The maximum pitching moment that is developed by the water on a flying boat as it lands is noted as c_max The following are the variables involved in this action:
α = angle made by flight path of plane with horizontal
β = angle defining attitude of plane
M = mass of plane
L = length of hull
ρ = density of water
g = acceleration of gravity
R = radius of gyration of plane about axis of pitching

a. According to the Buckingham p theorem, how many independent dimensionless groups should there be characterizing this problem?
b. What is the dimensional matrix of this problem? What is its rank?
c. Evaluate the appropriate dimensionless parameters for this problem.