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# Cosine Indicator

#50
12-18-2004, 04:04 PM
 Posts: n/a
Re: Cosine Indicator

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
#51
12-18-2004, 08:40 PM
 Silver Member Join Date: Nov 2004 Location: GF Montana Posts: 467
Re: Cosine Indicator

I see what your saying. I think you were thinking like a practical hunter [img]/ubbthreads/images/graemlins/cool.gif[/img] and I was an unclear ass-uming mathamatican [img]/ubbthreads/images/graemlins/frown.gif[/img] [img]/ubbthreads/images/graemlins/confused.gif[/img] 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
#52
12-18-2004, 08:57 PM
 Posts: n/a
Re: Cosine Indicator

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
#53
12-27-2004, 07:38 PM
 Posts: n/a
Re: Cosine Indicator

#54
12-30-2004, 01:33 AM
 Silver Member Join Date: Nov 2004 Location: GF Montana Posts: 467
Re: Cosine Indicator

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
#55
12-30-2004, 02:12 AM
 Posts: n/a
Re: Cosine Indicator

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... [img]/ubbthreads/images/graemlins/tongue.gif[/img] [img]/ubbthreads/images/graemlins/crazy.gif[/img] [img]/ubbthreads/images/graemlins/tongue.gif[/img]
#56
12-31-2004, 12:52 AM
 Silver Member Join Date: Nov 2004 Location: GF Montana Posts: 467
Re: Cosine Indicator

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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