Analogue aircraft navigation

Twenty years ago, I participated in a special software development with some Ukrainian and Russian fellows. We developed an aircraft for Microsoft Flight Simulator 2004 (also called FS9). Some designed the 3D model and rendering of the aircraft, including the cockpit equipment graphics. Others modelled the flight characteristics, electronic, hydraulic and other systems' behaviour. I participated in the navigation system development and also I was writing the documentation for the simulated aircraft: Antonov AN-24RV for FS 2004.

It was two decades ago, but it is still a good feeling to read this document. Hereby I recreate the part that describes the gyroscope-based navigation using the traditional Russian analogue equipment - mostly gyroscopes. See other part of the referenced document for more information about navigation.

Let's jump into the two propeller AN-24 aircraft and fly over the huge, frozen tundra. Read three chapters from my 20-year-old navigation guide for flight simmers.

Loxodrome and the Great Circle

If you maintain a specific heading (generally magnetic, but it could be true as well) while flying long distance you will follow a specific course over Earth surface called loxodrome (also called as rhumb line). It is not a strait line at all (and if you fly long enough you will end up at the magnetic North Pole in a spiral). By definition a loxodrome is intersecting each meridians by the same angle. If you want to fly from point P1 to point P2 than it is some dirty calculation to figure out what should be the correct loxodrome and heading, but once it is done, navigation is quite simple: just keep that (magnetic) course and you will end up at point P2.

If you want to fly from P1 to P2 on the shortest route you have to fly on a great circle course (orthodrome). Great circle is a circle defined by the intersection of the surface of the Earth and any plane that passes through the center of the Earth. There are infinite number of great circles on Earth - the Equator and all the meridians are specific examples for that. For us a single great circle is interesting; the one that goes through P1 and P2 points. Calculation of this great circle is rather simple using spherical trigonometry, but navigating is much more difficult. Great circles are intersecting the meridians by variable angles because of meridian convergence. You have to start with a specific course angle from P1, but along the course you have to change heading angle to remain on the great circle. This is practically impossible to do using a magnetic compass.

Great Circle is the shortest route on a globe. Earth is not a perfect globe. Its form is called geoid and on a geoid the shortest route is called geodesic and it is rather difficult to calculate. Anyhow the difference between the geodesic and the great circle is negligible in aviation.

Flying on the Great Circle (orthodrome)

Flying on an orthodrome instead of a loxodrome has several advantages. The generally known reason is that this is the shortest distance between any two points on Earth. In fact this difference is quite small on middle latitudes and shorter distances: on a 600 km flight the saving will be not more than 10 km. On longer distances the saving is increasing but as the maximal range of our AN-24 is around 2000 km the saving is not significant. On higher altitudes and near to the magnetic pole however the saving is quite important.

The other advantage of the orthodrome relates to radio transmitter radials. These radials are in fact orthodromes. If you would like to precisely follow a radial either towards or from a beacon you have to fly on a great circle. As the range of such transmitters are rarely larger than 300-400 km, the difference between a loxodrome and an orthodrome is not big, but in precision flights it could be important. On the other hand if you use a magnetic compass to follow a transmitter course, you might find that you have to adjust your magnetic heading time by time to maintain the needle of the VOR track indicator (HIS, KPPM) in the middle. This is especially important in AN-24 where the autopilot will not follow a VOR track automatically.

Orthodrome (great circle) flights are supported by special gyroscopes. At point P1 you spin the gyro, align it for example towards true North and you follow the calculated start angle on the route. The gyro will not point to North any more on the route (it will point to parallel of the meridian at P1 still), but it does not matter. Just follow that initial course angle and you will arrive to P2.

If from point P2 you would like to continue to point P3 on a great circle, you have to make some more trigonometry to calculate the start angle from point P2. This angle is to be measured from the meridian at P2. The problem is that our gyro is still aligned to the meridian in point P1 and it is obviously not aligned with the meridian in point P2 as the meridians are converging to the pole (that is why our start? and arrival angles differ).

We have two options now:

• When flying over point P2 we align the gyro to the meridian at P2 (as we did it at point P1 at the beginning) and than read the new calculated start angle directly (again as we did at point P1). You turn the plane to this new direction.
• We do not touch the gyro, but we calculate the drift of our gyro that was cumulated from P1 to P2 due to meridian convergence. This is called the fork (вилка in Russian) and it is basically the difference of our start and arrival angles. We do not re-align our gyro, but we add this fork angle to the calculated start angle from P2. The resulting angle is still relative to the meridian at P1 and we can read it from our gyro now.

Orthodromic Course Angle 2 = Course Angle 2 + Fork 2        

In Russian terminology (see explanation later):

OZIPU2 = ZIPU2 + Δa2        

We can continue with either methods when we reach point P3. Russian navigation use(d) this technics so much that they sometimes do not use magnetic compass at all. Before take-off they align the aircraft along the runway precisely. The magnetic direction and the declination of the runway is documented, so the true heading of the aircraft can be calculated easily. They align the gyro to the true North based on this and they follow the method described above along the route. Near to the destination airport they make a similar calculation based on the magnetic direction and declination of the runway, so keeping in mind the calculated cumulative fork they are able to define the final turn.

In the example above we aligned our gyro to true North (after calculating it form magnetic direction and from magnetic declination of the runway), thus we used true courses all along the route. If you prefer you might align the gyro to magnetic North at the take-off runway and use magnetic courses on the route. In this case however you should modify the above algorithm:

• Mathematical computations are still give true courses between P1 and P2 (as the geographical coordinates are based on the true coordinate system), thus you have to subtract magnetic declination from this course when starting from point P1.
• If you do not want to re-align your gyro at point P2, you have to calculate the fork as we did before. However the fork at point P2 will have a second component (the first one is because of meridian convergence as described above): the difference in magnetic declination in P1 and in P2. You add this fork angle to the calculated true start angle from P2.

It is basically your decision whether to use magnetic or true courses. True courses have the advantage that they are calculated directly from the equations and they are independent of the spatial and temporal changes of magnetic declination. Magnetic courses have the advantage that they are widely used in charts, maps for example in SIDs and STARs and in air traffic control (ATC) conversations.

VORs are "advertising" magnetic courses (bearing), but their Russian counterparts - RSBN beacons - use true courses. The complete RSBN-2 equipment on AN-24 is built around true directions, thus it could be quite ambiguous to align our gyro and define our courses relative to magnetic pole when we use RSBN. NAS-1 navigation system however is independent of external systems, thus it can be used with any reference directions.

Russian terminology

If you are challenged enough to read Russian documents you will realize that they are generally very precise in terminology. It is rather difficult to translate the terms to English. In fact they are not frequently using the terms but abbreviations instead. Hereby I summarize the most important terms.

The most annoying thing is the different use of the term "course". In English it means the track on which the aircraft is moving. May also mean the angle ("course angle") - the track's angle to the reference direction - true or magnetic North. Thus we can speak about true and magnetic course. In Russian the term "курс" (kurs) means "the angle between the reference direction and the extended longitudinal axis of the aircraft" - i.e. "heading"!

The Russian equivalent of "course" is "путевой угол" (track angle). The difference (angle) between the course and heading is called "slip angle" ("угол сноса") and is generally caused by cross-wind:

Course = Heading + Slip        

"Курс" (heading) is either true ("Истинный курс, ИК") or magnetic ("Магнитный курс, МК"). "Путевой угол" (course) is also either true ("истинный путевой угол, ИПУ") or magnetic ("магнитный путевой угол, МПУ"). If it is the planned (required) course than they call it "заданный истинный путевой угол, ЗИПУ" or "заданный магнитный путевой угол, ЗМПУ" depending on the reference direction. And finally if the course is measured relative to a reference meridian and not directly to the actual meridian, then it is called as "ортодромический заданный истинный путевой угол, ОЗИПУ" or "ортодромический заданный магнитный путевой угол, ОЗМПУ" respectively:

ОЗИПУ = ЗИПУ + вилка        

The course referred frequently within this document - ZPU is the "planned course" ("заданный путевой угол, ЗПУ"). However when used in conjunction with the RSBN navigation it has a special meaning: It is the course (angle) measured at the RSBN radio station between the true meridian and the line going through the RSBN station parallel with the "planned course" (see details later).