# Ballistics for Excel Forum

## BfX => Ballistics => Topic started by: 375CT on December 05, 2015, 06:02:54 AM

Title: Pejsa and 3DOF PM
Post by: 375CT on December 05, 2015, 06:02:54 AM
Folks, I have a friend asking for the main differences between Pejsa and Point Mass (3DOF), which are in your opinion those?

Besides the traditional answer, of a closed form vs a numerical approach, the slope (N) I'd like to have a summary of the differences and strengths of both if possible.

thanks in advance for the help.
Title: Re: Pejsa and 3DOF PM
Post by: admin on December 07, 2015, 03:44:22 PM
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.

Title: Re: Pejsa and 3DOF PM
Post by: 375CT on December 07, 2015, 11:17:45 PM
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.

Robert, thanks for the reply. But how would you compare Pejsa with PM beyond the flat fire approximation and the treatment of drag? I understand that BfX has many improvements over the traditional method. Perhaps I haven't got a full grasp of your text.
Title: Re: Pejsa and 3DOF PM
Post by: admin on December 08, 2015, 02:41:47 PM
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
Title: Re: Pejsa and 3DOF PM
Post by: admin on December 09, 2015, 11:00:26 AM
I would like to add a speculation,

given the purpose of Pejsa's applications in AA guns he probably has some formulas that work for large elevations too.