Firing Down/Up Slopes

[Whisker]

I couldn't find a section on Slope Adjustment except for in the RBC POI... Thought it should be clarified and discussed.

I'm trying to determine the correct and simple method for firing up or down slopes.  I have come accross a couple things.

First, a general rule.  

For every 10 degrees of slope, subtract 1 MOA per 100 yards

So say a target appears to be at 300 and on a 20 degree slope. 

I would subtract 6 moa, correct?

This seems excessive when considering this chart:

Slope Adjustment Formula

Range in Meters X Cosine of Angle= Modified Range
Angle Cosine/Compensation Constants
05 degree= .99  10 degree= .98  15 degree= .96  20 degree= .94  25 degree= .91
30 degree= .87  35 degree= .82  40 degree= .77  45 degree= .70  50 degree= .64
55 degree= .57  60 degree= .50  65 degree= .42  70 degree= .34  75 degree= .26
80 degree= .17  85 degree=.09   90 degree= .00

So, a target that appears to be at 300m target up a 20 degree slope would actually be 300(m)x.94=282m  So adjust for a 18m "closer" target.  Can that really be 6moa as calculated by the first "slope rule"?

Which is correct?

Maybe I'm using the bottom chart wrong.  How is it used?

[Fred]

   Whisker, when I long ago "checked this out", there were one conclusion I came to: Unless the target is 300 yards or more away, AND the slope is 45 degrees or STEEPER, you simply take the shot with normal sight pic.

    If the distance is more than 300 and the slope is steeper than 45 degrees, I would aim low on the target, as it doesn't matter if the slope is uphill or down, the bullet will strike high.

    Only in that 'corner' - steeper than 45 and beyond 300 - do you have to take the slope into account. (IIRC, at 300 yards a 45-degree slope made a difference in bullet strike of ONE MOA - not exactly anything to get excited about...)

    And I suspect aiming a half-target high at 500 would pretty well take care of things at that distance, although I'd like to see someone on here post what the calculated effect of slope at 500 would be to answer the question: "how much slope does it take to make a rifleman need to compensate for it on a 4 MOA target at 500 yards?"

     Therefore, for practical "rifleman" purposes, you can ignore the issue entirely unless you are dealing with a really strong steep slope on a target beyond 300 yards.

    There's a lot of things targets shooters have to fool with - after all, they are seeking 1 MOA or better - that 4 MOA riflemen don't need to worry about, unless they are persnickity: light, humidity, temp, etc.

[Spanner]

Whisker:

Fred is correct; for 30 cal the combination of both distance and slant angle being large enough for a need to whip out the tables tends to be rare.

When it isn't rare, you still have the situation that the "modified range" argument is based on bad physics (it isn't correct).  It turns out that the "rule of thumb" is straightforward, but requires knowing an extra thing or two about your rifle: the click-setting when the sight axis and barrel axis are parallel, and the sight offset. 

I've been meaning to typeset & post the "corrected" physics since last Fall, but didn't think there would be much interest.  I guess maybe I should stop procrastinating and just do it.

The situation where slant-angle adjustments would be fun to actually use is with a 22LR squirrel gun, because the bullet drop can be largish at shortish distances.

[staplegund]

FWIW, the trajectory calculator online at http://www.jbmballistics.com/cgi-bin/jbmtraj-5.0.cgi was adapted from a ballistics program developed by Ballistics Research Lab (reference:  "Mc Drag" - A Computer Program for Estimating the Drag Coefficients of Projectiles,
Robert L. McCoy, Technical Report ARBRL-TR-02293, February 1981, [ADA098110] -- More on estimating the drag coefficient for boattail and flat base projectiles. Includes a code listing and sample runs.  "Mc Traj" is the trajectory program developed by the same author, and is downloadable.).
According to the calculator I used, set for sight height of 1.5", 150gr .308 fmjbt at 2750fps, my elev of 4440, 29.92" Hg pressure, 59 degrees and 20% RH and a 45 degree slope, if the rifle is sighted in for 500y on flat ground it will strike 21.4" high at 500 slant range.  It was right on at 650y slant range at that slope.  Changing the zero range to 300, a 45 deg. slope caused the strike to be 7" high at 300, right on at 400, and 11.5" low at 500.  I didn't check for the difference between up and downslope, but it will figure it if you want (If downslope, the strike is only .2" higher than upslope at 500-650y).  There's actually more than one program on his site(there are several for different things), and he includes a bibliography, downloads, and much more.  Enjoy!  

[Spanner]

This should give an idea for when the slant angle adjustments are important.  Better yet, when it isn't important.  

These are the MOA=click come-backs for the (3,3,4,4,...) M14.



This is the same chart, but without the rounding down:



The "modified range" calculations that you see touted are a bit of an old-wives-tale.

I'll post the theory etc. on this when I get a little more time.

EDIT: These are "actual range" distances on the charts, not horizontal distance.

[Big H]

This should give an idea for when the slant angle adjustments are important.  Better yet, when it isn't important.   

These are the MOA=click come-backs for the (3,3,4,4,...) M14.

When using Spanner's chart, please use common sense:
DO NOT AIM STRAIGHT UP AT 90 DEGREES! 
What goes up must come down!
The consequences could be harmful or fatal!

[Spanner]

DO NOT AIM STRAIGHT UP AT 90 DEGREES! 
What goes up must come down!
The consequences could be harmful or fatal!

[jollynator]

......

[Nickle]

Funny how people complicate this.

The correct term is "slant range". I see someone used it already.

See, the bullet doesn't give two hoots what angle it's flying.

It never was about the angle, or the actual distance to the target.

It's about the exact horizontal distance to the target. The bullet drops based on that and that alone. X amount for Y amount of horizontal distance. PERIOD!

You calculate that, and use your usual come ups.

All that being said, unless it's an awfully STEEP angle, or you're out past 500 yards, or it's an awfully small target, it really isn't that important to correct. Make the quick and dirty compensation, and call it good, just like wind.

Snipers correct for this, not regular shooters.

[Spanner]

Funny how people complicate this.

See, the bullet doesn't give two hoots what angle it's flying.

It never was about the angle, or the actual distance to the target.

It's about the exact horizontal distance to the target. The bullet drops based on that and that alone. X amount for Y amount of horizontal distance. PERIOD!

That is incorrect.  Yes, I know that is what is in the manuals, and in the POI, but it is incorrect.

[Big H]

Funny how people complicate this.

The correct term is "slant range". I see someone used it already.

See, the bullet doesn't give two hoots what angle it's flying.

It never was about the angle, or the actual distance to the target.

It's about the exact horizontal distance to the target. The bullet drops based on that and that alone. X amount for Y amount of horizontal distance. PERIOD!

You calculate that, and use your usual come ups.

All that being said, unless it's an awfully STEEP angle, or you're out past 500 yards, or it's an awfully small target, it really isn't that important to correct. Make the quick and dirty compensation, and call it good, just like wind.

Snipers correct for this, not regular shooters.

That is the quick-and-dirty Rifleman's Rule, which is usually a reasonable approximation for 4 MOA shooting within the rifleman's quarter mile.

There is also the Improved Rifleman's Rule and the Sierra Rule, each progressively more complicated and more accurate. This article explains in more detail for those interested, with some examples.

http://www.exteriorballistics.com/ebexplained/article1.html

[TruckinMike]

This link will answer all of your questions. Have fun trying out the trajectory equations. Click here... http://hyperphysics.phy-astr.gsu.edu/Hbase/traj.html.

TMike



PS- Hi everybody

[Spanner]

One of the most interesting things I've seen in a long time is the wikipedia page for Rifleman's Rule.  I'm not sure if it is a hoax or not.

Big_H, I wish I had looked at that Sierra page before I rushed to make these pictures... I wouldn't have rushed.  But I think these will be easier to digest, so I'm gonna post them.

I'm really glad that everyone has a teachable attitude and is willing to help make Appleseed Instructors "the finest rifle marksmanship Instructors on the planet" instead of pouncing on them with a bunch of nonsense.  That would just be really sad.    






EDIT:  http://hyperphysics.phy-astr.gsu.edu/Hbase/traj.html i think is TMike's link.  (Hi TruckinMike!)

EDIT: fix the x/A typo to A/x, and Big_H's catch.

[Big H]

But I think these will be easier to digest, so I'm gonna post them.

You may want to relabel your first diagram, when alpha=0, the sight axis should be the horizontal black line pointed at the POA and the bore axis should be the brown line pointed upward. 

[didactic]

Those vector diagrams are really really close to right, but I don't think they account for the effect of slightly adjusted velocity due to climbing or descending (converting kinetic into potential energy).

The "horizontal distance" rule is much easier to use in the field, and is so doggone close to perfectly correct that it's more accurate than even a match rifle's shot-to-shot accuracy, so it's more than good enough to go with.

The quick-and-dirty method, ignore it inside of 300 yards and less than 45 degrees elevation, and adjust by a minute of angle if it's over either of those, is accurate enough to use in almost all situations with a 2-moa rifle.

So that's the practicality.  But it sure is an interesting subject to bat around, isn't it?

[TruckinMike]

edit

[Spanner]

You may want to relabel your first diagram, when alpha=0, the sight axis should be the horizontal black line pointed at the POA and the bore axis should be the brown line pointed upward. 

You are right.  Thanks!

[Another D.O.M.]

Great Job Spanner...  WoW!

It almost says it all. But where is your windage component...   



TMike

Guys - my brain is sore just from thinking about these calculations.  I must be getting old - I used to love math and physics.

     On the other hand, maybe I just need to get back into the habit...

[Spanner]

Those vector diagrams are really really close to right, but I don't think they account for the effect of slightly adjusted velocity due to climbing or descending (converting kinetic into potential energy).

The "horizontal distance" rule is much easier to use in the field, and is so doggone close to perfectly correct that it's more accurate than even a match rifle's shot-to-shot accuracy, so it's more than good enough to go with.

The quick-and-dirty method, ignore it inside of 300 yards and less than 45 degrees elevation, and adjust by a minute of angle if it's over either of those, is accurate enough to use in almost all situations with a 2-moa rifle.

So that's the practicality.  But it sure is an interesting subject to bat around, isn't it?

Fred already stated the practical usage.  My first post was to show that there are few situations where you need to make an adjustment, but where those situations do occur, if one is so "inclined".

On the other hand, I remember the first time as a student that I saw the slant angle taught at an Appleseed, and thinking "good grief, that doesn't make physical sense at all."  I didn't walk away disgusted or anything  , but... It got me thinking.

And then Big_H comes up with that Sierra link...

Yeah, it's fun to kick this stuff around.  The reason I put this off for so long is that the errors in the "slant range" version (I disagree with using that term, because it refers to a quantity that doesn't even appear in the analysis... but that's another story) get interesting as bullet drop increases but I didn't want to compute a table of come-downs based on that method for comparison to the method above.

The next question that one needs to ask (in order to start the next flame war   ) is why the "slant range" method doesn't work for larger angles, and why I published come-backs for up to 90 degrees.  

[staplegund]

Thanks for the effort in analyzing and putting it into graphical content here, guys.  Note to viewers:  FWIW, Sierra's results written up by Mr. McDonald are well worth a look, particularly if you will be involved with doing any military AS events for advanced shooters.  (whether you call it distance to target or slant range, you still have to know it)  One difference with Sierra:  In today's mountain warfare you can't dismiss the military shooter's chances of seeing angles over 30 deg. at long range over 500m. 
Here's the Sierra link again: 
http://www.exteriorballistics.com/ebexplained/article1.html

JBM's free trajectory calculator link again: http://www.jbmballistics.com/cgi-bin/jbmtraj-5.0.cgi

[Another D.O.M.]

Thanks for the effort in analyzing and putting it into graphical content here, guys. 

Yes - thank you all for this information.  I'll admit the subject matter hasn't been on my Christmas List of late, but now that it has been broached, I'm intrigued.  After all, shooting >210 is just the beginning, isn't it...

[Nickle]

Well, there's a lot of stuff here that may be true, but complicated.

Now, the bottom line is what I mentioned, whether right or wrong (it isn't 100% right) is not relevant.

It's close enough. http://www.snipercountry.com/SlopeShooting/shoot_on_slope_draft.pdf gives some thoughts on it, and it looks like the author put some effort into checking it.

You'll find the difference falls withing the tolerances of the ammo and rifle you're using. So you all know, I own exactly ONE rifle right now that could tell the difference. It's a .308 on a Rem 600, 24" Hart barrel, McMillan stock, and shoots under .5 MOA with better than match grade ammo. My M1, M14, M4 clone and PSL don't shoot well enough to take advantage of the extra work.



Now, to throw a damper on all this.

1. Don't let me catch you overcomplicating this to the shooters at an Appleseed. They need to learn how to shoot a Rack Grade 4 MOA Battle Rifle out to 500 yards. That's it. You can mention there is a complicated method using trigonmetry to calculate it, but the rule of thumb is close enough. We do the same thing about wind doping up my way, tell them there's a complicated method, and that the rule of thumb is close enough. We're teaching people to be Riflemen, not Snipers.

2. If you have time enough to discuss this kind of stuff, I think you might have enough time to spare to do more to fill some firing lines at Appleseeds near you. (In other words, SOMSOM, this is mission drift.)

[Spanner]

1. Don't let me catch you overcomplicating this to the shooters at an Appleseed. They need to learn how to shoot a Rack Grade 4 MOA Battle Rifle out to 500 yards. That's it.

Amen. 

2. If you have time enough to discuss this kind of stuff, I think you might have enough time to spare to do more to fill some firing lines at Appleseeds near you. (In other words, SOMSOM, this is mission drift.)

You had me right up to here, Cardinal.  How about a little less popery?    

[Nickle]

No harm, no foul yet, but so we all know, a long discussion on a subject like this has devolved into more than it should be before (40+ pages on how to tart up a 10/22 to use as a trainer is an example). Just trying to keep it from ending up the same way. 

Not popery, just a friendly reminder that we have lots to do and a short time to get it done in. 

[Spanner]

 
I just bought the Sierra Reloading manual, 5th edition, © 2003.  Starting page 1045, section 3.3 "Effects of Shooting Uphill or Downhill" confirms reply #12 above (see figure 3.3-1 on page 1048) except that it doesn't include the very small term due to sight height.  It's a pretty good discussion: almost six pages.