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Interpolation between verified elevaton drops

I have shot my gun at 100, 200, 300, 400, and 500. Based on my shooting, I know the "exact/precise" elevation turret settings at these distances. How can I use this actual data to come up with drops at the 25, 50, and 75 yard increments between each verified 100 yard increment; without shooting the incremental distances? Example 225 yards, 375 yards, 450 yards, etc.

Please don't suggest I just chrono the gun velocity and grab the bc and run through ballistic programs to get the drops. This has never worked well for me and I've found actual shooting often gives different dope than the programs.

Here is the information. I would be VERY grateful for the math formula, etc. that I could use for multiple guns to do the same thing by determining the correct dope for the unshot distances based on the precise hard data from my dope shooting the 100 yard distances.

Tikka T3 TCR .260 Rem.

Bullet: Hornady 129 grain InterLock SP

G1 BC = 0.445

Actual Correct Dial Setting for Elevations:

100 Yards = 0
200 Yards = 1.50
300 Yards = 3.75
400 Yards = 7.50
500 Yards = 11.25
 
If your Ballsitics program doesn't give the same drops as actual shooting, then you have bad inputs. Any decent program or app will give you the precise drops, but all the data must be correct:

Zero distance
Scope height
MV
BC
Temperature
Pressure
Altitude
Humidity (very minor factor, but plug it in anyway)
Wind (cross-wind all cause high or low impact due to aerodynamic jump)

If you have trouble assessing those numbers, you can "true" the model by tweaking MV and BC until it lines up with your real drops. Then you can interpolate using the tool.

However, it's better to have the best inputs possible, so that you can trust the model to correctly account for environmental changes.

The only reason the model will be off is if you have a bullet that doesn't track very well to either a G1 or G7 BC curve. This is basically a non-issue out to 500yd.
 
There is no formula. You need to get accurate inputs for a ballistics calculator and run the numbers. If you do everything right, it should match up with your data, and the ranges filled in by the ballistics calculator should be very accurate at the ranges you are talking about. Sometimes this is easier said than done, but basically, measure everything and it will work.
 
Just wanted to give a shout out to Bryan Litz who hooked me up with the math to make it work perfectly by using a Linear Interpolation Equation Calculator. Very grateful to Mr. Litz now my brain has peace.
light-bulb.gif
 
The most common reason people's actual drops don't match exactly with those predicted by a ballistic calculator typically has to do with the input data, as suggested above. Bryan was very kind to provide you with the solution, but there is a pretty simple method for anyone that has graphing software. Mathematically, the trajectory of a bullet should be closest to a parabola. If you plot your actual data in any programmable graphing software, input the equation for a parabola as the function, and have it plot the best line through your actual data, you can extrapolate the answers you want, at least to as fine a degree as most can likely shoot, because there are no "predictive" ballistic elements required; it's simply a graph of your actual distance vs drop data. Alternatively, you could do the "old school" method, which took me about 2 minutes by hand with a piece of graph paper :). Using this little graph, I estimated the following drops per your original post:

225 yd - 2.0 MOA
375 yd - 6.0 MOA
450 yd - 9.0 MOA

I'd be curious to hear back how these values compare to those you obtained using the Linear Interpolation Equation Calculator. The obvious advantage to doing this type of an exercise electronically is that you can solve for any intermediate value, which may be a little more challenging to estimate from a hand-drawn graph for very fine or unusual increment yardages (i.e. 373 yds). However, the difference in drop over a 5 yd increment is not likely to be one that you can reproducibly shoot.


Drop%20Graph_zpsl1d6jqx8.jpg
 
There are indeed a number of generalized polynomial forms that can be used for interpolation. Second order or parabolic general forms come immediately to mind.

Using your data, you come very close with the following very crude second order model -

(((d/100)^2*-10.4785714)+((d/100)*4.071428571)+6.75)/(d/100)

where "d" is the distance in yards.

I'm assuming your dial settings correspond to minutes of angle. The residuals (error) are greatest at shorter distances - the gap between the actual and predicted values close very quickly beyond values of 300 for "d".
 
The most common reason people's actual drops don't match exactly with those predicted by a ballistic calculator typically has to do with the input data, as suggested above. Bryan was very kind to provide you with the solution, but there is a pretty simple method for anyone that has graphing software. Mathematically, the trajectory of a bullet should be closest to a parabola. If you plot your actual data in any programmable graphing software, input the equation for a parabola as the function, and have it plot the best line through your actual data, you can extrapolate the answers you want, at least to as fine a degree as most can likely shoot, because there are no "predictive" ballistic elements required; it's simply a graph of your actual distance vs drop data. Alternatively, you could do the "old school" method, which took me about 2 minutes by hand with a piece of graph paper :). Using this little graph, I estimated the following drops per your original post:

225 yd - 2.0 MOA
375 yd - 6.0 MOA
450 yd - 9.0 MOA

I'd be curious to hear back how these values compare to those you obtained using the Linear Interpolation Equation Calculator. The obvious advantage to doing this type of an exercise electronically is that you can solve for any intermediate value, which may be a little more challenging to estimate from a hand-drawn graph for very fine or unusual increment yardages (i.e. 373 yds). However, the difference in drop over a 5 yd increment is not likely to be one that you can reproducibly shoot.


Drop%20Graph_zpsl1d6jqx8.jpg
 
Here is my actual chart, Gstaylorg:

500 11.25 4475 10.25 3.75450 9.50 3.5425 8.50 3.25400 7.50 3375 6.50 2.75350 5.50 2.5325 4.75 2.5300 3.75 2.25275 3.25 2250 2.75 1.75225 2.00 1.5200 1.50 1.5175 1.25 1.25150 0.75 1125 0.50 1100 0.00 0.75 YARDS ELEVATION WINDAGERANGE TURRET 10 mph
 
There are indeed a number of generalized polynomial forms that can be used for interpolation. Second order or parabolic general forms come immediately to mind.

Using your data, you come very close with the following very crude second order model -

(((d/100)^2*-10.4785714)+((d/100)*4.071428571)+6.75)/(d/100)

where "d" is the distance in yards.

I'm assuming your dial settings correspond to minutes of angle. The residuals (error) are greatest at shorter distances - the gap between the actual and predicted values close very quickly beyond values of 300 for "d".

Yes, MOA. Nightforce SHV 5-20
 
Here is my actual chart, Gstaylorg:

500 11.25 4475 10.25 3.75450 9.50 3.5425 8.50 3.25400 7.50 3375 6.50 2.75350 5.50 2.5325 4.75 2.5300 3.75 2.25275 3.25 2250 2.75 1.75225 2.00 1.5200 1.50 1.5175 1.25 1.25150 0.75 1125 0.50 1100 0.00 0.75 YARDS ELEVATION WINDAGERANGE TURRET 10 mph

Thanks for responding, but unfortunately that's complete gibberish at my end. It must have lost the formatting when you cut and pasted it.
 
Here is my actual chart, Gstaylorg:

500 11.25 4
475 10.25 3.75
450 9.50 3.5
425 8.50 3.25
400 7.50 3
375 6.50 2.75
350 5.50 2.5
325 4.75 2.5
300 3.75 2.25
275 3.25 2
250 2.75 1.75
225 2.00 1.5
200 1.50 1.5
175 1.25 1.25
150 0.75 1
125 0.50 1
100 0.00 0.75
YARDS - ELEVATION - WINDAGE RANGE TURRET 10 mph

Fixed the formatting of your dope chart for others to read.
 

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