Big, heavy arrows do not need as much velocity to get the hitting power and KE of a normal (lighter) arrow.
KE= penetration/damage.
Momentum = mv (mass x velocity) and is what you need for penetration with a set frontal area - the more mass you have, the higher the resistance to a change in velocity, whether due to air resistance or due to penetration into the target.
Kinetic energy = mv
2 (mass x velocity x velocity) and is what causes impact damage to the target (as distinct from penetrating/cutting tissue damage from the sharp edges of a broadhead).
Illustration:
2 arrows - one weighing 300gr travelling at 300 f/s, (carbon out of a compound?), the other weighing 600gr travelling at 150f/s (warbow?)
They both have the same momentum, but the lighter arrow has twice the kinetic energy of the heavier arrow at half the velocity.
If both arrows had the same point profile and cross-section (OK, unrealistic, but bear with me), they would penetrate to the same depth, but the lighter arrow would impart a heavier impact.
Switching back to Planet Reality, where the lighter arrow has a much smaller cross section, the lighter, faster arrow would quite possibly penetrate all the way through, whereat the extra kinetic energy would be less than gainfully employed in making a hole in the scenery. The heavy arrow, on the other hand, would be more likely to stop in the target, passing
all it's energy into the target - energy transfer is the key to stopping power.
Your 1/4lb warbow arrow hitting the aforementioned armoured knight downrange at 100f/s, not even penetrating the armour, but passing all it's kinetic energy to the target, would have the same energy of impact as a 12lb sledgehammer swung at 15f/s (try swinging one at this speed - it's hard work!) - more than enough to knock said knight over.