AB Bullet Drop Formula

[strikeeagle1]

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.

 

[_Windrider_]

I don't think it's proprietary
[IMG2=JSON]{"data-align":"none","data-size":"full","src":"http:\/\/www.softschools.com\/formulas\/images\/maximum_height_formula_1.png"}[/IMG2]
[IMG2=JSON]{"data-align":"none","data-size":"full","src":"http:\/\/www.softschools.com\/formulas\/images\/maximum_height_formula_2.png"}[/IMG2]



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?

 

[strikeeagle1]

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.

 

[_Windrider_]

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.

 

[strikeeagle1]

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.

 

[LastShot300]

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?

 

[strikeeagle1]

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).

 

[LastShot300]

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.

 

[strikeeagle1]

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

 

[DocUSMCRetired]

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.

 

[strikeeagle1]

^^^ 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 ?

 

[LastShot300]

^^^ 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.

 

[DocUSMCRetired]

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.

 

[LastShot300]

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

 

[strikeeagle1]

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

 

[LastShot300]

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.

 

[strikeeagle1]

^Thanks.

 

[DocUSMCRetired]

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:

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[IMG2=JSON]{"data-align":"none","data-size":"full","src":"https:\/\/s6.postimg.org\/45dbgn3hd\/image.png"}[/IMG2]

 

[DocUSMCRetired]

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

 

[LastShot300]

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
	(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

 

[DocUSMCRetired]

- 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.

 

[LastShot300]

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.