I just finished my XLR Chassis rifle build, and while planning and purchasing I did quite a bit of research and saw many questions asking what height rings are required for different scopes. After reading through the forums and reviewing the two formulas provided by XLR, I decided to draw the system out in some detail and figure it out for myself.
Below I provide two detailed methods for determining scope ring height for a chassis system; the first is a slight modification of XLR's method, the second is a closely related method to determine if your existing rings will work for the chassis. Both methods should work for any scope and just about any chassis system that employs a handguard around the barrel similar to that of the XLR Evolution chassis. All you need to do is find your hardware measurements (or measure accurately) and then do some arithmetic.
I'm sure some of you guys already know this stuff, but there are apparently many out there who don't... it certainly was new to me. So here goes.
I found two formulas provided by XLR's Kyle Miller for calculating ring height...
The first was:
Ring Height = (objective diameter/2) + 0.22 - base height
which was modified later to:
Ring Height = (objective diameter/2) + 0.9 - (action diameter/2) - base height
or, more algebraically:
Hr = (Do/2) + 0.9 - (Da/2) - Hb
My calculations use the second formula, which I have modified to use the exact geometry of any chassis:
Hr = (Do/2) + (Dg/2) - (Da/2) - Hb
See below for definitions of the variables and example calculations. And yes... I'm an engineer, so you'll have to excuse the rigorous explanations.
--------------------------
METHOD 1 - New Rings
If you plan to buy new scope rings (or mount) for your chassis, the basic formula for calculating ring height is:
Ring Height (Hr) = (Do/2) + (Dg/2) - (Da/2) - Hb
But, if you've added a top rail to the handguard that extends under the scope, and/or have a lens cap for the objective (I have both), those values need to be included as well. So now:
Hr = (Do/2) + (Dg/2) - (Da/2) - Hb + Hg + Hc
And if you use a sloped optics base (which I don't) you must account for the downward slope of the base as well.
This is calculated using the Tangent of the angle of the base multiplied by the distance
the scope projects beyond the end of the base (don't forget to include the sunshade).
For example, a scope extending 10" past the end of a 20 MOA sloped base will need an
additional ~0.06" clearance:
Fs = TAN(0.333) x 10" = 0.0582" [ where 20 MOA = 0.333 deg ]
So finally, the full generic formula becomes:
Hr = (Do/2) + (Dg/2) - (Da/2) - Hb + Hg + Hc + Fs
Where, for my rifle & equipment:
Do - Objective Bell diameter = 1.95" SWFA SS 10x42 scope
Dg - Handguard diameter = 1.75" XLR Evolution Chassis
Da - Action diameter = 1.36" Remington 700 SA
Hb - Optics Base height = 0.38" Warne 0-MOA base
Hg - Handguard Top Rail height = 0.25" XLR 11" top rail
Hc - Scope Cap rim thickness = 0.06" Butler Creek caps
Fs - Factor for sloped base = 0.0" Warne 0-MOA base
The example calculation for my rifle is then:
Hr = (Do/2) + (Dg/2) - (Da/2) - Hb + Hg + Hc + Fs
= (1.95/2) + (1.75/2) - (1.36/2) - 0.38 + 0.25 + 0.06 + 0.0
= 0.975 + 0.875 - 0.68 - 0.38 + 0.25 + 0.06
Hr = 1.10"
This represents the absolute minimum ring height and should leave the rim of the scope cap just touching the handguard top rail. But I want at least 0.05" (>1mm) clearance between the scope and the rail to provide some margin for error and ensure there is no contact, so I'll need rings at least 1.15" high.
------------------------------
METHOD 2 - Existing Rings
If you have already have a set of rings (or as in my case, a scope mount) and just want to determine if they will provide enough clearance, you can use the following:
Clearance = [ (Da/2) + Hb + Hr - Fs ] - [ (Do/2) + (Dg/2) + Hg + Hc ]
Here's how...
First, know (or accurately measure) the height of your rings. For my rig:
Hr - Ring Height = 1.25" Armalite scope mount
Next, calculate the height of the scope's optical centerline above the bore of the barrel:
Scope Centerline above bore (Hs) = (Da/2) + Hb + Hr - Fs
= 0.68 + 0.38 + 1.25 - 0.0
= 2.31"
Then, determine the overall height of the hardware stacked up between the scope centerline and the bore:
Hardware Stack-up (Hw) = (Do/2) + (Dg/2) + Hg + Hc
= 0.975 + 0.875 + 0.25 + 0.06
= 2.16"
Finally, the clearance between the scope and the rifle is the difference between the two:
(note that a negative value indicates interference)
Clearance = Hs - Hw
= 2.31" - 2.16"
= 0.15"
Only 0.1" higher than the minimum clearance I used in Option 1... almost perfect.
-------------------------
Notes:
Ring Height is measured from the top of the optics base to the centerline of the ring.
Objective diameter is the actual outside diameter of the objective bell, not the diameter of the aperture. For example, my scope's objective aperture is 42 mm, but the bell diameter is 49.5 mm.
If you can't get the dimensions of your equipment from the manufacturer or find them on-line you will have to measure them yourself. And accurate measurements are essential... don't just eyeball them with a cheap ruler.
My calculations are fairly precise, so given potential measurement errors and different hardware tolerances, you may want to include additional margin of clearance, as I did in the first example.
Below I provide two detailed methods for determining scope ring height for a chassis system; the first is a slight modification of XLR's method, the second is a closely related method to determine if your existing rings will work for the chassis. Both methods should work for any scope and just about any chassis system that employs a handguard around the barrel similar to that of the XLR Evolution chassis. All you need to do is find your hardware measurements (or measure accurately) and then do some arithmetic.
I'm sure some of you guys already know this stuff, but there are apparently many out there who don't... it certainly was new to me. So here goes.
I found two formulas provided by XLR's Kyle Miller for calculating ring height...
The first was:
Ring Height = (objective diameter/2) + 0.22 - base height
which was modified later to:
Ring Height = (objective diameter/2) + 0.9 - (action diameter/2) - base height
or, more algebraically:
Hr = (Do/2) + 0.9 - (Da/2) - Hb
My calculations use the second formula, which I have modified to use the exact geometry of any chassis:
Hr = (Do/2) + (Dg/2) - (Da/2) - Hb
See below for definitions of the variables and example calculations. And yes... I'm an engineer, so you'll have to excuse the rigorous explanations.
--------------------------
METHOD 1 - New Rings
If you plan to buy new scope rings (or mount) for your chassis, the basic formula for calculating ring height is:
Ring Height (Hr) = (Do/2) + (Dg/2) - (Da/2) - Hb
But, if you've added a top rail to the handguard that extends under the scope, and/or have a lens cap for the objective (I have both), those values need to be included as well. So now:
Hr = (Do/2) + (Dg/2) - (Da/2) - Hb + Hg + Hc
And if you use a sloped optics base (which I don't) you must account for the downward slope of the base as well.
This is calculated using the Tangent of the angle of the base multiplied by the distance
the scope projects beyond the end of the base (don't forget to include the sunshade).
For example, a scope extending 10" past the end of a 20 MOA sloped base will need an
additional ~0.06" clearance:
Fs = TAN(0.333) x 10" = 0.0582" [ where 20 MOA = 0.333 deg ]
So finally, the full generic formula becomes:
Hr = (Do/2) + (Dg/2) - (Da/2) - Hb + Hg + Hc + Fs
Where, for my rifle & equipment:
Do - Objective Bell diameter = 1.95" SWFA SS 10x42 scope
Dg - Handguard diameter = 1.75" XLR Evolution Chassis
Da - Action diameter = 1.36" Remington 700 SA
Hb - Optics Base height = 0.38" Warne 0-MOA base
Hg - Handguard Top Rail height = 0.25" XLR 11" top rail
Hc - Scope Cap rim thickness = 0.06" Butler Creek caps
Fs - Factor for sloped base = 0.0" Warne 0-MOA base
The example calculation for my rifle is then:
Hr = (Do/2) + (Dg/2) - (Da/2) - Hb + Hg + Hc + Fs
= (1.95/2) + (1.75/2) - (1.36/2) - 0.38 + 0.25 + 0.06 + 0.0
= 0.975 + 0.875 - 0.68 - 0.38 + 0.25 + 0.06
Hr = 1.10"
This represents the absolute minimum ring height and should leave the rim of the scope cap just touching the handguard top rail. But I want at least 0.05" (>1mm) clearance between the scope and the rail to provide some margin for error and ensure there is no contact, so I'll need rings at least 1.15" high.
------------------------------
METHOD 2 - Existing Rings
If you have already have a set of rings (or as in my case, a scope mount) and just want to determine if they will provide enough clearance, you can use the following:
Clearance = [ (Da/2) + Hb + Hr - Fs ] - [ (Do/2) + (Dg/2) + Hg + Hc ]
Here's how...
First, know (or accurately measure) the height of your rings. For my rig:
Hr - Ring Height = 1.25" Armalite scope mount
Next, calculate the height of the scope's optical centerline above the bore of the barrel:
Scope Centerline above bore (Hs) = (Da/2) + Hb + Hr - Fs
= 0.68 + 0.38 + 1.25 - 0.0
= 2.31"
Then, determine the overall height of the hardware stacked up between the scope centerline and the bore:
Hardware Stack-up (Hw) = (Do/2) + (Dg/2) + Hg + Hc
= 0.975 + 0.875 + 0.25 + 0.06
= 2.16"
Finally, the clearance between the scope and the rifle is the difference between the two:
(note that a negative value indicates interference)
Clearance = Hs - Hw
= 2.31" - 2.16"
= 0.15"
Only 0.1" higher than the minimum clearance I used in Option 1... almost perfect.
-------------------------
Notes:
Ring Height is measured from the top of the optics base to the centerline of the ring.
Objective diameter is the actual outside diameter of the objective bell, not the diameter of the aperture. For example, my scope's objective aperture is 42 mm, but the bell diameter is 49.5 mm.
If you can't get the dimensions of your equipment from the manufacturer or find them on-line you will have to measure them yourself. And accurate measurements are essential... don't just eyeball them with a cheap ruler.
My calculations are fairly precise, so given potential measurement errors and different hardware tolerances, you may want to include additional margin of clearance, as I did in the first example.
.
