Small Forward Speed Research Articles

Helicopter Landing Trajectory Optimization after Tail Rotor Control Failure in Different Collective Pitch

This paper studies helicopter optimal landing and control procedure after tail rotor control failure (TRCF) in different collective pitch. The optimal control problem of landing after tail rotor control failure was solved numerically by direct multiple shooting method and sequential quadratic programming. A sample helicopter optimal landing procedures after tail rotor control failure in large collective pitch and small collective pitch were investigated respectively. As can be seen from the results, when the tail rotor is stuck at large collective pitch, the tail rotor provides a large lateral force, which facilitates landing with small forward speed and descent rate in a large power state. The pilot can maintain stability of heading by side slipping. When the tail rotor is stuck at small collective pitch, the tail rotor provides a small lateral force, which is favorable for flying near economic speed, but difficult for a safe landing. A normal landing maneuver will cause a high yaw rate at touchdown, which is dangerous. Therefore, autorotation is preferred during touchdown because the landing is more secure with small yaw rate. The trajectory optimization method of helicopter safe landing after tail rotor control failure can provide a reference for flight test.

Seakeeping experiments on damaged ship

ABSTRACTThe aim of this paper is to present results of seakeeping experiments performed on a damaged ship hull and to compare them with numerical analysis results. The assumed damage opening in the ship hull, i.e. the damage extent, is determined based on probability distribution functions for damage size and location as specified by the Marine Environment Protection Committee. Two different sets of experiments are conducted in a large commercial towing tank. Firstly, rigid body motions of damaged and intact ship hulls in tow in head seas with small forward speed are measured for irregular waves. Secondly, ship motions and vertical wave bending moments are measured on the segmented model in regular waves. Experimental results are compared with the linear 3D Boundary Element Method using Hydrostar software. Satisfactory correlation of computations and experiments is achieved for ship in tow while discrepancies are found for the segmented model. An important finding of this experimental campaign is that measured vertical wave bending moments of the damaged ship considerably exceeds those of the intact ship.

The effect of small forward speed on prediction of wave loads in restricted water depth

Wave load prediction at zero forward speed using finite depth Green function is a well-established method regularly used in the offshore and marine industry. The forward speed approximation in deep water condition, although with limitations, is also found to be quite useful for engineering applications. However, analysis of vessels with forward speed in finite water depth still requires efficient computing methods. In this paper, a method for analysis of wave induced forces and corresponding motion on freely floating three-dimensional bodies with low to moderate forward speed is presented. A finite depth Green function is developed and incorporated in a 3D frequency domain potential flow based tool to allow consideration of finite (or shallow) water depth conditions. First order forces and moments and mean second order forces and moments in six degree of freedom are obtained. The effect of hull flare angle in predicting added resistance is incorporated. This implementation provides the unique capability of predicting added resistance in finite water depth with flare angle effect using a Green function approach. The results are validated using a half immersed sphere and S-175 ship. Finally, the effect of finite depth on a tanker with forward speed is presented.

Second-Order Diffraction and Radiation of a Floating Body With Small Forward Speed

The formulation of the second-order wave-current-body problem in the inertial coordinate system involves higher-order derivatives in the body boundary condition. A new method taking advantage of the body-fixed coordinate system in the near field is presented to avoid the calculation of higher-order derivatives in the body boundary condition. The new method has an advantage over the traditional method when the body surface has a sharp corner or high curvature. The nonlinear wave diffraction and forced oscillation of floating bodies are studied up to second order in wave slope. A small forward speed is taken into account. The results of the new method are compared with that of the traditional method based on a formulation in the inertial coordinate system. When the traditional method applies, good agreement has been obtained.

Semi-Analytical Methods for Different Problems of Diffraction-Radiation by Vertical Circular Cylinders

As in the other fields of mechanics, analytical methods represent an important analysis tool in marine hydrodynamics. The analytical approach is interesting for different reasons : it gives reference results for numerical codes verification, it gives physical insight into some complicated problems, it can be used as a simplified predesign tool, etc. This approach is of course limited to some simplified geometries (cylinders, spheres, ...), and only the case of one or more cylinders, truncated or not, will be considered here. Presented methods are basically eigenfunction expansions whose complexity depends on the boundary conditions. The hydrodynamic boundary value problem (BVP) is formulated within the usual assumptions of potential flow and is additionally simplified by the perturbation method. By using this approach, the highly nonlinear problem decomposes into its linear part and the higher order (second, third, ...) corrections. Also, periodicity is assumed so that the time dependence can be factorized i.e. the frequency domain formulation is adopted. As far as free surface flows are concerned, only cases without or with small forward speed are sufficiently simple to be solved semi-analytically. The problem of the floating body advancing in waves with arbitrary forward speed is far more complicated. These remarks are also valid for the general numerical methods where the case of arbitrary forward speed, even linearized, is still too difficult from numerical point of view, and "it is fair to say that there exists at present no general practical numerical method for the wave resistance problem" [9], and even less for the general seakeeping problem. We note also that, in the case of bluff bodies like cylinders, the assumptions of the potential flow are justified only if the forward speed is less than the product of wave amplitude with wave frequency.

Second-order horizontal steady forces and moment on a floating body with small forward speed

In a recent work, a simple formula was derived for the ‘wave drift damping’ in a two-dimensional floating body and the obtained expression is exact within the context of the related theory, where only leading-order terms in the forward speed are retained. This formula is now generalized for a three-dimensional problem and the coefficients of the ‘wave drift damping matrix’ are given explicitly in terms of the standard second-order steady forces and moment in the horizontal plane; Munk's yaw moment, related with the steady second-order potential and discussed in Grue & Palm (1993), is not analysed in this paper and the effect of an eventual small angular velocity around the vertical axis is also not considered.Numerical results agree in general with the proposed formula although in a specific case a consistent disagreement has been observed, as discussed in §5.

Wave forces on marine structures with small speed in water of restricted depth

Wave forces on three-dimensional bodies with small forward speed is considered. The water depth is allowed to be finite (or shallow), which is a generalization of existing theories. The problem is formulated consistently to leading order in the wave amplitude and the forward speed by means of integral equations. Linear forces and moments, second order horizontal drift force, yawing moment, and wave drift damping are considered. Results are presented for a half-immersed sphere, a vertical truncated cylinder and a ship. Considerable enhancement of the wave forces may occur when the wave number multiplied by the water depth is smaller than unity and the body draught is comparable to the water depth. The wave drift damping for a ship may then be up to three times larger than in deep water.

Wave forces on three-dimensional floating bodies with small forward speed

A boundary-integral method is developed for computing first-order and mean second-order wave forces on floating bodies with small forward speed in three dimensions. The method is based on applying Green's theorem and linearizing the Green function and velocity potential in the forward speed. The velocity potential on the wetted body surface is then given as the solution of two sets of integral equations with unknowns only on the body. The equations contain no water-line integral, and the free-surface integral decays rapidly. The Timman-Newman symmetry relations for the added mass and damping coefficients are extended to the case when the double-body flow around the body is included in the free-surface condition. The linear wave exciting forces are found both by pressure integration and by a generalized far-field form of the Haskind relations. The mean drift force is found by far-field analysis. All the derivations are made for an arbitrary wave heading. A boundary-element program utilizing the new method has been developed. Numerical results and convergence tests are presented for several body geometries. It is found that the wave exciting forces and the mean drift forces are most influenced by a small forward speed. Values of the wave drift damping coefficient are computed. It is found that interference phenomena may lead to negative wave drift damping for bodies of complicated shape.