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Vector lines are one of the tools available on many air traffic control radar display systems, to help air traffic controllers plan their traffic.

You have probably, at some point, seen an ATC radar display of some kind. Lots of moving blips surrounded by numbers. Each blip represents the location at which a radar wave reflected off an aircraft (and there are various tools to verify that those blips do in fact represent aircraft and not, for instance, GIANT ROBOTS BATTLING ALIEN INVADERS). Believe it or not, 'blip' has a legal definition. According to the International Civil Aviation Organization, a blip is:

The visual indication, in non-symbolic form, on a situation display of the position of an aircraft obtained by primary radar.

The blips—called 'PSR blips', in legalese, for Primary Surveillance Radar—usually have 'trail dots': a line of dots behind them. These dots show where the radar blip was for the last few sweeps of the radar. These are also very handy, because they give a rough indication both of manoeuvres the aircraft might be making, and of its speed—the trail dots of fast aircraft being more widely spaced than those of slower ones.

Vector lines are sort of the opposite of trail dots. While trail dots show the past, vector lines predict the future. They show the predicted position of the aircraft after a certain amount of time, based on the information present in the most recent radar sweep (the aircraft's direction and speed).

A couple of aircraft, without vector lines:

                                           *.. .. ..
                                            \
                                             \
                                              RYR123
                                              350
                 * 
                . \
               .   \
              .     BAW456
             .      350
ZOMG, they are totally going to hit each other. Wait, maybe I'm being paranoid. Let's toggle the vector lines:
                      /         -----------*.. .. ..
                     /                      \
                    /                        \
                   /                          RYR123
                  /                           350
                 * 
                . \
               .   \
              .     BAW456
             .      350
Hmm. So I was being paranoid. They're not going to hit each other. But they're still going to be pretty close, and we might lose separation. The identical flight level readouts of 350 under each callsign show we haven't got vertical separation, so we need at least five miles of horizontal separation. But wait, maybe this radar sweep doesn't tell the whole story. Let's give it another sweep:
                            /  -----------*.. .. ..
                          /                \
                        /                   \
                      /                      RYR123
                    /                        350
                  * 
                .  \
               .    \
              .      BAW456
             .       350
Aaaah. No, don't panic. Yes, the vector lines are almost intersecting, but I'm betting BAW456 is making a right turn. Let's give it another couple of sweeps:
                              --------/--*.. .. ..
                                  /       \
                              /            \
                          /                 RYR123
                      /                     350
                  .* 
                .   \
               .     \
              .       BAW456
             .         350
Yes, we're going to be fine. Even if BAW456 stops turning now, it's going to pass behind RYR123 and there's no chance of them hitting if RYR123 is locked on its heading. We might need to keep a protective eye on their separation (and our ATC licences) but we'll be fine. If you're extra paranoid, you might leave the vector lines on for a few more sweeps:
                              -----------*.. .. ..
                                          \
                                           \
                                            RYR123
                                            350
                     . *------------------
                  .     \
                .        \
               .          BAW456
              .           350
             .

See? Nothing to worry about.

Vector lines can usually be set to show predicted positions a variable amount of time in the future (up to about ten minutes), but will always use the same variable for each aircraft. They can usually be toggled to appear for all aircraft or just for controller-selected ones, and can be very handy. Doesn't half clutter up a busy display though, so you generally don't turn them on unless you specifically need them.



If you're wondering, BAW is Speedbird, aka British Airways, and RYR is Ryanair, aka money-grubbing lunatics.

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