Balor said:
Note: this is all for swinging a two handed sword with one hand.
You're forgetting a few things. First, I= 1/3*ml^2 + md^2, where d is the distance displaced from the pivot point, and 1/3*ml^2 is the moment of inertia for a rod through its end. You also need to factor in for the swinger's arm.
To be simple, if we assume the pivot point at a person's shoulder with a 5 kg, .7 m long arm -- mine is around 3.3 kg, and I am weak, skinny and not clad in armor -- then the values for your sample swords are 1.64 and 3.30 kg-m^2. So its about twice as tough to swing.
I'm not sure how you'd calculate how hard it would hit, but my best guess would be angular momentum. And angular momentum (L=Iω) depends on tons of factors. Using some kinematics, I found L=√(2τθI), so the bigger sword would probably hit about 41% harder. Using other equations, the time taken to swing should also be about 41% longer.
tl;dr for the non-science inclined
Difficulty to swing a 2 handed sword with one hand: Twice as hard as a one handed sword.
Damage: 41% More
Time: 41% More
My suggestions:
Raise damage for all 2 handed weapons (say, for a sword of war to 50).
Lower speed considerably when on horseback. Instead of a 10% penalty, make it around 40-50%. Remember, its 41% more time to swing
and to ready the sword. A better solution would be to raise the speed of one handed weapons by about 20% overall, and lower the speed for two handed weapons by about 20% on horseback.
This would make it so that two handed weapons are basically only for "drive by" attacks, and one handed weapons would be much more useful when stopped.
Note for people who will call me a nerd: All the calculations took under 5 minutes, and I needed the practice for my AP Physics test anyway.