Trajectory equation for long range

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FNFiveSeven

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Hey all,

Yesterday (and part of today) I decided to sit down and write a small "basic" program that allows you use your calculator (assuming it can be programmed, e.g. my Ti-82) to tell you how much elevation you need to hit your target based on its distance AND inclination/declination from the shooter. I used a cubic fit for the trajectory data (from Sierra) to provide the equations so that you have a continuous "drop" curve, i.e. you can figure out how much drop there is at in-between distances, like 772 yards. I made the program compatible in both metric and english measuring systems and it outputs the answer in both inches,MOA and cm,cm/100m you can use both American and Euro optics. The best part of this program is that it uses Sierra ultra-awesome formula for figuring out how to shoot at elevated/declinated targets, and this program should predict the strike of the bullet to less than 2 inches at all ranges and all angles up to 1000m. Less than 2 inches of error is pretty good at a km considering the error in the rifle will be far, far greater anyway. The parameters for the cubic equations will only work perfectly if you are shooting a 168 grain .308 match bullet out of a 24"bbl, with a scope mounted about 1.5" above the centerline of the bore, and assuming that you are shooting within a couple thousand feet of sea-level. If you want to tune the program to your load, you'll have to re-compute the parameters by doing cubic regression on the data corresponding to your load, which you can usually get from Sierra or whomever... but the rest of the program should still work just fine. Oh yeah, FYI the parameter "D" is absolute bullet drop, i.e. it's always negative at any distance from the muzzle, regardless of what range the rifle is zeroed at. The parameter "I" is the drop of the bullet (in inches) relative to the crosshairs, assuming a 100 yard zero. Good luck and let me know what you think and/or if you have any suggestions. With this program, all you have to do is attach an angle-cosine inclinometer to your rifle, and keep a programmable calculator and laser rangefinder in your rifle case, and you're ready to go shooting beyond 1km up a 45 degree hill.

-Robert

:ClrHome
:Menu("RANGE UNITS","YARDS",1,"METERS",2)
:Lbl 1
:Input "YARDS=?",Y
:Goto 3
:Lbl 2
:Input "METERS=?",M
:M*1.094 --> Y
:Lbl 3
:-3.350352E-7Y^3 - 5.895526E-5Y^2 - 0.0049468159Y + 1.246485221 --> I
:-3.34995E-7Y^3 - 5.901716E-5Y^2 - 0.0483006822Y + 2.994635349 --> D
:Menu("SLOPE CORRECTION","IGNORE",4,"cos @",5,"@",6)
:Lbl 4
:1--> C
:Goto 7
:Lbl 5
:Input "cos @=?",C
:Goto 7
:Lbl 6
:Input "@=?",A
:cos A --> C
:Lbl 7
:-D(1-C)+I --> P
:p*2.54 --> Q
:ClrHome
:(P*95.492966/Y) --> K
:Output(1,1,round(K,2))
:Output(1,9,"MOA")
:Output(3,1,round(P,2))
:Output(3,9,"INCHES")
:Q*(100/(Y/1.094)) --> L
:Output(6,1,round(L,2))
:Output(6,9,"CM/100M")
:Output(8,1,round(Q,1))
:Output(8,9,"CM")
:Stop
 
Last edited by a moderator:
dammit, the "unhappy face" was actually supposed to be a ":" followed by a "(", but the stupid thing decided to "override". Sorry about that.

-Robert
 
Great program!!! Many thanks.



Oh, can you tell me how to get the deer (elk/sheep/hog/lion) to stand still long enough for me to do all the needed cypherin'?
:D
 
Hey Charlie,

Glad you like it. I know it sounds kind of rediculous for hunting, but I wrote the program specifically to be fast. I even added the "IGNORE" option for the inclination/declination angle as default so you can by pass it just by hitting enter twice after entering the range. Heck, if you have a spotter/hunting partner, you can use the program faster than you can use the range finder or turn that elevation dial on your scope. Try it out, you'll see.

Thanks for the feedback,

-Robert
 
Very cool!

I like having thumbrules handy for elevation, wind, temp, altitude, uphill/downhill, etc... For lack of space on my buttplate, I have to distill them down to a couple of key ranges, then extrapolate or interpolate from there.

What I need is a tiny whizwheel (circular sliderule set up for ballistics) that I can tack onto my stock!

Ty
 
Excellent. I'll have to give that a try.

I'm using a Casio FX2.0 Plus and using raw data to find the curve. I zero at a distance, usually 100 yds, obtain distances of impact points away from zero (still set for 100 yds) at various ranges, usually 25 yds, 50 yds, and 200 yds, and let the calculator compute a curve to fit and graph it. (Also use the distance between the center of scope and bore axis for a starting point - 0 yds.) Best curves seem to be cubic. From there, I can pick any point on the curve at any distance and find the rise/drop.
 
Not a whiz-wheel...

But pretty close. I use both of these, one for my 700PSS in .308, one for my Interdiction Rifle in 6.5-06:

milmst.jpg

rifle_card4.gif
 
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