Department of Mechanical Engineering Massachusetts Institute of Technology 2.20 Marine Hydrodynamics, Sample Laboratory Assignment Laboratory Assignment B Surface Waves Kinematics and Added Resistance of Ship in Waves Introduction This lab is in an investigation into some of the properties of surface gravity waves and their effects in ship resistance. The purpose is to gain an understanding of some of the fundamental concepts and relationships of surface wave kinematics by means of an experimental study. The wave-making and wave-detection capabilities of the MIT Towing Tank will be used in conjunction with empirical observations. Pre-Lab Preparations You must submit a ”pre-lab” report of the following pre-lab prepa-rations at the beginning of the lab. Although you are encouraged to work the preparation as a lab group, your submitted ”pre-lab” must be done individually. In your final lab report you should include a copy of your ”pre-lab” (in addition to the one turned in the day of the lab) along with a short paragraph that discusses the lab preparation. (Time spent here will certainly save you many times the effort during and after the lab!) 1. Read through the entire lab carefully so that you have a clear idea of what has to be ac-complished. Be familiar with the expected results and calculations so that you can repeat suspicious measurements (during the lab). 2. Understand the relevant theoretical topics. Review the relevant topics in the course (Refer-ences: JNN pg. 237-266, Faltinsen pg.145-148 ) so that you understand the concepts, the methodologies, and what special care you have to take. Understand the derivation and phys-ical meaning of basic wave properties such as wave length, wave numb er, period, frequency, phase velocity, dispersion relation, etc. Make plots/sketches of the: wave length as a func-tion of frequency (dispersion relation); phase velocity as a function of frequency; and group velocity as a function of frequency. You should mark in each plot/sketch the areas (if those exist) where the previous functions have a linear behavior. Also, understand the significant dimensionless parameters in ship added resistance. 3. Think through and plan the lab with the other group members. Prepare an action plan for the lab including the number and range of measurements to be made and tables or graphs to roughly plot the data you anticipate. Plan and write a description of the method your group will use for determining the following wave characteristics using three wave probes and a controlled wavemaker. To be performed at the Ocean Engineering Towing Tank Room.2.20 Lab B . . . . . . . . . . . . . . . . . . . . . . . . . . Surface Waves Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . Page2 (a) Amplitude (b) Wavelength (c) Frequency (d) Phase speed (e) Group speed In addition plan and write a description of the measurements your group will need to de-termine the wave amplitude dependence of added resistance of a particular vessel in regular head sea waves. 4. As your pre-lab preparation submit to the lab staff copies of the plots asked in (2) along with the tables, graphs, action plan and short description asked in (3). Provide a checklist for experiments to be run and observations to be made. Be prepared to discuss with the lab staff your action plan when you enter the lab. Laboratory Assignment Equipment The towing tank is a long rectangular basin of water with a wave-maker at one end and a “beach” at the other. The wave-maker is a hydraulically driven vertical paddle with controllable amplitude and frequency. The “beach” is a region of absorbing material intended to prevent the reflecting of waves from this end of the tank. You will be using wave probes to measure the amplitude, or height, of the passing waves. The wave probes are a “resistance” type which produce a voltage proportional to the submerged length. This voltage can be logged by a computer at a prescribed sampling rate. As waves pass the probe, the computer can display the height of the free surface as a function of time. These data can then be stored electronically. Visual measurements will also be taken for corroboration of the methods and equipment. A stop watch and tape measure will be provided for such measurements. You will also be given measurements of the forces required to tow the ship at a given velocity with or without head waves. Objectives To measure the basic surface wave properties in terms of wave amplitude, period, wavelength, phase velocity, and group velocity. To measure the added resistance of a ship with no waves and in head waves. Measurements Towing Tank personnel will provide instructions for the operation of the wave-maker, towing and data collection system. Please follow their instructions. 1. Record the water depth h.2.20 Lab B . . . . . . . . . . . . . . . . . . . . . . . . . . Surface Waves Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . Page3 2. Calibrate the wave probes. The calibration of the probes consists of determining the rela-tionship between the voltage read by the computer and the submerged length of the probe. With the assistance of the towing tank operator, you will make measurements of the voltage corresponding to different depths of submergence. The following steps (3) through (6) are to be completed for a range of frequencies between 1hz and 2hz, for at least one amplitude. Plan your runs so that you cover a large range of frequencies first, then fill in interim frequencies for better resolution, as time allows. 3. Determine the amplitude, A, and the frequency, ω = 2π/T with T the period, of the wave using the wave probes. If η(x, t) is the free surface elevation, a good definition