SAM heliostats field layout

Dear all,
I would like to ask a question about SAM’s central receiver tower model.
About the SAM method of zone numbering :
SAM calculates ?R, which is defined as the Radial Step Size For Layout, using :
Equation1: ?R=(Rmax-Rmin)/(number of zones)

In Delsol, the method of zone numbering is different:
Equation2: ?R is calculated using: ?R=(Rmax-Rmin)/(number of zones - 1)
Then the layout of the zones is displayed and explained in Kistler B (1986), pp.30-31.
Which mean that the radial step size for the first and last zones is different than the radial step size of the other zones.

I made several tests considering the both zone organisations, and my results with Delsol method are closer to the results that SAM gives, than with the stated SAM method.

Although SAM states it uses the Delsol code to calculate the density of the field, Does those details have been changed?
Can you clarify the way the zones are displayed?
Thank you for your answers,
Best regards,
Clotilde

Dear Clotilde,

Can you tell me where you found Equation 1?

Best regards,
Paul.

Dear Paul,

In Field Parameters, SAM provides the Radial Step Size For Layout. I made several tests and analyzed the results and found out that they correspond to the equation 1. Please find on following one of my test example :
I based my calculations on SAM output :
- Data proposed by SAM
Radial Step size For Layout (?R) = 103.123 m
Max Heliostat Distance to Tower Heigh Ratio = 7.5
Min Heliostat Distance to Tower Height Ratio = 0.75
Tower Height = 183.33 m
Max. Dsitance From Tower (Rmax) = 1374.98 m
Min. Distance From Tower (Rmin) = 137.498 m
Max Realized Distance From Tower = 1374.98 m
number of zones = 12

- ?R calculated with equation 1 :
?R=(Rmax-Rmin)/(number of zones)=(1374.98-137.498)/12=103.1235

Thanks for you answer.

Best regards,
Clotilde