# Which map projection is typically used on ATC radar screens?

Displaying a (roughly) spherical surface on a flat map turns out to be pretty difficult. There are many different map projections, each with their advantages and disadvantages. Some of the most common ones are cylindrical (Miller), conical (Lambert) and azimuthal.

On aviation maps and charts, I often see the Lambert conical projection used. This made me wonder: on an ATC radar screen, which projection is typically used? It is important that the controller can easily estimate both headings and distance by looking at the screen. For large sectors especially, an inaccurate projection might make this difficult.

Clarification: The discussion of whether the choice of projection will have an operational impact at all is an interesting one. My question, however, is not about how important the choice of projection is, but rather what projections are commonly used. I have a professional interest in this, even if the choice of projections is not operationally important.

Maybe different standards are used in different companies or different regions of the world. If that is the case, a brief summary of the most commonly used standards would be appreciated.

• How large would a sector have to be before the inaccuracies become operationally significant? – Dan Pichelman Aug 29 '16 at 16:12
• Depends on which projection is used ... hence my question :) – J. Hougaard Aug 29 '16 at 16:15
• Stereographic, according to this document. More on stereographic. At least the projection must preserve angles (must be conformal) because different radars will see the target and the different displays (or portions) must be consistent. – mins Aug 29 '16 at 16:57
• Looks suspiciously like Eurocat... – Zeus Aug 30 '16 at 3:55
• I don't think there is a need for any projection, because radar output is not spherical. – Agent_L Aug 30 '16 at 10:30

Normally stereographic projection is used for ATC displays, especially if a multisensor tracker fuses data from multiple sources. The European surveillance data processing system ARTAS uses it internally and for output (unprojected WGS84 is also supported for displays doing their own projections & controller support tools). The Thales Eurocat/TopSky system also uses stereograhpic projection.

In older single radar systems, sometimes a simple local projection is used.

$X=\rho \sin(\theta)\\ Y=\rho \cos(\theta)$

With:

• $\rho$: measured range
• $\theta$: measured azimuth

Due to distortion caused by projection from 3D to 2D this only works for a single radar.

• Single-sensor SR radars are interesting because 2D radar plots do not contain altitude information, and plots are sometimes projected without height information. 3D SR radar plots can be corrected by taking height information (found by use of eg stacked beams, or even correlation with SSR Mode C data) into account. In a modern, multi-sensor "data fusing" environment, one can expect some kind of coordinate transformation into more "normal" maps such as Mercator etc, so that controllers can (also) perform accurate range and azimuth measurements. (I'm a former fighter controller.) – axd Aug 27 '18 at 6:51

I can only speak by experience, and this is relevant to PALLAS installed in Greek ACC and LGAV approach. What I concluded while discussing with ATCOs is that the projection used is gnomonic. Unfortunately I haven't read any document to prove it (this is pure observation) and even if I had I couldn't cite it (for obvious confidentiality-related reasons).

Anyway, gnomonic is the projection I've used while developing the PALLAS simulator for HCAA and the results were identical. So what characteristics has the gnomonic projection:

• Every straight line you draw on it, is part of great circle. This is of great importance since great circle arc between 2 points is the smallest distance between those 2 points. And when flying you want to avoid extra miles
• It heavily distorts areas of the map away of the projection center, but gives a very good approximation close to the center. That makes it suitable for relatively small geographical ares.
• You can never see a whole hemisphere. If you have a look at the article in Wikipedia, you will see why.

You might want to take a look at this picture which is not from the real system but the simulation. Unfortunately I don't have photo of the system that shows the concept, but I hope this does. Note the 19th and the 30th meridians that are straight lines (every meridian is a great circle arc) and how they converge to the north. Also note the blue-ish line measuring a random distance. This is guaranteed to be a great circle distance. So every straight line on the map, either from a tool like the one pictured or an airway, is a potential trajectory for an aircraft to follow. That way you see the "truth" each time you see a straight line.

PS: Now regarding your actual question of what projections are commonly used: others have mentioned stereographic while I mention gnomonic (and I'm pretty sure it is this one) for PALLAS. So there is no such thing as commonly. Projection is a tool. And as such you have to pick the right one for each situation. Now I don't know what your professional interest is, either a pilot, ATCO or a fellow developer wanting to write his/her own simulator (or even CWP???) in any case I would suggest you contact someone that knows the internals of the specific system you are interested in.

Regarding accuracy, you first need to address radar accuracy which is affected by coverage, track distance from the radar, atmospheric conditions and other factors that fall beyond the scope of the answer. Then you can wonder if it's worth the pain to analyze if the projection might trick the controller into errors.

• It might be useful to note that the map in your picture appears to be centered on the Aegean Sea. Took me a while to recognize the coastlines. (And I'm still not sure what the other less twisty white lines are; Greek airspace boundaries?) – Ilmari Karonen Aug 30 '16 at 13:38
• Downvoter cares to explain? – Stelios Adamantidis Apr 18 '17 at 8:44

Looks like @mins is correct. According to Stereographic Projection of Radar Data in a Netted Radar System by J.J. Burke,

In netted air defense and air traffic control systems, data from the long range radars are routed to a Sector Operations Center and stereographically projected onto a common coordinate plane for presentation to system operators on the display consoles.

Also, from On the Application of Stereographic Projection to the Representation of Moving Targets in Air Traffic Control Systems by Robert G. Mulholland:

an ARTCC is serviced by a multitude of radars, and control of aircraft in the horizontal sense is effected through stereographic representations of target locations in a single plane.

And,

Horizontal separation of aircraft under the control of a single Air Route Traffic Control Center in the National Airspace System (NAS) is accomplished by controlling the relative separation of points in a plane that represent actual aircraft locations. Such a representation is supposed to be the image of the orthogonal projection of an aircraft onto the mean sea level surface of the earth under a stereographic mapping.

• Not sure if this is what he is after, this is about the projection of aircraft onto the map not the physical world onto the screen. The "common coordinate plane" seems to be what he is looking for. – Ron Beyer Aug 29 '16 at 19:07

Map projections are notoriously bad at the edges of the area they represent.

Hence, when looking at a wall map of the globe, the area near the middle is fairly accurate, and near the top and bottom it gets screwy.

ATC Sector maps are always shown centered on their space. So the middle of their map is accurate, and, at worst, the extreme edges are a little distorted.

The biggest Centers I can find are about 1,000 miles from the center to an edge. (The Sectors will obviously be significantly smaller).

So while I cannot tell you the exact amount of distortion, I think the distortion over an estimated 500 miles on a scope would be pretty small.

• Thanks, you make an interesting point. However, my question is not about how significant any distortion is, but about which projection is actually used – J. Hougaard Aug 29 '16 at 16:57
• @J.Hougaard Does it matter though? For the short distances displayed on radar screens, unless you are near the "edges" for that particular projection, they should all be fairly similar. My guess is that because they need to be accurate with the paper maps they use the same Lambert Conformal Conic Projection system used by paper maps. – Ron Beyer Aug 29 '16 at 18:09
• @RonBeyer It matters to me, which is why I asked the question :) If you are not interested, feel free to ignore it – J. Hougaard Aug 29 '16 at 18:29
• @J.Hougaard Its an interesting question and it may benefit from the why, the only reason I can think of is to know the distortion over one side of the display to the other, which is why I said its probably insignificant. If you are trying to stitch together all the radar screens over the US, it would give more context. It may be the only way to know is to ask the manufacturer, I'm guessing even ATC operators don't know the answer for sure, I'm just guessing... – Ron Beyer Aug 29 '16 at 18:34
• As for why, the question came up the other day in class when we were discussing map projections. None of our ATC instructors were able to answer, so I thought I would ask here. Nothing more to it :) – J. Hougaard Aug 29 '16 at 18:37

I have some experience here. Based on my observation of actual radar, the placement of targets on a scope is based completely on slant range. Map items are based solely on distance from the sensor. When I first observed this, I was confused about the discrepancies which it would introduce. But the resolving factors are the limits on airspace dimensions and the fact that pilots are able to fly altitudes which are consistent. We never need to worry about seperating an aircraft at 20000 feet and 4 miles away from an aircraft that is 3000 feet and one mile away. The ranges are far more horizontal than they are vertical, and this minimizes the issues with separation.

• Welcome to Aviation SE. While your answer might be correct in the sense that it is not inaccurate, it does not answer the question itself. You might want to take a look at the help. – Stelios Adamantidis Aug 29 '16 at 23:30
• Yes, this does answer the question. The slant range data, projected onto a screen, represents a specific type of projection from 3-d to 2d. Which is the point of the question. The oldest radar units were pure analog and just showed reflection intensity on an analog CRT, and were simple time of flight vs antenna azimuth plots. That would be a type of projection. – Adam Aug 30 '16 at 13:04
• Contemporary systems integrating secondary data (transponders, ADS-B) with primary return data generally have processing to perform orthorectification which would make slant range arguments moot. But having said that, the number of installations which will display slant range still far exceeds those which have a more planimetrically corrected display. – mongo Apr 17 '17 at 17:07

This is not comprehensive, nor does it cover mappings of radar near the polar regions, but in CONUS and many other areas, the radar screen is approximately a Lambert projection. In reality, accurate measurements from ATC displays are not really needed, so there is little concern about the actual projection.

In targeting systems, the mapping is more closely managed, as part of the error budget in managing the targeting and navigation to the target (as in a missile guidance application).

Back to ATC, it approximates a Lambert, but the precise linearity of the projection is not critical on the screen.

Finally in center operations and in large area surveillance operations, displays covering large areas are composite displays, and once again, precise measurements are not taken from the screen, but rather from target metadata maintained by the computers.

There are three issues that must be considered in your question. Normally the projection used for paper chart plotting considers the maximum error that printing technology normally handles. This is, considering the thermal paper deformations due to heating sources/sinks and the mechanical tolerances at printing, this means like 0.1mm tolerances are allowed. On a normal 1:25000 chart this means an absolute error of 2.5m in the field. The counterpart issue to be considered is the display screen resolution. At resolutions of 4096 pixels by 4096 pixels, you have a relative error of 1/4096 you cannot fix, as a limitation of the display screen. This can make the error far greater in absolute units as you grow larger in map extension, which makes the projection absolutely effective by burying the errors inside the other errors.

Normal proyections do diverge normally from the point of construction (or the line in case of UTM, Lambert or Straight mercator) I consider each one.

Normally, in land places, the most commonly accepted (now) for its precission is UTM, which is not continous, as it consists in mapping the earth surface as a eliptical cilinder, with axis perpendicular to the rotating axis of the earth. In this cilinder, only a six degree huse in longitude is considered and the plane is tangent to a complete meridian. The maximum apart is 6 degree in longitude which makes it to deviate from the true point on less than 0.05% (and by that reason it gets scaled by 0.9995 to get half the deviation all the plane extension) Normally, a mapping of this class completely fits in the resolution of a normal display (even at resolutions of 4000x4000 pixels) without making any point to divert by one pixel apart from the surface of reference. This makes for a 0.03% max at aprox. 350km apart from the meridian.

Lambert, which uses a parallel of tangency, even having more diverting errors, is also far below the limit for a 4000x4000 pixel screen, even from departing from the parallel of tangency by more than 1000km. This makes an effective exact screen for maps with more than 2000km (N/S) coverage.

Finally, polar stereographic is normally used only for high latitudes (near the poles) and is not considered in most of the globe. Due to the elliptical surface of the earth is normally not used for representation at one point, due to the different curvature radii of the earth surface in the meridian and parallel directions.

Gnomonic projection has also been mentioned, for the properties that all the maximum circles map to straight lines (this makes normal straight approximations to map to straight lines) has similar deviations (like double, by not being a tangent line projection, but a tangent point projection it deviates more, but errors aprox. double the ones you have in tangential line projections)

It should be considered also that in case of a radar system, probably the most exact projection to achieve the best results should be a local UTM projection (with the central meridian passing through the radar rotating axis) as then you don't have any deviation from the north pole due to meridian convergence. It is remarkable that with this remarks, probably the differences between astronomical (the ones that you measure to the geoid) and geodesic coordinates begin to be significative at ranges well over 1000km.

On other side, radars make errors and you get on the screen normally points referenced by a distance and azimuth. As it has been said on other responses to this question. Distance is subject to meteorological perturbations that make errors to completely overrun the ones mentioned previously. And with angles the problem is even greater, as you can be affected by refraction issues in radar. This makes that some point acquisition be affected by errors far larger than the ones made in the projection (except in the case the projection is badly calculated) you can trust completely the used projection.

# CONCLUSION

Only in the case your projection is mistakenly selected or calculated, that you have to worry about the errors introduced by (at any range) for radar positioning. If the projecting software is well configured, the errors will be several orders of magnitude below the measurement ones and you can consider the earth surface as almost flat. (you have to make only the azimuth corrections due to meridian convergence anyway, as the projections are conformant only locally, but everithing you'll see in the screen will be exact as measured on the screen with the screen resolution capabilities)

# CLARIFICATION

As a software engineer, the most probable chartographic projection you have will be lambert conical or UTM mercator, independently on how then the coordinates are represented, as both combine the exactitude of the results with the conformant of data grids. But I recommend to read the radar screen manual to get the final response. UTM is official in the majority or countries in the world, but historically, lambert has been used for long time.

• Welcome to Aviation. SE. I'm sorry, but while you provide interesting background to the problem of map projection, I don't see how this is answer the question on an ATC radar screen, which projection is typically used? – Federico Aug 30 '16 at 8:37