Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010


conducted or reported, but the full-scale measurement process itself is beset with uncertainties. Therefore, it is important to define realistic limits for error bounds in each stage of manoeuvring prediction, in order to ensure practically reliable results.


This paper presents glimpses of the choices available to the designer / analyst at each of the stages for the manoeuvrability prediction process


vehicles, ranging from manned submarines to UUVs. Cases are presented illustrating the effects of


for underwater these


decisions and the effects of variation in parameters on the trajectory simulation for typical underwater vehicles. Based on these simulations, the effect of variation in values of HDCs can be appreciated. Finally, the paper presents error


measurements, which suggest the level of accuracy desirable for the preceding


bounds likely during full-scale stages


prediction and analysis. 2. FOCUS OF THIS STUDY Any study


of manoeuvring


important for underwater vehicles due to the relatively narrow band of water (in depth) within which they require to


operate. Therefore, the zigzag/overshoot


manoeuvre in the vertical plane is considered for this study.


In the zigzag manoeuvre, starting from a level submerged course, the control surfaces are set at constant angle δ1 as quickly and as smoothly as possible until the pitch angle (θ) becomes equal to the execute pitch angle (θe) decided for the manoeuvre. The planes are then deflected to an angle -δ1 until the original depth at the start of the manoeuvre is reached, or the execute pitch angle in the opposite sense (-θe)


is reached. The parameters of


interest are the time to reach execute (te), time to check pitch (tc), time to check depth (td), overshoot pitch angle (θO) and overshoot change of depth (zO), as defined in Figure 1. These values will depend upon the specified plane deflection, execute pitch angle and the speed at which the manoeuvre is conducted.


on the sensitivity of manoeuvring


characteristics to the many variables in the modelling process needs to be limited to certain cases in order to keep the scope of the study within reasonable length. In this study, therefore, two underwater vehicle hull forms have been considered and various trajectory simulations have been undertaken for one particular type of definitive manoeuvre.


2.1 UNDERWATER VEHICLES CONSIDERED Trajectory


• • Axisymmetric body of simulations were carried out for two


underwater vehicle geometries in this study, which are typical of UUV and submarine forms, respectively:


revolution with


cruciform control surfaces at stern [9, 10]. The length of the body considered is 10 metres and weight (m.g) is 196.5 kg.


SUBOFF body with appendages (fin and cruciform control surfaces) as described in [11]. Length of the body is 4.26 m and weight (m.g) is 18.1 kg.


The dimensions and weights of the bodies mentioned above were used for the trajectory simulation studies. The vehicle mass properties and HDC values determined by model


reported in [9, 11] were used in the trajectory simulation programs developed.


2.2 MANOEUVRE CONSIDERED


Definitive manoeuvres are carried out to characterise and compare the handling qualities of underwater vehicles. These include zigzag/overshoot, meander, spiral, pullout and turning circle manoeuvres [2, 12]. The depth- changing and depth-keeping abilities are particularly


Figure 1 Definition of parameters for Zigzag manoeuvre in vertical plane [2]


The variation in values of the above parameters for


standard 10/10 zigzag manoeuvre (i.e. δ1=10 degrees, θe =10 degrees) and 15/5 zigzag at speed 5 knots was examined in this study for various mathematical models and HDC values.


3.


MATHEMATICAL MODELS FOR TRAJECTORY SIMULATION


testing (Planar Motion Mechanism) and


The motion of an underwater vehicle can be described in terms of Newton–Euler laws of motion, where the rate of change of momentum of a rigid body is equated to the external forces/ moments causing the change. For an underwater vehicle such as a submarine or an AUV, controlled motion is possible with six degrees of freedom (6-DOF).


3.1 RIGID BODY EQUATIONS OF MOTION


The trajectory of the body at any instant of time is described by its linear velocities u, v, w, and by its angular velocities p, q, r, in the body-fixed frame of


δ1 – Initial Control Deflection Checking angle δ2 = δ1


θe θo


PITCH Time


zo te tc td DEPTH


PLANE DEFLECTION


A - 72


©2010: The Royal Institution of Naval Architects


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