spiral antenna description question

[yefj]

Hello , In CST i have the following menu,D=2*Coil Radius(major) C=pi*D
i think angle of increment tan_alpha=D/S.
The circomfrance of a helical has no roal inthe increment angle.
i cant understand the logic of the triangle shown bellow.
Why its tan_alpha=C/S?

 

[FvM]

The triangle is in the helix, but it's coiled. Look sharp!

 

[yefj]

Hello FVM, i cant see the logic of why they use the circumference of the coil as one side of the triangle?
Is there some intuition ?
Thanks.

 

[FvM]

Cut and flatten the helix cylinder and you get this planar structure

 

[vfone]

According to the history, John Kraus, the inventor of helical antenna in 1946, provided semi-empirical design formulas for input impedance, bandwidth, main beam shape, gain and axial ratio of helical antenna, based on a large number of measurements and antenna theory.