The present disclosure relates to systems and methods for controlling movement of a marine vessel in a body of water, and more particularly to controlling movement using a first propulsion device and a second propulsion device.
The Background and Summary are provided to introduce a selection of concepts that are further described below in the Detailed Description. The Background and Summary are not intended to identify key or essential features of the claimed subject matter, nor are they intended to be used as an aid in limiting the scope of the claimed subject matter.
The following U.S. Patents and Applications are incorporated herein by reference:
U.S. Pat. No. 6,234,853 discloses a docking system that utilizes the marine propulsion unit of a marine vessel, under the control of an engine control unit that receives command signals from a joystick or push button device, to respond to a maneuver command from the marine operator. The docking system does not require additional propulsion devices other than those normally used to operate the marine vessel under normal conditions. The docking or maneuvering system of the present invention uses two marine propulsion units to respond to an operator's command signal and allows the operator to select forward or reverse commands in combination with clockwise or counterclockwise rotational commands either in combination with each other or alone
U.S. Pat. No. 6,273,771 discloses a control system for a marine vessel that incorporates a marine propulsion system that can be attached to a marine vessel and connected in signal communication with a serial communication bus and a controller. A plurality of input devices and output devices are also connected in signal communication with the communication bus and a bus access manager, such as a CAN Kingdom network, is connected in signal communication with the controller to regulate the incorporation of additional devices to the plurality of devices in signal communication with the bus whereby the controller is connected in signal communication with each of the plurality of devices on the communication bus. The input and output devices can each transmit messages to the serial communication bus for receipt by other devices.
U.S. Pat. No. 7,267,068 discloses a marine vessel that is maneuvered by independently rotating first and second marine propulsion devices about their respective steering axes in response to commands received from a manually operable control device, such as a joystick. The marine propulsion devices are aligned with their thrust vectors intersecting at a point on a centerline of the marine vessel and, when no rotational movement is commanded, at the center of gravity of the marine vessel. Internal combustion engines are provided to drive the marine propulsion devices. The steering axes of the two marine propulsion devices are generally vertical and parallel to each other. The two steering axes extend through a bottom surface of the hull of the marine vessel.
U.S. Pat. No. 7,305,928 discloses a vessel positioning system that maneuvers a marine vessel in such a way that the vessel maintains its global position and heading in accordance with a desired position and heading selected by the operator of the marine vessel. When used in conjunction with a joystick, the operator of the marine vessel can place the system in a station keeping enabled mode and the system then maintains the desired position obtained upon the initial change in the joystick from an active mode to an inactive mode. In this way, the operator can selectively control the marine vessel manually and, when the joystick is released, the vessel will maintain the position in which it was at the instant the operator stopped control it with the joystick.
U.S. patent application Ser. No. 15/246,681, filed on Aug. 25, 2016, discloses a method for controlling movement of a marine vessel near an object, including accepting a signal representing a desired movement of the marine vessel from a joystick. A sensor senses a shortest distance between the object and the marine vessel and a direction of the object with respect to the marine vessel. A controller compares the desired movement of the marine vessel with the shortest distance and the direction. Based on the comparison, the controller selects whether to command the marine propulsion system to generate thrust to achieve the desired movement, or alternatively whether to command the marine propulsion system to generate thrust to achieve a modified movement that ensures the marine vessel maintains at least a predetermined range to the object. The marine propulsion system then generates thrust to achieve the desired movement of the modified movement, as commanded.
The present disclosure generally relates to systems and methods for controlling movement of a marine vessel that extends along a longitudinal axis between a bow and a stern and along a lateral axis between a port side and a starboard side, wherein the longitudinal axis is perpendicular to the lateral axis. A first propulsion device is located closer to the stern than to the bow and is steerable about a first steering axis that is perpendicular to the longitudinal and lateral axes. A second propulsion device is located closer to the bow than to the stern and is steerable at least 10 degrees about a second steering axis that is perpendicular to the longitudinal and lateral axes. A control module is configured to control steering of and thrust provided by both the first and second propulsion devices. An input device is configured to input a request for movement of the marine vessel to the control module, wherein based upon the request for movement, the control module is configured to control steering of and thrust provided by the first and second propulsion devices to thereby achieve a resultant movement of the marine vessel that is commensurate with the request for movement of the marine vessel.
Also disclosed is system for controlling movement of a marine vessel that extends along a longitudinal axis between a bow and a stern and along a lateral axis between a port side and a starboard side, wherein the longitudinal axis is perpendicular to the lateral axis, and wherein the marine vessel has a center of pressure located between the bow and the stern. A first propulsion device is located closer to the stern than to the bow and at a longitudinal distance (A) from the center of pressure, and is steerable about a first steering axis that is perpendicular to the longitudinal axis and perpendicular to the lateral axis. A second propulsion device is located closer to the bow than to the stern and at a longitudinal distance (B) in an opposite direction from the center of pressure as the longitudinal distance (A), and is steerable about a second steering axis that is perpendicular to the longitudinal axis and perpendicular to the lateral axis. A control module is configured to control steering of and thrust provided by both the first propulsion device and the second propulsion device, wherein a steering angle is defined as the angle that the thrust is provided relative to the longitudinal axis. An input device is configured to input a request for movement of the marine vessel to the control module. Based upon the request for movement, the control module is configured to control steering of and thrust provided by both the first propulsion device and the second propulsion device to thereby achieve a resultant movement of the marine vessel that is commensurate with the request for movement of the marine vessel. The request for movement of the marine vessel is one of movement of the marine vessel: parallel to the longitudinal axis; parallel to the lateral axis, without yaw movement with respect to the longitudinal and lateral axes; in translation at an angle to the longitudinal axis and at an angle to the lateral axis; parallel to the lateral axis, with yaw movement with respect to both the longitudinal and lateral axes; in rotation about the center of pressure; or parallel to the longitudinal axis, with yaw movement with respect to both the longitudinal and lateral axes.
A method for controlling movement of a marine vessel that extends along a longitudinal axis between a bow and a stern and along a lateral axis between a port side and a starboard side, wherein the longitudinal axis is perpendicular to the lateral axis, is also disclosed. The method includes: providing a first propulsion device located closer to the stern than to the bow, wherein the first propulsion device is steerable about a first steering axis that is perpendicular to the longitudinal axis and perpendicular to the lateral axis; providing a second propulsion device located closer to the bow than to the stern, wherein the second propulsion device is steerable at least 10 degrees about a second steering axis that is perpendicular to the longitudinal axis and perpendicular to the lateral axis; inputting, with an input device, a request for movement of the marine vessel to control module; and controlling, with the control module, steering of and thrust provided by both the first propulsion device and the second propulsion device to thereby achieve a resultant movement of the marine vessel that is commensurate with the request for movement of the marine vessel.
Various other features, objects and advantages of the disclosure will be made apparent from the following description taken together with the drawings.
The drawings illustrate the best mode presently contemplated of carrying out the disclosure. The same numbers are used throughout the Figures to reference like features and like components. In the drawings:
In the present description, certain terms have been used for brevity, clarity, and understanding. No unnecessary limitations are to be implied therefrom beyond the requirement of the prior art because such terms are used for descriptive purposes only and are intended to be broadly construed. The different systems and methods described herein may be used alone or in combination with other systems and methods. Various equivalents, alternatives, and modifications are possible within the scope of the appended claims. Each limitation in the appended claims is intended to invoke interpretation under 35 USC § 112(f), only if the terms “means for” or “step for” are explicitly recited in the respective limitation.
The marine vessel 10 has a bow 12 opposite a stern 14 and a port side 16 opposite a starboard side 18. As shown in
Returning to
The marine vessel 10 also includes various control elements that make up a marine propulsion system 11. The marine propulsion system 11 comprises an operation console 50 in communication with a control module 40 that contains a CAN bus 42 as described in U.S. Pat. No. 6,273,771, a processor 44, and a memory 46. As is conventional, the processor 44 can be communicatively connected to a computer readable medium that includes volatile or nonvolatile memory 46 upon which computer readable code is stored. The processor 44 can access and execute the computer readable code within the computer readable medium to carry out functions as described herein below.
In other embodiments, the CAN bus 42 may be external to the control module 40. In further embodiments, the operation console 50 and control module 40 may be connected via wireless communication rather than through physical wiring. It should be noted that the dashed lines shown in
The operation console 50 includes a number of input devices, such as a joystick 60, a steering wheel 70, one or more throttle/shift levers 52, and a keypad 80. Each of these input devices may provide a request for movement of the marine vessel 10 to the control module 40. The general process flow for maneuvering a marine vessel 10 according to the present disclosure is shown in
In some embodiments, the marine vessel 10 may also include sensors 13, 15, 17, and 19 (shown in
The steering wheel 70 and the throttle/shift levers 52 function in the conventional manner. For example, rotation of the steering wheel 70 may activate a transducer that provides a signal to the control module 40 regarding a desired movement of the marine vessel 10. The control module 40 in turn sends signals to activate steering actuators to achieve desired orientations of the first propulsion device 20 as known in the art. In accordance with the present systems and methods, the control module 40 also sends signals to activate steering actuators for the second propulsion device 30 in response to rotation of the steering wheel 70 for integrated control of both the first propulsion device 20 and the second propulsion device 30. The first propulsion device 20 and the second propulsion device 30 are independently steerable about the first steering axis 24 and the second steering axis 34, respectively. The throttle/shift levers 52 send signals to the control module 40 regarding the desired gear (forward, reverse, or neutral) and the desired thrust for each of the first propulsion device 20 and the second propulsion device 30. The control module 40 in turn sends signals to activate electromechanical actuators for shift and throttle, respectively.
A manually operable input device, such as the joystick 60, can also be used to input requests for movement to the control module 40. By integrating the control of the first propulsion device 20 and the second propulsion device 30 by way of a single input device (such as a joystick 60) or paired grouping (such as a steering wheel 70 and throttle/shift lever 52 pair), the marine vessel 10 can achieve purely longitudinal movement, purely lateral movement, purely rotational movement, or any combination thereof, as will be described below.
In some embodiments, additional input devices may be incorporated into a paired grouping such that traditional input devices may provide the functions of a joystick 60. For example, while a steering wheel is conventionally only capable of causing a rotational movement of a marine vessel, the present inventors had developed alternative methods and systems for using the steering wheel 70 to request other movements, such as a purely lateral translation movement. In one embodiment, the keypad 80 includes a translation switch 82. When the translation switch 82 is activated and the steering wheel 70 is rotated to either a left stop or a right stop (which are discussed below), the control module 40 identifies that the request for movement is for lateral movement to the port side 16 or the starboard side 18, respectively. In this configuration, the throttle/shift lever 52 is also used to control the magnitude of the thrust generated, thereby controlling the speed at which the marine vessel 10 moves laterally.
It should be recognized that other inputs may be incorporated in addition to, or instead of, those described in the previous embodiments. For example, input may come from other physical devices or from non-human sources, such as from station keeping, waypoint tracking, or heading control systems. Similarly, the control functions described in conjunction with control module 40 may be distributed across multiple control modules, such as separate control modules within the first propulsion device 20 and the second propulsion device 30 (not shown).
With reference to
The magnitude, or intensity, of movement represented by the position of the handle 61 is also provided as a request via the joystick 60. For example, if the handle 61 is moved slightly toward one side or the other, the requested thrust in that direction is less than if, alternatively, the handle 61 was moved by a greater magnitude away from its vertical position with respect to the base 63. Furthermore, rotation of the handle 61 about the pivot 62, as represented by arrow 66, provides a signal representing the intensity of desired movement. A slight rotation of the handle 61 would represent a request for a slight thrust to rotate the marine vessel 10. On the other hand, a more intense rotation of the handle 61 would represent a command for a higher magnitude of rotational thrust. In this regard, the joystick 60 provides both steering and thrust input.
The joystick 60 can also provide information to the control module 40 regarding its being in an active state or an inactive state. While an operator is manipulating the joystick 60, the joystick 60 is in an active state. However, if the operator releases the joystick 60 and allows its handle 61 to return to a centered/upright and neutral position above the pivot 62, the joystick 60 reverts to an inactive state. In one example, movement of the handle 61 away from the centered state or rotation of the handle 61 about pivot 62, or both, causes the control module 40 to determine that the joystick 60 is in the active state and to subsequently act on the commands from the joystick 60, regardless of the position of the throttle/shift levers 52 or steering wheel 70. In another example, either or both of the throttle/shift levers 52 and steering wheel 70 must be in a detent position before movement of the joystick 60 will result in the control module 40 determining that the joystick 60 is in the active state and subsequently acting on the commands from the joystick 60. In one example, the detent position of the throttle/shift levers 52 is a forward, neutral, or reverse detent position. For example, the first propulsion device 20 and the second propulsion device 30 must both be in neutral before the joysticking mode can be enabled. The detent position of the steering wheel 70 may be a zero-degree position as shown in
Thus, in a joysticking mode, the user may operate the joystick 60 to command the rotational and/or translational (lateral and/or longitudinal) movements described herein above with respect to
Returning to
As shown in step 300 of the flow chart of
In one embodiment, the modified movement may include controlling one or both of the first propulsion device 20 and the second propulsion device 30 to achieve one of a lateral movement, a longitudinal movement, or a rotational movement of the marine vessel 10, while cancelling or ignoring one or more of the other components of the movement requested that would cause the marine vessel 10 to move closer to the external object 100 than the permitted predetermined threshold distance. For example, if the request for movement includes both lateral movement and longitudinal movement components and the marine vessel 10 may only move in the longitudinal direction without violating the predetermined threshold distance between the marine vessel 10 and the external object 100, the modified movement selected by the control module 40 may control the first propulsion device 20 and the second propulsion device 30 such that only the longitudinal component of the requested movement is acted upon. Specifically, the steering angle Ae and thrust Me of the first propulsion device 20 and the steering angle At and thrust Mt of the second propulsion device 30 can be modified to partially accomplish the requested movement without moving the marine vessel 10 in the direction of the external object 100. As shown in step 330, the control module 40 subsequently controls the steering and the thrust of both the first propulsion device 20 and the second propulsion device 30 according to the selection of either the requested movement or the modified movement selected in step 320.
Note that other desired directions input to the control module 40, such as by way of the joystick 60 or from the station keeping section of the marine propulsion system 11, will be acted upon so long as they do not bring the marine vessel 10 within the predetermined threshold of the external object 100. In other words, in response to the marine vessel 10 being within the predetermined threshold of the external object 100, the method further comprises generating any thrust components that do not cause movement in the direction of the external object 100. The typical determination for controlling the steering and thrust of the first propulsion device 20 and the second propulsion device 30 without using sensors 13, 15, 17, and 19, or when the marine vessel 10 is not approaching the predetermined threshold distance relative to the external object 100, can be modified by the control module 40 to create a modified movement.
Both the magnitude and direction of the thrust, Me and the steering angle Ae, are determined by the control module 40 as described above. Based on the relationship between the thrust Me and the steering angle Ae, the thrust Me may be broken into its lateral component Se and its longitudinal component Fe or Re to determine the respective forces exerted by the first propulsion device 20 on the marine vessel 10 in the lateral and longitudinal directions. Furthermore, the rotational force on the marine vessel 10 caused by the first propulsion device 20 can be determined by multiplying the lateral component Se with the moment arm between the steering axis 24 of the first propulsion device 20 and the center of pressure CP, which is shown as longitudinal distance (A).
Similarly, the second propulsion device 30 is shown to generate a thrust Mt creating a force on the marine vessel 10. The thrust Mt is generated at the steering angle At from the longitudinal axis y. Based on this steering angle At, the respective lateral component St and longitudinal component Ft or Rt can be determined Likewise, the lateral component St can be used to determine the rotational force on the marine vessel 10 by multiplying the lateral component St with the longitudinal distance (B) between the steering axis 34 of the second propulsion device 30 and the center of pressure CP. In other examples, the distances (A) and (B) can be measured between the CP and the actual points where thrust is produced, although when compared to the length of the vessel 10, the differences between the actual points where thrust is produced and the locations of the steering axes 24, 34 are negligible.
The control configurations shown in
In the control configuration shown in
In one embodiment, as depicted in
Sequence 1:
The magnitude and direction of thrust Me and the steering angle Ae for the first propulsion device 20 to produce the Se portion of the desired translation thrust Sd can be determined from a lookup table or similar input/output map correlating a signal from the joystick 60 to calibrated values. The reverse thrust (Re) (lbf) of the first propulsion device 20 may be provided in a lookup table based on propeller versus engine speed data stored in the memory 46. The value of Re can then be used to calculate the thrust Mt and the steering angle At of the second propulsion device 30 according to the following equations:
Total lateral thrust acting on vessel 10:
Sdlbf=Selbf+Stlbf (Eq. 0)
Longitudinal thrust component Re or Fe for first propulsion device 20:
Relbf=Melbf×cos(Ae) (Eq. 1)
Lateral thrust component for first propulsion device 20:
Selbf=Meibf×sin(Ae) (Eq. 2)
Rotational or yaw component (moment) from first propulsion device 20:
Telbf·ft=−Selbf×A ft (Eq. 3)
Longitudinal thrust component for second propulsion device 30:
Ftlbf=Mtlbf×cos (At) (Eq. 4)
Lateral thrust component for second propulsion device 30:
Stlbf=Mtlbf×sin(At) (Eq. 5)
Rotational or yaw component (moment) from second propulsion device 30:
Ttlbf·ft=Stlbf×B ft (Eq. 6)
Solving for the second propulsion device 30 to eliminate yaw because no yaw was requested:
0 lb·ft=(Stlbf×B ft)−(Selbf×A ft) (Eq. 7)
Rearrange:
Stlbf=Selbf×(A/B) (Eq. 7.1)
Longitudinal thrust components must be equal because no longitudinal translation was requested:
Ft=Re (Eq. 8)
Resulting calculated second propulsion device 30 thrust:
Mtlbf=✓((Ftlbf)2+(Stlbf)2) (Eq. 9)
Second propulsion device 30 steering angle:
At=arctan(St/Ft) (Eq. 10)
Of course, in order to achieve the same marine vessel movement, the first propulsion device 20 need not be in reverse gear as shown in
Second propulsion device 30 steering angle when the first propulsion device 20 is in forward gear:
Ax=arctan(St/Ft) (Eq. 10.1)
Then, the steering angle used for control is:
At=180−Ax (Eq. 10.2)
The present inventors have found the configuration shown in
As shown in
As compared to the control configuration of
In one embodiment, as depicted in
Using the previous determinations from sequence 1 provided above (Eqs. 1-6), new determinations for controlling the second propulsion device 30 are provided by the following sequence. The value Fd, the desired forward translation, may be determined from a lookup table or similar input/output map that correlates a position of the joystick handle to a desired resultant force in the forward direction.
Sequence 2:
Because no yaw was requested:
Stlbf=Selbf×(A/B) (Eq. 7.1)
Solving for the second propulsion device 30:
Ft=Re+Fd (Eq. 8.1)
Resulting calculated second propulsion device 30 thrust:
Mtlbf=√((Ftlbf)2+(Stlbf)2) (Eq. 9)
Second propulsion device 30 steering angle:
At=arctan(St/Ft) (Eq. 10)
It should be noted that adjustments could be made to the control of the first propulsion device 20, or both the first propulsion device 20 and the second propulsion device 30, instead of those to the second propulsion device 30 above. For example, forward thrust of the first propulsion device 20 could be greater than reverse thrust of the second propulsion device 30.
Specifically, the integrated control from control module 40 causes the first propulsion device 20 and the second propulsion device 30 to output opposingly matching (i.e., of equal magnitude but opposite direction) longitudinal thrust components Re and Ft that are parallel to the longitudinal axis y, and lateral thrust components Se and St that are parallel to the lateral axis x and unmatched (i.e., of different magnitudes), but in the same direction. Thus, a first moment caused by the lateral thrust component Se acting at the longitudinal distance (A) from the center of pressure CP and a second moment caused by the lateral thrust component St acting at the longitudinal distance (B) from the center of pressure CP are unbalanced to thereby cause yaw movement of the marine vessel 10. While the lateral thrust components Se and St are shown to be in the same direction, these may also be in opposing directions.
It should be noted that while
In one embodiment, as depicted in
Using the previous second propulsion device 30 determinations from sequence 1 provided above (Eqs. 1-6), the new determinations for controlling the second propulsion device 30 are provided by the following sequence. The value Sd may be determined from a lookup table or similar input/output map that correlates a position of the joystick handle to a desired resultant force in the starboard direction. The value Td, desired rotational movement, may be determined from a lookup table or similar input/output map that correlates a rotation of the joystick handle to a desired resultant yawing force in the clockwise direction.
Sequence 3:
Solving for the second propulsion device 30:
Because a resultant moment has been requested:
Rdlbf·ft=(Stlbf×B ft)−(Selbf×A ft) (Eq. 7.2)
Rearrange:
Stlbf=(Selbf×(A/B))+(Rdlbf·ft/B ft) (Eq. 7.3)
Longitudinal thrust components must be equal because no longitudinal translation was requested:
Ft=Re (Eq. 8)
Resulting calculated second propulsion device 30 thrust:
Mtlbf=√((Ftlbf)2+(Stlbf)2) (Eq. 9)
Second propulsion device 30 steering angle:
At=arctan(St/Ft) (Eq. 10)
It should be noted that adjustments to the control of the first propulsion device 20, or both the first propulsion device 20 and the second propulsion device 30, could be made instead of these to the second propulsion device 30 as described above.
In one embodiment, as depicted in
Using the previous second propulsion device 30 determinations from sequence 1 provided above, the new determinations for controlling the second propulsion device 30 are provided by the following sequence. The value Td may be determined from a lookup table or similar input/output map that correlates a rotation of the joystick to a desired rotational movement, such as a yaw movement in the clockwise direction.
Sequence 4:
Solving for the second propulsion device 30:
Because there is no resulting lateral movement, but there is yaw:
Stlbf=Selbf (Eq. 7.4)
Because there is no longitudinal movement:
Ft=Re (Eq. 8)
Resulting calculated second propulsion device 30 thrust:
Mtlbf=√((Ftlbf)2+(Stlbf)2) (Eq. 9)
Second propulsion device 30 steering angle:
At=arctan(St/Ft) (Eq. 10)
In the embodiment shown, the moments created by the first propulsion device 20 and the second propulsion device 30 are both in the counterclockwise direction, providing the requested rotational movement of the marine vessel 10. Alternatively, the control module 40 may cause a rotation of the marine vessel 10 in the same counterclockwise direction by controlling the steering and thrust of the first propulsion device 20 and the second propulsion device 30 such that thrust is only generated by one of the propulsion devices. Specifically,
In addition to the control module 40 providing integrated control of the first propulsion device 20 and the second propulsion device 30 to accomplish movements not traditionally possible by a marine vessel 10, such as purely lateral movement, rotational movement about the center of pressure CP, or combination thereof, the present systems and methods also provide for enhanced steering at slow speeds over presently known marine propulsion systems.
In the configuration shown in
Through experimentation and testing, the present inventors have discovered that slow speed steering is optimized by the following configuration. The longitudinal components Fe and Ft have the same orientation in the forward direction, parallel to the longitudinal axis y. The lateral components Se and St have opposing orientations such that each creates a moment about the center of pressure CP in the clockwise direction, thereby causing a rotational or yaw movement of the marine vessel 10. The steering and thrust of the second propulsion device 30 can be optimized based on the turning radius (C) that corresponds to the steering angle Ae of the first propulsion device 20. The distance (C) is solved for by determining where a lateral line (L), which extends from the center of pressure CP parallel to the lateral axis x, intersects with a first steering line (D), which extends from the first steering axis 24 and is perpendicular to the steering angle Ae of the first propulsion device 20. In other words, the turning radius is a distance (C) from the center of pressure CP to the intersection. The control module 40 then controls the steering and thrust of the second propulsion device 30 such that a second steering line (F) that extends from the second steering axis 34 and is perpendicular to the steering angle At intersects with the lateral line (L) at the same point where the first steering line (D) intersects with the lateral line (L). While the inventors have found the previous configuration to be particularly advantageous, the control module 40 can control the movement of the bow 12 more aggressively by selecting a steering angle At for the second propulsion device 30 that is larger than the optimized value previously provided.
In one embodiment, as depicted in
The value Fd may be determined from a lookup table or similar input/output map that correlates a position of the joystick to a desired movement in the forward direction. The value Rd may be determined from a lookup table or similar input/output map that correlates a rotation for the joystick to a desired rotational movement, such as a yaw movement in the clockwise direction. If the distance (A) from the first steering axis 24 to the center of pressure (CP) and the steering angle (Ae) are known, then the length of (C) can be determined by:
Sequence 5:
The angle between lines C and D at the point of intersection is the same as the steering angle Ae of the first propulsion device 20 with respect to the longitudinal axis y.
AC-D=Ae (Eq. 11)
Angle between lines A and D at the first steering axis 24.
Ai=(90−AC-D) (Eq. 12)
Resulting calculated turning radius.
C=tan(Ai)×A (Eq. 13)
The angle of the second propulsion device 30 from the longitudinal axis y (steering angle At) is the same as angle AC-F (the angle between lines C and F at the point of intersection).
AC-F=arctan (B/C) (Eq. 14)
The angle of the second propulsion device 30 from the longitudinal axis y is the same as angle AC-F.
At=AC-F (Eq. 15)
Calculating the thrust required at the second propulsion device 30 (Mt) to perform a coordinated turn with the first propulsion device 20 requires the turning radius of the second propulsion device 30 (F):
F ft=√((B ft)2+(C ft)2) (Eq. 16)
The ratio of the thrust of the first propulsion device 20 (Me) to its turning radius (D) should be equal to the ratio of the thrust of the second propulsion device 30 (Mt) to its turning radius (F).
(Melbf)/(D ft)=(Mtlbf)/(F ft) (Eq. 17)
Solving for the magnitude of thrust of the second propulsion device 30.
(Mtlbf=(F ft/D ft)×(Melbf) (Eq. 18)
Thus, the thrust provided by the second propulsion device 30 is equal to the thrust provided by the first propulsion device 20 multiplied by the ratio of the distance (F) over the distance (D).
In the above description, certain terms have been used for brevity, clarity, and understanding. No unnecessary limitations are to be inferred therefrom beyond the requirement of the prior art because such terms are used for descriptive purposes and are intended to be broadly construed. The different assemblies described herein may be used alone or in combination with other devices. It is to be expected that various equivalents, alternatives and modifications are possible within the scope of any appended claims.
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Unpublished U.S. Appl. No. 15/246,681, filed Aug. 25, 2016 entitled “Methods for Controlling Movement of a Marine Vessel Near an Object”. |