Question $11$: On July $21$ at $12$:$00$ P$.$M$.$ solar time, what is the horizontal shadow length $()$ for a $1$ ft setback window in Shreveport, LA$,$ if:

The surface azimuth needs to be calculated for $10$ west of south.

The window height is $6$ ft$.$

There is a variable atmospheric scattering factor of $1\mathrm{.}3$ to be applied to the solar altitude angle $().$

The declination needs to be adjusted for an elliptical orbit factor of $0\mathrm{.}97.$

The window is inclined by $5$ from the vertical plane.

There is an additional factor of overhang tilt by $2$ from the horizontal plane.

Assumptions:

Latitude $()$: $32\mathrm{.}47$ N

Window dimensions: $4$ ft wide $($W$),6$ ft tall $($H$)$

Setback distance $()$: $1$ ft

Distance above window: $2$ ft

Declination $()$: Calculate with elliptical orbit factor

Hour angle $()$: $0\mathrm{.}0$

Surface azimuth $()$: Calculate for $10$ west of south

Additional Variables:

Variable atmospheric scattering factor of $1\mathrm{.}3$ to be applied to the solar altitude angle $()$

Adjust declination for elliptical orbit factor of $0\mathrm{.}97$

Window inclination by $5$ from the vertical plane

Overhang tilt by $2$ from the horizontal plane