There are several ways to plot a course in 3-dimensional space. One way is to provide a flight vector specified as an azimuth/elevation relative to another flight vector (usually the vessel's current orientation). This method, using the spherical coordinate system, gives the azimuth and elevation values as angles relative to another vector. These angles, the "bearing" and "mark", respectively, are given in degrees, with 360 degrees being equal to one full rotation.

This system can be show with some examples:

BEARING 019 MARK 038

BEARING 301 MARK 000

BEARING 329 MARK 322

MARK 010 BEARING 258

BEARING 087 MARK 030

How can trajectory paths be entered in the computer?

There are 5 basic input modes available for specification of spacecraft trajectory paths that may be entered into the computer.

• Destination Sector - For use with a frequently utilized designation or as an ID number for a specific sector. This would place the vessel at a same location in the targeted sector as it holds in the present sector.
• Destination Planet or System - Any celestial object or recognized facility in the navigational database is permissible. The computer calculates the proper direction automatically.
• Absolute Heading - A flight vector is specified as an azimuth/elevation relative to the center of the galaxy. ("Bearing 000, Mark 000" = Galactic center).
• Relative Bearing - A flight vector is specified as an azimuth/elevation relative to the vessel's current orientation. ("Bearing 000, Mark 000" = Straight ahead.)
• Spacecraft Intercept - For use with any vessel located by a sensor lock.

Spacecraft orientation

Federation starships navigate around the Galaxy by combining a massive database of information with sophisticated onboard sensors that can pinpoint the vessel's position accurately. Typically a Starfleet vessel can calculate its position relative to the galactic centre, or another 'fixed' reference point, such as earth, to within 10 kilometres; even at high warp speeds, the ship can determine its location to within 100 kilometres. In close manoeuvring of the kind required when docking, a starship can manoeuvre within distances as accurate as 2.75 centimetres.

To the casual observer, starship navigation appears a simple task. Navigational operations are controlled from the conn; a commanding officer can give a destination or heading in one of five ways. The easiest method is to give the destination. As soon as this is inputted into the conn, the ships computers consult the navigational database and automatically plot the ships trajectory. Destinations can be planets, systems or even orbital facilities. If an area as large as a sector is specified, the computers will generate a flight path to the centre of that area.

The conn can also be given a moving destination such as another spacecraft. As long as the vessel is within sensor range, the computers can plot an intercept course. This kind of order requires the conn officer to input either a velocity or an intercept time, so that the course can be calculated relative to the position of the other craft.

Giving Co-ordinates

Navigational instructions can be given by specifying a destination's galactic co-ordinates; however, this method of navigation is rarely used , as it requires personnel to either calculate or look up the relevant co-ordinate information. Navigational orders are often given as a relative bearing. This consists of two figures which relate to two perpendicular planes around the vessel; the first plane is horizontal, the second is vertical. Each plane is divided into 360 degrees, with 0 degrees deemed to be straight ahead. Thus a vessel given a heading of 000 mark 0 would not change its course. On the horizontal plane, values increase to the starboard; in the vertical plane , they increase in the direction above the ship. Therefore a heading of 150 mark 0 means that the ship will turn 150 degrees to starboard, a heading of 150 mark 20 means the ship will turn 150 degrees to starboard and then angle the nose up by 20 20 degrees.

Galactic Headings

Navigational orders can also be given as a heading. Again this is given as two figures, but these figures relate to two planes around a notional line which connects the vessel with the centre of the Galaxy. A heading of 000 mark 0 is directly toward the galactic centre. This system is very similar to that used in navigation on a planet's surface where headings are taken from the northern pole. The instructions given may be simple, but calculating a course across interstellar distances is an extremely demanding task. One has to know the position of the vessel, the speeds involved and the the position of the destination, but it is impossible to maintain an entirely accurate map of the Galaxy: all objects within the Galaxy are moving in their own direction and many methods of observation involve a noticeable time lag. Despite these difficulties, the Federation has charted a significant proportion of the Galaxy and uses information gathered from subspace relays, Federation vessels, probes and sensor platforms to ensure that its map, which is known as the galactic condition database, is as up to date as possible. Starfleet's Stellar Cartography division has plotted the position of stars well beyond the reaches of manned exploration. Facilities such as the Argus Array, located on the edges of Federation space, gather data on the position and activity of systems which are light years away from explored space. This data is constantly updated and the information transmitted back to Federation outposts. Starfleet regularly sends probes and deep space exploration vessels into 'new' regions of space. These vessels record detailed information back to other ships and Starfleet installations by subspace radio. Even in known space, Stellar Cartography departments on Starfleet vessels constantly observe changes in position and phenomena. When a ship is at a starbase of outpost, detailed logs are downloaded and transmitted to Starfleet and integrated into the galactic condition database which is, in turn, distributed to all Federation vessels. Where accurate real-time information is not available, computers predict conditions with reasonable accuracy. The information which vessels regularly receive from the galactic condition database is combined with data gathered by the ship's own sensors on the position of stellar phenomena such as nebulae, pulsars and subspace phenomena to calculate the vessel's location and the relative position of its destination.

Galactic headings rely on the ship knowing its relative position to the centre of the Galaxy; positions are given relative to a notional line drawn between the vessel and the galactic core. In this example, all the ships have a heading of 30 mark 0.

Some more examples on starship heading are below:

Keeping Track

Starfleet vessels are equipped with various external sensors which ensure that reliable positional data can be gathered even in difficult conditions such as magnetic storms or solar flares.

During travel, it is essential for a ship's computers to be able to calculate velocity accurately in order to plot the vessel's exact position and velocity. An extensive network of Federation Timebase Beacons allows ships to access absolute time values which are used to calculate speed. When the vessel is out of contact with the beacons, onboard timebase processors maintain records, but these are subject are subject to some temporal distortion phenomena and as soon as possible the ship will synchronise them with a timebase beacon. Time distortion is particularly extreme at high impulse speeds, but the ship's guidance and navigation subprocessors can largely compensate for this.

When calculating a course. Starfleet vessels plot a flight plan that avoids dangerous objects along the flight path, such as stars or other solid bodies. During travel, computers constantly update their flight plans, making course corrections as new information becomes available.

Flight Control (Conn)

Warp flight operating rules require Conn to monitor subspace field geometry in parallel with the Engineering department. During warp flight, the Flight Control console continually updates long-range sensor data and makes automatic course corrections to adjust for minor variations in the density of the interstellar medium.

Because of the criticality of Flight Control in spacecraft operations, particularly during crisis situations, Conn is connected to a dedicated backup flight operations subprocessor to provide for manual flight control. This equipment package includes emergency navigation sensors.

There are five major areas of responsibility for the Flight Control Officer:

• Navigational references/course plotting
• Supervision of automatic flight operations
• Manual flight operations
• Position verification
• Bridge liaison to Engineering department

During impulse powered spaceflight, Conn is responsible for monitoring relativistic effects as well as inertial damping system status. In the event that a requested maneuver exceeds the capacity of the inertial damping system, the computer will request Conn to modify the flight plan to bring it within the permitted performance envelope. During Alert status, flight rules permit Conn to specify maneuvers that are potentially dangerous to the crew or the spacecraft.

Flight Control Console (Conn)

The Flight Control console, often referred to as Conn, is responsible for the actual piloting and navigation of the spacecraft. Although these are heavily automated functions, their criticality demands a human officer to oversee these operations at all times. The Flight Control Officer (also referred to as Conn) receives instructions directly from the Commanding Officer.

Manual flight operations. The actual execution of flight instructions is generally left to computer control, but Conn has the option of exercising manual control over helm and navigational functions. In full manual mode, Conn can actually steer the ship under keypad control, and on ships such as the Sovereign-class, a control column is installed for full manual override in extreme situations.

Reaction control system (RCS). Although the actual vector and sequence control of the system is normally automated, Conn has the option of manually commanding the RCS system or individual thrusters.

Conn also serves as a liaison to the Engineering department in that he/she is responsible for monitoring propulsion system status and providing system status reports to the commanding officer in the absence of an engineering officer's presence on the bridge.

Navigational references/course plotting. The Flight Control console displays readings from navigational and tactical sensors, overlaying them on current positional and course projections. Conn has the option of accessing data feeds from secondary navigation and science sensors for verification of primary sensor data. Such cross-checks are automatically performed at each change-of-shift and upon activation of Alert status.

Flight Information Input

There are five standard input modes available for specification of spacecraft flight paths. Any of these options may be entered either by keyboard or by vocal command. In each case, Flight Control software will automatically determine an optimal flight path conforming to Starfleet flight and safety rules. Conn then has the option of executing this flight plan or modifying any parameters to meet specific mission needs. Normal input modes include:

Destination planet or star system. Any celestial object within the navigational database is acceptable as a destination, although the system will inform Conn in the event that a destination exceeds the operating range of the spacecraft. Specific facilities (such as orbital space stations) within the database are also acceptable destinations.

Destination sector. A sector identification number or sector common name is a valid destination. In the absence of a specific destination within a sector, the flight path will default to the geometric center of the specified sector.

Spacecraft intercept. This requires Conn to specify a target spacecraft on which a tactical sensor lock has been established. This also requires Conn to specify either a relative closing speed or an intercept time so that a speed can be determined. An absolute warp velocity can also be specified. Navigational software will determine an optimal flight path based on specified speed and tactical projection of target vehicle's flight path. Several variations of this mode are available for use during combat situations.

Relative bearing. A flight vector can be specified as an azimuth/elevation relative to the current orientation of the spacecraft. In such cases, 000-mark-0 represents a flight vector straight ahead.

Absolute heading. A flight vector can also be specified as an azimuth/elevation relative to the center of the galaxy. In such cases, 000-mark-0 represents a flight vector from the ship to the center of the galaxy.

Galactic coordinates. Standard galactic XYZ coordinates are also acceptable as a valid input, although most ship's personnel find this cumbersome.

Guidance and Navigation

Critical to the flight of any vehicle through interstellar space are the concepts of guidance and navigation. These involve the ability to control spacecraft motions, to determine the locations of specific points in three and four dimensions, and to allow the spacecraft to follow safe paths between those points.

The theater of operation for federation ships take them through both known and unknown regions of the Milky Way galaxy. While the problems of interstellar navigation have been well-defined for over two hundred years, navigating about this celestial whirlpool, especially at warp velocities, still requires the precise orchestration of computers, sensors, active high-energy deflecting devices, and crew decision-making abilities.

Navigation

The whole of the galactic environment must be taken into account in any discussion of guidance and navigation. The Milky Way galaxy, with its populations of stars, gas and dust concentrations, and numerous other exotic (and energetic) phenomena, encompasses a vast amount of low-density space through which Federation vessels travel. The continuing mission segments of Federation starships will take them to various objects within this space, made possible by the onboard navigation systems.

Transwarp

The founding of the United Federation of Planets was made possible by the invention of the warp drive. Equipped with this device, starships can travel at velocities faster than the speed of light. With this development, supply and communication lanes between widely separated star systems were opened up, but with conventional warp drive, a starship is limited to speeds of approximately warp 9.6. Transwarp normally refers to a journey above this speed. The laws of physics have always suggested that faster,, more direct 'short cuts' may be possible and in 2369 the federation becomes aware of one such method, which is dubbed the transwarp conduit.

The Physics of Speed

Reaching warp speed is made possible by the application of Zephram Cochrane's mechanism of continuum distortion propulsion (CDP), which became nicknamed 'warp' drive because of the way the energy field, generated by the CDP engines, distorts the space-time continuum. This distortion allows the starship to make the transition into subspace, effectively reducing the mass and allowing it to be impelled to large velocities. The ultimate warp speed velocity in subspace translates into approximately 1,000 times that of light. In principle, however, even higher velocities are attainable by distorting subspace; these ideas are collectively known as transwarp theory. The attractive thing about transwarp theory is that, whereas the energy requirements necessary to travel through subspace eventually prevents a starship from approaching Eugene's limit of warp factor 10, the variables with govern transwarp theory have no such limitations. To understand the relationship between sublight, warp and transwarp travel it is necessary to consider the passage of starships through the universe. The trajectory of an object can be placed on a space-time diagram. These graphs have one axis which denotes time and another which gives distances between objects. Trajectories show as diagonal lines and are known as geodesics. Sublight velocities give rise to 'time-like' geodesics which are always inclined at less than 45 degrees to the vertical. Light rays (and starships travelling at warp 1) follow lines known as 'null' geodesics which are precisely 45 degrees from the vertical. Finally, superluminal velocities (those greater than the speed of light), follow 'spacelike' geodesics which are always inclined by more than 45 degrees to the vertical. Spacelike geodesics can be further split into warp-speed and transwarp geodesics.

Wormhole Similarities

Transwarp

The length of the geodesic between two points in the Galaxy (such as two star systems) indicates the amount of space-time which has to be travelled in order to journey from one to the other. On a space-time diagram, the horizontal separation of the points is the effective distance between them, the vertical separation gives the time taken to travel between them. Thus, comparing the geodesics to get from star system 'A' to star system 'B', transwarp travel can be seen to be like a neat sideways step through the universe, rather than travelling the complete route.

Another way of imagining this is that a transwarp conduit can be thought of as being analogous to a wormhole. A wormhole is a distortion of the space-time continuum through a higher dimension such that two widely separated regions become close. A transwarp conduit is exactly the same only, instead of space-time being distorted, it is subspace which is folded over on itself. In order to penetrate subspace and open a conduit from normal space, special particles known as tachyons need to be produced. These subatomic particles are incapable of travelling at velocities slower than the speed of light, i.e. they follow spacelike geodesics and hence allow communication with other dimensions of the universe such as subspace. Once the correct frequency of tachyons has been found their emission causes a resonant oscillation in subspace, which can first be detected as a subspace distortion. This opens a rent from normal space through subspace, allowing access to the transwarp conduit. The flow of subspace energy is so great that anything close by is dragged in and immediately accelerated to extreme velocities, in the same way a stick that falls into a river is swept along by the current. After a brief, rough ride through the conduit, the starship is then deposited back in normal space, many light years from its point of origin.

Experiments with Transwarp

Starfleet scientists and engineers feel that after an intense period of developing the theory, their transwarp hypotheses are testable. To this end, they construct an experimental starship, the U.S.S. Excelsior in 2285. Unfortunately the testing fails; starfleet is unable to break the transwarp barrier successfully and the project is abandoned. In 2369, however, the U.S.S. Enterprise witnesses and actually uses a transwarp conduit while in pursuit of a marauding Borg vessel which had created it, proving that the theory can be put into practice.