Why tilted rows need room to breathe
The trigonometry behind row spacing
A tilted panel's back edge rises above the row behind it, and that height casts a shadow whose length depends on how low the sun sits and how far off south it is. The clear gap between rows equals panel height times the sine of the tilt, times the cosine of the sun's azimuth from south, divided by the tangent of the sun's altitude. At solar noon the azimuth is zero and the cosine drops out. Adding the panel's tilted footprint, height times the cosine of the tilt, turns the clear gap into front-to-front row pitch, which is the figure the ground mount vs roof mount space calculator needs for land area. The geometry behind that formula is the same one NLR's PV shading documentation uses to model row-to-row shade.
Why sloped roofs mostly skip this problem
On a standard pitched residential roof, panels mount flush with the roof's own slope, so there's no raised back edge casting a shadow onto the row behind it. Row spacing becomes a real design factor mainly on flat commercial roofs and ground-mount systems, where racking tilts panels up independently of the surface beneath them, a decision the commercial roof mount vs ground mount cost tool weighs from the cost side.
Solar noon is the easiest moment to design for, not the hardest
The lowest sun altitude of a winter day comes at sunrise and sunset, so a design that clears shade only at solar noon leaves the rows shading each other in the morning and afternoon. At latitude 40, the noon altitude on December 21 is 26.6 degrees, but at 9 AM it is 14.0 degrees with the sun 42 degrees off south, and that pushes the clear gap for a 65-inch panel at 30 degrees from 65 inches to 97. Designers use different windows: the common winter solstice rule asks for no shading of neighboring modules at 9 AM, while a stricter reading extends the clear window further into the morning and afternoon. The strictest window is a conservative choice, not a requirement. The NOAA solar calculator gives the sun's altitude and azimuth for any date, time, and location, so you can check the 9 AM winter angle for your own latitude.
Panel-to-panel gaps matter too, for a different reason
Beyond row-to-row spacing, individual panels within the same row need a small 0.5 to 1 inch gap between them. This isn't about shading, it's about thermal expansion and room for mounting clamps. Aluminum expands about 23 millionths of its length per degree Celsius, so a frame 44 inches wide that warms 60 degrees Celsius grows only about 0.06 inch, which a 0.5 inch gap covers comfortably. That is a separate physical constraint from the fire-code clearances the fire code setback calculator covers.
The shade shrinks as the season changes
Row spacing is set for one worst-case day, December 21. On any other day the sun climbs higher and the shadow gets shorter, so rows that clear shade on the solstice are clear for most of the year. The seasonal shading variation calculator shows how quickly that shading changes month by month, and when land is tight the usable roof area calculator helps weigh a tighter spacing against the shading it would allow.