calculating height over bore

[taliv]

this is somewhat easy to estimate, and it's a bit forgiving if you get it wrong, but i just thought i would share anyway, how to calculate it more precisely

so i happen to know (because i texted them and asked) that my surgeon 591 is .9" from top of pic rail to center of the bore. you could measure this yourself pretty easy on your action.

i also took the nominal spec for my spuhr 4002 mount, which is 1.5" and added them together. the result is 2.4". easy, huh?

except, that is at the face of the action. and the ballistic calculators use height over bore from the muzzle. (we're assuming here your barrel isn't banana shaped, which it probably is)

so to figure that out, we use the trig formula for tangent (theta) = opp / adj

we know the angle theta is 20 MOA (it's a 20MOA base) which means 1/3rd of 1 degree.

so the first step is to figure out the "adjacent" length of the triangle which is basically how far away the barrel and scope would intersect if they were infinitely long. So I solve that equation for adj by dividing 2.4" by tan(1/3) and the result is 412.535"

now to find out the height over bore at the muzzle, i'm going to subtract my barrel length from 412.535". my barrel is 25" but part of it is sticking into the action. I happen to know that from the face of the bolt to the face of the action is .950" on the surgeon 591. (you just have to know these things...) so i subtract .950 from 25 and then subtract the result from 412.525 to get the new adjacent value.

now i solve the equation again for opposite by multiplying tan(1/3) x adjacent and the result is 2.26" which is my height over bore at the muzzle. .14" closer together than they are at the face of the action.

doesn't really make much of a difference, but you know precision shooting and math...

 

[Bart B.]

Remember that the line of sight angle to the scope axis moves opposite to the direction adjustments are made.

With the scope's line of sight now parallel with the scope tube and rail it's set for zeroing a .308 Win load at 600 yards with a 120 inch drop that far away assuming the bore axis is at the same place when the bullet exits.

Click elevation up 20 minutes for a 900 yard zero and the LOS height above the muzzle will go lower .14 inch.

If you bore sight the rifle/scope at infinity, the LOS above the bore axis at the muzzle will go higher .14 inch.

If you're using metallic sights and the front sight aperture/post is directly above the bore axis 1.5 inch, that system's LOS above bore axis will stay at that amount as the rear sight's moved up and down for zeros at different ranges. The rear sight aperture will also be 1.5 inch above bore axis when boresighted at infinity.

The shorter the range, the more sight height effects trajectories. Here's two trajectories for 22 rimfire zeroed at 100 yards; one with sight height above bore at muzzle at 1 inch and the other at 12 inches:

 

[murf]

this doesn't make sense. the ballistics program doesn't know if you are using a 20 moa base, or not. if you are shooting at 50 feet with a 20 moa base your sights are still going to be the height of the center (front to back and top to bottom) of the scope above the bore. you will probably run out of adjustment on the scope, but, again, the program doesn't care. i don't think the program knows how long the barrel is, either.

can you clarify, taliv? i know this doesn't make a whole lot of difference at 400 yards, but i don't know about 1,000 and beyond.

thx,

murf

 

[taliv]

murf, if you mount your scope parallel, like say, on an AR15 flat top, the height over bore is the same at the front of the scope and at the back of the scope and at the muzzle.
when you mount it at an angle, the front of it is closer to the barrel than the back of it. make sense so far? so if you measured height over bore at the front of the scope and at the back of the scope, you'd get two different numbers. so which value would you use?
the answer is neither, you would use the value at the muzzle because that's where the exterior ballistics start. so you have to draw an imaginary line from the center of the scope out to the muzzle, and then see what the height is there, because that's where the calculator starts.

 

[Bart B.]

Taliv, if you draw an imaginary line from the center of the scope out to the muzzle, and then see what the height is there, that height will change if you adjust the scope elevation so the 20 degree angle of LOF down to LOS is lessened for shorter ranges. (Line of) sight height above the muzzle will now be greater. Ballistic calculations assume the sight height is where the LOS is above the bore axis at the muzzle. It doesn't take into account what height the rear iron or scope sight is; just where the LOS is above the muzzle axis. If you bore sight the scope to parallel the LOS to the LOF, the sight height will equal scope axis height above bore.

Did you read what I mentioned in post 2 about the LOS changing from the scope when adjustments were made?

I think it's a waste of time to calculate what the exact sight height is for scope sighted rifles. Just use the scope axis height above bore and use that. A 1/4 inch difference at the muzzle is insignificant for different ranges from zero to over 1000 yards where the real LOS position above bore at the muzzle will be.

Besides, the LOS will be 10 MOA off horizontally from the bore vertical axis with that much wind correction and that's never calculated for in ballistic programs that show wind drift.

 

[JDGray]

Man, I just eyeball a set of calipers from center of my barrel, to the center of my scope!
Boy was I off base.

 

[Bart B.]

JD, you're close enough measuring as you state. Your not off base but hitting a home run in any ball park.

A 1/8 inch error will not make any meaningful difference for trajectory calculations for any sight height. Unless you want your hold over or under amounts at ranges other than what the zero's for to be more precise than that 1/8 inch error will cause. And that's 1/8 inch maximum error.

The details I mention earlier were for folks wanting exact and precise information on sight height used for ballistic data. For me and everyone else, even a 1/4 inch error in measuring the height of your scope axis above bore center is not going to be noticed unless you shoot your stuff no worse than 1/8 MOA through 200 yards.