Optics Math Homework.

[fonzy]

Ok guys plz correct me or show me where I'm wrong so that I can learn. I'm throwing out a hypothetical scenario (equation). I've watched the videos but I'm not sure if I interpreted or comprehended it right.

How I came about this was I need a scope for my Savage fvsr. I was thinking of going fixed power mil-dot. That way from 0-50 I can use my crosshairs beyond that I can mil it and use the appropriate mildot for hold over.

Hypothetically I have a 4x fixed mildot. I'm shooting 36gr CPHP Mini-Mag. I'm zeroed for 50yrds. I'm aiming at a target that's 200 yrds. According to my ballistics report (Nikon Spot On) the round should drop 68 inches. Average mil dot scope contains 5 mildots on each side of intersection. Each mil equal 3.6 inches at 100 yds at 200 I assume 7.2. So on each side I have 5mil x 7.2 = 36 inches to play with.

So far is my math correct?

Now 68 inches minus 36 =32 inches short. So now I have to spin my turrets 4.5 moa which equal 4.5 x 7.2= 32.4 And I should be on target on the last mil dot.

And the scopes are 1/4 moa at 100 yds. I assume at 200 they are half moa. So I would turn 9 turns? .5moa x 9 clicks = 4.5 moa.


Sorry for the long posts guys. I assure 100 percent it's appreciated. No one I know at work shoots or in the family shoots. The ones at work that hunt say " I just aim in the middle".

I want to start my lil log book. I just bought this rifle and looking for a scope to get on it. Thanks a million again guys.

[RuskieShooter]

Near as I can tell, your math looks good to me.

Question: Why don't you zero at 100yds then adjust for 200yds and 50yds? Doing so may allow to leave the turrets alone.

-Ruskie

[ar15barrels]

And the scopes are 1/4 moa at 100 yds. I assume at 200 they are half moa. So I would turn 9 turns? .5moa x 9 clicks = 4.5 moa.

moa is an angle, not a distance.
moa is the same angle at all distances.



9moa at 100yds is the same as 9moa at 200yds.
Angle has nothing to do with inches of drop until you introduce a distance into the equation.
The picture above shows how much scope adjustment you get with each angle measurement system at each distance.
Ignore inches of drop from ALL figuring and work purely in angles and your life will be much easier.

So, look at your bullet drop in ANGLE and then figure out how much ANGLE you need to dial and hold from there.
Don't make it more difficult or confusing by adding in inches when you really don't need them.

1 mil is 3.438 moa.
Round to 3.5 for quick math...

My 22 is zeroed at 50yds.
To hit at 100yds, I need to dial about 7 moa to get re-sighted.
I could also just hold over 2 mils without dialing.
To hit at 200yds, I need to dial about 25 moa to get re-sighted.
Note that inches of drop never was even part of my thinking.

Here are my 22 dope cards: www.ar15barrels.com/data/22dope.pdf

[therealnickb]

How do you measure the bullet drop angle without knowing how many inches or mils it fell?

[ar15barrels]

How do you measure the bullet drop angle without knowing how many inches or mils it fell?

Inches and Mils are completely different units of measure.
It's like comparing a tape measure to a measuring cup.
How long is a gallon of water?
How many fluid ounces in a foot?

The ballistics calculator does all the math.

Start here:

http://www.jbmballistics.com/ballistics/calculators/calculators.shtml

Or, you can simply OBSERVE the drop angle through your scope using the reticle to measure where a shot lands after you fire it.

[therealnickb]

Inches and mils both measure length.

[advocatusdiaboli]

Inches and mils both measure length.

Um, not really. mil is short for milliradian (thousandths of a radian) which is an angle measurement (2xPi radians = 360 degrees). MOA (a minute is 1/60 of a degree) and mil are both measures of angle. Trig tells us that angles remain constant even as the sides of the triangle (distances) grow which is what Randall was trying to get across.

[therealnickb]

Mil is short for a lot of things. I never had a mil dot scope and assumed wrongly it was linear. Thanks for educating me.

So back to my first question. How can you determine angle if you don't know how far the bullet drops?

[advocatusdiaboli]

Mil is short for a lot of things. I never had a mil dot scope and assumed wrongly it was linear. Thanks for educating me.

No problem—glad I could help. That is what continues be great about this site—people helping each about our common interest in firearms. I get schooled more often than I'll admit here too.

So back to my first question. How can you determine angle if you don't know how far the bullet drops?

Keeping the in-flight ballistics model simple by neglecting higher order terms, a bullet's flight is basically a parabola from the time it leaves the muzzle gaining altitude because your zero aims it upward until it stops gaining as it loses energy and momentum and drops to terminal impact—it is always being pulled downward by the gravitational constant (g) as it's dissipates it forward momentum losing it energy. It crosses your zero point twice if the range is long enough: once on he way up (your zero) and again as it drops back through your secondary zero on it's way to the earth. In between it is above you zero point and below from the muzzle to the first zero and below from the second zero to impact.

It boils down to a simple physics differential equation vector problem easily solved with trigonometry when you know: mass, energy, angle, and distance. Any good ballistics calculator will plot that trajectory based on bullet weight, ballistic coefficient (drag estimate, etc.), muzzle velocity, and zero. You input your data, it spits out a curve tellings you inches above or below your zero at a given distance. You then either hold-over or under the right angle (MOA or mil) that will give you that many inches at the range or adjust you BDC (bullet drop compensation) on your scope and aim center cross hairs (well maybe left or right for windage). Notice I said "at the range" because 1 mil means a different vertical distance at any given range.

Randall gave you a link to one program and gave you a chart that converts MOA and mil fractions to vertical distance—you can also do it with a calculator and it's built in to some longer-range (and progressively expensive) range finders.

There are also programs for iOS and Android phone, tablets, and even free open source programs that do it, many allow you to include those higher order terms we neglected at first blush (humidity, altitude, temperature, wind speed and direction, etc.). Heck you can even add in the Coriolis spin of the earth on some if you want to split hairs (hairs on the head of a tango at 3,000 meters that is)—it offsets you about a couple inches at 1,000 meters and more beyond and the math is not simple for you—but it is for the calculator.

SF spotters use ballistic calculators or calculating range finders to get the answer for specific ranges when speed and accuracy save lives but they and the sniper can do it the old fashioned way (they need to be able to—equipment can fail in battle). You should learn too so you don't lose the Antelope, Ram, or Elk shot of a life time because you forgot to put in a fresh battery or moisture or cold caused failure. Shot angle matters too by the way if you are shooting down or up, the flat shot mil value will be wrong—enough to miss a longer shot.

Well, I've droned on too long & the wife is telling me breakfast is ready and the Springers need a run. Google is you friend and you'll find YouTube and other resources. Good luck and good, accurate shooting.

[therealnickb]

Wow. Thanks for all the effort.

Here's the deal though. I'm pretty familiar with the math & zero process. I was trying to ask ar15 how he calculated his angles while disregarding the distance a bullet dropped.

I know there are calculators to do the math for you, but you need to know the drop to set your angle. (As you pointed out in your reply.) right?

[ar15barrels]

Inches and mils both measure length.

Can you show me a tape measure marked in milradians?
I would like to measure a room in my house for some new carpet.

[ar15barrels]

I was trying to ask ar15 how he calculated his angles while disregarding the distance a bullet dropped.

I know there are calculators to do the math for you, but you need to know the drop to set your angle. (As you pointed out in your reply.) right?

Incorrect.
You don't need to know the inches of drop.

The ballistics calculator that determined the drop gave me the output in an angular measurement for each specific distance that I asked for.
Look at the 22dope cards I posted a link to above.
It is in 5 yard steps which is quite precise enough for 22 at any distance you would expect to make hits.
Scopes work with angular measurements.
Only angular measurements are useful.
Any ballistic calculator that does NOT give you angular measurement results is useless to me.
Inches of drop are useless to me.
I can't dial my scope knob to correct for 68 inches of drop without first converting it to an angle.

[advocatusdiaboli]

Wow. Thanks for all the effort.

Here's the deal though. I'm pretty familiar with the math & zero process. I was trying to ask ar15 how he calculated his angles while disregarding the distance a bullet dropped.

I know there are calculators to do the math for you, but you need to know the drop to set your angle. (As you pointed out in your reply.) right?

[advocatusdiaboli]

Randall,

What is a good BC to use for 22LR? I have Rem Golden Bullets plated HP and CCI mini-mag Round Nose cartridges. I am setting my Sig 522 up for some squirrel shooting at a friend's ranch tomorrow so I am going to change the zero to 100 yds (at 50 yds it's all drop IIRC). I just bought a new-fangled green-laser bore sight to zero at home instead of the old fashioned shooting way (though I know I'll need to tune it on the range at some point). I don't have a scope only pop-up irons so need to hold over or under in Squirrel Head units (couldn't find a scope calibrated in those)

[Izzy43]

Randall,

What is a good BC to use for 22LR? I have Rem Golden Bullets plated HP and CCI mini-mag Round Nose cartridges. I am setting my Sig 522 up for some squirrel shooting at a friend's ranch tomorrow so I am going to change the zero to 100 yds (at 50 yds it's all drop IIRC). I just bought a new-fangled green-laser bore sight to zero at home instead of the old fashioned shooting way (though I know I'll need to tune it on the range at some point). I don't have a scope only pop-up irons so need to hold over or under in Squirrel Head units (couldn't find a scope calibrated in those)

This is not a BDC scope but 1/2 Mildot but may work for your application. Several different magnification ranges are available. I have no idea of the quality of these scopes. http://www.eabco.com/mildotriflescopes.htm

There is also the Nikon Prostaff Rimfire 3-9x40mm with parallax set @ 50yds and a BDC reticle. Nice glass and the BDC works well. I had one and was able to shoot out to 150yds using the reticle and squirrel's head accurate for a good shooter. The Nikon website has a ballistics calculator for all their scopes and reticles which allows you to calibrate the reticle for the type of ammo that you use and it works well. You have to register to use it but no cost. You might want to try out the calculator before buying a scope to see if it works for you.