An excel implementation of the following article.
https://www.sciencedirect.com/science/article/pii/S2214914717301459

See attached excel file.

Happy shooting ...

I've made a very simple excel file in order to calculate Velocity, Energy and TOF for shotgun BB's.
1. What is the BB's ballistic coefficient ? Can it be calculated ?
2. Any idea how to make this simple excel file more reliable according to atmospheric conditions and the subsonic, transonic and supersonic region ?

Thank you in advance,
Bill

BC=Ballistic coefficient
Cd=Zero-yaw drag coefficient
M=projectile mass
D=Projectile diameter (caliber)
P=air pressure
T=air temperature
H=air humidity
shape=Geometric shape (form) of the projectile
u=projectile velocity
us=sound velocity at the projectile's atmosphere
u/us=projectile velocity/sound velocity ratio
SD=Projectile sectional density
i=form factor


Are the following points true or false ? (with the approximations used in BfX)

- us(P, d_air)

- d_air(P,T,H)     =>     us(P,T,H)

- BC(M, D, shape, u, P, T, H) or BC(M, D, shape, u/us)

- Cd(shape, u, P, T, H) or Cd(shape, u/us)

- SD=M/D²

- BC(M, D, shape, u/us)=SD/i(shape, u/us)

- i(shape, u/us)=Cd_projectile(shape, u/us)/Cd_{standard projectile}(u/us)

- Standard Gx projectiles always have diameter 1" and mass 1 lb

- A projectile with the exact same shape with the standard projectile (of the Gx drag function), but with different dimensions and weight, has a BC=SD at the same drag function, at all velocities

- Two projectiles with the same shape but with different dimensions and weights have the same Cd in the same velocity and at the same atmosphere.

- Lets say that we have a projectile with unknown BC ... the right way to build the BfX model for it is:
1. Compare the shape of the projectile with the Gx shapes and select the one more close to it.
2. Measure the BC near the muzzle (higher velocity with e.g. velocity differences at 2 points) according to Gx drag model selected in step 1.
3. Build the BfX model with the BC measured in step 2 and the drag function selected in step 1.


- Last question: why the BfX custom drag functions need as an input the length of the projectile ?

mman can you please re-upload the file .. thanks

mman, just a confirmation if the following terms-effects are the same ...

Crosswind drift = Aerodynamic jump = Magnus effect ?
Coriolis @vertical axis = Eotvos effect = vertical component of Coriolis force ?
Coriolis @horizontal axis = horizontal component of Coriolis force ?
Spin drift = Gyroscopic drift ?

thanks ...

a little correction to your 6dof workbook

in cell p11 you entered
=0,00007292*E16*T10*SIN(E19)*1000/H4

the correct is
=0,00007292*E16*T10*SIN(E19*pi()/180)*1000/H4

Quote from: mman on May 28, 2013, 06:45:58 PM
Nice! Isn't it fun to make your own calculator? Commercial versions always lack something or you would like to do something differently.

yes you are right !!!
The only thing that I want now is to print my scope's elevation turret tape ... (see attachment)
Now I do it via chairgun ... do you have any other idea ? (excel ... other free software ? ... maybe i'll give it a try via excel's graphs)

Quote from: mman on May 28, 2013, 06:45:58 PM
Is there also options for these mentioned on "about" sheet:

Wind weighting factors (McCoy)
Effect of atmospheric conditions to vertical zero range
Possibility to use horizontal zero to compensate spin drift for short ranges

I'm not sure what you mean by "Is there also options for these mentioned on "about" sheet:"
the "about" term in my workbook is inaccurate ... I just copied your post and paste it on a sheet in order to remember the factors ...
The term "about" came to my mind out of the blue  so I wrote it ...

If you mean that I must include also the remain 3 factors .... may I'll do it when I find some time ...

mman can you please give some info about the formulas you used for
Spin drift (Litz)
Vertical and horizontal Coriolis (Litz)
Up/downhill shooting (Litz's improved riflemans rule)
Range wind drift (McCoy)
Aerodynamic jump aka crosswind vertical drift (Litz)

you google it or the formulas are written in a book ?

Thank you again ...

my mistake ... sorry ...

Dear admin,
what formula do you use for length to angle conversion?

In the attached file you will see a difference between drop (in moa) in a distance of 500m with your formula and the cosines law ...

Thank you,
Bill

thank you ...

Quote from: mman on May 27, 2013, 09:34:20 PM
Thanks for info gvp. That's nice update for chairgun. Perhaps I give it a try. And impressive work with your own spreadsheet.

Try my latest version 27 (I've included YOUR impressive work)

Quote from: mman on May 16, 2012, 06:25:41 PM
Includes following 6-dof corrections to vertical and horizontal deflections:

Spin drift (Litz)
Vertical and horizontal Coriolis (Litz)
Up/downhill shooting (Litz's improved riflemans rule)
Range wind drift (McCoy)
Aerodynamic jump aka crosswind vertical drift (Litz)
Wind weighting factors (McCoy)
Muzzle velocity temperature coefficient (linear inter/extrapolation)
Effect of atmospheric conditions to vertical zero range
Possibility to use horizontal zero to compensate spin drift for short ranges

fantastic job mman, thank you !!!

can you please explain me the "Effect of atmospheric conditions to vertical zero range" ... I think it's the "Constant zero" cell.
when I must set yes or no ?

@admin
Which book did you used for BfX ?

Modern Practical Ballistics by Arthur J. Pejsa ?

Quote from: mman on May 17, 2013, 05:03:13 PM
As far as I know Chairgun fits pellets to a drag function A which is constant as a function of mach number. This is not a good drag function profile to fit any projectile. Drag of every projectile changes wildly close to speed of sound. If your gun shoots pellets at speed of 280 m/s or faster drag function A (chairgun) is not a good fit. I tried to explain this to the programmer of chairgun but I guess he didn't understand what I meant. Or is this problem corrected recently?

This is corrected ... at least in chairgun 4.0.8
see attached photo

as I said I compared my excel file v22 with chairgun (with GA drag) and JBM (with G1 drag) and I'm satisfied with the results.
The only problem I noticed was that chairgun POI differs from BfX and JBM when I change the temp from 20C (see JBM-CHAIRGUN-BfX.xlsx).
Anyway I use chairgun now only for printing my turret scope tape ... 

new version ... checked with
chairgun 4.0.8
plus
http://www.jbmballistics.com/cgi-bin/jbmtraj-5.1.cgi
and results are almost perfect.

In drag function cell @"Ballistics" and "BC from drop" sheets you can use GA for chairgun diabolo pellet drag function.