You will use the functions from the Wave Greens Function notebook to check the data from the roll damping lab and predict the damping characteristics of a 2D ship section across a range of parameters.
To be completed per 7 or 8-person lab session: Determine the natural frequency $\omega_n$ of the model and damping ratio $\zeta$ at this frequency using both the free-decay and forced oscillation roll data. Approximate the model midship geometry, and predict the added-inertia and damping coefficients $A_{44},B_{44}$ at the observed natural frequency. Use the model's bouyant stiffness $mgl_{GM}$ and moment of inertia $I$ to compare the calculated and measured natural frequency $\omega_n^2=\frac{mgl_{GM}}{I+A_{44}}$ and damping ratio $\zeta=\frac 1{2\omega_n} \frac{B_{44}}{I+A_{44}}$. Discuss the potential sources of error in this approach.
To be completed per 2 or 3-person group: Create a "maritime section" of your choice and demonstrate how the geometry changes over a dimensionless geometric parameter. An example is the aspect ratio of an semi-submerged ellipse, although you may not use this shape as your geometry. Determine the surge, sway, and/or roll added mass and damping coefficients as a function of the nondimensional frequency and the geometric parameter. Discuss any important changes in the coefficients and their physical cause. Identify a worst-case excitation for your geometry and a potential mitigation.
# Import functions
import requests
url = 'https://raw.githubusercontent.com/weymouth/MarineHydro/master/src/WaveMethod.py'
exec(requests.get(url).content)