William Guanglin Liu's description of the Song shi as 75 liters of rice/wheat comes close to Deng's 46.2kg, assuming 75/70kg for 100 liters. That would make the Song shi 50.25kg (rice) or 46.9kg (wheat). 46.9kg is awfully close to Deng's 46.2kg.
Did the Song shi (石

have the same meaning for the sort of economic grain measures as for bow/crossbow draw weights, or did it mean something different in that context?
In part I'm curious about the Song scroll-53 range difference for bows and crossbows. The ballistic info in the appendix of The Great War gives an idea of how much range reduces kinetic energy. Assuming a four-shi crossbow bolt has the same energy at 100 paces as a 1.2-shi bow has a 60 paces, that implies the crossbow the crossbow has least 15% more kinetic energy to start with. Of course, the real numbers depend on various aerodynamic factors.
Assuming the 1-shi-2-dou draw weight as 71kg, that probably means an initial kinetic energy of around 155 J, using
Turkish bow numbers and assuming a medium-weight arrow. It'd be less with a lighter arrow and more with a heavier arrow. So the Song crossbow would be approximately 180 J, maybe more or less depending on projectile weight. Now, a Manchu-style bow would deliver much more energy, but I don't think the Song used such bows.
Also note that 春秋戰國 of the
Great Ming Military blog expresses skepticism about the ability of hypothetical heavy-long crossbows to perform. We really need reconstructions and tests of so many types of historical crossbows.