Abstract:
A method for assisting tug boats, work boats and other vessels to navigate no-passing zones, such as narrow channel areas, along an inland and other waterways to avoid passing or overtaking other vessels having the right-of-way according to established waterway rules of the road within the no-passing zones. The method is implemented within an executing computer program, using a database of mile mark distances and of no-passing zones along the length of the waterway.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]    Priority is claimed to the filing date of provisional application, No. 61/417,168, entitled “Navigation in No-Passing Zone,” filed on Nov. 24, 2010. 
     
    
     BACKGROUND  
       [0002]    Rivers, bays, estuaries, inlets and harbors comprise some of the inland waterways used by marine vessels to move various goods into and from the interior of a continent. These inland waterways often have a channel, comprising that part of the lateral width of the inland waterway with sufficient depth to accommodate the draft of marine vessels. The channels often are dredged to maintain sufficient depth for marine vessels. In the United States, dredging and maintaining the navigability of inland waterways is the responsibility of the US Army Corps of Engineers. 
         [0003]    A common type of marine vessel operating on inland waterways is a towboat, pushing a number of barges secured together, called a barge tow. The barges can contain various bulk products, such as fuels, petroleum products, chemicals, ores, coal or grain. On the lower Mississippi River south of St. Louis, barge tows may be as large as 40 to 50 barges. Larger towboats, called line boats, are used to push these larger barge tows up and down the river. 
         [0004]    Along the Mississippi River are a number of bends in the river. There are also sections of the river in which sediment has accumulated or where a sunken wreck may be found. In these sections of the river, the channel width is constricted or navigation of a large barge tow is difficult, thereby making passing or overtaking another barge tow excessively hazardous of running aground. Therefore, if a vessel skipper feels or determines that a section of the river is insufficiently wide or otherwise too hazardous to safely pass an oncoming, opposing barge tow, he will stop and wait until the oncoming barge tow has cleared the narrow or hazardous area. 
         [0005]    On the Mississippi River and its major tributaries, commercial tow boats, line boats and other vessels traveling downstream or with the current have the right-of-way over vessels traveling upstream or against the current. Therefore, if an upstream-bound line boat with a barge tow is approaching a narrow channel area from downstream and learns of another barge tow coming towards him from upstream, the downstream line boats will slow or, if necessary, stop to allow the upstream barge tow to continue to ply downstream until it clears the narrow channel area. Hereinafter, the upstream-bound vessel which must adjust its course and/or speed to accommodate a downstream-bound vessel having the right-of-way is referred to as a “burdened” vessel. The vessel bound downstream having the right of way over a vessel located further downstream and bound upstream is referred to as a “privileged vessel.” 
         [0006]    Presently, burdened line boats navigating upstream, when nearing a narrow channel area, will call out on the marine radio to learn of any privileged vessels with barge tows proceeding downstream and approaching the same narrow channel area. The burdened line boat skipper will inquire of the upstream line boat&#39;s estimated time of arrival at the narrow channel area. If the privileged vessel is too close to the narrow channel area, the burdened vessel skipper will then adjust his speed accordingly to allow or wait for the privileged vessel to pass through and clear the narrow channel area before proceeding through it himself. Similarly, if the skipper of a privileged vessel learns of a burdened vessel approaching a narrow area from the downstream side, the skipper can call to the burdened vessel by radio and demand it yields the right of way and not enter the narrow area until the privileged vessel passes. 
         [0007]    Many line boats, tow boats and other commercial maritime vessels operating on the inland waterways have a radio system called an Automatic Identification System, or AIS. An AIS system automatically transmits on a VHS band a data packet containing a unique ID for the boat, its location, course, and speed along with possibly with other information. A vessel with an AIS system can receive the AIS transmissions from other vessels within the radio range of the AIS transponder. The AIS information from other vessels can then be displayed on a monitor or electronic chart. The skipper of a burdened vessel navigating upstream can then see the information on upstream privileged vessels heading towards his position. If the skipper of the burdened vessel knows the location of narrow channel areas, he can then predict when privileged vessels will enter and exit the narrow channel areas. He can then adjust his speed appropriately, either higher or lower, to avoid passing the privileged vessels within the narrow channel areas. 
         [0008]    This method of adjusting a vessel&#39;s speed to avoid passing opposing vessels or barge tows is adequate when the downstream vessel captain is very familiar with the channel condition ahead of him, and if there is only one vessel or barge tow heading downstream towards him. If the channel conditions upstream are unknown, if visibility is low or if there are more than one vessel or barge tow heading towards him, then determining the boundaries of narrow channel areas and the times when the area may be clear of downstream-bound traffic becomes too difficult and problematic. This method can be further inaccurate because the skipper must visually judge distances along the river channel. This is often difficult and inaccurate when the river course undulates and meanders across its river plain. 
       SUMMARY OF THE INVENTION 
       [0009]    In the method described herein, several electronic databases related to the course of a navigable waterway are accessible to a computer. One database contains the result of a survey of the river, in which points, called mile markers, are identified at intervals along the course of the river from a fixed reference point. 
         [0010]    Another database contains records of the narrow channel areas along the course of the river, where tow boat skippers generally do not want to pass an opposing barge tow, either as passing in opposite directions or overtaking when travelling in the same direction. These narrow channel areas are hereinafter identified as “no-passing zones.” Each record of a no-passing zone contains the mile marker distance of the upstream and downstream boundaries of the no-passing zone. Each record may contain additional information regarding that no-passing zone, such as any required or practical restrictions on the speed of a vessel navigating through the no-passing zone. This database can be used to visually plot the narrow channel areas of the river on a nautical chart. As used herein, “no-passing zones” may include a system of one or more locks. 
         [0011]    In the preferred embodiment, an AIS transponder is provided on the burdened vessel which can receive AIS transmissions from other vessels on the river similarly equipped. The data from the AIS transponder is communicated to a computer, in which a program is executed comparing the received AIS information with the mile marker and no-passing zone databases. The program identifies those vessels upstream of user&#39;s vessel travelling downstream, i.e., privileged vessels with respect to this burdened vessel. Then, all no-passing zones between the burdened vessel and the foregoing privileged vessels are identified. For each upstream privileged vessel, its scheduled entering and exiting times at each no-passing zone between it and the burdened vessel is determined. From these schedules, the speed of the user&#39;s vessel is adjusted so that the burdened vessel passes through each no-passing zone during time periods when no other privileged vessel will be present in the no-passing zones. 
     
    
     
       DESCRIPTION OF THE DRAWINGS  
         [0012]      FIG. 1  is an illustration of an inland waterway on which one burdened vessel and several privileged vessels are navigating towards no-passing zones. 
           [0013]      FIG. 2  is a plot of the time-vs.-mile mark distance of a burdened and privileged vessel approaching opposite ends of a no-passing zone, illustrating speed changes to the burdened vessel resulting from the present method. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0014]    As used herein, “burdened vessel” refers to a vessel navigating upstream and required, under maritime rules of the road, to yield the right-of-way to another vessel. 
         [0015]    As used herein, “privileged vessel” refers to a vessel travelling downstream or with the current and having the right-of-way over a vessel located downstream from it. Privileged vessel may also refer to another upstream-bound vessel located further upstream from a burdened vessel and being overtaken by the burdened vessel. 
         [0016]    As shown in  FIG. 1 , a burdened vessel  101  bound upstream is located in the channel of a mainland waterway  101  such as a river. One or more other privileged vessels  104  are located further upstream from the upstream-bound burdened vessel, but proceeding downstream towards the burdened vessel. Between the upstream bound vessel and the one or more downstream bound vessels are one or more restricted no-passing zones  102 ,  103 . 
       AIS Transponders  
       [0017]    In the preferred embodiment, the burdened vessel and one or more privileged vessels are equipped with AIS transponders. The Automatic Identification System (AIS) is an automated tracking system used on ships and by Vessel Traffic Services (VTS) for identifying and locating vessels by electronically exchanging data with other nearby ships and VTS stations. AIS information supplements marine radar, which continues to be the primary method of collision avoidance for water transport. 
         [0018]    Information provided by AIS equipment, such as unique identification, position, course and speed, can be displayed on a display screen or an ECDIS. AIS is intended to assist a vessel&#39;s officers and allow maritime authorities to track and monitor vessel movements. AIS integrates a standardized VHF transceiver with a positioning system such as a LORAN-C or GPS receiver, with other electronic navigation sensors, such as a gyrocompass or rate of turn indicator. Ships outside AIS radio range can be tracked with the Long Range Identification and Tracking (LRIT) system with less frequent transmission. 
         [0019]    The information in the messages transmitted by an AIS transponder may include one or more of the following:
       MMSI: A nine-digit identification number;   The vessel&#39;s navigational status, e.g., “at anchor”, “underway with engines;”   The vessel&#39;s rate of turn;   The vessel&#39;s speed over ground;   The vessel&#39;s position, in latitude and longitude;   The vessel&#39;s course over ground;   The vessel&#39;s true heading; and       
 
         [0027]    The transmission of an AIS transponder is in the form of a stream of text messages. The stream of text messages from another vessel are received by the AIS transponder on the burdened vessel and communicated to a computer. A program running on the computer can then parse the information from text stream and note the time the message was received. It may also display the information contained in it in a more useful graphic format on a display. Such a graphic format could include, for example, displaying an icon on an electronic nautical chart, the icon located in relation to the actual location of the transmitting vessel. The information from the text stream can be displayed in various formats. The identification, bearing, and speed can be displayed in a text box next to the icon; a text box can the pop up when the mouse cursor rolls over the icon; or the text box can pop up when a user clicks with a mouse button on the icon. Alternatively, different shapes, sizes and/or colors may be used for the vessel&#39;s icon to represent the vessel&#39;s data. For example, a vessel may be indicated by an arrowhead, its direction equivalent to the bearing of the vessel and its size or color indicative of its speed. 
         [0028]    If the particular AIS transmitter does not transmit all the data listed above, specifically the course and speed over ground, then the computer into which the data is imported can interpolate that information from a series of positions for the vessel. 
         [0029]    An AIS transponder can receive the transmissions of another AIS transponder directly if the two transponders are within VHF radio range. This range is typically about 20 miles, depending on the surrounding terrain. For receiving AIS transmissions from further ranges, retransmission means may be used, such as using a network of radio repeaters, using satellites, using cellular telephony data connections or using various wireless internet connections. Other embodiments of the invention include other radio transponders capable of transmitting data or information on a vessel&#39;s location, including cellular phones or GPS receivers. 
       Mile Marker Database  
       [0030]    Several computer databases related to the course of a navigable river are provided in or communicated to the computer. One database contains the result of a survey of the river, in which points called mile markers  105  are specified along the waterway  100 , representing a certain distance along the course of the waterway  100  from a fixed reference point. The fixed reference point is usually the downstream end of the waterway  100 , such as the mouth of the river or its confluence with another river. The fixed reference point may also be at the furthest upstream navigable port along the waterway. The identified mile markers  105  in the database are usually at whole integral distance measures from the fixed reference point, using common units of distance, such as miles (either statute or nautical) in the United States or kilometers in Europe and elsewhere. The database also contains the geographic location of each mile marker  105 , expressed as latitude and longitude. The database may also contain other information from a survey, such as the width and depth of the channel and the direction of the course of the waterway  100  at the mile marker  105 . 
         [0031]    In sections of the waterway  100  having turns or tight bends, the database may contain additional mile markers  105  at fractional unit distances between two integral distance mile markers  105 . The number and locations of additional mile markers  105  would be provided such that straight lines between two adjacent mile markers  105  would lie substantially within the channel of the waterway. 
         [0032]    This database permits any point along the course of the waterway  100  channel to be expressed in terms of its mile marker distance, i.e., its distance from the same fixed reference point used by the mile marker database. If the object&#39;s mile marker location must be more precise than that provided by the database, the object&#39;s mile marker location can be determined using its geographical coordinates (i.e., latitude and longitude) by interpolating between the geographical coordinates of the adjacent mile markers in the database. 
         [0033]    Because a waterway such as a river is dynamic and its course may alter and change over time, especially after floods, the database of mile markers  105  should be periodically updated from new surveys. 
         [0034]    The mile marker database may be stored in the computer&#39;s memory, including its random access memory, read-only memory, an internal or external hard disk drive, a portable memory stick or USB drive, or other forms of digital data storage well known in the art. In other embodiments, the mile marker database is stored on a remote server in communication with a network, such as the Internet, and its records are retrieved from the remote server by the computer using wireless means to access the network. 
       No-Passing Zone Database  
       [0035]    The computer program is also provided with a database of records describing the no-passing zones  102 ,  103  of the waterway. Each record of this database would contain at least the upstream and downstream boundaries  106 ,  107  of the no-passing zone  102 ,  103 , expressed as mile marker distances. If the mile marker distances of the upstream and downstream boundaries  106 ,  107  need more precision than the integral distances between mile markers, as contained in the mile marker database, then the locations of the boundaries  106 ,  107  can be interpolated based on the geographic coordinates of the boundaries  106 ,  107  and the adjacent mile markers  105 . Other information for each no-passing zone record could include the maximum safe speed for proceeding through the region or the present speed reduction necessary to proceed through the region. 
         [0036]    The no-passing zone database may be stored in the computer&#39;s memory. In other embodiments, the no-passing zone database is stored on a remote server and its records are accessed including wireless means across a network, such as the Internet. 
       Locating Objects by the Mile Marker Database  
       [0037]    The method for navigating through no-passing zones  102 ,  103  usually requires knowing the position of mile markers  105  of the relevant burdened and privileged vessels  101 ,  104  and the boundaries  106 ,  107  of no-passing zones  102 ,  103 , usually with a precision of 0.1 miles. Since the database of mile markers  105  typically records the distance of each mile marker  105  in integral units of either miles or kilometers, the mile marker distance of an object must be determined by interpolation between two adjacent mile markers  105 . To interpolate the mile marker distance of an object a computer program could, for example, calculate the distances from the object to each mile marker using the latitudes and longitudes of the object and the two adjacent mile markers. Using Pythagoras&#39; Theorem, the distance between two points on the earth&#39;s surface (for small distances) equals the square root of the sum of the squares of the longitudinal (east-west) distance and the latitudinal (north-south) distance between the two points. For accuracies sufficient for this method, the latitudinal distance is the difference in their latitudes, expressed in decimal degrees, multiplied by 69.172 miles. The longitudinal distance between two points is the difference in their longitudes, expressed in decimal degrees, multiplied by 69.172 miles, multiplied by the cosine of their mean latitude. To interpolate the mile marker distance of the object between the two mile markers  105 , the distance between the downstream mile marker  105  and the object is divided by the distance between the two mile markers  105  (which will typically be 1 mile). A more accurate method would be to calculate the dot product of the direction vector from the downstream mile marker  105  to the object with the direction vector from the downstream to the upstream mile marker  105 . 
       Determining the Next Two No-Passing Zones  
       [0038]    In another embodiment of the invention, the method may involve an iteration of the steps concerning the privileged vessels  104  between the next two no-passing zones  102 ,  103  upriver of the burdened vessel  100 . These two no-passing zones  102 ,  103  will have the next two sets of downriver and upriver boundaries  107 ,  106  subsequent to the current location of the burdened vessel  100 . 
       Identifying Privileged Vessels of Interest  
       [0039]    Data received by the burdened vessel&#39;s  100  radio transponder is routed to a computer able to communicate with the mile marker database and the no-passing zone database for the section of waterway  100  on which the burdened vessel  101  is navigating. From that data, the computer&#39;s program determines those vessels which are upstream of the burdened vessel  101  and are travelling downstream towards the burdened vessel  101 . These vessels would be privileged  104  and have the right-of-way with respect to the burdened vessel  101 . 
         [0040]    Because inland waterways  100  often meander, sometimes very significantly, identifying the privileged vessels  104  located upstream on the waterway  100  and travelling downstream is not obvious or readily apparent from that vessel&#39;s course. Of the vessels from which AIS or other radio transponder transmissions are received, those vessels upstream of the burdened vessel  101  must first be identified by finding the mile marker distance of each vessel. This may be done by searching the mile marker database and finding the mile marker  105  with the shortest distance from the vessel in opposite directions. The vessel&#39;s mile marker distance is then determined by interpolation from the two mile markers  105 , as described above. If the mile marker database reference point is the furthest downriver point of the waterway  100 , such as its confluence with another river, those vessels with higher mile marker distances than the burdened vessel are upriver of the burdened vessel. 
         [0041]    The travel direction of the upstream vessels, with respect to the river, is determined, i.e., whether the upstream vessel is travelling upstream or downstream. This can be done in two steps. First, the course of the waterway where the upstream vessel is located is determined. This course may be contained in the mile marker database for the mile marker nearest the upstream vessel. If the mile marker database does not contain information about the waterway&#39;s course, then that course may be determined by determining the vector between the mile marker locations on either side of the upstream vessel. The vector from the higher to the lower mile marker represents the directions of the course of the waterway, if the mile marker reference point is the furthest downstream point of the waterway 
         [0042]    Second, the course of the upstream vessel is determined. If the vessel&#39;s bearing is in the same direction as vector determined from the nearest upstream mile marker to the nearest downstream mile marker from the vessel, the vessel is travelling downriver, and is a privileged vessel  104 , with respect to the burdened vessel  101 . If the radio transponder information received from the upstream vessel does not contain its course information, then the upstream vessel&#39;s course can be determined by the computer by fitting a vector to the latest series of positions and the times of those positions. The upstream vessels having a course substantially parallel to the waterway&#39;s course are making way downstream and are privileged vessles  104  with respect to the burdened vessel  101 . It is with these privileged vessels  104  that the method herein avoids passing in no-passing zones  102 ,  103 . These privileged vessels  104  are preferably sorted by their proximity to the burdened vessel  101 . 
         [0043]    In the next step, those privileged vessels  104  on the opposite side of the no-passing zone  102  nearest the burdened vessel are selected. Preferably these privileged vessels  104  are sorted by their proximity to the burdened vessel  101 , as determined by their mile marker distances. Then, the times at which each of these privileged vessels  104  will enter and exit the next no-passing zone  102  upstream of the burdened vessel  101  are determined In the preferred embodiment of this invention, the mile markers reference the distance from the mouth or most downstream end of the subject River. 
         [0044]    From the upstream  106  and downstream  107  boundaries of the next no-passing zone  102 , the time at which an upstream privileged vessel  104  will enter the next no-passing zone  102  equals the difference in the mile marker distances between the privileged vessel  104  and the upstream boundary divided by the speed of the privileged vessel. The time at which the privileged vessel reaches the downstream boundary  107  the next no-passing zone  102  equals the time to cross the upstream boundary  106  of the next no passing zone  102  plus the distance between the upstream  106  and downstream  107  boundaries divided by the speed of the privileged  104  vessel through the next no-passing zone  102 . The speed of the privileged vessel  104  for the no-passing zones  102 ,  103  generally will equal its prior speed adjusted for any restrictions necessary for proceeding through the no passing zone  102 ,  103 . The periods between when a privileged vessel  104  will enter and exit the next no-passing zone  102  represent a temporal window during which the burdened vessel  101  cannot be within the no-passing zone  102 . 
         [0045]    If several privileged vessels  104  are heading towards the next no-passing zone  102 , then the time periods when each will cross the upstream boundary  106  and downstream boundary  107  of the next no-passing zone  102  are determined. The time periods when no privileged vessel  104  is within the no-passing zone  102  represent when the burdened vessel  101  can traverse the no-passing zone  102 . 
       Determining the Minimum Speed for the Burdened Vessel  
       [0046]    Each privileged vessel approaching the next no-passing zone is examined in turn. First, the minimum speed necessary for the burdened vessel  101  to cross and exit the next no-passing zone  102  is determined. This equals the distance between the upstream boundary  106  of the next no-passing zone  102  and the present position of the burdened vessel  101  divided by the time for the first privileged vessel  104  to reach the upriver boundary  106  of the next no-passing zone  102 . If this minimum speed is greater than the maximum cruising speed of the burdened vessel  101 , with any barge tow, then the burdened vessel  101  must wait for the first privileged vessel  104  to pass through the next no-passing zone  102 . The overall maximum speed to pass this first privileged vessel  104  at or below the downriver boundary  107  of the next no-passing zone is determined. The speed of the burdened vessel can be set at or below this overall maximum speed, depending on the preferences of the burdened vessel&#39;s skipper. Based on this chosen speed, the position of the burdened vessel when the first privileged vessel exits the next no-passing zone  102  can be determined. 
         [0047]    This step is repeated with the second privileged vessel  104 , aft of the first privileged vessel  104 , using the burdened vessel&#39;s  101  new position at the time when first privileged vessel  104  passes the downriver boundary  107  of the next no-passing zone  102 . It may be necessary for a burdened vessel  102  to wait for the second privileged vessel  104  to clear the no-passing zone  102 , as well, depending on the distance of the second privileged vessel  104  behind the first, and on the length of the no-passing zone  102 . 
         [0048]    When the minimum speed to successfully traverse the first no-passing zone  102  found for the nth vessel is within the capability of the burdened vessel, the speed of the burdened vessel  101  is set at least to this minimum speed. The burdened vessel  101  will clear the no-passing zone  102  and pass its upriver boundary  106  before the nth privileged vessel  104  reaches the upriver boundary  106  of the next no-passing zone  102 . 
         [0049]    In other embodiments of the invention, the above steps may be repeated for the subsequent no-passing zones  103  once the minimum speed for the next no-passing zone  102  has been determined. The identity and order of privileged vessels  104  upriver of the subsequent no-passing zone  103  are found and their times of arrival and departure through the subsequent no-passing zone  103  are found. From these, the minimum speed to reach and pass through the subsequent no passing zone  103  is set. If the minimum speed is greater than the burden vessel&#39;s current speed navigating through the next no-passing zone  102 , it can increase its speed to assure reaching and traversing the subsequent no-passing zone 103  . Determining the necessary minimum speed for crossing the subsequent no-passing zone while still at or near the next no-passing zone assures the minimum speed for each no-passing zone, while reducing the times a burdened vessel must unnecessarily stop at the downriver boundary of any no-passing zone. 
         [0050]    These steps are repeated as the burdened vessel  101  proceeds upriver. As the method reaches a solution for traversing the next no-passing zone  102  without passing a privileged vessel, it begins solving for passage through the subsequent no-passing zone  103  . If the solution for the subsequent no-passing zone  103  is within the solution of the next no-passing zone  102 , the speed of the burdened vessel  101  is adjusted accordingly to satisfy both solutions to travel at the most efficient speed without unnecessary stops and delays. As the burdened vessel  101  passes through the next no-passing zone 102 , the subsequent no-passing zone  103  becomes the next no-passing zone  102  in the above methodology, and the no-passing zone further beyond becomes subsequent no-passing zone  103 , as those terms are used in the methodology above. 
         [0051]    On occasions, an upriver-bound vessel trailing behind another, slower moving upriver-bound vessel or barge tow desires to overtake that vessel ahead (not shown in  FIG. 1 ). In this situation, the vessel overtaking the other is the burdened vessel, and the vessel being overtaken is the privileged vessel with the right of way. In such a situation, the burdened vessel desires to complete the overtaking maneuver while there are no downriver vessels passing them and outside of a no-passing zone. 
         [0052]    To determine the minimum speed necessary to complete an overtaking maneuver, the necessary distance to overtake the privileged vessel is calculated, based on the geographical positions of the two vessels and the necessary distance must be ahead of the privileged vessel to complete the overtaking maneuver. First, the distance between the privileged vessel and the next no-passing zone is determined. The time available equals that distance divided by the speed of the privileged vessel. The minimum speed equals the distance of the burdened vessel to the no-passing zone divided by the available time. If that minimum speed is greater than the capability of the burdened vessel, the burdened vessel must wait to overtake until passing through the no-passing zone. 
         [0053]    After determining the minimum speed with respect to the privileged vessel, any possible meeting with a downriver-bound vessel must be determined, from their AIS transmissions. Using the current location and speed of any downriver-bound vessel, its position at the end of the overtaking maneuver is projected. If this position is at or beyond that of the burdened vessel, then the overtaking maneuver cannot be completed at the aforementioned minimum speed. 
         [0054]    A new minimum speed may be calculated to both overtake the burdened vessel before passing any approaching downstream-bound vessel. First, the position and time at which the burdened vessel and approaching vessel meet is calculated. If this point is beyond where the privileged vessel will pass the burdened vessel, and the time to meet the approaching vessel is greater than the time necessary to overtake the privileged vessel, then the burdened vessel may proceed to overtake the burdened vessel. 
         [0055]    If, however, the approaching vessel will meet the burdened vessel prior to overtaking the privileged vessel, then a new, higher speed may be calculated. To overtake the privileged vessel before passing the approaching vessel, the burdened vessel must reach the position that the approaching vessel passes the bow of the privileged vessel &amp; barge tow, plus a margin of safety, before the approaching vessel reaches it. This point will be reached in a time period equal to the net closing speed of the approaching and burdened vessels, divided by the current distance between the two vessels minus any distance allowed for their barge tows and for a safety margin. If this time period is longer than the prior time period for overtaking the privileged vessel at the minimum necessary speed, then the approaching vessel will have no effect on overtaking the privileged vessel. 
         [0056]    The location of this new overtaking point equals the speed of the burdened vessel multiplied by the new time period, plus the length of the privileged vessel&#39;s barge tow and any safety margin. The new minimum speed for the burdened vessel equals the distance between the burdened vessel and the new overtaking point, divided by the new time period. If this new minimum speed is greater than the capabilities of the burdened vessel, then the burdened vessel must wait until the approaching vessel passes, and the process is repeated. If not greater than the vessel&#39;s capability, the speed of the burdened vessel is adjusted to at least the new minimum speed and the overtaking maneuver is carried out. 
         [0057]    The various geographic points at which the burdened vessel will overtake another upriver bound vessel or will pass a downriver bound vessel can be displayed on the electronic navigational chart. 
       EXAMPLE 
       [0058]    An example of the method in practice is illustrated in  FIG. 2 . In the graph of  FIG. 2 , the horizontal axis represents clock time, and intervals are labeled according to military or GMT time. The vertical axis represents distance along a waterway, with intervals shown in mile marker distance. The track of a burdened vessel proceeding upstream is shown as  202 , while the track of a privileged vessel proceeding downstream is shown as  201 . Just prior to 15:00 hours, the AIS transponder of the privileged vessel comes within range of that of the burdened vessel. The computer programmed to implement this method receives the text messages from the transponder of the privileged vessel, and determines it will enter the next no-passing zone  203  at about 15:30 and exit it about 16:45. The projected path  207  of the burdened vessel will enter the no-passing zone at about 15:20 and exit at about 16:40, crossing the privileged vessel at about 16:00, in the middle of the no-passing zone. 
         [0059]    Accordingly, the computer running the program which implements the present method calculates the maximum speed for the burdened vessel to enter the no-passing zone at or after the privileged vessel enters the no-passing zone. This maximum speed track  205  crosses the track of the privileged vessel immediately after it exits the no-passing zone.