Angles are viewed as having two components- horizontal and vertical. Gravity only acts upon the horizontal component. That is why a bullet traveling 45-degrees to a target at 1000 yards (uphill or downhill) only has an equivalent gravitational effect (drop) as that at 707 yards, as 707 yards is the horizontal component of 1000 yards at 45-degrees.

The time of flight (wind effect) will still be based on the actual travel distance of 1000 yards. The bullet doesn't magically go faster to reach that 1000 yards in the time it would normally take to reach a target at 707 yards.

 

[flounderv2]

Waiting on mil-coder

 

[goodgorilla]

That's because you're going to have a tough row to hoe around here to convince us that a bullet adjusts its speed depending on what angle the barrel is when fired. 1000 yards distance is 1000 yards distance, and the time of flight will be (essentially) the same in any case, whether 45-degrees uphill, horizontal, or 45-degrees downhill.

Angles are viewed as having two components- horizontal and vertical. Gravity only acts upon the horizontal component. That is why a bullet traveling 45-degrees to a target at 1000 yards (uphill or downhill) only has an equivalent gravitational effect (drop) as that at 707 yards, as 707 yards is the horizontal component of 1000 yards at 45-degrees.

The time of flight (wind effect) will still be based on the actual travel distance of 1000 yards. The bullet doesn't magically go faster to reach that 1000 yards in the time it would normally take to reach a target at 707 yards.

What he said could still be true after what you said. He didn't clarify what distance he was talking about. I'm pretty sure he was just saying that you never use the adjusted distance for wind corrections and/or you use the strait line distance for that. The adjusted distance does not reflect the time of flight of the bullet, but the strait line distance does.

 

[flounderv2]

I think we are both right in a way just saying it differently. 1. drop and wind holds are based on time of flight I think we can all agree with that distance is just what we use as a reference. If I shoot at a target straight up 1000 yards away my drop is zero and yes my wind will be for the 1k yards as that's the tof for the bullet to get there. With that being said I'll give you that the wind hold would be based on the distance or tof that the bullet is in the air. Agreed?

 

[Darkside-Six]

Watch this. he explains it very well.

 

[M40_A1]

I think we are both right in a way just saying it differently. 1. drop and wind holds are based on time of flight

YES AND NO! Drop is only based entirely on time of flight if the straight line to target is HORIZONTAL. All other angles have vector components that must be considered.

If I shoot at a target straight up 1000 yards away my drop is zero

But, wait. You just said that drop is determined by time of flight! So the time of flight to a target 1000 yards away, but straight up, is ZERO??? I DON'T THINK SO! The reason a bullet going straight up does not have any "drop" is because THE HORIZONTAL COMPONENT OF A VERTICAL ANGLE IS ZERO.

and yes my wind will be for the 1k yards as that's the tof for the bullet to get there. With that being said I'll give you that the wind hold would be based on the distance or tof that the bullet is in the air. Agreed?

And, yes, I can agree with this part, but it's not what you were saying before, which was the whole basis of your disagreement...

I believe you are incorrect. Wind effect is not a component of distance.....

However, this thread has gone off-topic. I respectfully suggest you open another thread if you need to explore this further.

 

[CoryT]

I suggest you have a look at the Sierra ballistics web article on Inclined fire. The cosine of the angle, as applied to the range is the least accurate method of correction, applying the cosine to the elevation setting is better, but still not really precise.

 

[goodgorilla]

I had some thoughts about the flight time with respect to flight angle. I'm pretty sure if you shoot a bullet strait up in the air say 2k yards, it will take longer than shooting the bullet strait down 2k yards. Ignoring wind resistance on both bullets, the bullet shot strait up will be slowing down at a rate of 9.8m/s (32.15 feet per second) and the bullet shot strait down will not be slowed down.

 

[LRShooter101]

Pandoras Box!

You are really opening a whole can of worms if you want to dig deep into this issue.

For example:
- as the bullet flight path increases or decreases in altitude, it can travel through a completely different set of environmental conditions. Wind (speed & direction) and Density Altitude are two things that can change and impact the bullets flight path. Trying to figure out how much, is pretty much a SWAG IMHO, unless you have your own personal Doppler Radar weather station onsite.

Per above, compensating for the distance/flight time is what most shooters will be able to deal with, but it is not everything that is going on. Inside of 1,000 yards and at minimal altitude changes the other factors can have little to no impact, but ignoring those factors when shooting on a mountainside at extreme ranges can easily lead to a miss.

The more extreme your shooting conditions, the more the "Devil is in the details".

 

[Strykervet]

OK, I've read that when shooting up hill and down hill gravity affects the bullet drop equally.

I'll try to keep this simple, you'll need a working knowledge of trig. Not theoretical, but a working knowledge, how to apply a few basic ideas. Shooter's trig is a few applied ideas vs. university math where you learn every detail.

You want to isolate the cosine element from the trig equations and dial that in. In a nutshell. Uphill and downhill shots include the sine and cosine elements and line of sight is along the hypotenuse, which is longer than the sine or cosine alone and is the square root of the sum of the sine and cosine elements each squared. You need to measure the line of sight to the target, then isolate the cosine element and use that distance to dial in.

The sine component only considers distance in the vertical whereas cosine considers only distance in the horizontal. Since we can eliminate the vertical component as all it does is affect the drop (which will be the same regardless given a particular round) we need only concern ourselves with the cosine element, or the distance to the target assuming there is no elevation.

The cosine element is shorter than line of sight and due to the sine element being a constant, we can make our adjustments using only the cosine measurement. In essence, a shot adjusted using the hypotenuse will be adjusted too long whereas a shot adjusted using only the cosine element will yield a shot spot on.

 

[goodgorilla]

And while everyone is worried about and doing the numbers, the target says I'm out of here.

There's nothing to worry about? So we just use the strait line distance for wind correction? I'm fine with using what works.

I found the equation for the time of flight:
http://en.wikipedia.org/wiki/Projectile_motion

It's near the middle. Looks like a function you need a graphing calculator for. Yeah so, even if you know the time of flight. How would you use that with wind correction? I can see where this is going and it isn't pretty. I don't think I can go further without knowing how the ballistic calculator does it. Or perhaps it don't matter, perhaps all we got to do is feed the machine the variables it wants.

 

[Rthur]

If the bullet travels 1000 yards but the dope is 707 you hold wind for 1000 yrds. The time of flight will be very close to a 1000 yrd flat shoot. Hence the wind hold for 1k. The dope change is a direct result of how far the bullet travels against gravity perpendicular to the source of gravity.


R

 

[M40_A1]

And while everyone is worried about and doing the numbers, the target says I'm out of here.

And while you're trying to get closer, the target says I'm out of here. You're crackin' me up! I guarantee I can "do the numbers" much, much faster than you can get closer!

 

[M40_A1]

I had some thoughts about the flight time with respect to flight angle. I'm pretty sure if you shoot a bullet strait up in the air say 2k yards, it will take longer than shooting the bullet strait down 2k yards. Ignoring wind resistance on both bullets, the bullet shot strait up will be slowing down at a rate of 9.8m/s (32.15 feet per second) and the bullet shot strait down will not be slowed down.

Which really brings us back to the op's question.

 

[Pinecone]

Uphill/downhill ballistics explained:

exterior ballistics

Interesting. I always wondered why the drop would change for the same slant range, as drop is time of flight and gravity (constant).

That link explains the that drop does NOT change, but the relationship between the line of sight and the trajectory DOES change.

 

[goodgorilla]

Interesting. I always wondered why the drop would change for the same slant range, as drop is time of flight and gravity (constant).

That link explains the that drop does NOT change, but the relationship between the line of sight and the trajectory DOES change.

The cosine equation isn't good enough?

edit:
I've read that if your angle of fire is extreme, you have to use an advanced rifleman's rule and change your B.C. to account for the change in altitude. If you don't change your B.C. over a 1000 yard strait line shot, your shot will only be off by like a few inches. The advanced rule is you take your bullet drop for 1000 yards and multiply it by the cos of your firing angle. That number will give you your correct bullet drop, and from there I don't know what to do. I don't know how to use bullet drop in firing solutions yet. Anyhow, if you want to change your B.C. the formula goes:

height = strait line distance in ft * sin (angle)

correction factor = 1 + 1.3 x (10 to the negative fifth power) X height

Corrected B.C. = un-corrected B.C. X correction factor

 

[Killer Spade 13]

Trust me, I know trig and geometrey.
The thing here is the vector of gravity. Gravity is pulling the projectile downwards at 32 ft/sec/sec. If you hold a projectile in you hand an let it go, it falls. That same gravitational force is acting in the same manner as a bullet fired at a downward angle, therefore the velocity of the projectile will not diminish as rapidly as if it were fired in an upward angle.

Yes, this has an affect upon the time of flight, although I'll admit it is functionally insignificant, it has an affect none the less.

Just wondering what the minute difference would be say, at a 1000 m shot on angles of +/- 30 degrees from the horizontal.

 

[ShtrRdy]

Trust me, I know trig and geometrey.
The thing here is the vector of gravity. Gravity is pulling the projectile downwards at 32 ft/sec/sec. If you hold a projectile in you hand an let it go, it falls. That same gravitational force is acting in the same manner as a bullet fired at a downward angle, there for the velocity of the projectile will not diminish as rapidly as if it were fired in an upward angle.

Yes, this has an affect upon the time of flight, although I'll admit it is functionally insignificant, it has an affect none the less.

Just wondering what the minute difference would be say, at a 1000 m shot on angles of +/- 30 degrees from the horizontal.

I would suggest trying a simulation with a Ballistic program.

 

[mark5pt56]

While I have no dog in the pen here, how many actually have the skill and equipment to know the difference?

 

[LRShooter101]

. . . . . how many actually have the skill and equipment to know the difference?

Texas Shooter Nails Target at 3650 Yards with .375 CheyTac « Daily Bulletin

I am not 100% sure on all of the "skill level" details here, but it obviously has to be well beyond the basics of just applying a cosine modifier to your normal DOPE.

Shooting like this is what will be pushing the boundaries of "shooting science".

You can also look at what is going on with Extreme Long Range Hunting https://www.youtube.com/results?search_query=long+range+hunting
Not looking to start a debate on the ethics of long range hunting, but making the point that hunters are routinely making shots well beyond 1,000 yards in extreme conditions (angles, winds, etc).

Obviously there are NOT a lot of shooters who are operating at these extremes, and per my earlier comment, a simple angle cosine modifier will work just fine for most shooters. But for those who are going beyond the "norm", it is going to take way more than a simple math/calculation to make consistent hits based on something other than luck.

 

[Pinecone]

Trust me, I know trig and geometrey.
The thing here is the vector of gravity. Gravity is pulling the projectile downwards at 32 ft/sec/sec. If you hold a projectile in you hand an let it go, it falls. That same gravitational force is acting in the same manner as a bullet fired at a downward angle, therefore the velocity of the projectile will not diminish as rapidly as if it were fired in an upward angle.

Yes, this has an affect upon the time of flight, although I'll admit it is functionally insignificant, it has an affect none the less.

Just wondering what the minute difference would be say, at a 1000 m shot on angles of +/- 30 degrees from the horizontal.

Did you read the link?

The drop remains the same, based on slant range. BUT, where the bullet is at that range, versus the line of sight is different.

 

[Sterling Shooter]

The USAMU has a good video out on this subject, search: USAMU Praslick on angle shooting.

 

[NevadaZielmeister]

Trust me, I know trig and geometrey.
The thing here is the vector of gravity. Gravity is pulling the projectile downwards at 32 ft/sec/sec. If you hold a projectile in you hand an let it go, it falls. That same gravitational force is acting in the same manner as a bullet fired at a downward angle, therefore the velocity of the projectile will not diminish as rapidly as if it were fired in an upward angle.

Yes, this has an affect upon the time of flight, although I'll admit it is functionally insignificant, it has an affect none the less.

Just wondering what the minute difference would be say, at a 1000 m shot on angles of +/- 30 degrees from the horizontal.

So the three most important factors affecting bullet path:

1.) Gravity - by a very large margin.
2.) Atmospherics - a much lesser effect on the bullet path.
3.) Rotation of the earth - very minimal, maybe 1-2 inches per 1000 yards.

When you take your example of 1000 yards at +/- 30 degrees means that you have a ballistic range of 700 yards. So you are asking then what the effect would be at the last 300 yards between the atmospheric and gravity. Very very little, if measurable. Yes, the bullet travels through the atmosphere an extra 300 yards, but when compare to the gravity, the effect is very very minimal.

To further illustrate: Using my TRUSTED Kestrel with Applied Ballistics, using a .308 155 grain scenar with typical atmospherics here in Nevada, I used both scenarios you describe, 1000 yards out, one at +30 degrees and one at -30 degrees:

+30 degrees has an elevation call of 7.62 milliradians and wind holds of 1.00 and 2.25 for 5mph and 10mph 3/9 o'clock wind ranges, respectively.
-30 degrees has an elevation call of 7.56 milliradians and wind holds of 1.00 and 2.27 for 5mph and 10 mph 3/9 o'clock wind ranges, respectively.

So that means you will see a difference of .06 milliradians elevation difference and .02 wind hold difference. In real terms, that equates to 2.1 inches of elevation and .72 inches of wind hold at 1000 yards. That is VERY minor and not even worth worrying about on most applications.

 

[goodgorilla]

Texas Shooter Nails Target at 3650 Yards with .375 CheyTac « Daily Bulletin

I am not 100% sure on all of the "skill level" details here, but it obviously has to be well beyond the basics of just applying a cosine modifier to your normal DOPE.

Shooting like this is what will be pushing the boundaries of "shooting science".

You can also look at what is going on with Extreme Long Range Hunting https://www.youtube.com/results?search_query=long+range+hunting
Not looking to start a debate on the ethics of long range hunting, but making the point that hunters are routinely making shots well beyond 1,000 yards in extreme conditions (angles, winds, etc).

Obviously there are NOT a lot of shooters who are operating at these extremes, and per my earlier comment, a simple angle cosine modifier will work just fine for most shooters. But for those who are going beyond the "norm", it is going to take way more than a simple math/calculation to make consistent hits based on something other than luck.

He said his kestrel was doing the math. The more I read, the more it seems like I should use ballistic programs and print outs.

 

[LRShooter101]

So the three most important factors affecting bullet path:

1.) Gravity - by a very large margin.
2.) Atmospherics - a much lesser effect on the bullet path.
3.) Rotation of the earth - very minimal, maybe 1-2 inches per 1000 yards.

When you take your example of 1000 yards at +/- 30 degrees means that you have a ballistic range of 700 yards. So you are asking then what the effect would be at the last 300 yards between the atmospheric and gravity. Very very little, if measurable. Yes, the bullet travels through the atmosphere an extra 300 yards, but when compare to the gravity, the effect is very very minimal.

To further illustrate: Using my TRUSTED Kestrel with Applied Ballistics, using a .308 155 grain scenar with typical atmospherics here in Nevada, I used both scenarios you describe, 1000 yards out, one at +30 degrees and one at -30 degrees:

+30 degrees has an elevation call of 7.62 milliradians and wind holds of 1.00 and 2.25 for 5mph and 10mph 3/9 o'clock wind ranges, respectively.
-30 degrees has an elevation call of 7.56 milliradians and wind holds of 1.00 and 2.27 for 5mph and 10 mph 3/9 o'clock wind ranges, respectively.

So that means you will see a difference of .06 milliradians elevation difference and .02 wind hold difference. In real terms, that equates to 2.1 inches of elevation and .72 inches of wind hold at 1000 yards. That is VERY minor and not even worth worrying about on most applications.

Issue here is ASSUMING that the environmental conditions are the same along the flight path and not just the difference in terms of corrected or uncorrected distance. With square flat ranges, you have a much better chance of that being the case. Shooting at angles which implies some form of drastic change in terrain, also usually implies a drastic change in environmental conditions especially in terms of wind speed & direction.


(pardon my grade school graphics!)

Not saying that Gravity is not the major player, but in many instances the environmental factors can also be a deciding factor, how much depends on where you are shooting?

Not trying to sidetrack this, but you have to watch that you are not trying to apply a "flat square range mentality" to the real world which is angle shooting, especially if you are talking over long distances.

As a LE Sniper, this also get interesting when you start talking about shooting from structures in urban areas, and everything that can come into play there.

 

[NevadaZielmeister]

LR,

I agree with everything that you say, completely. You are correct, I did make an assumption regarding the conditions being consistent. I was just trying to get to the OP's question regarding the angle difference and keeping all other variables constant.

Good job taking this to a whole new level, which supports my point even more, that with all of the other factors to consider that I left constant, the differences are MINIMAL at best regarding the difference in angle changes.

We could also get into mirage effectiveness between ridges, aerodynamic jump in the bullet, etc. Good discussion LR, thank you.

 

[M40_A1]

The op was talking about the effect of gravity when shooting uphill versus shooting downhill. Shooting uphill, gravity will be slowing the bullet down more quickly than when shooting downhill where gravity aids in maintaining velocity. But here's the big secret no one knows about. Although the earth's gravity works against the bullet being shot uphill, the closer the bullet is to the sun, the more the sun's gravitational field will pull the bullet up. Therefore, the gravity from the earth and the gravity from the sun counteract eachother, and there is no difference whether shooting uphill or downhill. But, this only applies at solar noon. You have to take the cosine of the angle of the sun, subtracted from the tangent of the shot angle, and added to the cubed root of the sine of the magnetic azimuth for any other time of day. Don't forget to use negative values for the angle of the sun at night.

 

[mark5pt56]

Pretty amazing that there are so many variables involved. Very interesting points to learn from.

 

[Sterling Shooter]

Pretty amazing that there are so many variables involved. Very interesting points to learn from.

There does seem to be a lot to learn for a shooter who wants to know everything there is to know about good shooting. Countering for wind and weather effects, as well as slope are no doubt important . Thing is you don't need to know much about the effects of slope shooting to get a good hit in most any scenario. Earlier, I posted that the USAMU has a shooting tip video on angle shooting. This video provides enough instruction on the matter for most anyone to master slope shooting without having to go for more degrees on the subject.

 

[LRShooter101]

Sorry, once again, not trying to muddy the waters,

The OP's questions in regards to angle shooting was a "Distance / Gravity / Time of Flight" based question, and that is the primary foundation/fundamental of angle shooting.

Per many excellent responses above, that aspect and how it can be dealt with are all well explained.

That being the case, I have seen more shots missed in the "real world of angle shooting" because of other environmental factors which I also tried to cover.

External Ballistics covers a broad range of variables, and the bottom line is you can't afford to ignore any single component. Where I frequently see newer shooters struggling is when they make the transition from a "square flat range" into the "real world" and they find themselves dealing with variables that they had never previously dealt with (like angle & cosines), or are having to deal with variables in a different manner (like multiple wind speeds & directions or varying atmospheric conditions).


Looking at Shot 1 & Shot 2 above, they could both be the exact same shot in terms of Distance & Angle, however if the conditions are significantly different and it is a long range shot, you would need two different sets of corrections in order to make the shot because of the different environmental conditions involved in each shot.

Many shooters are familiar with compensating for different environmental conditions, for example starting off shooting early in the morning (cool/thin/dry) versus shooting later in the afternoon (hot/dense/humid). What many shooters will not recognize, is that you can have both of these conditions at the same time in an angle shooting scenario due to the changes in altitude and the impacts of the topography.

Making a first round hit in the situations above can obviously be very challenging because determining all of the conditions along the bullet's flight path can be almost impossible. The key is when the first round goes long or comes up short, that you can figure out what component of External Ballistics is making that happen? If all you focus on is Angle & Corrected Distance, then you may well be missing the real cause like a wind conditions running up the face of the slope causing lift or a drastic change in other environmental conditions.

If you can rapid fire your shots and call your misses, you can always just correct off of your previous shot. However if you need a first round hit, or you can't call your misses, then being able to read the variables and adjusting as needed becomes critical. Also knowing what variables to watch/consider for changes between your shots can also be critical.

Apologies again for the sidetrack, hopefully there was some benefit to it, and it didn't just derail the topic.

 

[goodgorilla]

I didn't see anyone else mention that air resistance has more of an affect on a bullet than gravity. The air resistance gets thinner as you shoot up, and thicker as you shoot down. So if gravity is slowing down the bullet while the air is getting thinner, it's not so different from the bullet not fighting gravity while getting into thicker air. Some other things to consider: wind gradient, and your physical/equipment ability to shoot high angles.

 

[Ledzep]

For example, consider a 700yd (shooter to target distance) 45 degree shot. This is some pretty serious incline. I've yet to shoot over 25 degrees. Some sort of crazy mountain shooting. I'm going to use my .260 data. 140 amax @ 2740fps.

Shooting up hill:
Distance to target- 700yd (LRF the target)
Angle up 45 degrees
Elevation difference from you to the target- 495 yd (1485 ft)
Gravity effect on the bullet- 495 yd

So at 700yd, what is the difference in your dope for 1500ft? For me, about .1 mil. If I was going to go at it, knowing that there was a 1485 ft difference in elevation between me and my target, I would take the data from the halfway point (my elevation + 743ft). The net effect of air resistance change is less than .1 mil. Almost a wash IMO, unless you're doing ELR stuff.

Also, if I use simply the flat-shooting range of 495yd, I need to use 2.7 mils to get there. However, if I shoot 45 degrees [MENTION=100785]700[/MENTION]yd (495yd gravity pull), I need 3.0 mils.

Why? Because gravity is only pulling for 495 yd, but the bullet is still pushing through 700yd of air, and has a 700yd-long flight time.

Now compare to down hill, -45 degrees @ 700yd. Gravity still pulling 495yd, this time partially "helping" the bullet along.

495 flat-line remains 2.7 mils, but 700yd @ -45degrees is 2.9 mils. Again, the 1500ft change in altitude (air density) is going to affect it less than .1 mils.

So 2.9 and change up and 2.9 and change down (air density helps shooting up hill, hurts downhill, gravity hurts uphill, helps downhill).

Playing with some numbers on JBM, it would appear that this rule of thumb works fairly well (in my limited number playing). When shooting at an angle, take the flat-line dope for the gravity-span of your up/down angle shot, then multiply your DOPE by 110%.

Maybe make a chart starting at 20 degrees and do every 10 degrees to 60 for a coefficient to multiply your LRF-range (hypotenuse) by to get gravity-range (base or adjacent), then take your flat line dope and multiply drop/correction in Mil/MOA by 1.1. That will get you within .1 mil.

This is assuming you want to do it electronics-free. Otherwise just plug the shit into a ballistic calculator.

 

[NevadaZielmeister]

Shooting at 45 degrees out to 700 plus yards. Sounds like Himalayan combat to me.. or Afghanistan.

 

[Ledzep]

Yeah I tried to push the limits of what anyone can realistically expect. I'm sure someone out there has done more "extreme" in both angle and range, but I've shot quite a bit in mountainous areas and like I said only ever approached 30 degrees, though I would love to get some more experience at higher angles.

Anyway my main point was that the change in air density and the effect of gravity nearly cancel each other out, to the extent that it's negligible to the shooter. I agree with previous posts that your environmental effects (updrafts, boils, wind gradient, eddies etc.) will probably have more effect on your POI than will the correlation between air density change and gravity's pull.

edit to add: And that's just one example with MY data. Take a couple hours, do some trig (A^2 + B^2= C^2, and SOH CAH TOA), Get on JBM and play with temps and pressure, and range and angle, up and down hill, compare it to the flat-line distance of gravity etc. etc. It doesn't take too long to notice patterns that can be helpful to generating your own "rule of thumb" that you can go out in the field and test.

 

[ptosis]

Some time ago I have put together a series of articles on this very subject.
Here:
1. Basic physics (+ some definitions)
2. The whole series as one page
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EDIT: oops, sorry, I have misread the original post. The links above don't actually have the answer (heuristic to estimate difference between uphill and downhill).

But, as others have already suggested above, it is relatively easy to come up with by playing with a decent ballistic calculator. (My guess would be: roughly proportional to ToF, heavily dependent on calibre).

This being said, I can see little practical value in such heuristics -- if you are using one, that means that a ballistic calc is not there to help, that means that you have to rely on approximations/heuristics with a much larger margin of error than the difference between uphill and downhill at reasonable angles and distances.

 

[LRShooter101]

https://www.youtube.com/watch?v=riAqarCH9sI&list=PLDF39D15BC04BFB86#t=254

Another one, from the Long Range Hunting perspective.