A couple of other things in choosing a hoe size are breakout power and lifting capacity.
The breakout force is how hard a material it will tear loose. Pond slime, earth, hard soil, soft rock, or hard rock.
Typically there is more breakout force as the hoes get larger and also the penetration force should increase.
Lifting capacity is generally limited by the weight of the machine. Most hoes should have the power to lift enough to tip the machine so the more it weighs the more it lifts before it wants to tip.
