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  • AB Bullet Drop Formula

    Does anyone know the actual formula used to calculate the output result "Drop (inches)" that appears in the data table generated
    by AB Solution software? Thanks.

  • #2
    I don't think it's proprietary





    H = maximum height (m)

    v0 = initial velocity (m/s)

    g = acceleration due to gravity (9.80 m/s2)

    θ = angle of the initial velocity from the horizontal plane (radians or degrees)


    DocUSMCRetired or BryanLitz am I close?
    Last edited by TacticalDillhole; 09-13-2017, 11:38 AM.
    The lyf so short, the craft so long to lerne
    "Do not pray for an easy life, acquire the strength to endure a difficult one" -Bruce Lee

    Comment


    • #3
      1+ - thanks. I am trying to reconcile output data differences. I was examining a .308 175 SMK @ 2450 fps @ 600 meters with similar atmospherics.
      When I use the iPhone AB app and input the variables the data table indicates ~142" of path inches v. AB Solution where I use their custom drag curve for the same round the data table indicates ~ 182" of drop. The TOF's are virtually identical, as are vertical mil holds. I was surprised to see 40" of difference between the two solutions.

      Comment


      • #4
        Originally posted by strikeeagle1 View Post
        1+ - thanks. I am trying to reconcile output data differences. I was examining a .308 175 SMK @ 2450 fps @ 600 meters with similar atmospherics.
        When I use the iPhone AB app and input the variables the data table indicates ~142" of path inches v. AB Solution where I use their custom drag curve for the same round the data table indicates ~ 182" of drop. The TOF's are virtually identical, as are vertical mil holds. I was surprised to see 40" of difference between the two solutions.
        Well there may be something more to it. If the mil holds are the same and velocity is the same the drop should be the same since those are the only 2 variables in this equation. I may have the wrong formula too. I tagged Bryan and Doc, hopefully one of them will see this and give you some feedback.
        The lyf so short, the craft so long to lerne
        "Do not pray for an easy life, acquire the strength to endure a difficult one" -Bruce Lee

        Comment


        • #5
          Those formulas referenced above are partial solutions for straight forward rectilinear kinematics. I am pretty sure they are using some calculus based iterative solution sets, but a first-order approximation equation would be useful. As the TOF's are virtually identical, it implies the bullet trajectory is subjected to gravity for similar flight duration thus I was expecting closer bullet drop results.
          Last edited by strikeeagle1; 09-13-2017, 01:58 PM.

          Comment


          • #6
            Originally posted by strikeeagle1 View Post
            1+ - thanks. I am trying to reconcile output data differences. I was examining a .308 175 SMK @ 2450 fps @ 600 meters with similar atmospherics.
            When I use the iPhone AB app and input the variables the data table indicates ~142" of path inches v. AB Solution where I use their custom drag curve for the same round the data table indicates ~ 182" of drop. The TOF's are virtually identical, as are vertical mil holds. I was surprised to see 40" of difference between the two solutions.
            Clearly an error. At that distance it's impossible to observe such difference in drop, no matter CDM or not. Are you sure you are not taking drop, in one case and path in the other?

            Comment


            • #7
              Last shot you are exactly correct. I was looking right at the table headings and still didn't see that one was labeled Path and the other Drop. I have been using AB Mobile and Strelok Pro but just began using AB Solutions the other day. Which seems odd that the AB tables would be constructed differently. Now please correct any misunderstanding I have as to bullet drop / path (see below). Screen Shot 2017-09-13 at 6.38.57 PM.png
              IMG_6629.PNG





              I thought the bullet path crossed the line of sight twice whereas the bullet drop (distance below the zero range) did not.
              Thus the bullet path value should always be larger than the bullet drop. The table calculations indicate otherwise.
              This is not the best diagram but I was trying to illustrate trajectory differences ignoring all the #'s. Bullet Path v. Bullet Drop.png
              Last edited by strikeeagle1; 09-13-2017, 07:18 PM.

              Comment


              • #8
                Strikeeagle1:

                I agree, the inconsistency between the terminology in the two programs is very odd to say the least, error prone I'd say. BTW, Path is often confused and incorrectly labeled as Drop, which is, as you posted, another view of the trajectory with just a different baseline reference. Boreline vs sightline. Thanks for sharing the graph it's very helpful and I'm sure many should take a look at it.

                Comment


                • #9


                  I am trying to construct a diagram to illustrate most if not all the common ballistic trajectory terms. This is a prototype. Corrections welcomed.

                  Screen Shot 2017-09-14 at 8.51.12 AM.png
                  Attached Files
                  Last edited by strikeeagle1; 09-14-2017, 08:49 AM.

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                  • #10
                    Drop is the physical drop of the bullet, uncorrected for the line of sight.

                    Path or Elevation is the firing solution needed to impact the target.

                    As far as the calculated firing solution, there is more than just drop going on. Our engine makes adjustments to the density of the air based on the bullets change in elevation. For example, if you were to tell the program you are shooting at an upward angle of 15 degrees it would account for the less dense air during the bullets flight and vice versa for downhill shooting. Just as an example of part of the complexity.
                    Last edited by DocUSMCRetired; 09-14-2017, 10:05 AM.

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                    • #11
                      ^^^ Thanks for the response.

                      Some additional queries.
                      Is the sum of the Maximum Ordinate plus the drop of the bullet below the optical axis roughly equal to the magnitude of Bullet Drop" ?
                      Using common gravity kinematics equation for vertical drop, Dy = 1/2*g*t^2 where "t"=TOF -0.05 gives a pretty good first-order approximation of bullet drop magnitude ?
                      Last edited by strikeeagle1; 09-14-2017, 11:24 AM.

                      Comment


                      • #12
                        Originally posted by strikeeagle1 View Post
                        ^^^ Thanks for the response.

                        Some additional queries.
                        Is the sum of the Maximum Ordinate plus the drop of the bullet below the optical axis roughly equal to the magnitude of Bullet Drop" ?
                        Using common gravity kinematics equation for vertical drop, Dy = 1/2*g*t^2 where "t"=TOF -0.05 gives a pretty good first-order approximation of bullet drop magnitude ?
                        I don't think so since the real calcs are very involved and far from being that simple as far as I can tell.

                        BTW, every decent program out there acccounts, in the right way, for slope shooting, Strelok, AE, JBM, iSnipe, etc since all are based on the same engine with minor touches here and there.

                        Comment


                        • #13
                          Originally posted by LastShot300 View Post

                          I don't think so since the real calcs are very involved and far from being that simple as far as I can tell.

                          BTW, every decent program out there acccounts, in the right way, for slope shooting, Strelok, AE, JBM, iSnipe, etc since all are based on the same engine with minor touches here and there.
                          A number of them are based on the same type of solver (Point Mass) however to say they are based on the same engine is misleading at best. That would be like saying that a Ferrari Formula 1 V12 currently sitting on a race track is the "same engine" as a 1962 Ford Taunus V4 because they are both "V Blocks". While its true they are both V designs, they are not the same engine.

                          Comment


                          • #14
                            Originally posted by DocUSMCRetired View Post

                            A number of them are based on the same type of solver (Point Mass) however to say they are based on the same engine is misleading at best. That would be like saying that a Ferrari Formula 1 V12 currently sitting on a race track is the "same engine" as a 1962 Ford Taunus V4 because they are both "V Blocks". While its true they are both V designs, they are not the same engine.
                            Well, I said with minor touches here and there, not "exactly the same" which is pretty much obvious. Just for the sake of comparing "similar if not equal" engines here goes a simple exercise regarding AB and Hornady solvers, in both cases with the following input. Note the 30° slope.

                            Honestly the minor differences shown here are academic, because we have no real world dope to confirm their respective trueness (which one is better than the other). I still wonder where AB is so different to make it "special" and please no need to mention SD and AJ, it's a moot point not worth a line to comment about for the simple reason they are not part of the 3DOF Point Mass solver that AB or Hornady (or Strelok, JBM, etc) rely upon. I see no evidence whatsoever that either AB or the other solvers (based on the same Point Mass method) are that much different.

                            Ballistic Coefficient: 0.5
                            Velocity (ft/s): 3000
                            Weight (GR): 155
                            Maximum Range (yds): 2000
                            Interval (yds): 100
                            Drag Function (): G1
                            Sight Height (inches): 1.5
                            Shooting Angle (Deg.): 30
                            Zero Range (yds): 100
                            Wind Speed (mph): 10
                            Wind Angle (Deg.): 90
                            Altitude (ft): 0
                            Pressure (hg): 29.92
                            Temperature (F): 59
                            Humidity (%): 0

                            AB Hornady
                            Range Vel MOA Wind MOA Range Velocity MOA Wind MOA
                            0 3000 0.0 0.0 0 3000 0.0 0.0
                            100 2804 0.3 -0.6 100 2805 -0.3 1.0
                            200 2617 -0.9 -1.2 200 2618 0.9 1.0
                            300 2437 -2.6 -1.8 300 2439 2.6 2.0
                            400 2265 -4.7 -2.5 400 2266 4.7 3.0
                            500 2099 -7.1 -3.3 500 2100 7.1 3.0
                            600 1940 -9.8 -4.1 600 1941 9.8 4.0
                            700 1789 -12.8 -5.0 700 1790 12.8 5.0
                            800 1646 -16.2 -5.9 800 1647 16.2 6.0
                            900 1512 -20.1 -6.9 900 1513 20.0 7.0
                            1000 1390 -24.4 -8.0 1000 1391 24.3 8.0
                            1100 1281 -29.3 -9.2 1100 1281 29.3 9.0
                            1200 1186 -34.9 -10.4 1200 1186 34.8 10.0
                            1300 1109 -41.2 -11.7 1300 1108 41.2 12.0
                            1400 1047 -48.4 -13.0 1400 1046 48.3 13.0
                            1500 996 -56.4 -14.2 1500 996 56.3 14.0
                            1600 953 -65.2 -15.5 1600 953 65.1 16.0
                            1700 915 -75.0 -16.8 1700 916 74.9 17.0
                            1800 881 -85.7 -18.0 1800 882 85.5 18.0
                            1900 850 -97.3 -19.2 1900 851 97.1 19.0
                            2000 821 -109.8 -20.4 2000 822 109.6 21.0

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                            • #15
                              Curious why the 30 degree slope and G1 parameters were chosen for comparison.

                              Comment


                              • #16
                                Originally posted by strikeeagle1 View Post
                                Curious why the 30 degree slope and G1 parameters were chosen for comparison.
                                The basic purpose of the example was to debunk hype, said here before.

                                Any drag function will show the same output when doing the comparison, G1, G7 or else. G1 was chosen for no special reason. The reason behind the 30° slope was because, as it was stated before, AB is somehow "special" in the way it solves for uphill or downhill shooting making the necessary compensations for the incline. Well, truth be said, it's not. Period.

                                Comment


                                • #17
                                  ^Thanks.

                                  Comment


                                  • #18
                                    Originally posted by LastShot300 View Post

                                    Well, I said with minor touches here and there, not "exactly the same" which is pretty much obvious. Just for the sake of comparing "similar if not equal" engines here goes a simple exercise regarding AB and Hornady solvers, in both cases with the following input. Note the 30° slope.

                                    Honestly the minor differences shown here are academic, because we have no real world dope to confirm their respective trueness (which one is better than the other). I still wonder where AB is so different to make it "special" and please no need to mention SD and AJ, it's a moot point not worth a line to comment about for the simple reason they are not part of the 3DOF Point Mass solver that AB or Hornady (or Strelok, JBM, etc) rely upon. I see no evidence whatsoever that either AB or the other solvers (based on the same Point Mass method) are that much different.
                                    Ballistic Coefficient: 0.5
                                    Velocity (ft/s): 3000
                                    Weight (GR): 155
                                    Maximum Range (yds): 2000
                                    Interval (yds): 100
                                    Drag Function (): G1
                                    Sight Height (inches): 1.5
                                    Shooting Angle (Deg.): 30
                                    Zero Range (yds): 100
                                    Wind Speed (mph): 10
                                    Wind Angle (Deg.): 90
                                    Altitude (ft): 0
                                    Pressure (hg): 29.92
                                    Temperature (F): 59
                                    Humidity (%): 0
                                    AB Hornady
                                    Range Vel MOA Wind MOA Range Velocity MOA Wind MOA
                                    0 3000 0.0 0.0 0 3000 0.0 0.0
                                    100 2804 0.3 -0.6 100 2805 -0.3 1.0
                                    200 2617 -0.9 -1.2 200 2618 0.9 1.0
                                    300 2437 -2.6 -1.8 300 2439 2.6 2.0
                                    400 2265 -4.7 -2.5 400 2266 4.7 3.0
                                    500 2099 -7.1 -3.3 500 2100 7.1 3.0
                                    600 1940 -9.8 -4.1 600 1941 9.8 4.0
                                    700 1789 -12.8 -5.0 700 1790 12.8 5.0
                                    800 1646 -16.2 -5.9 800 1647 16.2 6.0
                                    900 1512 -20.1 -6.9 900 1513 20.0 7.0
                                    1000 1390 -24.4 -8.0 1000 1391 24.3 8.0
                                    1100 1281 -29.3 -9.2 1100 1281 29.3 9.0
                                    1200 1186 -34.9 -10.4 1200 1186 34.8 10.0
                                    1300 1109 -41.2 -11.7 1300 1108 41.2 12.0
                                    1400 1047 -48.4 -13.0 1400 1046 48.3 13.0
                                    1500 996 -56.4 -14.2 1500 996 56.3 14.0
                                    1600 953 -65.2 -15.5 1600 953 65.1 16.0
                                    1700 915 -75.0 -16.8 1700 916 74.9 17.0
                                    1800 881 -85.7 -18.0 1800 882 85.5 18.0
                                    1900 850 -97.3 -19.2 1900 851 97.1 19.0
                                    2000 821 -109.8 -20.4 2000 822 109.6 21.0
                                    I input the information, given what you provided in to our solver. As you can see, the firing solution you provided, and the results given the same inputs you provided are not the same. Since firing direction was not supplied, I have also zeroed out any Coriolis Effect in this demonstration. The difference here is roughly 3 2/3rd moa. Screen Shots provided here:






                                    Last edited by DocUSMCRetired; 09-18-2017, 01:32 PM.

                                    Comment


                                    • #19
                                      I also placed this same information in to our online free calculator, and did not end up with the same results you have published. Here is a screen shot including all the information provided in the firing solution:



                                      You can use this solver for yourself here: www.appliedballisticsllc.com/ballistics

                                      Comment


                                      • #20
                                        Let me clarify some points that I see as important info for the sake of fairness. BTW, I'm not trying to diminish AB, it's a fair program, just not particularly outstanding, it's just another Point Mass solver, not any better. That's all there is about the purpose after the exercise.

                                        1) The first exercise was run with the AB program that came with the book. (superseded?)
                                        2) In your examples AJ was factored in. Not in my sample (see below)
                                        3) Hornady run did not accounted for the zero range, same option as in JBM ( I think Hornady should revise this asap)
                                        4) In the following example I have corrected AB output for AJ
                                        5) Once again, I don't see any significant difference between AB and JBM or Nimoh, so the claim that AB is somewhat "special" is quite over-exaggerated in my opinion.
                                        Ballistic Coefficient 0.500 Muzzle Velocity 3000 fps
                                        Bullet Weight 155 grains Zero Range 100 y
                                        Bullet Diameter 0.308 inches Sight Height 1.50 inches
                                        Bullet Length 1.240 inches Twist Rate 10.00 inches
                                        Wind Speed 10.00 mph Heading 0 degrees
                                        Wind Direction 3 o'clock Inclination 30 degrees
                                        Pressure 29.92 inHg Target Speed 0 mph
                                        Humidity 0 % RH Air Density 0.07654 lb/ft^3
                                        Form Factor 0.467 Stability Factor (Sg) 2.230
                                        AB JBM Nimoh
                                        Range TOF Velocity Elevation Windage Range Time Velocity Drop Windage Range Time Velocity Drop Windage
                                        (y) (s) (fps) (moa) (moa) (yd) (s) (ft/s) (MOA) (MOA) (yd) (s) (ft/s) (MOA) (MOA)
                                        0 0.0 3000.0 -0.4 0.0 0 0.0 3000.0 0.0 0.0 0 0.0 3000.0 0.0 0.0
                                        100 0.1 2805.0 0.3 -0.6 100 0.1 2805.3 0.3 0.6 100 0.1 2806.2 0.3 0.6
                                        200 0.2 2618.0 -0.9 -1.2 200 0.2 2619.7 -0.9 1.2 200 0.2 2620.5 -0.9 1.2
                                        300 0.3 2441.0 -2.6 -1.8 300 0.3 2442.1 -2.6 1.8 300 0.3 2442.1 -2.6 1.8
                                        400 0.5 2270.0 -4.7 -2.4 400 0.5 2272.1 -4.7 2.5 400 0.5 2270.5 -4.7 2.5
                                        500 0.6 2108.0 -7.1 -3.1 500 0.6 2109.2 -7.1 3.2 500 0.6 2105.6 -7.1 3.2
                                        600 0.7 1952.0 -9.8 -3.8 600 0.7 1953.7 -9.8 4.0 600 0.7 1947.7 -9.8 4.0
                                        700 0.9 1804.0 -12.8 -4.5 700 0.9 1805.8 -12.7 4.9 700 0.9 1797.4 -12.8 4.9
                                        800 1.1 1665.0 -16.2 -5.3 800 1.1 1666.2 -16.1 5.8 800 1.1 1655.6 -16.1 5.8
                                        900 1.3 1535.0 -19.9 -6.2 900 1.3 1535.8 -19.9 6.8 900 1.3 1523.4 -19.9 6.8
                                        1000 1.5 1415.0 -24.2 -7.1 1000 1.5 1415.7 -24.1 7.8 1000 1.5 1402.6 -24.2 7.9
                                        1100 1.7 1308.0 -29.0 -8.1 1100 1.7 1307.4 -28.9 8.9 1100 1.7 1295.1 -29.1 9.0
                                        1200 1.9 1214.0 -34.4 -9.1 1200 1.9 1212.5 -34.3 10.1 1200 1.9 1202.9 -34.6 10.2
                                        1300 2.2 1135.0 -40.5 -10.1 1300 2.2 1132.6 -40.5 11.3 1300 2.2 1127.7 -40.8 11.5
                                        1400 2.5 1071.0 -47.4 -11.2 1400 2.5 1067.8 -47.3 12.6 1400 2.5 1067.8 -47.8 12.7
                                        1500 2.7 1019.0 -55.1 -12.2 1500 2.7 1015.4 -55.0 13.8 1500 2.8 1018.8 -55.5 13.9
                                        1600 3.0 976.0 -63.6 -13.2 1600 3.0 971.7 -63.5 15.0 1600 3.1 977.1 -64.1 15.1
                                        1700 3.4 937.0 -72.9 -14.1 1700 3.4 933.8 -72.9 16.2 1700 3.4 940.4 -73.5 16.3
                                        1800 3.7 904.0 -83.1 -15.1 1800 3.7 900.1 -83.2 17.4 1800 3.7 907.0 -83.8 17.5
                                        1900 4.0 873.0 -94.2 -15.9 1900 4.0 869.3 -94.3 18.6 1900 4.0 876.2 -94.9 18.6
                                        2000 4.4 845.0 -106.1 -16.8 2000 4.4 840.8 -106.4 19.7 2000 4.4 847.3 -106.8 19.7
                                        Last edited by LastShot300; 09-18-2017, 03:23 PM.

                                        Comment


                                        • #21
                                          Originally posted by LastShot300 View Post
                                          - Snip
                                          The first table that was published clearly said Hornady, and matched the results that I was able to pull from Hornady's website. While the AB Table did not. AJ was factored in (see in the table where you -0.3 at your zero range). Hornady didn't account for the zero range? AJ is present in both solutions. You can clearly see the table lines up, with a zero range of 100 yards. How did you "correct" the AB output for AJ? Did you simply remove the wind to see how the results changed?

                                          In your second example, I simply went to the last number. Which is 106.1, however I did provide a screen shot of the solution which shows uncorrected for AJ it should be 105.93. Small difference, but when the numbers don't match, it calls in to question the other information. No need to worry about breaking it down, when the information doesn't line up in either case by looking at only 3 numbers in the data.

                                          Comment


                                          • #22
                                            Originally posted by DocUSMCRetired View Post

                                            The first table that was published clearly said Hornady, and matched the results that I was able to pull from Hornady's website. While the AB Table did not. AJ was factored in (see in the table where you -0.3 at your zero range). Hornady didn't account for the zero range? AJ is present in both solutions. You can clearly see the table lines up, with a zero range of 100 yards. How did you "correct" the AB output for AJ? Did you simply remove the wind to see how the results changed?

                                            In your second example, I simply went to the last number. Which is 106.1, however I did provide a screen shot of the solution which shows uncorrected for AJ it should be 105.93. Small difference, but when the numbers don't match, it calls in to question the other information. No need to worry about breaking it down, when the information doesn't line up in either case by looking at only 3 numbers in the data.
                                            Of course it's Hornady, no mistake here. Just read my comment about how I think it's working. You can try that yourself.

                                            I don't have the AB package, which, as posted, shows essentialy the same solution as the free online one. In the AB package you can clearly see that Drop was adjusted by AJ. So, what I did was just to remove it. Nothing fancy. I think my notes were clear enough, if not let me know.

                                            BTW, unfactoring AJ is extremely simple and it's not wind-related.
                                            Last edited by LastShot300; 09-18-2017, 04:47 PM.

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