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Internal and external ballistics spreadsheet

I said I'd release this in May last year, just never said which year. Maybe its 2022? I built this all in 3-4 months during the beginning of the pandemic, but have kind of slept on it for the last year due to burning out on it, it is/was quite overwhelming. Its 98% complete and fully in beta testing. I cannot promise any release dates.



If I get enough interest I may put forth a bit of more time and energy into finalizing and releasing this sooner than later...otherwise this post is just a reminder this beast still exists.



This is a big project for a single individual, and I put a lot of my time, energy and heart into it, which is also hard to give away, even harder when its not complete.



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List of features

-Sheet automatically saves/stores data when needed
-Sheet automatically resizes to fit the data on the sheet (on 100% zoom, this function will break at any other and you will have to manually resize, its better to use the zoom function via your operating system (windows) under display settings if you find text small), also the big shot string can be maximized up to 4k displays for FULL viewing potential on large strings.


Main:
-Store data from up to 10 guns to be able to compare them or review them on the fly!
-Customize gun names, ie: gun model
-Copy a guns data to another guns data
-Calculate peak fps/energy from a given combination of pressure/barrel length/port size/caliber/pellet weight/reg volume
-Show pressure gradient from both tune and plataeu, both are close approximations that give you an idea of whats happening internally, as well as residual muzzle pressure
-Adjustable projectile friction
-Adjustable valve close @ peak (nominal is 45-50%)
-Calculate efficiency from a current tune/string
-Tons of data including cc use per shot, fpe per gram of air, mg ejection, air density, pressure drop, ports max flow (mg/ms), and more.
-Fpe losses from barrel length / port size / pressure drop caused by regulator
-Hammer data including: Energy / Lock time / Velocity
-Allows you to add a 'balanced valve' ratio which applies to hammer data only
-Compare strings+tunes, rifles, projectiles, and hammer data + more!
-Metric + Imperial input+outputs with option to convert current inputed data to desired setting
-Load Projectile Data directly from stored data
-Calculates ideal barrel twist rate, ballstic coefficient, sg factor, tank fills, max shot count (based on current air use + assumed fill range),wound depth, fps loss from creep, ideal pressure based on desired fps, and much more!
-Calculates optimal Valve Throat OD based on current porting and your stem's OD in throat!
-Light + dark mode
-Hide advanced data, string graph, comparison and slim it down extra with a click of a button, there are 16 possible configurations total.

String shot analyzer:
-10 guns, 10 strings per gun, 100 shots per string. Thats 10,000 shots!
-Ultra wide screen mode, can be displayed in 1080, 1440p, and 4k resolutions
-Splatter target graph that shows your extreme spreads variation at whatever distance is set by the user. Two modes, randomized 5 shot group with fps within your string or 2 shot high/low from your string!
-Compare any two strings from the same or different guns. side by side, including the splatter target!
-Side by side or split graph mode when comparing two strings!
-Calculate loss from chronograph distance and optionally add it to the entire string automatically!
-Custom es range (graph will give a good visual of what is within and what is outside of said custom es)
-fps high, fps low, fps within, fps outside and longest sequence of shots within es% graph markers, and an option to turn them off
-Shows the % below your setpoint achieved
-Calculates shots on/off regulator for you
-Dynamic FPS list that is created upon user request, no more staring at a bunch of strings while trying to enter data for just one
-Add fps simply one by one by looking at the graph and using the provided textbox and add button, or one by one using the FPS list (sheet detects edits in that column/row set)!
-Shows ES while on reg, ES while off reg, and ES from the entire string, to help anaylze whats going on while on/off reg and as a whole!
-Automatically finds the longest streak wtihin your custom ES and tells you the shot #'s + streak count
-Shows the most duplicated fps in a string and the amount of times it was duplicated.
-Save custom notes (string dependent)
-Copy string data straight to clipboard to share in the following format!

Marauder
Date: Temp: 60
Chronograph distance: 0ft
Loss from Chrono Distance: 0 fps
Chrono Loss Added: No

Projectile Mass: 33.95 - Ratio to Air: 71.5% / 28.5%
Psi Start: 3100 - Psi End: 1700 - Airuse: 1400 psi
Psi / Shot: 46.7 - CC / Shot: 5.04 - Fpe / Psi: 0.34
Res Vol: 190cc - Reg Vol: 53cc - Setpoint: 1925psi
Shots On Reg: 25 - Shots Off Reg: 5 - Total Shots: 30

Efficiency: 1.45 fpe/ci
Valve Close @: 29%

ES: 19 fps ( 2.16%) - Std Dev: 4

Total Energy: 1709 - Fpe Per in/Barrel: 2.99

Total Shots < 1% ES: [22/30] best streak: [10] shots [#12-21]

Fps/Fpe High Fps/Fpe Avg Fps/Fpe Low
879 - 58 869 - 57 860 - 56

(1-10) 877 - 872 - 872 - 866 - 873 - 875 - 879 - 868 - 873 - 868
(11-20) 877 - 865 - 869 - 868 - 870 - 864 - 866 - 868 - 869 - 870
(21-30) 863 - 872 - 867 - 864 - 868 - 868 - 872 - 868 - 865 - 860

Most repeated: [868] Duplicates: [7]


ProjectileDB
-Store up to 20 projectiles, and their needed data
-150+ presets from the most common available pellets
-APMR MIL Reticle with a visualization of where the shot placement should be! (used due to popularity and its clarity in producing a good visual)
-Displays units in CLICKS/MIL/MRAD
-Extreme spread markers, reticle will display two fine lines showing spread in MIL from fps variation.
-Graph that shows projectile drop in absolute inches, poi inches, MIL drop, retained energy, and penetration with custom start/end and incriment ranges
-Applies wind speed, wind angle, shot slope, scope height, and bullet spin into trajectory calculations (also temp + altitude, bc, ect..)
-Calculates ideal twist rate, projectile sg, hits number, wind drift per mph @ a common range set by user, retained fpe/fps at target, wound depth into flesh, projectile rpm, and more!
-Calculates optimal zero based on height of projectile path
-bc calculator (near/far velocity + the difference in distance between the two)
-Compare 2 projectiles side by side
-3 size configuration, full size, minimized list, and hide graph+reticle to help reduce clutter when focusing on one area!
-Save custom notes (projectile dependent)
-Current Local Weather based on your City/State (conditions/temp/rh/wind/uv index/ change of perciptation) and elevation query!
-Show a table with all the data you need for a custom range card, can add/remove whatever units you desire!

Extras:
-Calculate optimal balanced valve specs, such as vent OD, chamber volume (cc), and balance % + poppet OD, as well as current o-ring squeeze for a dynamic o-ring!
-Extra large graph for fps/fpe gains based on one parameters, and also pressure gradients / valve dwell model
-Extra large shot string graph that can edit string data just like the main page, with splatter target showing extreme spread for strings
-Extra large reticle display on seperate sheet for those hard of seeing or those that just want an exploded view from the projectileDB
 
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Reactions: fe7565
I am interested. It is a lot of hard work and amazing details and depth. I think many of us do not yet realize the utility of this excellent project. Probably many are wondering what it does and how it can help the average shooter in a simpler layman-type of explanation? 

What I was particularly interested, (if I remember correctly) there is a way to calculate fps from just the internal parameters. Is that still the case? How accurate is it? How does one measure the internals to such precision to make sure the data will be correct? Especially, if the internals are modified and not factory? 
 
I’m totally interested too. The more information we have available, the better off we’ll be. There is another person doing some great work on pellet destabilization and finding the exact velocity the pellet will destabilize based on just a few variables. All of that information is not available yet either but I look forward to reading over it too. I know it’s a lot of work doing this kind of thing. I appreciate it!

Thanks, Stoti
 
wow! Cool spread sheet. What software language did you use to write it up? Is it Open Source so we can fine tune it to our specific guns such as caliber, pellet/slug mass, barrel length, transfer port diameter, regulator valve orifice area, barrel number of lands and grooves and their depth, twist rate, choke, coefficient of friction both static and dynamic of projectile to barrel, temperature, humidity, elevation, latitude, Coriolis, magnus, earth curvatures, projectile spin such as RPM, jump effects, etc...

It seems like a very useful tool to further understand the laws of thermodynamics that involve our airgun sport and understanding of internal, intermediate, external and terminal ballistics. 

Can your program be connected to Bluetooth and an external apparatus that measures many of the said variables such as a doppler radar unit?

What value do you use for the average air molecule? I use 28.96546 daltons, and 207.2 daltons for the lead atom using the exact values for Avogadro's number and Boltzmann's constant to get the exact value for the Universal gas constant and I set it to sea level at 45 degrees latitude. Then I make the minor changes based on my location.

Do you use the published ballistic coefficient of the projectile because it varies with speed and based on a particular range. I use the drag coefficient because it does not change, but is a bit more tricky to calculate.

I think your program would be a marvelous addition to AGN.

Thank you for all your hard and dedicated work in the project and please advise when we can download to play with it and add comments on our findings based on your program.

Stay safe and God speed.

FJB Out!


 


Do you use the published ballistic coefficient of the projectile because it varies with speed and based on a particular range.

I use the drag coefficient because it does not change, but is a bit more tricky to calculate.



icuppu,

please tell us more about where you get the drag coefficient! 👍🏼😊



Do you have custom drag models for one or more pellets/slugs?

I'd love to see them. And hear the details of how you got your data and calculations. Very interested! 👍🏼



Matthias


 
ackuric,

your ballistic calculator looks like a VERY POWERFUL TOOL!

Please, do complete it. We need good tools. 👍🏼

THANK YOU for all the time you already invested into it.

As we reach out farther and farther, the importance of precise and accurate ballistic data and calculations becomes more and more important.

There will always be the backyard squirrel shots to 25 yards that could care less about external ballistics. But that's just one of many shooting scenarios.

Keep up the good work!

I saw something on the screenshot about randomize and simulation. Are we talking about a shot probability calculation based on a Monte Carlo simulation? If yes, then that raises my interest even more! 😊

Matthias




 
Matthias,

The coefficient of drag will be applicable to the projectile being studied as it will change with shape as it comes out of the muzzle. You could average it for a particular projectile coming out of the same barrel (caliber and type due to rifling lands and grooves width, depth, and number).

Instead of getting into a long lecture, here is a pictorial to give you an idea:

th
 Notice the sphere and the half sphere Coefficient of drag for each (Cd); also, the diamond and halved diamond, aka: pyramid on its side.

Next, the formula that only requires a little algebraic gymnastics: 

th
 The average density of an air molecule is approximately 28.96546 daltons, so if you were to pack 28.96546 grams of air molecules, they would equal one mole (6.02214076x10^23 air molecules, exact, by definition). 

One mole of air at STP (0 oC) is approximately 24.414 Liters in volume, at 20C (68F) it occupies 24.055 Liters. Translating to our airgunning, approximately 525 grains of air mass per cubic foot (0.075 lbs. per cubic foot). Note: when converting air volume to mass, make sure you use psia and not psig; therefore, add 14.6959494 to your psig to get psia (absolute), else you will get an erroneous answer from that point and forward to the end of your calculation.

For example, I calculated ackuric's spread sheet output, from another post, in fpe/gr air mass and I got 3.436 fpe per grain of air mass used per shot, which is very very good efficiency for a regulator set at 131 Bar (170 Bar will give you approximately 1 fpe/grAir, and 100 Bar will give you approximately 5 fpe/grAir, of course, from well tuned guns).

This is how I crunch the formula to understandable numbers and using constants I calculated from another of Ackuric's post:

(250 Bar x 14.603774393 + 14.6959494) x 0.00126 x 190 cc = 871.5691 grains of air at tank fill

(131 Bar x 14.603774393 + 14.6959494) x 0.00126 x 190 cc = 458.37688 grains of air at tank when reach regulator set point of 131 Bar, which is the preload pressure for the shot pressure.

Now, 871.5691 - 458.37688 = 413.2 (rounded) grains of air available for shot count down to regulator

Then divide by the 25 shots taken on regulator pressure 413.2 / 25 = 16.5277 grains of air used per shot

Then calculate the fpe and divide by the grains used per shot and you get the fpe/grAir

If I remember right, the mass was 33.95 gr, and the most repeated velocity was 868 fps, so:

33.95 x 868^2 / 450,436.6798 = 56.78655 fpe

56.78655 / 16.5277 = 3.436 fpe/grAir

That was just a snap shot of a quick and dirty calculation. There are hundreds of equations, which is why I can appreciate the work Ackuric has put in his program.

In essence, you think you load 33.95 grains of lead, but in actuality, you are shooting 33.95 + 16.53 = 50.48 grains of mass, and to add insult to injury, the speed of sound is the limiting velocity of the air molecules which is approximately 20 x sqrt absolute temperature, which looks like this:

20 sqrt (273.15 + 5/9 x (77F-32) = 20 x sqrt (298.15) = 20 x 17.267 = 345.34 meters per second

divide by 0.3048 you get 1,133 fps (approximately the speed of sound at 77F, or 25C temperature), so

the pellet is travelling not at 868 fps through the barrel, but out the muzzle, and it starts at 0 fps, so a quick average is to divide by 2; even though, the velocity is geometrically reducing in acceleration and thus speed to a plateau that is never reached, mathematically speaking. When the trigger is pulled and the air comes out, it comes out as a sound shock wave that will be reverberating to and fro until it escapes out the muzzle behind the turtle moving pellet at averaged 434 fps (from zero to 868, 2 x 434 = 868). Don't touch that channel! Then we have the shock wave that also reverberates back and forth on the metal barrel that travels approximately four (4) times faster than the speed of sound, or faster.

Then we wonder why we have such poor precision and poor accuracy down range. There are all these reverberating waves going over each other that you would need a Fourier analysis on each pellet to make any exact prediction. One tenth of a grain will change the frequencies.

Numbers do not lie, but you can lie with numbers, and the laws of physics are not just really good ideas. 

I hope I partly answered your question Matthaeus, but it takes a lot of empirical testing and averaging out using mechanical statistics.

FJB Out!
 
Numbers do not lie,

but you can lie with numbers.





And you can impress with numbers.

In fact, so much "press" can happen that I find myself simply flattened! 😄

Very cool, Francisco/ icuppu! I'm so glad that playing with numbers seem natural to you as your post clearly shows. You and some of the other math and/or ballistic cracks should be swapping notes to crunch the numbers for the mortal masses like me! 👍🏼



Man, I wished numbers and formulas had been natural for me while in highschool...! My science and math teachers would have liked me so much more. (And I, them.)

As it so happens, when it comes to numbers I still manage to avoid getting my pant legs wet in the numbers ocean — by simply letting the ballistic calculators do the heavy lifting. 



🔸BUT: I do get my feet wet! I use BC numbers, velocity dependent hollow point expansion percentages, ranges, wind speeds, and projectile velocities to feed them into Strelok Pro. Even an occasional standard deviation and circular error probable CEP enriches my numbers diet (crunched by EBC* and TargetScan**). 🤣 



*EBC app = Exterior Ballistics Calculator, here:

https://sites.google.com/site/scixddevexteriorballistics/home

**Target Scan app, here:

https://targetshootingapp.com





🔷 The latter really is the concern of my question in the post — I'd like something to help me calculate HIT PROBABILITIES (coveniently) for my shooting system.

•Now Brian Litz's Applied Ballistics program is sold at a price in line with the money PRS shooters spend on ammo, so, NO, as an airgunning spending less than 5c per shot, I have not given in to the temptation.

•EBC has that function, but it has not received any updates in years, and is somehow limited. 😟 



Anyhow, I'm really excited about all this stuff! Had my math and physics teacher told me that what they were teaching would help with shooting guns — I'm sure I would have paid more attention!! 🤣



Matthias