Lets say a balloon with a certain amount of buoyant lift has a 2 kg mass strapped to it (including engines) and accelerates enough that it perceives a positive 2.5 g inertial force (2.5g * weight) acting downwards. Lets say initially the amount of buoyant force is equal to 50% of the perceived weight during no acceleration (1 kg total weight).
Because weight equals: mass * gravity (2.0 kg * 9.81)
And the g factor due to acceleration is applied to the weight to get g force: 2.5g * weight = Force
Then the g force would become 2.5g * 2.0 kg * 9.81 = 49.05 N
Is the g factor due to acceleration only applied to the resultant weight minus the helium buoyant force?
2.5g * 1kg (resultant weight) * 9.81 = 24.525 N
If the first case is true, the buoyancy becomes much less effective under an acceleration inertial load. If the second case is true, can someone show me mathematically or explain why the g factor is not multiplied by the entire mass?