Sight Height and Elevation Required to Target

[Vio515]

Hello Hide Members,

I was asked this question the other day at my local rifle club and I did not have a good answer. I am hoping the collective can help educate me on this.

The question was “Why does sight height affect how much elevation is required to be dialed into the scope at long distances?”

I drummed up some sample ballistic data using a 175 SMK @ 2650 MV, 100 yard Zero, so everything is approximate.

Example:

Sight height of 1 inch

MOA @ 1000 yards = 36.9 minutes

Sight height at 2.5 inches

MOA @ 1000 yards = 35.7

36.9 - 35.7 = 1.2 MOA Difference @ 1000 yards due to Sight Height (all other variables were the same)

Can someone provide the technical explanation as to why sight height changes how much elevation is needed to reach a certain distance?

Thanks,
Matt

 

[Pink_Mist]

Your solver is taking the sight height into consideration to align the point of departure and line of sight as zero. Notice when you view your trajectory graph it starts at 0 inches not your sight height (inches). The solver is making all calculations from your bore but you are making the measurements from a few inches above this. That distance grows expediently from 0 yards to 1000. Your bullet is not making a more efficient path what you are seeing is mathematical offset.

36.9 MOA @ 1000 yards = 10.47"x 36.90 = 386.343 inches
35.7 MOA @ 1000 yards = 10.47"x 35.70 = 373.779 inches

386.343" - 373.779" = 12.564" difference at 1000 yards

12.564" = 1.2564" difference at 100 yards (your calibration distance) I expected this to equal 1.5 moa but there is trigonometry that I cannot solve. This is as deep as I can take it but will be returning to complete the challenge.

Look at it this way. If your scope is sitting at exactly 2000 feet of elevation and looking at a target 1000 yards away at the exact same altitude (down to the inch) then place the rifle under the scope, the lower the point of departure is below the sightline the shorter the trajectory path will be because its impacting higher on its arch. That is my theory and I am sticking with it.

 

[Vio515]

Thank you for your time and the explanation on the mathematical offset.

I suspected it had to do with trigonometry however, that math is beyond my knowledge.

I am very interested to hear what else you find on the topic.

 

[theLBC]

simple answer is your 100 yard zero takes into account the angular difference of the sight and barrel.
this angluar difference, usually expressed in sight height in your ballistic calculator, makes a bigger difference the farther you go out.
the greater that angular difference (height) the more that difference is expressed at 1000 yards (or any distance).

 

[Vio515]

Thank you LBC. That is a concise answer and avoids a lot of the nitty gritty math that I have no doubt is quite complex.

 

[Pink_Mist]

Show your math - you only summarized what I just posted.

 

[Pink_Mist]

Vio, we both joined the hide 9 years ago and 9 days apart. And we are both from WI. weird.

 

[Gustav7]

Your solver is taking the sight height into consideration to align the point of departure and line of sight as zero. Notice when you view your trajectory graph it starts at 0 inches not your sight height (inches). The solver is making all calculations from your bore but you are making the measurements from a few inches above this. That distance grows expediently from 0 yards to 1000. Your bullet is not making a more efficient path what you are seeing is mathematical offset.

36.9 MOA @ 1000 yards = 10.47"x 36.90 = 386.343 inches
35.7 MOA @ 1000 yards = 10.47"x 35.70 = 373.779 inches

386.343" - 373.779" = 12.564" difference at 1000 yards

12.564" = 1.2564" difference at 100 yards (your calibration distance) I expected this to equal 1.5 moa but there is trigonometry that I cannot solve. This is as deep as I can take it but will be returning to complete the challenge.

Look at it this way. If your scope is sitting at exactly 2000 feet of elevation and looking at a target 1000 yards away at the exact same altitude (down to the inch) then place the rifle under the scope, the lower the point of departure is below the sightline the shorter the trajectory path will be because its impacting higher on its arch. That is my theory and I am sticking with it.

Your math looks right... but i'm thinking about it in MOA.

12.564" = 1.2564" at 100yds. 1.2564/1.047 = exactly 1.2moa.... which is exactly the difference between the two sight height DOPEs.

I try to think of it like this: The higher the scope, the MORE moa you're accounting for BEFORE 100yds. Your ballistic calculator is only telling you what to dial AFTER 100yds. So it tells you less moa since your zero at 100yds with a higher sight height accounts for more of the overall bullet path than a sight at a lower height.

I could be wrong....but I feel like I'm right lol

 

[theLBC]

another way to picture it is that imagine if the bullet traveled in a straight line with no drop.
now imagine a laser come from both the scope and the barrel.
when you are zeroed for 100 yards, the only time those lasers cross will be at 100 yards, and the farther out you go, the farther apart those laser beams will be.
one part of the ballistic solution is to calculate the distance between those two beams at a given distance.
the second part we think more about is how much the bullet drops from that laser path at that distance.

 

[Vio515]

Per usual, the Hide delivers. Thank you all for the time spent thinking about this question.

 

[Gustav7]

Per usual, the Hide delivers. Thank you all for the time spent thinking about this question.

The Hide abides....dude lol