As aircraft mass increases, the stopping distance from 'x' knots increases (because the force provided by the brakes is fixed, regardless of mass, and therefore the decelerating effect is less on a heavy aircraft). Therefore V1 reduces as aircraft mass increases - because you have to abort earlier in the takeoff run in order to stop.
Acceleration = force / mass. Ignoring the effects of derated takeoffs, a heavier aircraft will accelerate more slowly, so will eat up more runway in reaching 'x' knots - again this reduces the stopping distance available, so V1 reduces. These 2 effects are compounding.
Vmcg is a function of rudder and nosewheel steering authority against asymmetric thrust moment. Mass doesn't come into it.
Last edited by Easy Street; 2nd Mar 2013 at 23:23.