Effects of Rifle Canting on LR Accuracy

[Brent]

I have been looking at the effects in great detail today, and they are most dramatic to say the very least.

For the example I'm using a bullet with a G1 BC of .588 at 3100 fps at 300' ASL, 59 deg F, 29.53 BP.

With only 6 degrees of cant, which is only 1 minute on a clock face, at 100 yds it will cause less than .1 MOA POI divergance from POA "with a 100 yard zero".

Now, here's where things get worse, much worse I might add, and I hadn't really thought of it until I stumbled upon it when I moved my 100 yd zero out to 750 yds and noticed the chart change by "many, many" inches when I zeroed the wind out and typed in 6 degrees of cant for kicks and giggles. After all, I was looking at 1.0 inch of error at 1000 yards when I was looking at the cant effect on the chart with the 100yd zero, not bad I thought, even though I'd have been holding over some 241" unless I rezeroed for a 1000yd shot. After rezeroing it to 1000yds, man did the cant induced error jump up!! Now at 1000 yards it was 28", up from an inch!

Now these are pretty small numbers you might say.... Well, lets put it in perspective a bit more and see just how significant it really is.

First, I'll presume without a bubble level, we could realistically be maybe + or - 12 degrees off of of vertical, or canting a couple of minutes off to either side, maybe even more, especially if on a hill or without some sort of visual frame of referance. I do a pretty good job by eyeball at keeping real close to level, and also leveling my scopes on the rifle initially (which is just as important), so I never figured I was off much.... BUT

At 1000 yards, with 12 degrees of left cant (2 minutes till

) the program says POI be 56.47" or 5.39 MOA off to the right, and 2.08" or .20 MOA low!

Now them numbers are pretty darn significant! 5.39 MOA off on the horizontal is insane! This isn't even mentioning the wind either...

The same 12 degrees of cant at a mere 500 yards is going to still kill you by 10.70" or 2.04 MOA on the horizontal, still nothing to blow off.

Now, you can see that is close to 1" off for every degree with a 500yd zero, and 4.7" per degree for a 1000 yard zero. With 360 degrees to a circle, a few degrees of cant could easily go unnoticed.

Thought I'd share with you what really kind of surprized me, I really thought I'd looked at it closer along time ago... I seen really small error numbers and basically discounted it as a minor effect out to 800 yards or so.

A side note. Who knows anything about laser printing a reticle on overhead projector type plastic film, cutting the top half of the reticle off, leaving a half moon type piece to tape to the lower half of the scopes objective bell away from the glass and using it to read mirrage?

I'm told the European sniper/tactical competition teams are using it in place of other methods we all know about, and it works much better, as I'm told they're winning all the time with it now?

 

[Dave King]

Let me think on this for a little while...something seems out-of-place.

Couple questions for clarification.

1. Are you speaking of rifle cant or scope mounting cant? IAW Does the scope track true on elevation or is it inducing windage error because of scope mounting cant?

From my testing in the field I believe that the maximum linear cant error at 100 yards (with a 100 yard zero) will be in the area of 3.5 (call it ~ MOA as were talking of 100 yards) inches of vertical displacement and about an equal amout of horizonal displacement. This would be with a 90 degree cant on the rifle. As I see it there can be no scope mounting cant error at the "base zero" range (100 yards for my rifles).

I'll get back to this thread in a little bit.

/r

 

[Brent]

This is zeroed at 1000 yards, then 12 degrees of cant were added to see its effects. As you can see, it altered the zero range by 5yds also.

CALIBER: 300 Ultra Mag
MUZZLE VELOCITY: 3100 fps
BULLET WEIGHT: 200 gr.
BALLISTIC COEFFICIENT: 0.588
SIGHT HT.: 1.76 in. (1.8"/12°)
ZEROED AT: 995 Yds.
INCLINE ANGLE: 0 deg.
WIND: 0 mph
STANDING TARGET
ATMOSPHERE: Std. 300 ft.
59° F./300 ft./29.53 in. HG/78% R.H.
'G1' STANDARD FLAT BASE

Range- Vel.- Energy- Drop- Path---- Defl.- Time- Lead-
Yards- fps- Ft.Lbs.- Inches- Inches- Inches- Sec.- Inches-

000 3100 4268 0.00 -1.76 -0.37 0.000 0.0

100 2934 3822 1.88 24.00 5.31 0.099 0.0

200 2774 3417 7.79 45.72 10.99 0.205 0.0

300 2620 3047 18.23 62.91 16.68 0.316 0.0

400 2471 2710 33.74 75.04 22.36 0.434 0.0

500 2326 2403 54.95 81.46 28.05 0.559 0.0

600 2187 2124 82.60 81.45 33.73 0.692 0.0

700 2052 1870 117.52 74.17 39.42 0.834 0.0

800 1922 1641 160.70 58.62 45.10 0.985 0.0

900 1798 1436 213.30 33.65 50.79 1.146 0.0

1000 1680 1253 276.67 -2.08 56.47 1.319 0.0

TRAJECTORY CROSSES LINE OF SIGHT AT 6.4 & 995 yds.
PATH IS 82.31 IN. OVER LINE OF SIGHT AT 551.8 yds.


Testing to see how this chart posts.

Dave,
you're right. I'm refering to actual rifle canting, scope cant when mounting will also have an effect when dialing out to a farther range, bullet deflection just is not the same amount as canting the rifle for the same degree of cant... or is it?

The RSI Shooting Lab program predicts "rifle cant", with a properly aligned scope, at what ever the range, only now you just tell it how much the rifle is canted. The program will calculate the cant in the "deflection" column, adding or detracting from the wind deflection value, if wind is also entered. For this chart, wind is set to zero and cant is the total deflection cause. Canting is entered - for left cant, + for right cant.

A 12 degree cant error in the mounting of the scope would be relative to the range it was zeroed at, and error would only begin to increase with distance beyond that if the rifle is level and if elevation setting is adjusted and the only cause for it... effective windage would be changed from the vertical adjustment by an amount relative to the cant angle in the scope. Vertical MOA calibration would, at some point, be noticably affected as the adjustment isn't perfectly vertical anymore, and has some hoizontal movement.

Lets assume the scope is mounted perfectly, with the vertical hair intersecting the bore line and just look at the rifle canting effect, I'll have to think a bit more on the scope canting and how you'd figure that closely. Dave, any ideas?

I'm fixing to look at a 175gr SMK at 2600 fps, G1 BC of .505 and get back to this thread. I know you're familiar with it well. At 100 yards, canting over the rifle 90 degrees error, horizontal deflection should be equal to the bullet drop plus the scope height in inches, vertical drop would be actual for a 100yd shot... if the gun's perfectly zeroed at 100 yards.

Back in a few...


Here's another chart, same as above only with a 100 yard zero, same 12 degrees cant.


CALIBER: 300 Ultra Mag
MUZZLE VELOCITY: 3100 fps
BULLET WEIGHT: 200 gr.
BALLISTIC COEFFICIENT: 0.588
SIGHT HT.: 1.76 in. (1.8"/12°)
ZEROED AT: 103.4 Yds.
INCLINE ANGLE: 0 deg.
WIND: 0 mph
STANDING TARGET
ATMOSPHERE: Std. 300 ft.
59° F./300 ft./29.53 in. HG/78% R.H.
'G1' STANDARD FLAT BASE

Range- Vel.- Energy- Drop- Path---- Defl.--- Time- Lead-
Yards- fps- Ft.Lbs.- Inches- Inches- Inches- Sec.- Inches-

000 3100 4268 0.00 -1.76 -0.37 0.000 0.0

100 2934 3823 1.88 0.01 -0.06 0.099 0.0

200 2774 3417 7.79 -2.27 0.25 0.205 0.0

300 2620 3047 18.23 -9.07 0.56 0.316 0.0

400 2471 2710 33.74 -20.93 0.87 0.434 0.0

500 2326 2403 54.95 -38.50 1.18 0.559 0.0

600 2187 2124 82.59 -62.50 1.49 0.692 0.0

700 2052 1870 117.51 -93.78 1.80 0.834 0.0

800 1922 1641 160.70 -133.32 2.11 0.985 0.0

900 1798 1436 213.30 -182.29 2.42 1.146 0.0

1000 1679 1253 276.68 -242.02 2.73 1.319 0.0


VITAL ZONE = 0 IN. POINT BLANK RANGE = 105.7 yds.
TRAJECTORY CROSSES LINE OF SIGHT AT 90 & 103.4 yds.
PATH IS 0.01 IN. OVER LINE OF SIGHT AT 96.9 yds.

[ 09-25-2003: Message edited by: Brent ]

[ 09-25-2003: Message edited by: Brent ]

[ 09-25-2003: Message edited by: Brent ]

 

[Brent]

Here's a chart from 0-100yds with the rifle held with 90 degrees of cant, 308 win 175gr SMK at 2600 fps.

CALIBER: 308 Win
MUZZLE VELOCITY: 2600 fps
BULLET WEIGHT: 175 gr.
BALLISTIC COEFFICIENT: 0.505
SIGHT HT.: 0 in. (1.8"/90°) -Note the scope is level with the bore and is at 0 in. with the 1.8" hight at 90 degrees.

ZEROED AT: 100 Yds.
INCLINE ANGLE: 0 deg.
WIND: 0 mph
STANDING TARGET
ATMOSPHERE: Std. 300 ft.
59° F./300 ft./29.53 in. HG/78% R.H.
'G1' STANDARD FLAT BASE

Range- Vel.- Energy- Drop- Path---- Defl.--- Time- Lead-
Yards- fps- Ft.Lbs.- Inches- Inches- Inches- Sec.- Inches-

00 2600 2627 0.00 0.00 -1.80 0.000 0.0

10 2582 2591 0.03 -0.03 -1.52 0.012 0.0

20 2565 2556 0.10 -0.10 -1.25 0.023 0.0

30 2548 2522 0.23 -0.23 -0.97 0.035 0.0

40 2530 2488 0.42 -0.42 -0.69 0.047 0.0

50 2513 2454 0.66 -0.66 -0.42 0.059 0.0

60 2496 2420 0.95 -0.95 -0.14 0.071 0.0

70 2479 2387 1.30 -1.30 0.14 0.083 0.0

80 2462 2354 1.71 -1.71 0.41 0.095 0.0

90 2445 2322 2.17 -2.17 0.69 0.107 0.0

100 2428 2290 2.69 -2.69 0.97 0.119 0.0




TRAJECTORY DOES NOT CROSS THE LINE OF SIGHT

 

[Brent]

Here's a chart at 1000 yards for the 308 win and a 175gr SMK with 12 degrees of rifle cant for comparison. More error is the result of much more MOA needed to zero it at 1000 than the other one.

CALIBER: 308 Win
MUZZLE VELOCITY: 2600 fps
BULLET WEIGHT: 175 gr.
BALLISTIC COEFFICIENT: 0.505
SIGHT HT.: 1.76 in. (1.8"/12°)
ZEROED AT: 997.9 Yds.
INCLINE ANGLE: 0 deg.
WIND: 0 mph
STANDING TARGET
ATMOSPHERE: Std. 300 ft.
59° F./300 ft./29.53 in. HG/78% R.H.
'G1' STANDARD FLAT BASE

Range- Vel.- Energy- Drop- Path---- Defl.-- Time- Lead-
Yards- fps- Ft.Lbs.- Inches- MOA- Inches- Sec.- Inches-

000 2600 2627 0.00 0.00 -0.37 0.000 0.0

100 2428 2290 2.69 38.49 8.85 0.119 0.0

200 2262 1988 11.29 36.51 18.08 0.247 0.0

300 2102 1717 26.70 33.68 27.30 0.385 0.0

400 1949 1477 49.99 30.39 36.53 0.533 0.0

500 1804 1264 82.44 26.66 45.76 0.693 0.0

600 1666 1079 125.60 22.47 54.98 0.866 0.0

700 1537 918 181.31 17.77 64.21 1.054 0.0

800 1419 782 251.74 12.48 73.44 1.257 0.0

900 1312 669 339.47 6.54 82.66 1.477 0.0

1000 1219 577 447.41 -0.15 91.89 1.714 0.0

TRAJECTORY CROSSES LINE OF SIGHT AT 3.9 & 997.9 yds.
PATH IS 141.97 IN. OVER LINE OF SIGHT AT 566.4 yds.


After some figuring, I figure that a scope to rifle mounting angle error of 1 degree would equal .01111 MOA windage deflection for every 1 MOA elevation dialed for a farther range beyond the 100yd zero.

A 90 degree angle mounting cant error would obviously cause a 1 MOA windage correction if dialing in 1 MOA elevation. Half that cant angle, 45 degrees, would cause .5 MOA deflection and so on. So 1/90th of that is equal to .01111 MOA deflection per 1 MOA elevation dialed in if the scope is canted only 1 degree.

So if the "scope" alignment instead is off the same 12 degrees from the rifle when installed, the error at 1000 yards with the 38.61 MOA needed to rezero there, there would be .01111 * 12 * 38.61 * 10 = 51.47" or 4.91 MOA deflection error introduced.

That 4.91 MOA error would not be accross the board all the way to 1000 yards and beyond tho, that MOA number is merely a result of the number of MOA needed to dial in for elevation at a given range, and the range itself with a given cant angle to the scope.

Any thoughts or corrections.

 

[Dave King]

Brent

Okay... you've got me doing cartwheels in Excel...

I was doing this/these calulation once before and now I'm getting the hang of the problem.

I believe the magnitude of the problem with cant is that it's contrary to inclined fire (cosine) logic solution. The cosine as used in inclined fire indicates that when deviating from a 90 degree from the horizontal the initial "gradiant/step" values are small and the final steps are large. The degree of deviation for a 45 degree inclined fire problem is 1 - .707 or .293. BUT the deviation for a cant problem (as I see it) is greatest at the onset so a 45 degree cant produces a deviation error of .707 not the .293 I had expected.

A cant angle of 30 degrees produces a windage error of 50%, as a result as rifle zeroed at 100 yards with the scope set at 100 yards will have a deviation for elevation and windage. For my 308 Win with a 1.75" scope height and 2.7 inches of TOF drop I'll have a 2.225" windage error and a -.6" elevation error.

Now if I think of what happens when (we) add elevation to a scope. The termination of the line-of-sight departure angle should now become the basis for the error determination. (View this as a cone of departure, point at the muzzle with the depth of the cone equal to the yardage value and the base of the cone double the elevation requirement.) So your ~276 inches of drop and 12 degrees of cant produce a (276 + 1.76) * .2079 (the Cosine of 90-12 or 78 degrees) = 57.75 inch windage error at 1000 yards. The elevation error is the reciprocal of the windage error (I believe) so (276 + 1.76) * .021852 ( 1 minus the cosine of 12 or .978148) for an elevation deviation of about 6.06 inches.

Does any of this make sense? Hope I'm about on the correct train of thought.

BTW... Thanks for getting me back onto this puzzle.

[ 09-25-2003: Message edited by: Dave King ]

 

[Brent]

Dave,

I understand most of what you are saying, but a few things I'm not sure of. I'll have to read more after I get some coffie.

This part here was one that kind of threw me off until I thought about it a little while, I wasn't exactly thinking about it in the way you were at first.

The degree of deviation for a 45 degree inclined fire problem is 1 - .707 or .293. BUT the deviation for a cant problem (as I see it) is greatest at the onset so a 45 degree cant produces a deviation error of .707 not the .293 I had expected.

Man am I glad you've worked with angles so much!

I hadn't figured the drop at distance from LOS, cosine of 78 degrees for the simple solution. Thanks Dave!

For my 308 Win with a 1.75" scope height and 2.7 inches of TOF drop I'll have a 2.225" windage error and a -.6" elevation error.
For some reason, I'm having a hard time duplicating that, maybe I missed something?

The elevation error is the reciprocal of the windage error (I believe) so (276 + 1.76) * .021852 ( 1 minus the cosine of 12 or .978148) for an elevation deviation of about 6.06 inches.

That is another one I'm not sure I'm seein completely, then again I ain't awake yet, or been through geometry either.

6" is more than this program figured so I don't know what to think yet. 1 - the cosine of 12... what is "1" and why are we subtracting the cosine of 12 from it to get the vertical error, that is the part I'm missing, probably some more too. Wish I knew more geometry, I have a feeling I'll figure it out but I'm having a serious brain freeze right now!

 

[Brent]

I've kind of got the 1 - 12 and 78 reciprical deal figured out, but I'm not sure the end result is correct, or not. Are we on the faster rate of deviation end of the angle range when we should be on the slower end for elevation, like the incline angle is? Brain freeze!

[ 09-26-2003: Message edited by: Brent ]

 

[Dave King]

Brent

I did these calculation quickly in Excel and there is the likelyhood that they are off a bit but that error sholdn't be more than 1 order of magnitude.

They are more for concept and should probably be tweaked a bit...of course I could be all wet too.

Let's talk about this...

That is another one I'm not sure I'm seein completely, then again I ain't awake yet, or been through geometry either. 6" is more than this program figured so I don't know what to think yet. 1 - the cosine of 12... what is "1" and why are we subtracting the cosine of 12 from it to get the vertical error, that is the part I'm missing, probably some more too. Wish I knew more geometry, I have a feeling I'll figure it out but I'm having a serious brain freeze right now.

I used a graphic example to visualize the error/deviation propogation. Get a 8 x 11 sheet of paper... I'll wait.......................... Okay.

Fold the paper in half in both planes (quarter the paper to get reference marks). Use one of your handy CD's and place the center of the spindle hole over the central intersection on the opened sheet of paper. Draw a circle on the paper using the CD's outer edge as a guide. You should now have a circle and in it's center a 90 degree intersection of the fold marks. Call this central intersection the muzzle of the rifle. Call the intersection of the line (fold) going in the 12 oclock direction and the line draw on the outer edge of the CD the POI of the bullet OR the central point in the rifles' scope. For a -0- cant solution the "drop" is directly downward (relative) on the 12 o'clock line...back toward the muzzle. For a canted shot we need to move the POI or POA in the direction of the cant and then plot a line perpendicular to the "drop" line (the 12 o'clock line from the muzzle) AND a line perpendicular to the horizontal line. The vertical line will intersect the horizontal line and indicate the windage deviation... the horizontal line will intersect the vertical line and indicate the elevation deviation. I'll need to scan in a graphic as it'll be too confusing to verbally explain this.

Sorry... gotta run again. Let me know if this helps or hinders.

[ 09-26-2003: Message edited by: Dave King ]

 

[Brent]

Perfect example Dave! You basically painted a picture of what I was visualizing taking place, so I'm right with you.

I see the 30 and 70 as I saw the 12 and 78 so here's what I was trying to say in my last post; The vertical error is more pronounced in the later part of the cant, or more error per degree, while the windage is more pronounced from the onset as you said.


Gotta run for now...

 

[MAX]

Either way or both ways, cant will kill your shot, not the quarry. I think most deal with it fairly well on paper with grids assuming they are in fact properly oriented. In the field or other targets, not so good.