10.1 Circles drawn on the surface of

10.1 Form of The Earth
The Earth is neither flat, nor completely round but rather what is known an oblate spheroid. This simply means that the planet is slightly flat at the poles – and not a perfect sphere as one might imagine. This compression results in the polar diameter being approximately 23 nautical miles shorter than the equatorial diameter. For practical purposes however, the earth is assumed a perfect sphere for ease of calculations.

Circles on the Earth:
A Great Circle (GC) when drawn on the surface of a sphere, will have the same center and radius of the sphere itself. So only one GC can be drawn between two points unless they are absolutely opposite sides of the planet, such as the North and South poles. In which case any number of great circles can be drawn between them.

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The shorter arc between two points on a great circle will represent the shortest distance over the surface of the earth and therefore the shortest time between the two points. Radio waves or radio frequencies follow great circle paths over the Earth and if we are to plot radio bearings we need first be able to plot great circles.

Small Circles drawn on the surface of the Earth is any circle whose center and radius are not those of the Earth itself. Parallels of Latitude are small circles. These are used for position finding.

Accurate position finding on Earth’s surface is achieved with the use of a simple cross-referencing system using both great circles (connecting the North and South Poles) and small circles (running from East to West). A simple cross reference allows us to plot specific accurate locations.

Lines of Longitude connect North and South Poles. Each of these great circles is divided into two halves, a Meridian and an anti-Meridian. Lines of longitude are referred to as Meridians. These Meridians run 180 degrees East and West of the Prime Meridian (this is the Greenwich Meridian which runs through the Greenwich Observatory in England).

The equator is the first Parallel of Latitude, and the only parallel to be a Great Circle. As the Parallels move 90 degrees North or South of the equator they reduce in size as they move towards the poles (all of which are small circles)
By bringing the two together we are able to plot accurate coordinates, or positions on the Earth’s surface. This is a combination of Latitude and Longitude, for example
260S 290E. This position can be made more accurate by breaking the degrees down into minutes and then the minutes into seconds. One degree therefore consists of 60 minutes and each minute is 60 seconds. A more accurate position could now be given as:
260 08′ 02” S and 290 14′ 33” E. It is important to remember that latitude is always given first.

Meridians are semi great circle, all meeting at the poles. Since the Earth is a sphere it follows that these meridians converge as they run towards the poles. This convergency is measured in terms on an angle of inclination, small at the equator and increasing in significance towards the poles.

This becomes important when plotting bearings on a chart. We have seen that the shortest arc between two points on a great circle will provide the shortest distance, however the angle at which this line cuts through the various Meridians will vary quite significantly, the extent of which depending on the changing convergency.

When plotting on charts, we draw a straight line between two points (a great circle representing the shortest route we wish to fly). This is called a track, and the angle between the track and a meridian relative to True North gives us our bearing. As our track line passes through different meridians, the bearings are bound to change because of the change in convergency. Unless we are following the equator (at which point convergency is zero). Since this is rarely the case, we will need to constantly alter our heading to remain on track, which is an inconvenient means of navigation.
The solution to this is the Rhumb Line which cuts the meridians at a constant angle, however this rhumb Line is no longer the shortest distance or straight line but rather a curved one, increasing our distance travelled over the ground. Whether we choose to plot rhumb Lines or great circle tracks will depend on our latitude and distance travelled. In South Africa we tend to plot great circle tracks as we don’t experience substantial convergence. Remember;
Meridians are great circles and rhumb Lines as they are a constant North/ South direction (as is the equator).

All parallels of latitude are rhumb Lines.

10.2 Time
Earth’s Orbit
The Earth revolves around its axis from west to east. One full revolution taking approximately 24 hours known as a mean solar day. Simultaneously the Planet is revolving around the sun, completing an elliptical orbit in about 365 and one quarter days. Although this is inconvenient, it explains the intention of a leap year every 4 years to adjust for the additional quarter day.
The N/S axis of the Earth is tilted, and remains fixed throughout its orbit, giving the illusion of the sun moving from the Tropic of Cancer (23.50 North) to the Tropic of Capricorn (23.50 South) and back within a year giving us the changing seasons.

Local Mean Time (LMT)
The time at a particular meridian is known as the local mean time (LMT) and is the same for the entire length of the meridian. One rotation of 3600 takes 24 hours, therefore in one-hour Earth will have rotated 150. With the position and time of any location, we can now calculate the time at another known location.

EXAMPLE: LMT at Position X (longitude 300 East) is 1130, calculate the LMT for Position Y
(Longitude 750 East).

SOLUTION: Change in Longitude (75-30 = 45 E). *Position Y is East, therefore later in the day
45 150 (1 hour) = 3 hours
Position Y LMT = 1430
Standard Time
Due to the time differences within the same country (almost an hour difference between South Africa’s East and West coast) a need for standardization becomes apparent. The first consideration for this is a standard starting point. Since time changes with longitude and longitude starts at the Greenwich Meridian (Latitude 000), it makes sense to use this as our datum. The LMT at the Greenwich Meridian is now called Universal Time Coordinated (UTC). Remember time East of the Greenwich Meridian will always be later whereas time to the West will be earlier.

The principle of standard time is based on the concept of time zones. Basically, the earth is divided into zones, each comprising 150 – one hour. Standard time is flexible in that it allows a country to adopt one zone as its standard time. Going back to the South African example, Alexander Bay is situated in a different zone to the rest of South Africa, however we have a standard time factor (STF) meaning the entire country is UTC + 2 hours (effectively one zone). In other words, if the time at Greenwich is 1000, the time in South Africa will be 1200.

Problems still exist with international travel and all these different time zones. Standardization regarding time reporting is therefore necessary.

First off, we make use of military time or the equivalent of a 24-hour clock. Midnight being 0000, midday 1200 and 6 pm as 1800. To standardize this for international travel, Pilots refer to Universal Time Coordinated (UTC). A pilot departing from South Africa at 0600 (LMT) would report departure time as 0400 (UTC).
Sunrise and Sunset
It is important to have an understanding of these two terms, as they are used in the regulations governing and distinguishing between day and night flight. The times of sunrise and sunset vary with latitude, altitude and according to the seasons as well. In order to fly at night, pilots must hold the required rating, without which he/she should stay within the bounds of the law with sufficient planning. Contact your local aviation meteorology office for a table of local sunrise and sunset times.

Sunrise: When the very first part of the sun appears above the horizon
Sunset: When the very last part of the sun is above the horizon
Twilight: Period of light before the sun rises and after it sets
Daylight: From beginning of morning twilight to end of evening twilight
Official Day: 15 minutes before sunrise to 15 minutes after sunset
Official Night: 15 minutes after sunset to 15 minutes before sunrise
10.4 Direction
Direction on the Earth is measured clockwise from True North (0000 – 3600). North (0000 T), East (0900 T), South (1800 T) and West (2700 T) are known as the Cardinal Points.
Quadrantal Points lie between the Cardinal Points –
i.e. NE (0450), SE (1350), SW (2250) and NW (3150).

When plotting tracks on aviation maps, we need to determine the magnetic heading used in the aircraft to maintain this desired track with a compass. First thing we need to do, is measure the angular difference between the nearest meridian and our track line to determine our true bearing (always measured clockwise from true North). Since all meridians point to true North, we need to adjust this angle for magnetic North. Depending on our position on the Earth, magnetic North could lie either East or West of true North. Fortunately, this is provided for on our chart by means of isogonal lines which indicate the angular difference between magnetic and true North, or Variation. With variation expressed as west by means of a curved broken line on the chart, we can expect magnetic North to be West of true North.

Looking at an example below, we can see with a magnetic North west of true North, we need to add the variation to our true bearing to give us a magnetic bearing from which we can navigate using our compass.
To help remember, use the rhyme:
Variation West, Magnetic Best (add variation)
Variation East, Magnetic Least (subtract variation)

10.5 Aircraft Magnetism
In order to successfully navigate we need a reference system that can be used to consistently indicate direction. There are no instruments to indicate true north, however a magnet when freely suspended will align itself with the earth’s magnetic field. This provides a constant indication of magnetic north, thereby allowing us to navigate on the ground and in the air. Unfortunately, magnetic north is not the same as true north as we have discussed, there is an angular difference (variation) which we need to account for.

Compass Construction
The magnetic compass used in the aircraft consists of two bar magnets attached to a compass card, mounted on a pivot within a glass bowl. This glass bowl is filled with a petroleum based clear fluid which has dampening properties to prevent excessive oscillations. Heading reference is aided through the use of the lubber line – a vertical line positioned within the case.

The compass card is marked with the four cardinal points, labeled; N, E, S, W.

Every 300 thereafter is marked (3=300, 6=600 etc.) with long lines indicating 100 and short lines marked in 50 intervals. Looking at the compass card, it is easy to be confused at first, this can be avoided by remembering that you are in fact looking at the back of the compass card. When on a Northerly heading (as indicated by the compass above), we know we need to make a heading change to the right to intercept heading 300. However, 300 is marked to the left of our current heading 0000. So as a rule of thumb, always turn away from your desired heading and the compass will swing as required.
Compass Errors
This is a deflection away from magnetic north due to the electrical circuits, moving engine components and radio equipment within the aircraft that deter compass accuracy. Without correction, instead of pointing to magnetic north we now have what is called a compass north reading. Since these magnetic fields are relative to the aircraft itself, this deviation is not constant and varies from heading to heading. To reduce this effect, small adjustable compensating magnets are placed within the compass itself. However, this does remove the error completely and a compass card can be found near the compass itself to help account for the residual deviation.

As with variation, we also need to make a correction for deviation (the angular difference between magnetic heading and compass heading):
Deviation West, Compass Best
Deviation East, Compass Least
Therefore, if we wish to maintain a magnetic track of 0000, we need to correct for 30E deviation (compass north lies 3 degrees east of magnetic north).
Deviation East, Compass Least:
0000 (M) – 30 (Dev.) = 3570 (C)
So, for 0000 we need to steer 3570
Now when plotting a track, we will first adjust true bearing to magnetic bearing taking into account the local variation. Thereafter, we will need to correct this magnetic heading for the appropriate deviation leaving us with a compass heading we can reference in the aircraft.

Magnetic Dip
Earth’s magnetic field of attraction is strongest at the poles, resulting in a freely suspended magnet to dip, or point downwards the nearest pole. At the equator, this effect is negligible as the magnetic field is parallel to the surface. The magnetic compass is designed with a high pivot point and the magnets situated well below which results in a pendulum effect opposing this magnetic dip – keeping the magnets horizontal. Residual dip still remains and this displacement of the center of gravity brings about to more momentary errors:
Acceleration and Deceleration Errors: Only occur on East/ West headings and is due to the displaced center of gravity from directly below the pivot because of the magnetic dip. As the aircraft accelerates, the pivot moves forward too. A force equal in strength but opposite in direction will act on the center of gravity because inertia exists. This results in a turning of the needle; the compass now indicates slightly different to what is actually being flown. Once speed stabilizes, the needle will settle back to the correct heading. The same is true for deceleration.

Accelerating on an E/W heading will indicate a turn to the South
Decelerating on an E/W heading will indicate a turn to the North
Turning Error: The displaced center of gravity of the needle is also subject to centrifugal forces in a turn. This causes the compass to lag behind the turn because of the inertia that is experienced. This error is most significant on North and South headings. The acronym ONUS will help here.
Overshoot a Northerly heading and Undershoot a Southerly heading or, more simplified (Overshoot North – Undershoot South). The amount of overshoot or undershoot should never be more than 200. As you roll out, you will notice the lag in the compass as it swings back to the desired heading.

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