the effect of the flat fire approximation is that it simplifies the math.
That is why Pejsa is able to give formula's.
Formula's can speed up the computation quite a lot - and could be programmed in the computers of the early sixties

BfX, due to the flat fire formula's can be used to 15 degrees.
Due to progress in computing, however, PM can be done at an instant, compared to the early sixties
In priciple I can switch BfX to point mass as I already have the technology to do that.
yet I do not want to support applications that go beyond 15 degrees - these have nothing to do with target shooting

Pejsa makes two assumptions to derive his formulas:
1) at a given mach interval the drag function can be approached by a power of the mach number g(m)=a*m^b a and b are real numbers. With the custom drag funtions BfX determines for each interval a and b. Then applies Pejsas method. Numerical integration assumes a constant drag value for a given interval.

2) a flat fire approximation

ad 1) if the  mach interval is small enough Pejsa method, and the software has to sum the effects over many intervals, Pejsa method becomes is equivalent to a numerical integration, probably equalling the accuracy of a  runge kutta integration. BfX has the ability to use a measured drag function, e.g. the ones of lapua. BfX results matches here  the ones of a 3dof model, see the workbooks mman posted.

ad 2) a 3dof is able to go beyond the flat fire approximation

BfX is all about generating tables. However, Pejsa publishes many simple formulas which one can use with an electronic calculator are sufficiently accurate for most purposes. In that case it is much faster than 3dof.

I have updated BfX to support Excel 2015.
Fixed also a bug that might prevented it to support Excel 2013. I cannot test this...

Dear all,
It is getting a mess. Let us collect what we have produced during the years.

can you post your best spreadsheets and a small description here, status 2015?

Some of them I will put them on the download page of www.bfxyz.nl

... nice to have ...
http://www.mylabradar.com/#Home

I think I have missed this request.

On my downloads page you can download a workbook, here a screen copy.
http://www.bfxyz.nl/pics/bcfromvelocitysimplelarge.PNG
It uses velocity measurements at several distances, yet one can apply the same method to a single measurement.
Yet the more measurements (at the same or different disatances) the better the results/

Alternatively you might post your data and I reply with an excel document that does the job.

Years ago I was puzzling with these matters, should altitude be a paremeter?
Yet it is much easier to measure pressure and calculate the density from it. Hence I removed the altitude parameter.

Clearly one can study the sensitivity of a path to atmospheric conditions via BfX_C. Yet, in al those years I have used BfX, I seldom used it. And, if so, mostly for rather academic purposes, to develop an intuition.

Some of the guys on the forum, shooting long range in Australia and Finland, at extreme temperatures, might be devoted users.

Measuring pressure certainly does not require devices that exceed 20 Euro's. For that price I have a electronic weather station over here (not measuring wind speed)

Furthermore, I think that the influence of temperature on the burning of the powder might cause more deviation  than through density fluctuations. However, I am not able to do te calculations. The aformementioned forum users keep their amunition in a  coolbox. In Finland to keep them warm, in Australia to keep them cool 

Thanks for the compliments,

Fine that you managed to install. I certainly wouldn't be able to help you with XP and Office 2003 anymore.

Robert

Currently I am working on an update.

this would ensure that you run the latest MS software in Excel.

BfX_U will get the possibility to do scoring on several targets: e.g. BfX_U("300mI";12;"cm") would return 8, as the eight ring on that target has a radius of 15 cm and the nine ring has  10 cm radius.

From BfX/Forum users I got several requests  to extend BfX, e.g. spin drift.
Some of you manufactured some Excel software for this.
Please mail me your wishes and the corresponding algorithms.

Robert

Quote from: mman on July 01, 2014, 09:12:33 AM

This input field allows you to move group center in relation to target, if that is what you meant?

Yes. I our case, at 300m, people aim with their telecopes at a white sticker 20cm below the electronic target center.

Cool.

would it be possible to include the effects of a  hold over/under (and the horizontal equivalent)? (in combination with cant)

From Bfx_help(...)
90   ==========================Non volatile random numbers===========================
91   i is a positive integer number, b is the bottom value, t (>b) is the top value
92   <r> is an optional range
93   random_number = BfX_Ran(i; <r>) 0 <= random_number <= 1]
94   b <= random_number <= t = BfX_Ranb(i; b; t; <r>)
95   c and s are center and width of normal distribution
96   normal distribution b <= random_number <= t= BfX_Rang(i; c; s; b; t; <r>)
97   use <r> to link cells to guide Excels calculation order

i is the seed.

<r> is a cell or a range

B   C   D
2   seed   1234567
3      
4   0,051118901   =BfX_Ran(seed)
5   0,207298019   =BfX_Ran(seed;C4)
6   0,529684412   =BfX_Ran(seed;C5)
7   0,164931189   =BfX_Ran(seed;C6)
8   0,760708209   =BfX_Ran(seed;C7)
9   0,711878956   =BfX_Ran(seed;C8)
10   0,434484066   =BfX_Ran(seed;C9)
11   0,032066679   =BfX_Ran(seed;C10)
12   0,018770791   =BfX_Ran(seed;C11)
13   0,197369616   =BfX_Ran(seed;C12)
14      
15   bfx_ran    refers to the previous cell in order to force
16      a specific order of random number (cell) processing

My random number is non volatile.
Volatile means according to MS:
Excel supports the concept of a volatile function, that is, one whose value cannot be assumed to be the same from one moment to the next even if none of its arguments (if it takes any) has changed. Excel reevaluates cells that contain volatile functions, together with all dependents, every time that it recalculates. For this reason, too much reliance on volatile functions can make recalculation times slow. Use them sparingly.

The following Excel functions are volatile:

    NOW

    TODAY

    RAND

    OFFSET

    INDIRECT

    INFO (depending on its arguments)

    CELL (depending on its arguments)

1) My random number generator generates the same output sequence for the same seed.
2) My random number generator is not recalculated if somewhere else on the spreadsheet an (unlinked) cell is recalculated.

In visual basic and as an Excel function I have published random number generators, two of them generate numbers with a constant probability ("flat").
The other one. =bfx_rang(....) generates numbers according to a gaussian distribution.
The properties of Excels random generators did not suit my purpose.

The "flat" distribution is the basis for generating numbers distributed according to another distribution.
For gaussian distributions efficient algorithms can be googled.

Nevertheless, the more random variables involved in a simulation, the less details of a certain random variable matter.

Ok,
I understand what you understand - nothing special meant here. Let me make things less abstract.

Basically what Monte Carlo does is to generate "outcomes", e.g. where a  bullet ends, for, varying conditions - the input parameters. The input parameters are varied according to a certain probability distribution. If for example a shooter is able to aim with an accuracy of 1 MoA then people like me model that as a bell-shaped (Gaussian) probability distribution that averages to 1 MoA mean inaccuracy. With this we acknowledge the fact that in some cases the shooter aims very well and in others badly. 

In a Monte Carlo simulation then, the computer draws a random number and converts that to an inital horizontal and vertical aiming angle. This is done in such a way that average inaccuracy is 1 MoA. After the horizontal and vertical launch angles are chosen, the bullets trajectory is calculated.

If, for instance, in addition the effects of a non-constant wind is being studied, one might model that primitively as a wind distribution that is half of the time zero and the other half 1 m/s. In a Monte Carlo calculation then one first draws a random number that determines the launch angle, and an another random number is used to determine if there is wind or not in the trajectory calculation (with the afforementioned spreadsheet I deal on a more sophisticated way with non constant wind along a trajectory). Hence we end up with a set of bullet end coordinates that  were affected by both wind and the shooters abilities.

In practise, the more inputs one generates according to a probability distribution, the less the details of a probability distribution matters. The distribution might as well be flat, meaning that the probability for a certain input value is constant in a certain range and zero elsewhere.