How to calculate double area distance for conical horns?

[Petter Persson]

I try to calculate at what distance the double area occurs in rectangular conical horns. The rund case was rather simple but now I'm stuck with math. Please help. See the enclosed image and find x expressed in a1, b1, tan(Theta a1) and tan(Theta b1).

The scenario is simplyfied by that the horn is divided into 4 quarters.

Thanks
Petter

 

[scottjoplin]

Couldn't you draw it to scale and measure?

 

[Petter Persson]

Yes, but I wish to implement the solution in an excel spreadsheet to aid synergy horn calculations.

 

[nc535]

the area is proportional to axial distance squared in a conical horn so every time you move 1.414 times further away from the throat the cross sectional area doubles.

 

[Lojzek]

This may be of help.

 

[nc535]

the area is proportional to axial distance squared in a conical horn so every time you move 1.414 times further away from the throat the cross sectional area doubles.

Correction. 1.r14 times further away from the apex. Not the throat, that being where the cone of pyramid would one to a point if extended backwards far enough

 

[Petter Persson]

Thanks guys, luckily it was not that difficult... The trickey thing was to formulate the problem.

 

[Lojzek]

Luckily we have fora where we can present our desire to find a solution and then people happen. Cheers.