# What method does ATC use to calculate distance between two aircraft?

The distance between aircraft must be larger than the minimum separation all the time and is therefore quite important for Air Traffic Control (ATC). As I need to calculate the distance between aircraft for my research, I'm wondering if there are any regulations (in Europe) about how exactly the distance is determined.

How exactly does ATC determine the distance between two aircraft?

I suppose that they are working with latitudinal and longitudinal coordinates and probably the altitude to determine great circle distances. To get the coordinates, they could use either radar or the position which is communicated by the aircraft.

The task to calculate the distance from coordinates is not that trivial as it may sound from the first impression. One method to calculate the distance is the haversine formula. In all methods, the assumed earth radius is rather crucial. If the distance is calculated in that manner:

1. Which value is used as the earth radius?
2. Are the different earth radii from the equator to the meridian regarded?
3. Is the altitude of flights included in the calculation?
• Using a range/azimuth calculation from radar returns would probably be a lot simpler than doing it from coordinates. I don't think they are looking for precision beyond ~25 feet or so. Commented May 5, 2015 at 14:02
• @JoelM.: You are overestimating the precision. The radar target on the scope is about a mile wide in the scale of the scope (for radars monitoring en-route traffic). Commented May 5, 2015 at 14:12
• Does ATC radar provide any data other than the scope display? I would expect that the system has better range resolution than one mile. Commented May 6, 2015 at 14:48

The things you mention would matter, if you wanted to know the distance to 6 or more significant digits. But ATC does not need that precision. They need to be able to tell whether it's 4 nmi (too close), 5 nmi (still sufficient, but getting in trouble) or 10 nmi (no worry, but should not be heading directly towards each other). That is one significant digit.

The controller does not use any formula. They just look at the distance of the targets on the radar scope (which is drawn properly to scale). And possibly use the grid that is drawn over it or compares to the leader lines (indicating velocity) or history trail. The controller doesn't need precision, they need to look and see. And they are not getting any precision; on centre station (controller handling en-route traffic) the radar target blob is about a mile wide.

Until recently, aircraft did not broadcast position at all. Many still don't; not all aircraft are equipped with ADS-B. For those that don't, the interrogator may have precision similar to DME (~ 0.1 nmi) in range and a degree or two in angle. Not great precision either. The radar also has single rotating antena that takes couple of seconds to scan the whole circle, so the position of the aircraft is only updated once every few seconds. Jet airliner in cruise moves some 700 m in 3 s.

On such radar, the scope most likely transforms directly from the angle and distance reported by the radar to the screen coordinates. Altitude was usually not taken into account (so higher targets appear further than they really are!) in the older systems.

New radars with ADS-B support (less busy areas don't need it) need to combine the radar data with coordinates reported by ADS-B, which are in WGS84, so WGS84 is usually used as intermediate format for the collected data. But shortcuts can still be taken in the software.

I don't know what which radar system manufacturer uses, but I work on navigations and we tested the precision. By assuming Earth is flat and the coordinate system is orthogonal and using simple Pythagorean formula, you can still get 3-4 significant digits (unless you are working around north or south pole) for points tens of miles apart, which is more than enough for the radar screen. So the system can simply multiply longitude and latitude with appropriate factors (that depend on latitude of the sector centre) and get sufficient precision.

• The shortcut is usually map it to a distance equivalent (or near enough) projection centered on the airspace and then hypot(dx, dy) Commented May 5, 2015 at 14:23
• @ratchetfreak: Yes, that's the one I mentioned. Commented May 5, 2015 at 14:25
• Radar systems don't report in WGS84, they report in azimuth and range. The downstream processing system does the conversion into WGS84 and combines data of multiple surveillance systems into single tracks for each aircraft. The display is often in stereographic projection. The display software incorporates features such as grids and rulers to measure exact distance if needed (e.g. distance to navaid), but eye-balling should be sufficient for spacing. Commented May 5, 2015 at 14:28
• "They need to be able to tell whether it's 4 nm (too close)" I've always hated seeing the symbol for nautical miles without capitalisation until today. Commented May 6, 2015 at 0:04
• @dougk_ff7 These are called "history dots / trail" and "leader line" (usually set to 5nm, 3nm or 1min, controller's preference). +1 or using nmi instead nm. ;) Commented May 6, 2015 at 8:28