Engineers/Math People Get In Here

[Precision Underground]

I asked this question a while back and didn’t get any responses so I’m still curious.

When I set a rifle up I get comfortable on the rifle and then level my scope to that position. Some guys spend hours and $$ trying to get their rifle and scope level to each other. The way I understand it in my head, it doesn’t matter if your scope and rifle are level as long as the scope is level to the earth/target.

So the question is, what(if any) deviation would show up at long range if a rifle is canted but the scope is level? Is it there a point where X amount of cant starts to matter even if the scope is level? What’s the layman’s calculation/illustration of this?

@Jack Master
@C.R. Adams
@Rocketmandb

ETA- I’m picturing that as long as your barrel and your line of sight though the scope are parallel or all but parallel to one another the deviation at distance would be zero or minimal.

 

[J-Ham]

I've wondered the same thing, that's why I level the scope to the rifle. It just seems to me that I am going to be the thing adding the most variation to the equation... So if the reticle is level in say the prone, I feel like there's a good chance that won't be the case off a barricade since my body position is so different. So with the scope level to the rifle, I just try to level the rifle (or the reticle depending on the situation) in a given shooting position. Maybe that's not a good approach though, hell I don't know.

 

[CoryT]

Absent a real measurable offset between the scope center and the bore centerline, you won't see any real deviation. Suppose however, you cant the rifle so far that the centerline of the scope is two inches left of the bore center. If you then zero POI = POA, then you have two inches of windage applied to get to the scope center and now you have a 'converging zero'. The bullet will now be either left or right of the POA except at the zero distance, and the distance offline will depend on the distance from the zero range.

It's probably pretty hard to get a 'normal' shooting position where the centerline of the scope is outside the diameter of the receiver, maybe 1/2 an inch off the barrel center. The error is there, but it's lost in the noise not worth wasting brain cells on anyway.

 

[SWFShooter]

The scope elevation will be skewed from vertical, which shows up at distance. Search for "tall target" video by Bryan Litz to see the impact it will have.

 

[Nik H]

@Precision Underground

Read the resource I posted some time ago. It is perfect at explaining it

Errors due to cant

@lowlight has spoken about this topic about 1,000 times as well.

I've attached another useful file from here. Not sure who put it up

 

[Alan Warner]

Mounting sights and scopes to a canted rifle is a norm in order to allow the shooter the hold the rifle in the most natural position. Once the cant angle is established, a base is made to bring the sight level when shooter and rifle are in position.
Most of the time by rotating the base or rail.
Offset sights for one eyed shooters is another set of details that require a bit more design. They also can be canted.
I have made quit a few over the years.
Alan

 

[_Windrider_]

I asked this question a while back and didn’t get any responses so I’m still curious.

When I set a rifle up I get comfortable on the rifle and then level my scope to that position. Some guys spend hours and $$ trying to get their rifle and scope level to each other. The way I understand it in my head, it doesn’t matter if your scope and rifle are level as long as the scope is level to the earth/target.

So the question is, what(if any) deviation would show up at long range if a rifle is canted but the scope is level? Is it there a point where X amount of cant starts to matter even if the scope is level? What’s the layman’s calculation/illustration of this?

@Jack Master
@C.R. Adams
@Rocketmandb

ETA- I’m picturing that as long as your barrel and your line of sight though the scope are parallel or all but parallel to one another the deviation at distance would be zero or minimal.

@Jack Master has a sheet with good info and the values of can’t error at distance. @Nik H resource is a good discussion on the math and theory.
All I will say is u want the reticle level not the scope. In a perfect world they should both be level but the reticle is the critical piece.

 

[CoryT]

It's not really cant, it's offset. You don't have cant until the sights are actually attached. We see the rifle as canted if the trigger and pistol grip don't point straight down, but the reality is that's not relevant to the trajectory at all.

If the sight is not mounted directly above the center of the bore, but that sight is always held level, then all you have is offset, not cant. Look at a Vickers or BREN gun, the sights are a fair bit off center. You just zero that much off center and you now have a parallel bore zero.

In the case of a shoulder fired rifle, it's hard to have very much offset, an inch would be quite a lot, look for example at an M1D. Normally, the offset is probably less than half the diameter of the barrel, and meaningless in the scheme of things. If you manage to somehow setup several inches of offset, and then make a converging zero, you'll have offset at ranges other than the zero range.

 

[CoryT]

@Jack Master has a sheet with good info and the values of can’t error at distance. @Nik H resource is a good discussion on the math and theory.
All I will say is u want the reticle level not the scope. In a perfect world they should both be level but the reticle is the critical piece.

Is it though? It certainly would be if you planned to hold for elevation. If you dial everything that the erector cell needs to be square, the reticle could form an X and it matters not at all.

Personally I'm more concerned that the scope (erector mechanism) is square to gravity, as I dial more often than not, sometimes quite a bit of elevation (25+ mils) and I want POA=POI. If I'm holding, it's because of speed, and I can accept somewhat less precision. If the reticle is canted in the tube enough to cause measurable error at distance, then the scope is defective and gets returned.

 

[_Windrider_]

Is it though? It certainly would be if you planned to hold for elevation. If you dial everything that the erector cell needs to be square, the reticle could form an X and it matters not at all.

Personally I'm more concerned that the scope (erector mechanism) is square to gravity, as I dial more often than not, sometimes quite a bit of elevation (25+ mils) and I want POA=POI. If I'm holding, it's because of speed, and I can accept somewhat less precision. If the reticle is canted in the tube enough to cause measurable error at distance, then the scope is defective and gets returned.

I agree. If a reticle is canted send the scope back. Period.

 

[Jack Master]

Here is the post I made in 2019 with the math for this.

Having your scope centerline match your rifle centerline is not required. (0.2" offset is 1.8" at 1000yds)
Having your rifle plumb is not required. If your rifle is canted but your scope if vertical to gravity an offset of the scope over the bore is created. A 5 degree rifle angle is 1.5" at 1000yds
Having your reticle and scope adjustments plumb is what really matters. canting the scope 2 degrees of rotation is is about 10" at 1000yds

Everyone loves to argue about how to mount a scope but the truth is: If you level the reticle when your are shooting nothing else matters.

So after reading 400(ish) posts about scope mounting and leveling I had to do the math.

Every time a scope mounting or leveling thread is posted it usually leads to conversations about weather the rifle needs to be level when the scope is mounted level. And sometimes is goes into weather the scope needs to be mounted directly over the bore and not offset from the bore. Well, math 'never' lies. So... attached is a sheet I put together for the down range effects of...1) mounting your scope with an offset from the bore, 2) mounting the scope level with the rifle not level, and 3) effects of a canted reticle dues to not being mounted correctly or canting the entire system.

I was very surprised to find the offsets due to mounting or rifle cant (with level scope) are very minimal. especially when compared to the canting of the scope. I could understand needing to worry much more about the offsets when shooting over... maybe 3000 yards, but even then its a strech then compaired to wind calls or actual scope cant.

Conclusions:
We need to have a level reticle or level tracking (not always the same) but don't fret over the mounting offsets (case 1) or canting the rifle with a level scope (case 2). Do worry about canting the scope.

View attachment 7074705

 

[HousePlant]

I'd be more concerned about an optic with a canted (defective or incorrectly made) reticle/reticle image against the actual windage or elevation adjustment direction. As long as your scope is level to how you hold or position the rifle, it doesn't really matter. If you mount your scope to the side of the rifle for some odd reason but also hold the rifle such that the scope is straight vertical above the bore... ain't no difference. Weird... but... it'll shoot.

 

[Sheldon N]

@CoryT and @Jack Master have it right.

Rotating the scope to induce cant is bad, because it rotates an entire plane - the imaginary vertical line the reticle tracks when you dial up from zero to add elevation. That vertical plane needs to stay true to gravity or the trajectory goes to hell (as nicely explained in @Nik H 's paper).

Rotating the barrel does nothing, it's a round tube and there's no such thing as cant for the barrel.

Rotating the entire weapon system just repositions the barrel underneath the scope, creating horizontal offset between the barrel and scope. If you re-level the scope after canting the weapon system, all the vertical stuff is sorted out. What you are left with is two non-parallel lines (scope line of sight + barrel POA) that converge left/right and come together at your 100 yard zero, then diverge at an equal rate thereafter. So if there was 1/4 inch of left/right offset between your barrel and scope, that would work out to no error at 100 yards, 1/4" error at 200 yards, 1/2" error at 300 yards, 3/4" at 400 yards, etc.

As Cory pointed out, the amount of offset is minimal unless you dramatically cant the weapon system.

 

[Rocketmandb]

So the question is, what(if any) deviation would show up at long range if a rifle is canted but the scope is level? Is it there a point where X amount of cant starts to matter even if the scope is level? What’s the layman’s calculation/illustration of this?

Man, you always come up with these things that make me kick out some graphics (or a video)! I'll start something today - I've actually been meaning to put together a video on this because there's a lot of confusion around this subject by newer folks getting into the discipline.

Short answer is that if you use a level, you want it leveled against the reticle/scope. The barrel is a tube - it doesn't care what orientation it's in. What's happening with the action and rest of the rifle is EDIT: ALMOST irrelevant for the purposes of sighting and ballistics - though not for practical feel and ergonomics, which can have an impact.

EDIT: I added the ALMOST because in extreme, unrealistic circumstances, you start getting left/right offset of the scope vs. the barrel and less vertical offset.

 

[Nik H]

I'd be more concerned about an optic with a canted (defective or incorrectly made) reticle/reticle image against the actual windage or elevation adjustment direction.

The implicit assumption behind the mathematics and physics of the situation is that the reticle and erector are aligned properly and working normally. If the erector does not move in a purely vertical direction when the elevation is adjusted or the reticle is not aligned properly, you're screwed and the scope is junk.

This is fundamentally why the job of setting up your scope properly does not end when you level the reticle. I always follow this process:

1. Level the reticle so that it is consistent with the pull of gravity
2. Do so WITH the rifle in position in YOUR shoulder and on your @Precision Underground rear bag . Yes it may take two people to do it right but so be it. That is what wives, kids or buds are for.
3. Run a tall target test to ensure the reticle moves in a purely vertical direction over the range of travel that you will use in the field.
4. Do a Box test to ensure that the windage adjustment moves in a purely horizontal fashion.

At this point, you will be FAR ahead of 90% of the shooters you will encounter

 

[smoothy8500]

A short test at long distance using the same rifle with "offset" level scope. There was only minimal change in POI. After seeing this, I quit stressing about mounting scopes:

 

[Precision Underground]

Here is the post I made in 2019 with the math for this.

Having your scope centerline match your rifle centerline is not required. (0.2" offset is 1.8" at 1000yds)
Having your rifle plumb is not required. If your rifle is canted but your scope if vertical to gravity an offset of the scope over the bore is created. A 5 degree rifle angle is 1.5" at 1000yds
Having your reticle and scope adjustments plumb is what really matters. canting the scope 2 degrees of rotation is is about 10" at 1000yds

Everyone loves to argue about how to mount a scope but the truth is: If you level the reticle when your are shooting nothing else matters.


View attachment 7535242

For sure. I knew the important part is the reticle and erector movement but my question is at what point does a canted rifle/level scope start to matter? Your chart is the exactly what I was looking for. How much of a difference does scope height make?

 

[Precision Underground]

Man, you always come up with these things that make me kick out some graphics (or a video)! I'll start something today - I've actually been meaning to put together a video on this because there's a lot of confusion around this subject by newer folks getting into the discipline.

Short answer is that if you use a level, you want it leveled against the reticle/scope. The barrel is a tube - it doesn't care what orientation it's in. What's happening with the action and rest of the rifle is EDIT: ALMOST irrelevant for the purposes of sighting and ballistics - though not for practical feel and ergonomics, which can have an impact.

EDIT: I added the ALMOST because in extreme, unrealistic circumstances, you start getting left/right offset of the scope vs. the barrel and less vertical offset.

Yep that’s what I was pondering - how much cant would it take to make a difference if the scope level. The chart by Jack is good info!

 

[Rocketmandb]

Yep that’s what I was pondering - how much cant would it take to make a difference if the scope level. The chart by Jack is good info!

Maybe we should start a gansta style long range movement

 

[_Windrider_]

For sure. I knew the important part is the reticle and erector movement but my question is at what point does a canted rifle/level scope start to matter? Your chart is the exactly what I was looking for. How much of a difference does scope height make?

Shouldn’t matter until you start changing the system. It would effect the offset but not enough to matter at the traditional ring heights we used until the offset was 45 degrees or more. Seen a few stages where 90 degree cants are part of the stages. ETA, these were gas gun stages.

 

[Precision Underground]

Maybe we should start a gansta style long range movement

Lol I just pictured what that would look like and chuckled. I ask because I keep canting my rifles more and more toward my head. It’s never shown up on target but I’m curious as to the math. Or should I say curious as to the geometry because math seems like work.

 

[Precision Underground]

@Precision Underground

Read the resource I posted some time ago. It is perfect at explaining it

Errors due to cant

@lowlight has spoken about this topic about 1,000 times as well.

I've attached another useful file from here. Not sure who put it up

Yep that all good info. I’m clear on how to set up just was curious as to what point is too much cant. I’ll start tagging you on my random questions to fill in the missing “whys” in my head lol.

 

[Rocketmandb]

Lol I just pictured what that would look like and chuckled. I ask because I keep canting my rifles more and more toward my head. It’s never shown up on target but I’m curious as to the math. Or should I say curious as to the geometry because math seems like work.

Did you ever see the Mythbusters test of gansta pistol vs. standard?

 

[carbonbased]

Neat interactive flash animation showing how cant affects your shot. I “can’t” vouch for its accuracy, but I think it gets the general idea across.

http://www.arld1.com/images/swfs/impactpointvscantangle.swf

 

[Jack Master]

For sure. I knew the important part is the reticle and erector movement but my question is at what point does a canted rifle/level scope start to matter? Your chart is the exactly what I was looking for. How much of a difference does scope height make?

Yes. Height over bore will technically make a difference. For the sheet I made I assumed 2" as the height over bore. Changing the height over bore will make a very very small change to the center line of scope to center line of bore offset (laterally). Going from 2" to 1" of height over bore will half the values in the chart for cant of the rifle with a level scope. But even this amount is likely lost in your zeroing ability.

Here is a way to correlate your height over bore to the chart above.
(Your height over bore) / 2" x ( the listed bore offset) = your bore offset. -->Then look this value up in the top chart of the page.
_______________________________________________________________________________
Example for a 2.5" height over bore with a 5 degree rifle cant (level reticle)
2.5/2 = 1.25 --> 1.25 x 0.174 = .218 <-- look the value up in the first chart. = 0.191 MOA of windage added to your rifle.

2.5 = my height over bore
2" = table's height over bore
0.174 = Listed offset for 5 degree cant
0.191 = listed MOA of windage for a 0.2 scope to bore offset in the first table.
________________________________________________________________________________

The difference of 2 to 2.5" height over bore is 0.166 to 0.191 MOA shift. This is 0.025moa difference and why height over bore changes are very negligible and gets lost in your zeroing ability. Does is effect the offset yes, but our human error will be much bigger.