Is this acceptable for a high end ring manufacturer?

[randello88]

Hi everyone, i already posted a similar thread on another forum (more hunting oriented). I know you guys are more knowledgeable about precision shooting so i will ask here for more insight.

I recently bought several sets of rings from a reputable brand, very appreciated on forums. They look good quality. They have an integral level in the base. I opted for that model based on reputation and onnthe fact that the level, placed in the base of the front ring on the left, looked like a good compromise for a 450 yards max hunting rifle (take note that i will shoot up to 800-1200 meters at the range with this same gun but the main use of the rifle is to hunt roes, boars and fallow deer). This way i am able to check the level when rarely needed but at the same time the level doesn't stick out too much, keeping the rifle convenient to carry.

I made a test and found out that ALL the 4 rings i have, bought in a 1 year timespawn, have the level.. out of level! It's just a matter of half a degree and i know that, as long as the reticle is plumb to the bubble level, the level being off (and thus the rifle being canted) 0.5 degrees is no big deal, especially for the distances i am shooting at. That said, every one of the level is canted in the same exact direction and everyone is off by 0.5 degrees (this value was tested with reliable equipment and was the same also on my colt le6921 rail). I checked with rings mounted and torqued on a high quality integral scope base (defiance) and using multiple levels i know to be on spot as a reference). Also when leaning on a flat surface and not clamped to the rail, the rings showed the same exact cant.
The fact that all the ring levels are off by the same exact amount in the same directions tells me that the manufacturing of these rings is very consistent.. consistently wrong though!

How is this possible? For at least 1 year a reputable brand (i will not say the name of the brand because they have been great in assisting me and accorded a full refund) produced defective rings?

Thanks guys!
greetings from Italy

 

[Edsel]

Those bubble levels are a dime a dozen, regardless of having come from "top tier scope ring manufacturers."

Amazon.com

A proper bubble level costs around $50 on its own, and quite honestly I'm not even sure if they're truly accurate despite the price tag.

Only if you had one of these as a reference...

Amazon.com

...could you say for certain which bubble level was "true..."

All that being said, one really has no idea how level the scope ring would end up when mounted onto your rifle - the rifle of the guy next to you - or mine.

 

[randello88]

View attachment 8497307

View attachment 8497309

Those bubble levels are a dime a dozen, regardless of having come from "top tier scope ring manufacturers."

View attachment 8497310

Amazon.com

A proper bubble level costs around $50 on its own, and quite honestly I'm not even sure if they're truly accurate despite the price tag.

Only if you had one of these as a reference...

View attachment 8497313

Amazon.com

...could you say for certain which bubble level was "true..."

All that being said, one really has no idea how level the scope ring would end up when mounted onto your rifle - the rifle of the guy next to you - or mine.

if i took 5 levels of different manufacturer and all of them are basically perfectly giving the same reading and then 4 levels of the same brand are off, i assume that is very unlikely that 5 diffierent manufacturer made a canted level, canted in the same exact way. The "wrong ones" must be the ones from the same manufacturer.

Those levels you showed in the pic, one next to the other, are much less out of level than the ones of the rings but much less consistently so. All the bubbles in the rings are that much off that the level passes the right reference line when action of the rifle is plumb. The ones you showed are slightly out of level in comparison, but htey are more erratic. So i assume in your pic we are talking about low quality bubble levels, in the case of my rings we are talking about a manufacturing problem which consistently put those levels canted in the same exact direction everytime. I assume the reference lines are there for a reason and if a ring should be level but the bubble passes a line, this can be considered a defective product. What do you think?

i know the actual impact on the shooting is negligible but this makes me wonder about the quality of QC of this specific brand. And i am sorry because i liked the design and the function on the other hand but i won't put rings with a so and so QC on a 14k dollars rifle setup.

Anyway yes, probably i had too big expectations, this is minblowing to me that you pay 300 dollars for rings and the manufacturer don't even care to put the bubble level...leveled!

 

[pangris]

I'd return them and ask for levels that have been verified, and that demonstrate consistency.

 

[spife7980]

I’m every bit as suspect of the test “proving” things aren’t level as the tests saying that they are level.

 

[Aftermath]

if i took 5 levels of different manufacturer and all of them are basically perfectly giving the same reading and then 4 levels of the same brand are off, i assume that is very unlikely that 5 diffierent manufacturer made a canted level, canted in the same exact way. The "wrong ones" must be the ones from the same manufacturer.

Those levels you showed in the pic, one next to the other, are much less out of level than the ones of the rings but much less consistently so. All the bubbles in the rings are that much off that the level passes the right reference line when action of the rifle is plumb. The ones you showed are slightly out of level in comparison, but htey are more erratic. So i assume in your pic we are talking about low quality bubble levels, in the case of my rings we are talking about a manufacturing problem which consistently put those levels canted in the same exact direction everytime. I assume the reference lines are there for a reason and if a ring should be level but the bubble passes a line, this can be considered a defective product. What do you think?

i know the actual impact on the shooting is negligible but this makes me wonder about the quality of QC of this specific brand. And i am sorry because i liked the design and the function on the other hand but i won't put rings with a so and so QC on a 14k dollars rifle setup.

Anyway yes, probably i had too big expectations, this is minblowing to me that you pay 300 dollars for rings and the manufacturer don't even care to put the bubble level...leveled!

For shits and giggles (no, I'm. not talking about Biden/Harris) do the plumb bob thing to get your scope plumb and make sure that it is also plumb to the bore at the same time. Now, place your bubble level across some point you believe should be perpendicular to the that plumb line.

 

[Mulepackhunter]

My opinion is unless you want more than one level on your rifle to match this means zero. Its a reference for repeatability not for measureing level.
Expecting something to be level off of a 1/4 in plastic tube 1/4 in long is asking alot.

 

[Holliday]

To check level’s level I place it on a flat surface. Note the bubble position. Then I spin it 180° to see that it reads exactly the same.

The only non-adjustable level that I have never personally seen a failure of that test is stablia.

Hell Starrett hand picked for me one of those short aluminum ones at the factory and it still fails that test…..nimrods

 

[Aftermath]

To check level’s level I place it on a flat surface. Note the bubble position. Then I spin it 180° to see that it reads exactly the same.

The only non-adjustable level that I have never personally seen a failure of that test is stablia.

Hell Starrett hand picked for me one of those short aluminum ones at the factory and it still fails that test…..nimrods

I have a Sands 4' that has been true since the day I bought it maybe 35 years ago.

 

[Slides]

As above, a bubble level is generally just a checking device and I don't ever assume "centered" is level, if the offset is the same when you turn it 180 degrees the surface should be level on that axis. The 360 ones on scales etc should at least put you in the same orientation as calibrated for repeatability.

 

[Baron23]

I have one of the short Starrett's pictured above...I don't use it as its off IMO.

Also, without very expensive test equipment like the type used to certify traceable to NIST standards, my view is you need to pick a level you think is close and go with it. I choose to use an iGaging AngleCube as a standard as it also matched my Send-it level. I also do have a spirit level that matches these two electronics.

Close enough for me.

 

[randello88]

I have one of the short Starrett's pictured above...I don't use it as its off IMO.

Also, without very expensive test equipment like the type used to certify traceable to NIST standards, my view is you need to pick a level you think is close and go with it. I choose to use an iGaging AngleCube as a standard as it also matched my Send-it level. I also do have a spirit level that matches these two electronics.

Close enough for me.

We can all agree that finding a almost perfectly leveled level is very difficult but a 0.5 degree cant is a pretty big cant in my opinion..
I mean, the bubble, when the rings are (more or less) on level (i mean, within +/- 0.1 degrees, as all my reference levels are), is crossing on of the reference lines.

Do you think this should make me question the overall quality of the rings, being a sign of poor QC?

 

[Makinchips208]

From a manufacturing aspect, measuring half degree off on most parts of a scope ring is not that hard with manual measuring equipment, and downright easy on a cmm.

 

[Edsel]

Do you think this should make me question the overall quality of the rings, being a sign of poor QC?

Not really.

Just placing too much faith on a cheap bubble.

It’s just a crude reference.

 

[Secant]

I think you'd be time and money ahead to go for a tube mounted level (something like a Flatline Ops) or an adjustable level (Send IT). Also, if you want to get nitpicky about canting, have you checked your reticle relative to the scope's tracking axis? Which one do you wanna match-up with your level?

 

[randello88]

I think you'd be time and money ahead to go for a tube mounted level (something like a Flatline Ops) or an adjustable level (Send IT). Also, if you want to get nitpicky about canting, have you checked your reticle relative to the scope's tracking axis? Which one do you wanna match-up with your level?

The reason why i choose to use a ring integral level is that i will shoot oretty often inside 300 m, almost always. When i get a longer shot it's because i can't get closer and in this case i will check the level. So a level is a not so important piece of kit for me but i still want to be able to make sure not to be too much off level (talking about the reticle of course) when i shoot further away. And also at the range.

I opted for a integral level because i loke the fact that it is flush with the rings and doesn't stick out, leaving the rifle convenient to carry without stuff sticking out to the side or to the top. I may be wrong though

 

[pangris]

US Optics will put a level in the scope for you. So far so good...

 

[Makinchips208]

@randello88
TLDR? The half degree won’t matter.

And as for quality? It’s a dumb piece of aluminum (hopefully 7075) that clamps to a rail and a tube. Simple.

Checking level as mounted isn’t a very precise test either. There is like .01” of tolerance allowed on a pic rail. That’s a lot. Just cause the rail is level does not mean the ring will mount level.
Someone already questioned your measurement method, no insults, but it’s possible that the mounting surfaces of the ring are perfect to the bubble, and off as mounted to the pic rail.

mount the ring and level the bubble, then true the reticle to your bubble (Or something like that). In practice it will likely be more consistent than you.

 

[randello88]

@randello88
TLDR? The half degree won’t matter.

And as for quality? It’s a dumb piece of aluminum (hopefully 7075) that clamps to a rail and a tube. Simple.

Checking level as mounted isn’t a very precise test either. There is like .01” of tolerance allowed on a pic rail. That’s a lot. Just cause the rail is level does not mean the ring will mount level.
Someone already questioned your measurement method, no insults, but it’s possible that the mounting surfaces of the ring are perfect to the bubble, and off as mounted to the pic rail.

mount the ring and level the bubble, then true the reticle to your bubble (Or something like that). In practice it will likely be more consistent than you.

200 dollars is quite a bit for a raw chunk of aluminum. What are we paying for then?

 

[Makinchips208]

200 dollars is quite a bit for a raw chunk of aluminum. What are we paying for then?

Depends on the brand.

R&D,
Aluminum,
Machining,
Inspection,
Anodizing,
Titanium hardware,
Crooked bubble levels,
Packaging,
Advertising,
Storage,
Shipping,
Profit margin,
Warranty,

To name a few.

 

[Secant]

The reason why i choose to use a ring integral level is that i will shoot oretty often inside 300 m, almost always. When i get a longer shot it's because i can't get closer and in this case i will check the level. So a level is a not so important piece of kit for me but i still want to be able to make sure not to be too much off level (talking about the reticle of course) when i shoot further away. And also at the range.

I opted for a integral level because i loke the fact that it is flush with the rings and doesn't stick out, leaving the rifle convenient to carry without stuff sticking out to the side or to the top. I may be wrong though

Understood, I get why you picked what you did, but a level mounted in the stock/chassis, an optics rail, or a ring base is counting on a lot of shit to be perfect (or tolerances to cancel out).

• Do you cant your rifle at all when you address it? If yes, are you able to cant the buttstock to correct? Do you ever shoot "weak" side, and does that can’t vary?
• Does the action sit ‘perfectly’ in the stock/chassis?
• Does the pic rail sit perfectly on the action or is the integral pic rail milled 'perfectly'?
• Are the rings milled 'perfect'/how do they pair to the rail? Is your scope set perfectly square/plumb in the rings or do you otherwise intentionally rotate the scope to counter your natural cant of the rifle (see first question above)?
• Is the reticle canted at all inside the scope?

Sorry, those are all rhetorical questions. I'm just trying to make the point that this is all a compromise. You can set-up the rifle to your body and then set-up the scope to your body, and then buy the right level to index off of the scope (and even then you are picking between the reticle and the tracking axis - if we are being nitpicky)
OR
You can buy a level that is mid-stream in your 'system', and you will get what you get.

 

[randello88]

Understood, I get why you picked what you did, but a level mounted in the stock/chassis, an optics rail, or a ring base is counting on a lot of shit to be perfect (or tolerances to cancel out).

• Do you cant your rifle at all when you address it? If yes, are you able to cant the buttstock to correct? Do you ever shoot "weak" side, and does that can’t vary?
• Does the action sit ‘perfectly’ in the stock/chassis?
• Does the pic rail sit perfectly on the action or is the integral pic rail milled 'perfectly'?
• Are the rings milled 'perfect'/how do they pair to the rail? Is your scope set perfectly square/plumb in the rings or do you otherwise intentionally rotate the scope to counter your natural cant of the rifle (see first question above)?
• Is the reticle canted at all inside the scope?

Sorry, those are all rhetorical questions. I'm just trying to make the point that this is all a compromise. You can set-up the rifle to your body and then set-up the scope to your body, and then buy the right level to index off of the scope (and even then you are picking between the reticle and the tracking axis - if we are being nitpicky)
OR
You can buy a level that is mid-stream in your 'system', and you will get what you get.

I see your point and I agree. I was just wondering if those rings are defective or not. In the case they are, i will not use this brand because it means they made defective rings for at least 1 year and this would make me doubt the whole brand. I sent the rings back for a full refund, let's see what they tell me. I will update you.

 

[mewillis]

So the lesson is levels may not be level or even necessary on a rifle?? Whooda thunk it.........

 

[hlee]

Put everything (rifle/scope/rings) together. Hang a plumb Bob. Align the vertical stadia of the reticle to the plumb Bob. Mark the bubble level. Now you have a reference for the reticle being level, which is what you care about.

 

[Harman117]

Yeah like others have said. The bubble level serves as a reference point. In your case, you'll have to rotate the scope in the rings for adjustment.

With the bubble level centered, rotate your scope until the reticle aligns with a plumb bob. Torque up and confirm alignment.

Now that bubble level is a reference for your reticle being aligned to gravity. You can't assume the reticle/tracking is perfectly perpendicular to the bottom of your scope or top of your scope turrets.

It's always good to then check/confirm with a tall target test:

 

[TheOE800]

Hell Starrett hand picked for me one of those short aluminum ones at the factory and it still fails that test…..nimrods

Those Starrett mini levels are fucking trash. I use a Stabila pocket level; not as small, but I don’t worry about it being a piece of shit.

 

[Kiba]

As Confucius wisely said:

"A man who owns one level knows what is level, a man who owns more than one level is confused."

Most non-adjustable levels are "pretty close."

For most shooting use, given all the other variables involved (wind, ammo variation, rifle accuracy/uncertainty, etc) "pretty close" typically gets the job done within the margin of error of everything else in the system unless the level is way out of whack.

Keep in mind every machined part in the assembly, including the level itself, is subject to manufacturing deviations and tolerance stacking that can throw things off. The only way to avoid that is an adjustable level that you can set up to match the erector and reticle. This is why a scope tube mounted level is typically the best option, as then you can shoulder the rifle as normal and rotate the reticle to match a plumb line, then rotate the level to match, and then do a tracking test to make sure the reticle isn't canted to the erector. If the rail or the action is a little out of square it's not a problem as you adjust the level to match the optic.

With a non-adjustable level mounted on the base or a level built into in the bottom of the ring or in the ring cap, if that level is off compared to the rail on the action, sure you can set the scope up so the erector/reticle matches that built in level but then your rifle will be canted, and possibly canted in a direction that's not conducive to natural point of aim and your regular hold.

Also keep in mind levels can be made with different graduations and sensitivities, and most levels provided for scope levels aren't that sensitive as then you would be constantly chasing center on the bubble. You really need a "close enough" sanity check that you're not holding the rifle way out of level in an odd firing position, you don't need to know when it's level to within 0.0001" per foot.

I have one of the Mitutoyo Pro 360 digital levels that someone linked above that I use quite often for general fab work, but you do have to calibrate it somewhat regularly as it can drift if knocked or if the temperature changes significantly from the last time it was calibrated.

For really, really accurate stuff I have a Starrett 199Z master level that's accurate to 0.0005" per foot. Total overkill for rifle or scope mounting use, but nice for leveling precision machinery and surface plates. Maybe I should whip up a picatinny mount for it and attach it to my rifle as a joke, but then I'd never end up taking a shot as there's no way I can hold the rifle steady enough to keep the bubble in the center with 0.0005" per foot sensitivity, lol

 

[randello88]

Thanks guys, you are amazing. A last question: i am not gonna adventure myself in math.
A 0.5 degree cant of the rifle with a reticle (and erector) perfectly plumb to gravity how much will impact poi at 400, 500, 600, 700 and 800 yards? Assuming the rifle is zeroed at 180 (mpbr for my rifle and the animals i hunt) and that I would dial for elevation for further distances?

Thanks

 

[hlee]

Thanks guys, you are amazing. A last question: i am not gonna adventure myself in math.
A 0.5 degree cant of the rifle with a reticle (and erector) perfectly plumb to gravity how much will impact poi at 400, 500, 600, 700 and 800 yards? Assuming the rifle is zeroed at 180 (mpbr for my rifle and the animals i hunt) and that I would dial for elevation for further distances?

Thanks

For a scope mounted 3 inches from the bore, 0.025 inch per “zero yardage increment.” In this case 0.025 inch per 180 yards. Less if the scope is closer to the bore. More if further away.

 

[stanley_white]

I run four levels on my scope.

Two left, two right, one up and one down on each side.

I need four to account for the possible non-uniform finish on the scope body.

All four have a bubble of hydrogen from Jupiter suspended in liquid unobtanium.

I divide the average bubble position by four before every shot.

This system has helped me go from dead last to bottom quarter.

-Stan

P.S. I am also a liar.

 

[randello88]

For a scope mounted 3 inches from the bore, 0.025 inch per “zero yardage increment.” In this case 0.025 inch per 180 yards. Less if the scope is closer to the bore. More if further away.

So at 180x3=540 yards the poi would be moved by 0.075?
This is almost nothing

 

[Secant]

Thanks guys, you are amazing. A last question: i am not gonna adventure myself in math.
A 0.5 degree cant of the rifle with a reticle (and erector) perfectly plumb to gravity how much will impact poi at 400, 500, 600, 700 and 800 yards? Assuming the rifle is zeroed at 180 (mpbr for my rifle and the animals i hunt) and that I would dial for elevation for further distances?

Thanks

Depends on time of flight, so it’ll vary based on bullet, MV, environmentals, etc. Also dependent on scope height over bore, scope offset,

Google "Estimation of Shot Error Due to Rifle Cant" by Dr Lyman Hazelton.

VERY ROUGHLY, you will be off horizontally by a tenth or two at 1,000 yards with a 0.5* cant, and vertical will really be negligible.

 

[Harman117]

For a scope mounted 3 inches from the bore, 0.025 inch per “zero yardage increment.” In this case 0.025 inch per 180 yards. Less if the scope is closer to the bore. More if further away.

Above is correct, if you are looking only at the horizontal offset of the scope and bore. (Which won't matter much)


But what really matters (and is the reason people put levels on their gun) is below.

Depends on time of flight, so it’ll vary based on bullet, MV, environmentals, etc. Also dependent on scope height over bore, scope offset,

Google "Estimation of Shot Error Due to Rifle Cant" by Dr Lyman Hazelton.

VERY ROUGHLY, you will be off horizontally by a tenth or two at 1,000 yards with a 0.5* cant, and vertical will really be negligible.

 

[Baron23]

We can all agree that finding a almost perfectly leveled level is very difficult but a 0.5 degree cant is a pretty big cant in my opinion..
I mean, the bubble, when the rings are (more or less) on level (i mean, within +/- 0.1 degrees, as all my reference levels are), is crossing on of the reference lines.

Do you think this should make me question the overall quality of the rings, being a sign of poor QC?

First, having the scope vertical stadia (vertical line in the reticle) absolutely in line with the bore and canting the rifle/scope together will result in far greater error down range than merely have a scope be a small bit rotated out of level. Far greater. Give the attached a read....no, I didn't write it (not sure who...maybe @Jack Master ???).

Here is the tldr conclusions:

Second, a .5 degree of cant of the scope in relation to the rifle is absolute insignificant. Note, in the document attached they are calculating a full 2 degrees and the error at 1k yards is practically zip (if you can shoot better than .622" at 1k you should try out for a international shooting team! haha).

And, though I found it difficult to find too many references that aren't way too deep scientific papers, between your eyes and vestibule system (balance in the ears), you should be able to get your reticle aligned with gravity to 1-2 degrees....without any external level.

Third, as I mentioned in my post above (or at least I think I did), you need to pick a level and consider it the standard that you are going to use. You will have a hell of a time getting any set of different spirit levels (levels with bubbles, right?) to agree. If you want a calibrated spirit level....that is, one traceable to the National Institutes of Standards & Technology (NIST) to an absolute value of accuracy...that will cost you far more than you wish to spend.

I guess, fourth...you returned a set of $200 rings (which from that price I take them to be from a high quality rifle manf) because you determined...with some rando other level...that the level built into their rings is .5 degree off? 1/2 of a degree? Do I have that right? If so, I'm going to bet you are not going to make it to their Christmas card list this year.

Cheers

 

[hlee]

Above is incorrect


Below is correct

0.5 deg is insignificant.

 

[mewillis]

Obviously if you aren't running lasers on all 4 quadrants of your scopes, rings AND mounts you are definitely NOT snipers LOL...........

 

[TheOE800]

Just use a high power construction laser level Arca clamped to your rifle after you level your scope to your rifle, right?

 

[Nik H]

All I can say about this entire thread is LOL

 

[Rob01]

All I can say about this entire thread is LOL

 

[Harman117]

View attachment 8498985
0.5 deg is insignificant.

Whoops my bad, I re-read the post where OP asked for calculation. OP was specifically asking about the calculation that doesn't matter. This is correct, I edited my original post

 

[randello88]

First, having the scope vertical stadia (vertical line in the reticle) absolutely in line with the bore and canting the rifle/scope together will result in far greater error down range than merely have a scope be a small bit rotated out of level. Far greater. Give the attached a read....no, I didn't write it (not sure who...maybe @Jack Master ???).

Here is the tldr conclusions:

View attachment 8498972

Second, a .5 degree of cant of the scope in relation to the rifle is absolute insignificant. Note, in the document attached they are calculating a full 2 degrees and the error at 1k yards is practically zip (if you can shoot better than .622" at 1k you should try out for a international shooting team! haha).

And, though I found it difficult to find too many references that aren't way too deep scientific papers, between your eyes and vestibule system (balance in the ears), you should be able to get your reticle aligned with gravity to 1-2 degrees....without any external level.

Third, as I mentioned in my post above (or at least I think I did), you need to pick a level and consider it the standard that you are going to use. You will have a hell of a time getting any set of different spirit levels (levels with bubbles, right?) to agree. If you want a calibrated spirit level....that is, one traceable to the National Institutes of Standards & Technology (NIST) to an absolute value of accuracy...that will cost you far more than you wish to spend.

I guess, fourth...you returned a set of $200 rings (which from that price I take them to be from a high quality rifle manf) because you determined...with some rando other level...that the level built into their rings is .5 degree off? 1/2 of a degree? Do I have that right? If so, I'm going to bet you are not going to make it to their Christmas card list this year.

Cheers

I probably won't but at the time i thought the impact would be much more significant. I asked them and they told me to send everything back so..

I was more interested in understanding if this cant in their rings (which I didn't assest randomly) could reflect a lack in QC. I like companies that try to make everything as precise as they can

 

[randello88]

All I can say about this entire thread is LOL

Ibam happy to see i brought some fun to your life man! Sometimes can happen that someone doesn't know such a particular detail. I don't find it funny but if you do i am happy for you

In the meantime i will go back killing stuff with my 4 levels i just installed

 

[randello88]

Thanks to everyone guys, as i expected snipershide delivers good technical informations.

I am also happy for the ones who had so much fun for my goofy question!

Greeting from Italy and good hunting to everyone

 

[Nik H]

Ibam happy to see i brought some fun to your life man! Sometimes can happen that someone doesn't know such a particular detail. I don't find it funny but if you do i am happy for you

In the meantime i will go back killing stuff with my 4 levels i just installed

The level built into your brain is the best one to use. As you shoot more, you will see that.

 

[Baron23]

I asked them and they told me to send everything back so..

Then I apologize. I thought you were demanding they take them back.

Best of luck.

 

[fx77]

Great thread, great proofs, and responses

 

[GO@HORNS]

Did you ever check each level at the same place on the rail?

 

[randello88]

Did you ever check each level at the same place on the rail?

Yes, actually a little update. The manufacturer checked the bubbles and admitted theynare off. They found a good one and sent it to me for free

 

[Aftermath]

View attachment 8498985
0.5 deg is insignificant.

Math.
It's not really just something you had to study in high school.