Range math?

[RidgeRebel]

How do I figure out true ballistic range w/o range finder or slide rule? Can somebody give me the actual equation to figure this? Like say I am at 3000 feet and I know my target is at say 4500 feet. Using my reticle I figure the target is 800 yards. How do I find the angle and the true range of the taget?
Sorry if this is an old question I couldn't find the answer using the searche function.
Thanks
Elksniper

 

[Strangedays]

Re: Range math?

Are you trying this with a mil dot scope?

 

[RidgeRebel]

Re: Range math?

Yes, Using mil dot scope to find the line of sight range.

 

[Strangedays]

Re: Range math?

buy a mil-dot master. If not give me the ranges you wish to know at what angle and I will give you the actual shooting distance.

 

[RidgeRebel]

Re: Range math?

I would like to know how to do the math without a mil dot master. What's the equation?

 

[Chiller]

Re: Range math?

Are you discussing a high angle shot? or straight line of sight?

 

[Chiller]

Re: Range math?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: elksniper</div><div class="ubbcode-body">How do I figure out true ballistic range w/o range finder or slide rule? Can somebody give me the actual equation to figure this? Like say I am at 3000 feet and I know my target is at say 4500 feet. Using my reticle I figure the target is 800 yards. How do I find the angle and the true range of the taget?
Sorry if this is an old question I couldn't find the answer using the searche function.
Thanks
Elksniper </div></div>

I can only assume I understand the following;
You are at elevation 3000’
Target is at 4500’
The difference being 1500’ or 500 yards
You say that you have ranged the target to be 800 yards
Using Pythagorean theorem you need to solve for the unknown length. You know the hypotenuse and the opposite sides of the triangle (solve for the adjacent)
a^2+b^2=c^2
(500)^2+b^2=(800)^2
b^2=((800)^2-(500)^2)
b=((800)^2-(500)^2)^.5
b=624 yards
angle of 39 degrees
the interesting thing that I still need to learn is how time of flight is dealt with.

 

[Chiller]

Re: Range math?

for the dope it is the cosine x dope

your 800 yards may become a issue in my reading most examples were in the 5-600 yards range. As th bullet slows down time of flight might become more significant.

 

[Shiraz]

Re: Range math?

I'm not sure you can do what you are asking without more equipment.

But here is the formula.
your scope adjustment =
distance to target(a straight line, if you will through the air)
times the cosine of the angle from your position to the target.

so for example.... You lase a target at 941 yards. You measure the angle to the target (up or down, does not matter).
The angle to target is exactly 35 degrees. The cosine for 35 degrees is .81915.

so 941y times .81915 gives you a gravity range to target of 770.8 yards. Dial in 770 yards to your scope, fire score a hit.

the end.

 

[Chiller]

Re: Range math?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Shiraz</div><div class="ubbcode-body">I'm not sure you can do what you are asking without more equipment.

But here is the formula.
your scope adjustment =
distance to target(a straight line, if you will through the air)
times the cosine of the angle from your position to the target.

so for example.... You lase a target at 941 yards. You measure the angle to the target (up or down, does not matter).
The angle to target is exactly 35 degrees. The cosine for 35 degrees is .81915.

so 941y times .81915 gives you a gravity range to target of 770.8 yards. Dial in 770 yards to your scope, fire score a hit.

the end.
</div></div>

First round hit on how large of a target?
Time of Flight and the related drop of the bullet somehow needs to be dealt with.
In your example you used your 770 yards dope but the bullet time of flight is 941 yards.

 

[Lindy]

Re: Range math?

Multiplying the actual range times the cosine of the angle, and then using the dope for that range is called the Rifleman's Rule - and it will not work for a shot at that range and angle. The Rifleman's Rule was used when snipers shot at typically short ranges with angled shots.

The Improved Rifleman's Rule is to multiply your <span style="font-weight: bold">dope</span> for the actual range by the cosine of the angle.

If you want to know why, see this reference from Sierra Ballistics:

Inclined Fire by William McDonald

 

[Shiraz]

Re: Range math?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Chiller</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Shiraz</div><div class="ubbcode-body">I'm not sure you can do what you are asking without more equipment.

But here is the formula.
your scope adjustment =
distance to target(a straight line, if you will through the air)
times the cosine of the angle from your position to the target.

so for example.... You lase a target at 941 yards. You measure the angle to the target (up or down, does not matter).
The angle to target is exactly 35 degrees. The cosine for 35 degrees is .81915.

so 941y times .81915 gives you a gravity range to target of 770.8 yards. Dial in 770 yards to your scope, fire score a hit.

the end.
</div></div>

First round hit on how large of a target?
Time of Flight and the related drop of the bullet somehow needs to be dealt with.
In your example you used your 770 yards dope but the bullet time of flight is 941 yards.
</div></div>

How large of target depends on how accurate you and your rifle are. 2MOA is the standard.
No, time of flight is a consideration for hit probablilty, but not trajectory.
The trajectory is a result of the gravity range, time of flight is not a driving factor in this scenerio.
[I skipped barometric pressure and air temp in this example for simplicity.]

 

[Lindy]

Re: Range math?

Consider the example you posed above, a 941 yard shot at a 35 degree angle, and let's assume a .308 175SMK fired at 2600 on a standard day.

Using the Rifleman's Rule, my ballistic program gives me an elevation of 25 MOA.

Using the Improved Rifleman's Rule, my ballistic program gives me an elevation of 29.75 MOA.

My ballistic program gives me an elevation for the angled shot of 28.9 MOA.

So, assuming that the ballistic program calculated the shot correctly, the Rifleman's Rule is off by 3.9 MOA.

The Improved Rifleman's Rule is only off by 0.85 MOA.

And that almost 4 MOA of error for the Rifleman's Rule amounts to a 39 inch miss at 941 yards.

I think if you need to use one of those, the one to use is obvious.

However, the Sierra reference above has another method which produces a more accurate result, and which can be implemented using a scientific calculator, a slide rule, or even a set of cosine tables.

 

[Chiller]

Re: Range math?

Lindy,

As always. Thank you

 

[RidgeRebel]

Re: Range math?

Thanks for your help guys. Thats the formula I was looking for. Still needs some work on my end.

 

[Chiller]

Re: Range math?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: elksniper</div><div class="ubbcode-body">Thanks for your help guys. Thats the formula I was looking for. Still needs some work on my end. </div></div>

My question would be are you going to use the "rifleman" of "improved rifleman"?

 

[Pat M]

Re: Range math?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lindy</div><div class="ubbcode-body">Multiplying the actual range times the cosine of the angle, and then using the dope for that range is called the Rifleman's Rule - and it will not work for a shot at that range and angle. The Rifleman's Rule was used when snipers shot at typically short ranges with angled shots.

The Improved Rifleman's Rule is to multiply your <span style="font-weight: bold">dope</span> for the actual range by the cosine of the angle.

If you want to know why, see this reference from Sierra Ballistics:

Inclined Fire by William McDonald </div></div>

Bump for the post - a good read

 

[Shiraz]

Re: Range math?

yes,
Please post your test results.

 

[RidgeRebel]

Re: Range math?

I,m going to try the improved riflemans rule hopefuly this weekend I will post my results. There are lots of good places to test these kind of shots. Let me make sure I have this right.
So I have figured the true range of my target to be 900 yards and the angle of the shot to 40 deg. My dope for that distance is 31.5 moa. So I take 31.5 multiply by 0.766044443 the cosine of 40 deg and I get 24.28 moa?

 

[srt_1]

Re: Range math?

Do you know the size of your target?

Height of target (in) / Number Mils x 27.8 = distance to target

Height of target (yrd) / Number Mils x 1000 = distance to target

I use these two formulas to find my range.

 

[Lindy]

Re: Range math?

My calculator says the result of that is 24.13, but you have the method correct.

 

[Chiller]

Re: Range math?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: elksniper</div><div class="ubbcode-body">I,m going to try the improved riflemans rule hopefuly this weekend I will post my results. There are lots of good places to test these kind of shots. Let me make sure I have this right.
So I have figured the true range of my target to be 900 yards and the angle of the shot to 40 deg. My dope for that distance is 31.5 moa. So I take 31.5 multiply by 0.766044443 the cosine of 40 deg and I get 24.28 moa? </div></div>

Correct DOPE to 24.1

Assuming all your other dope is good.

 

[Chiller]

Re: Range math?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: elksniper</div><div class="ubbcode-body">I,m going to try the improved riflemans rule hopefuly this weekend I will post my results. There are lots of good places to test these kind of shots. Let me make sure I have this right.
So I have figured the true range of my target to be 900 yards and the angle of the shot to 40 deg. My dope for that distance is 31.5 moa. So I take 31.5 multiply by 0.766044443 the cosine of 40 deg and I get 24.28 moa? </div></div>

900 is the hypotenuse or the adjacent?
If it is the adjacent that would make the hypotenuse 1,175 yards. 40 degrees is a steep shot. Best of luck, would love to hear how this goes. You will need some pretty good skills to make a first round hit with distance, angle, and atmospheric all well in play.

Curious what caliber you are using.

 

[Chiller]

Re: Range math?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lindy</div><div class="ubbcode-body">My calculator says the result of that is 24.13, but you have the method correct.
</div></div>

Agreed

 

[RidgeRebel]

Re: Range math?

If I can get out early in the morning there should be little to no wind to contend with but in the afternoons it gets pretty rough. I will start out with some closer ranges to work on my skills. I have not shot to 1000 yet. Those numbers were just hypothetical I will be using a 308 w/ 168 grain GMM ammo I will try to get some good pics to post while I'm out.

 

[viav13]

Re: Range math?

Great topic, i always find this confusing too. So I just use the mildot master

Its good to see the actual math behind it all.

 

[Chiller]

Re: Range math?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: elksniper</div><div class="ubbcode-body">If I can get out early in the morning there should be little to no wind to contend with but in the afternoons it gets pretty rough. I will start out with some closer ranges to work on my skills. I have not shot to 1000 yet. Those numbers were just hypothetical I will be using a 308 w/ 168 grain GMM ammo I will try to get some good pics to post while I'm out. </div></div>

YOu have the areas that will allow you to go that far. Please just dont try your dope and I am going through the virgin river....

 

[RidgeRebel]

Re: Range math?

Change in plans: I will now be using a 223 this weekend with 69 SMK's out of RRA Coyote carbine. There won't be as much change in POI at the closer ranges (300-400) but it will still be a good chance to test out what I have learned. Sorry been trying to sell my rifle and am now parting it out. Sold a few parts this morning so I can't use the rifle. But I will definitely get out and do some more testing when I get the new rifle set up. I'll keep an eye out for you chiller.