Source: AD0389304 – ORDP 20-245 Ordnance Engineering Design Handbook, Artillery Ammunition Series, Section 2, Design for Terminal Effects (11.5~ MB PDF) which in turn, references Abbott, K. H., Full Caliber Vs. Sub-Caliber Steel Shot for the Defeat of Armor, Watertown Arsenal Laboratory, Report No. WAL 762/595, January 1952.

When estimating the muzzle velocity of a sub-caliber projectile from known data for a full-caliber projectile, you must take into account the energy used to accelerate the propellant gases. The following empirical equation, developed by the British (in WAL 762/592, Jan 1952), takes the gas acceleration into account. In effect it assumes that half the weight of the charge is being accelerated along with the projectile:

Where:

V_S = Muzzle Velocity of sub-caliber projectile (m/sec)
V_O = Muzzle Velocity of full caliber projectile (m/sec)
M_O = Weight of full caliber projectile (kg)
M_S = Weight of sub-caliber projectile (kg)
M_P = Weight of Sabot (kg)
M_C = Weight of Propellant Charge (kg)

When the known data for the 17 pdr gun (900 m/s full caliber velocity, 7.7 kg full-caliber projectile mass, 3.7 kg mass of propellant charge, 0.4 kg sabot mass and 3.1 kg sub-caliber projectile mass) are input into the above equation, it results in a V_S of 1,202.45 m/sec; very close to published figures of 1,200 m/s for WW2 British APDS shot, proving the validity of the equation for estimation.

NOTE: Because the equation simply adds Sabot Weight and Sub-Caliber projectile mass together, it's not super critical if you don't know the sabot's mass itself -- you just need the total mass of the combined sub-caliber projectile system for estimation.

BIG IMPORTANT NOTE: As the subcaliber penetrator's velocity increases; it approaches the shatter region where velocities are high enough for a given projectile construction that it shatters upon striking a solid enough target.

Why is this important? In theory if you put the 3.7cm PzGr40 (APCR) projectile with a mass of 0.368 kg and estimated a total mass of 0.45 kg for the sabot/projectile complex into the Panther's 7.5cm KWK 42, you would get about 1,763+ m/sec from it -- significantly faster than the 1990 Desert Storm M829 APDFS round of 1,670 m/sec -- and thus in significant danger of shattering. There's a reason US/UK experimental sabot rounds in WWII trended towards using 57mm (6 pdr) shells as the subcaliber projectile, as that was about the limit of what WW2 materials science and analysis could support in regards to the shatter gap.