# MIT 13 42 - FORWARD SPEED EFFECTS AND MODEL TESTING (11 pages)

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## FORWARD SPEED EFFECTS AND MODEL TESTING

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## FORWARD SPEED EFFECTS AND MODEL TESTING

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Pages:
11
School:
Massachusetts Institute of Technology
Course:
13 42 - Design Principles for Ocean Vehicles
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13 42 LECTURE 17 FORWARD SPEED EFFECTS AND MODEL TESTING SPRING 2003 c A H TECHET M S TRIANTAFYLLOU 1 Model Testing of Seakeeping z xm t Us bow x Towing tank experiments can be done to determine the characteristics of a model vessel in waves 1 Place a fixed model at position along the tank 2 Generate a regular incident wave train with frequency and amplitude a 3 Measure the surface elevation at xm far from the model 4 Measure the heave force F3 t and pitch moment F5 t wave amplitude at the model 5 Compare the surface elevation at xm with the force signal to determine the phase offset between the two signals t1 13 42 Spring 2003 1 2 c A H TECHET M S TRIANTAFYLLOU SPRING 2003 6 Take x 0 at the midship point So that the surface elevation at the ship is e 0 t a ei t And the elevation at xm is e xm t a ei t kxm e 0 t e ikxm If xm 0 then the surface elevation at xm lags the surface elevation at x 0 by a phase of 1 kxm else if xm 0 then the surface elevation at x 0 lags the surface elevation at xm by a phase of 1 kxm 7 The phase lag between the forcing signal and the amplitude of the waves at the body can be found simply by combining the phase shift between the elevation at xm and the force with the expected phase shift in surface elevations due to location difference between x xm and x 0 0 1 t1 k xm n F3 t Re Fb3 ei FbI3 FbD3 t 0 o Fb3 a ei 0 Where the LHS of this equation is the excitation force In order to find the added mass and damping coefficients we can force the body in calm water and measure the forces FORWARD SPEED EFFECTS MODEL TESTING i t x t x b cos t Re x be n F3 t Re Fb3 ei t Fb3 e i x b m A33 2 i B33 C33 x b Separating the real and imaginary part of the above equations Fb3 cos 1 1 Fb3 sin x b m A33 2 C33 x b x b B33 we can use this data to get the added mass and damping coefficients 3 4 SPRING 2003 c A H TECHET M S TRIANTAFYLLOU 2 Speed Effects z a x Take a ship moving with speed U cos against waves with wavelength amplitude and frequency a These waves have a phase speed the speed at which each crest moves Cp k and the ship has a forward speed relative to the phase speed Urel U cos Cp Since the ship is moving an observer on this ship s bow would observe waves coming in at a frequency e the encounter frequency leading to an apparent wave phase speed Cpe e U cos Cp k e U k cos Using the deep water dispersion relationship kg we can rewrite the encounter frequency as a function of the incident wave train frequency and forward ship speed e U cos g FORWARD SPEED EFFECTS MODEL TESTING 5 Typically an observer on the ship will report back with his or her observed frequency e and wish to translate that information to arrive back at the wave frequency g 2U cos 1 s U cos 1 4 e g provided 4 e U cos 1 g In a head seas configuration the incident wave angle is between 2 so that cos 0 and e 0 always for all In following stern seas the incident wave angle is between 3 2 and 2 so that cos 0 When U cos Cp the ship is overtaking the waves and e 0 and when U cos Cp then the encounter frequency is zero It is possible to meet some ambiguity when observing incident wave trains For example if the magnitude of the encounter frequency and angle are measured it may be possible for the sign of e to be uncertain This could result from a misdiagnosis of the incident wave angle versus The idea of encounter frequency e has implications on the sea spectrum analysis of ship motion in waves Since the spectrum is representative of the available energy in the waves we can write a relationship between the spectrum on the waves with frequency and the complementary spectrum with encounter frequency e such that energy is preserved S e d e S d S e S d e d For deep water 2 d e 1 U cos d g Such that the spectrum in terms of the encounter frequency is 6 SPRING 2003 c A H TECHET M S TRIANTAFYLLOU S e S 1 2 g U cos From the equation above we can see that S e goes to infinity as the denominator goes to zero at 2 U cos 1 g Given the forward velocity U and the incident wave angle again e U cos g If is in 2 2 then e 0 for 0 and e 0 for 0 If is in 3 2 2 then e 0 for 0 and g 1 U cos FORWARD SPEED EFFECTS MODEL TESTING 7 8 SPRING 2003 c A H TECHET M S TRIANTAFYLLOU 3 Speed Effects on Forces With respect to the ship s reference frame for a ship in head seas U x s x y z T x y z t where the first term is solely the potential due to the forward motion of the ship or in the reference frame of the ship the apparent speed of the oncoming water the second term is the contribution from steady diffraction and the final term is unsteady term The body boundary condition for a vessel in both heave and pitch can be written in familiar terms B n n b V b FORWARD SPEED EFFECTS MODEL TESTING 9 where n b is the unit vector normal to the body surface and is only used to get the correct velocity direction For small angular motions we can write the normal vector as n b n b0 n b0 B n V b Ubi s n b0 Ubi s T b n0 n b0 0 In the perpendicular direction to the surface normal n b s is negligible and we arrive at the condition In heave and pitching motions B n T n b0 Ubi n b0 V b0 bi n b0 x5 nz x6 ny Vertical velocity is x 3 U and we can get T B n V b0 U x5 nz x6 ny n 10 SPRING 2003 c A H TECHET M S TRIANTAFYLLOU 5 05 F Z Z SB pn b dS Z Z SB U 0 i 3 T T U t x From Salvensen Tuck Faltinsen Trans SNAME 1970 Vol 78 n b0 dS F h 3 1 Heave U 0 m A33 x 3 B33 x 3 C33 x3 F3 t FORWARD SPEED EFFECTS MODEL TESTING 11 3 2 Heave U 6 0 The ship is moving at velocity U such that …

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