Cosine Indicator

With the example I wrote previously:

<font color="red"> 10.63 MOA - 2.954 MOA = 7.676 MOA (corrected MOA you'd now dial) My RSI Ballistics Lab program for example predicts the corrected drop to be 7.68 MOA too.
</font>

Now instead, use the method that takes the bullet path MOA and multiply it by the cosine of the incline angle.

What you get is 8.7 MOA not 7.68 MOA... which is a 7.8" deviation at 770 yards... Now remember, none of our rifles shoot one hole groups at 770 yards, so factor in the additional error due to the rifle and your inability to shoot in one hole at that range and you have the true picture. Did you miss? At 1200 yards it would be MUCH further off than that, using this method it would... even further off multiplying the range by the cosine for a "corrected range"... this is just a fact.

The steeper the angle, and/or farther the distance, the more error these two methods introduce.

How precise do you need to be? Or really, at what point do you find out the method you've been using has failed you as a result of their inherant inaccuracy.


BC,

Your calculation <font color="red"> 1.0 minus 30 degree cosine of .87 = .13 X actual drop of 5.73 MOA = .745 subtracted from 2.9 MOA bullet path = 2.2 MOA </font> is correctly done.

Sorry I wasn't more clear.



Hunter,

The angle should be in reference to the bore line, and set to zero when leveled... has nothing to do with some angle the scope tube happens to be setting at, 20 MOA base or not. The asymmetrical force of gravity changes trajectory when we change the bore angle from the level fire position, which is 90 degrees to this force of gravity.

The 20 MOA base only allows you to elevate the bore line more while maintaining the same POA, or thus compensate for more bullet drop etc.
 
Brent: I agree with you; the software programs are a bit more accurate. At least they are with Exbal.
Also, not to confuse the matter, however when the sun light is behind you, your shot will hit approx 1/4 moa low. To the right and it will impact approx 1/4 moa left and left, 1/4 moa right. Heavy overcast? Your bullet will impact 1/2 moa low. A medium (4-6 mph) tail wind? Bullet impact will be 1/2 moa low. Some of the finer attributes of Precision Shooting.

As far as how to mount the ACI... The bore of the barrel must be level. Once the ACI is mouinted, loosen the screw on the side an rotate the body as needed, until the 0 cosine lines up with the index mark. To level the bore of the barrel, pull your bolt out, place a bubble level on the inside rail (that the lugs ride on) until it is level. Then make the adjustment.
 
ricka's simple COS example
I posted my EARL a couple days ago but some 2nd ammendment lover /ubbthreads/images/graemlins/blush.gif 1st amm hater /ubbthreads/images/graemlins/frown.gif nuked it.
As W says:
[ QUOTE ]
shooting and the difference between MOA and inches of drop; they do not work the same

[/ QUOTE ]
MOA = Drop in inches/yds*100 - (1.04" would be ridiculous for the field)
So they are directly related.

Do any of the ballistics packages account for uphill vs. downhill? Shooting my 50 BMG 40 degrees up or down at a target 1300 yds away makes a difference.

I was poking fun of the company for the way they mis-spelt COS as cosign. Not sure what value a useless dictionary def gives other than SPAM. It's not what we mathematicians use.
 
B1g_b0re: It is not simple to explain this principle and would take me almost two, maybe three pages to do so, and then it would still be difficult for most people to grasp. So… The bottom line is; NEVER use hold-over's in inches of drop when shooting on angles. If you want to hold-over, ONLY use Mil Radians or Minute of angle.

-W
 
Are you trying to tell a mathematican that 1 MOA is not equal to 1.04" at 100 yards? That angles can't be resolved by vertical and horizontal components?
I think you might be confusing bore line with scope line - the only reason we need the more complicated formula.
I never use hold overs, I have 20 MOA precant on most of my long range guns &amp; 40 MOA on my nightforce equiped 50 BMG's. I simply figure out the drop in inches and calculate the MOA. It works, what should I do, calculate in 1/8 MOA ticks (on my nightForce)?
Now I'm convinced that I need to upgrade to the 2 variable COS formula and aquire ACI.
The 82nd kicks butt - if it works for them, ... well, they are better trained than me - it might work for me /ubbthreads/images/graemlins/cool.gif
 
You guys holding up okay??

These angle discussions get long sometimes /ubbthreads/images/graemlins/smile.gif and I'm a little suprised I missed out on this one... should have been looking around a little more I guess.

Nice deer up above, the guy looks a little like Gort from The Day the Earth Stood Still with that blacked out face.
 
b1g_b0re:
[ QUOTE ]
Are you trying to tell a mathematican that 1 MOA is not equal to 1.04" at 100 yards? That angles can't be resolved by vertical and horizontal components?

[/ QUOTE ]

In a way (excluding the fact that 1 moa = 1.047" at 100 yards) I geuss that's exactly what I have been trying to do only in regards to shooting on angles. However, I think that for some reason we are not conecting. Perhpas you would like to give it a try? Since you are a mathematician, perhaps you can prove to me that a measurement in linear inches of drop is equal and substantive to an angular measurement such as mil-radian or minute of angle when shooting on angles.

-W
 
B1g_b0re… The arced flight of the bullet is not equal to linear inches of drop when shooting on angles. The changing constants of gravity, velocity, ballistic coefficients, and time of flight of the bullet, surpass the non three dimensional models, making multi-dimensional technology necessary. Everything has an equation and since you are a mathematician, you can certainly see the complexity of those values.

But to make this all clearer and easier, I suggest utilizing a ballistic targeting software programs such as "Exbal." Just plug in the temperature, barometric pressure and humidity at your location and it will tell you your holds in either moa, mil-rad or click value. It is shooting made easy and should be utilized before starting your hunt. You can purchase this through Night Force
Night Force Web Site or Perry-systems direct; Perry-systems Web Site
 
I see what your saying. I think you were thinking like a practical hunter /ubbthreads/images/graemlins/cool.gif and I was an unclear ***-uming mathamatican /ubbthreads/images/graemlins/frown.gif /ubbthreads/images/graemlins/confused.gif Yes, you can't linearly map MOA to 1" - actually MOA comes from
SIN(1/60*PI()/180)*100*3*12= <font color="red"> 1.047197536
</font> (well to as many digits as Excel will go. And yes those factors come into play.
Suppose you move the target @ 100 yds up 150 yards. (pointing above 45 deg up (actuall atan(150/100) = 56deg)

150yards * 3ft/yard * 12"/foot = 5400 inches.
Now move your scope up 5400 MOA - and you get your scope pointing 90 degrees up - as 90 degrees * 60min/degree = 5400 MOA.

So what's the best way to use the cos level do ma jig when you're in the hills? I could write a program for WinCe PDA's that uses the improved formula. Or you could just sight your rifle in at the bore (not 100 yards) so drop = path, then you can use the simple cos formula. See my web page and please offer improvements to it.

ricka's explaination of the improved cos formula
 
b1g_b0re:

Personal Data Assistant's, otherwise known as "PDA's" have been around for several years, and have had their place with anyone that needs personal data at their fingertips. These electronic notebooks are manufactured by "Palm", "Dell", and a host of others and are relatively small and convenient to use. They are in use as language translators, calendars, and phone and address books; and are also in use as word processors. They have add ons such as GPS units for getting around town and most importantly, for a hunter's needs, run specialized ballistic targeting software such as "Perry-Systems Exbal."

Exbal for Dell's pocket PC's or Palm's PDA's are an absolute gem and a hunters friend. By inputting the pertinent data before you begin your hunt, you will save countless hours of stalking, greatly increase your hit ratio and learn the fundamentals of external ballistics; hence the name, "Exbal." These hand held devices use the same rigorous ballistic motion equations that are used on the PC version. Like the PC version, both the Pocket PC and the Palm version are very efficient and do not require much memory at all (approximately 40K). It has been validated on Palm OS 3.1, 3.5, 4.0 and 5.2 using systems with at least 1 MB of memory. In addition, it accurately determines where your bullet will go in relation to the line of sight and performs three dimensional motion equation calculations that account for air resistance, gravity, and wind drift.

This is cutting edge technology that takes about ten minutes to learn and provides the hunter with real time, in the field holds, delivered in either "Minute of Angle, Mil Radian or clicks." Once the cosine value is entered into the software, it will then compute the corrected for gravity distance to target, incorporating the bullet's time of flight commingled with gravity and other entities into the equation.

When speaking with other hunters about all of this, their usual response is, "I don't have time to do all of this! I just aim and drop em;" or, "sounds like an awful lot of stuff to remember to me…"

This is where I usually take a deep breath and think to myself, "Exbal" is synonymous with shooting made easy. How can I show this guy that "Exbal" is not a stumbling block, but a stepping stone?

Several times a month I teach a Precision Shooting 1 class, which includes "Exbal" ballistic targeting software as part of the curriculum. I do this contrary to methods taught by other instructors who spend a day having their students zero their rifles out to six hundred yards, only to have the weather conditions change, altitude change, along with their previously acquired, now obsolete zeros. With Exbal, they are on target in moments, not hours; and in any environment.

This software is robust and feature rich. To break it down, there are three main windows or forms, each with its own instruction set. The first form contains your ballistic data such as bullet weight, site in distance, sight height above bore, muzzle velocity and the ballistic coefficient of your bullet; all of which you input; and of-coarse, you can do this with any of your loads and save them all for future use.

The second window or form is your current field data and contains the current weather conditions such as temperature, barometric pressure and humidity; again, all of which you input.

The third window or form is the target data and contains areas for target distance, wind speed and direction at the muzzle, target speed, and cosine number of the angle that you are holding on or the angle itself (your choice).
There are other additional forms provided such as multiple ballistic coefficients and more. If you don't know the ballistic coefficient of a certain bullet, it is there for you to look up.

Once this information is inputted into the software it will calculate and display your holds for elevation, windage and leads, either in Minute of Angle, Mil Radians, or Clicks. The software will also calculate and display a complete data card with your distance depicted in yards or meters, in 10, 25 or 50 yard increments out to two-thousand yards.

The way that I instruct my students to use this is pretty straight forward. To begin with, the user must know the velocity of the cartridges that they are using. So, the student must chronograph their loads. The student must also know what the ballistic coefficient of the bullet is. To do this they either have to know what bullet is being used, so that they can look it up on the ballistic coefficient library that is available in the software, or call the manufacturer. And of-coarse, the student needs to know the bullet weight and the distance that they have zeroed their rifle at. This information can be saved to a file within the software and referenced at anytime.

With that data inputted and stored into the software they are ready to move onto the next step, which is inputting the current field meteorological (weather) conditions for where they are right now. This consists of temperature, barometric pressure and humidity. Unless it is raining, humidity really doesn't have too much of an effect on the bullet. But because it is part of the equation, we will input it. Humidity, (other than rain or a heavy drizzle) affects the bullet about 1/10th of 1% or roughly 1/100th of an inch at one thousand yards. So we take a quick weather reading which includes as mentioned before, the temperature, uncorrected for altitude barometric pressure, and humidity and input that into the software.

Uncorrected for altitude barometric pressure simply means that we set the instrument to a constant elevation of zero feet. This is because we want a true barometric pressure reading. 28.27 bar at sea level is the same as 28.27 bar at 10,000 feet. The instrument that I use to accomplish this is a small handheld weather station such as a Kestrel 4000 or the Brunton Sherpa.

The next step is to move onto the target data form. Here we input the distance to target, (even though we have not began our hunt), wind speed (I use a standard 10 mph), wind direction (I use a standard full value wind from 3 O'clock), target speed of 1mph and although there is a place for the cosine number or angle of hold to be inputted, I leave that out for now. The last step here is to click on the calculate button. The software will deliver a hold for what ever distance you inputted, however the final step is to click on the make table button. This will deliver all of your elevation, windage and lead holds as far out as two-thousand yards and as previously mentioned, in Minute of Angle, Mil Radian or Clicks. Once these steps have been accomplished, copy your data onto a write in the rain paper or notepad and either place it in your pocket, tape it to the side of your rifle or where ever you prefer to store it.

When you get into the field and spot your quarry, all you have to do is take three readings; 1) range your distance to target, 2) obtain a wind reading, and 3) the cosine number of the angle that you are holding on. Pull out your data card and do a couple of equations and hold on target where your card tells you to. It is pretty much that simple.

There is other targeting software available on the market, however Exbal utilizes up to date ballistic tables based on current drag models; which is one of the main reasons that I use it and highly recommend it, especially if you shoot at different elevations. The software also contains a ballistic reticle analysis and trajectory validation if you care to use it. If there is one thing you can do to improve your shooting ability, eliminate the guesswork and assist you in making your hunts more successful, it is utilizing Exbal. Understanding the physics of ballistics can give you a whole new approach and perspective to hunting. If you happen to be a LE Shooter, this approach will alleviate additional stress and liability issues as well.

The suggested retail price for "Exbal," is $70.00, and can be purchased through Light Force USA.



Light Force USA
Exbal Ballistic Targeting Software
1040 Hazen Lane
Orofino, Idaho 83544
(208) 476-9814
http://www.nightforceoptics.com


Perry Systems
My address is PO Box 581
Bishop, TX 78343
Phone: 361-584-1424
www.Perry-Systems.com
 
Yes, thanks.

If you're hunting in an area where there is a good chance of uphill or downhill shooting, why not sight your rifle in for 0' in lieu of 100 yards, that way the more complicated formula is reduced to the simple formula, ie
a = d*(1-cos(w)) - p
becomes
a = d*cos(w)
where a = actual drop
d = drop
p = path

see the bottom of ricka's COS page
 
b1g_b0re: You still need to take into account the bullets time of flight as it is still traveling the entire length of the sloped distance... Just purchase Exbal and a good pocket PC. COME ON MAN... /ubbthreads/images/graemlins/tongue.gif /ubbthreads/images/graemlins/crazy.gif /ubbthreads/images/graemlins/tongue.gif
 
Does Exbal take into account the longer TOF shooting uphill vs. down - or like most ballistics programs that do angles, does it consider a 1000 yard 30 deg incline the same as 1000 yard decline?

I expect the worst case for me would be 750 yards @ 25 deg - I doubt TOF would contribue more than a std dev of my shots.
 
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