I'm unfamiliar with an easy way to work this out
Assuming there is 0 deg AoB / Sideslip, load factor will depend on: velocity (in both x and z body axis directions), acceleration (in both x and z body axis directions) and pitch rate (q). If the reference point (i.e. the location of the cart) does not coincide the CoG, pitch acceleration (q dot) will also play a part.
A level banked turn is quite straight forward. This scenario is a little more complex.