Calculating the Pitch

EasilyFound_2

. . . on this topic, so I'm going to just post my question again.

How much pitch is needed for a horizontal runout that feeds a riser for radiators in three apartments?

Looking through Dan's steam book, it seems to say one-half inch of pitch per foot of pipe. My pipe is roughly seven feet, so that would mean about 3.5 inches of pitch.

But according to Dan's "The Golden Rules of Hydronic Heating for pipe sizes based on connected load," the pitch should be one inch per foot back to the main.

One more thing: my runout needs to be pitched back to another riser that is connected to the end of the steam main in the basement. That other riser feeds a radiator on the first floor before it is connected the the horizontal runout.