Table of the NAC Character and Integer Correspondences =========================================================== ||Character|Integer||Character|Integer||Character|Integer|| ||---------|-------||---------|-------||---------|-------|| || 0 | 0 || B | 10 || N | 20 || || 1 | 1 || C | 11 || P | 21 || || 2 | 2 || D | 12 || Q | 22 || || 3 | 3 || F | 13 || R | 23 || || 4 | 4 || G | 14 || S | 24 || || 5 | 5 || H | 15 || T | 25 || || 6 | 6 || J | 16 || V | 26 || || 7 | 7 || K | 17 || W | 27 || || 8 | 8 || L | 18 || X | 28 || || 9 | 9 || M | 19 || Z | 29 || ===========================================================
A Natural Area Code (NAC) consists of three character strings separated by blank spaces. The first character string represents longitude, the second string represents latitude, and the third string represents altitude. The system divides the whole range of longitude (0 - 360 degrees), latitude (0 - 180 degrees) and altitude (from the earth center to the infinite outer space) into 30 discrete divisions respectively, each of which is named by one character from the character set according to the order of the characters. And each resulting division is divided into 30 subdivisions, and each of the subdivisions is named by one character. The division process can continue to the third , fourth, and other levels. The resulting divisions in three dimensions form many regions called NAC blocks. Therefore, a first level NAC block can be represented by a NAC of three characters separated by blank spaces, each of which represents the character string for longitude, latitude and altitude respectively, for example, NAC: 5 6 7. A second level NAC block can be represented by a NAC of six characters to form three character strings: the first two characters form the longitudinal string, the third and fourth characters form the latitudinal string, and the last two characters form the altitudinal string. A blank space is placed between these strings, for example, NAC: JB KH LN represents a NAC block at the second level, in which the characters J, K and L represent coordinates of a first level NAC block which contains the second level NAC block, and the characters B, H and N are the relative coordinates of the second level NAC block in the first level NAC block. A region formed by sides at different division levels is called a NAC region and can be represented by a single NAC too. Any three NAC character strings can form a NAC which represents a completely defined region in the universe.
If the third string of a NAC is omitted, the resulting NAC represents an area on the earth surface, called a NAC area if the number of characters in the two coordinate strings are different, and called a NAC cell if the number of characters in the two coordinate strings are the same. Any two NAC character strings can form a NAC representing a completely defined area on the earth. When the sides are very different in length, a rectangular area will turn out to be a line section automatically. When the sides are relative small, a rectangular area will become a geodetic point.
Therefore, a NAC can represent a geodetic point anywhere in the universe, a line section of constant longitude or constant latitude on the earth, an area bounded by constant longitude and constant latitude anywhere on the earth and a three-dimensional region bounded by constant longitude, constant latitude and constant altitude anywhere in the universe.
The NAC of a region that contains a geodetic point expressed by the longitude, latitude and altitude coordinates in the WGS-84 system[1] can be determined by the following algorithm:
LONG = (Longitude + 180)/360
x1 = Integer part of( LONG*30)
x2 = Integer part of(( LONG*30-x1)*30)
x3 = Integer part of((( LONG*30-x1)*30-x2)*30)
x4 = Integer part of((((LONG*30-x1)*30-x2)*30-x3)*30)
...
LAT = (Latitude + 90)/180
y1 = Integer part of( LAT*30 )
y2 = Integer part of(( LAT*30-y1)*30)
y3 = Integer part of((( LAT*30-y1)*30-y2)*30)
y4 = Integer part of((((LAT*30-y1)*30-y2)*30-y3)*30)
...
ALT = Arctan((Altitude + R)/R )/90
z1 = Integer part of( ALT*30)
z2 = Integer part of(( ALT*30-z1)*30)
z3 = Integer part of((( ALT*30-z1)*30-z2)*30)
z4 = Integer part of((((ALT*30-z1)*30-z2)*30-z3)*30)
...
where Longitude is positive in the eastern hemisphere but negative in the western; Latitude is positive in the northern hemisphere but negative in the southern; both Longitude and Latitude are in degrees plus decimals; Altitude is measured along the gravitational force line from the geoid surface of the earth in kilometers; Altitude is positive above the geoid surface and negative below the surface; the symbol * is the multiplication sign; x1, x2, x3, x4, ..., y1, y2, y3, y4, ..., z1, z2, z3, z4, ... are integers ranging from 0 to 29 here; Arctan( ) is the arctangent function with value in degrees; R is in km the distance from the earth center along the gravitational force line to the geoid surface and can be approximated by the earth radius at the location:
f = (a - b)/a ; e = 2*f - f^2 ; N = a/sqrt(1 - e^2*sin^2(Latitude)) ; R = N*sqrt[1- e^2*(2-e^2)*sin^2(Latitude)]
where a is the semi-major earth axis (ellipsoid equatorial radius) equal to 6378.1370 km; b is the semi- minor earth axis (ellipsoid polar radius) equal to 6356.7523 km; sqrt( ) is the square root function; sin( ) and cos( ) are triangular functions; the symbol / is the division sign; the symbol ^ is the exponential operator.
Once x1, x2, x3, x4, ..., y1, y2, y3, y4, ..., z1, z2, z3, z4, ... are calculated, the corresponding characters can be found from the Table of the NAC character and integer correspondences: X1, X2, X3, X4, ..., Y1, Y2, Y3, Y4, ..., Z1, Z2, Z3, Z4, .... Then, the Natural Area Code of the region is written as NAC: X1X2X3X4... Y1Y2Y3Y4... Z1Z2Z3Z4... with a blank space between any two character strings. The first character string of a NAC represents longitude, the second string represents latitude, and the third represents altitude.
If a NAC has only two character strings, then the NAC represents an area on the earth surface and the two character strings represent the longitude and latitude respectively, as defined in the beginning of this chapter. For example, NAC: 8KD8 PGGK represents a 25 by 50 meter area in the White House, while NAC: 8KD8 PGGK H000 represents a region 25 meters wide, 50 meters long and 25 meters high measured from the geoid surface under the White House.
The number of characters to be used in a character string of a NAC representing the geodetic point is determined by the required resolution or the resolution of the original coordinates of the longitude, latitude and altitude. A NAC using more characters represents a smaller area or region. The smallest area or region containing the geodetic point is the one of the size equal to the error range of the coordinates. Therefore, when a NAC is used to represent a geodetic point, it has both the information of the location and its error range.
If the NAC of a region is known, then the longitude, latitude and altitude of the southwestern lower corner of the region can be calculated by the following procedure:
First, convert all characters X1, X2, X3, X4, ... Y1, Y2, Y3, Y4, ... Z1, Z2, Z3, Z4, ... into integers x1, x2, x3, x4, ... y1, y2, y3, y4, ... z1, z2, z3, z4, ... according to the Table of the NAC Character and Integer Correspondences.
Then use the following formulae to calculate coordinates:
Longitude = (x1/30+x2/30^2+x3/30^3+x4/30^4+...)*360-180 Latitude = (y1/30+y2/30^2+y3/30^3+y4/30^4+...)*180-90 f = (a - b)/a ; e = 2*f - f^2 ; N = a/sqrt(1 - e^2*sin^2(Latitude)) ; R = N*sqrt[1 - e^2*(2-e^2)*sin^2(Latitude)] Altitude = R*tan((z1/30+z2/30^2+z3/30^3+z4/30^4+...)*90)-R
The northeastern upper corner of the region can be calculated by repeating the same procedure with the same integers except adding 1 to the integer corresponding to the last character of each string of the NAC. Then, the region can be completely determined by the coordinates of these two geodetic points.
In the Natural Area Coding System, several algebraic rules have been introduced to simplify the notations and operations of NACs. Some of the rules are defined in the following, where symbol = represents the equivalency and symbol + represents the sum of two NAC regions or areas.
Definition a If there are a series of neighboring NAC regions in the universe, which exactly fill a region bounded by surfaces of constant longitude, constant latitude and constant altitude, then the whole region can be represented by a single group NAC which uses a hyphen to link the relative coordinate characters of the first NAC with the relative coordinate characters of the last NAC in each direction with multiple NAC regions respectively, for example:
NAC: NHJ-L TH KJH = NAC: NHJ TH KJH + NAC: NHK TH KJH + NAC: NHL TH KJH
NAC: NHJ-L TH-J KJH = NAC: NHJ TH KJH + NAC: NHK TH KJH + NAC: NHL TH KJH
+ NAC: NHJ TJ KJH + NAC: NHK TJ KJH + NAC: NHL TJ KJH
NAC: NHJ-L TH-J KJH-J = NAC: NHJ TH KJH + NAC: NHK TH KJH + NAC: NHL TH KJH
+ NAC: NHJ TJ KJH + NAC: NHK TJ KJH + NAC: NHL TJ KJH
+ NAC: NHJ TH KJJ + NAC: NHK TH KJJ + NAC: NHL TH KJJ
+ NAC: NHJ TJ KJJ + NAC: NHK TJ KJJ + NAC: NHL TJ KJJ
The number of characters after the hyphen in a character string represents the
number of the characters of the relative coordinate. The characters before the
hyphen in a character string represent the first NAC region coordinate in this
direction. The characters before the hyphen with its last characters replaced
by the characters after the hyphen in the character string represent the last
NAC region coordinate in this direction. For example, NAC: NHJ-LZ TH KJH
represents a three-dimensional region which starts from the region of
NAC: NHJ TH KJH and ends by the region of NAC: NLZ TH KJH, that is,
NAC: NHJ-LZ TH KJH = NAC: NHJ-Z TH KJH + NAC: NK0-Z TH KJH + NAC: NL0-Z TH KJH
It is the same for NACs with hyphens in two or three character strings, such as:
NAC: FP-GZ TH-ZK HJK = NAC: FP-Z TH-Z HJK + NAC: G0-Z TH-Z HJK
+ NAC: FP-Z V0-Z HJK + NAC: G0-Z V0-Z HJK
+ NAC: FP-Z W0-Z HJK + NAC: G0-Z W0-Z HJK
+ NAC: FP-Z X0-Z HJK + NAC: G0-Z X0-Z HJK
+ NAC: FP-Z Z0-K HJK + NAC: G0-Z Z0-K HJK
When a NAC with 0-Z at the end of its character string, these three characters can be omitted in the character string provided there are some characters left in the character string, for example:
NAC: JJ0-Z KKL HG = NAC: JJ KKL HG NAC: JJ0-Z KKL0-Z HG0-Z = NAC: JJ KKL HG
An exponent has been introduced to represent the repetition of one same character in a NAC coordinate string, for example:
NAC: RGJJJJK RDF FDS = NAC: RGJ(4)K RDF FDS NAC: RGGGH HFF ZZZZZ = NAC: RG(3)H HF(2) Z(5)
The exponential expressions will be very useful in representing far distant objects in the universe.
Definition b If there are a series of neighboring NAC areas on the earth which exactly fill an area bounded by lines of constant longitude and constant latitude, then the whole area can be represented by a single group NAC which uses a hyphen to link the relative coordinate characters of the first NAC with the relative coordinate characters of the last NAC in each direction with multiple NAC areas respectively. The exponential expression can be applied to the two-dimensional NAC too.
There are special cases which need be further explained. NAC: RGJ-H WDF is not defined because there are no divisions after division H but before division J in the same higher level division. A group NAC such as NAC: HJ K0-Z can be simplified as NAC: HJ K since 0-Z covers all NAC divisions in the higher level division, but NAC: 0-Z HF is not allowed to be written into NAC: HF because any simplication is only to shorten the coordinate string but not remove the whole string.
With the above definitions, the concept of NAC regions has been extended to include any regions in the universe, bounded by surfaces of constant longitude, constant latitude and constant altitude, and the concept of NAC areas has been extended to include any areas on the earth, bounded by lines of constant longitude and constant latitude. Every NAC region or NAC area can be expressed by a single group NAC. Since the side ratios and size of a NAC area or region can be any values, a NAC in fact can represent any point in the universe, any line section of constant longitude or constant latitude on the earth, any area bounded by lines of constant longitude and constant latitude on the earth, any region bounded by surfaces of constant longitude, constant latitude and constant altitude in the universe.
If the NACs of any two areas on the earth surface have been given as: NAC1 and NAC2, then the earth surface distance between the centers of these two areas can be calculated as follows:
1. First, calculate the longitude, latitude and the
local earth radius of NAC1 and NAC2: a1, b1, R1 and a2, b2,
R2 respectively using the above formulae;
2. Then calculate the distance S between them
approximately as follows:
S = Rav*Arccos(cosb1*cosa1*cosb2*cosa2+cosb1*sina1*cosb2*sina2+sinb1*sinb2)
where Rav = (R1 + R2)/2.
Calculation of the Time Difference between Two NACs
The natural Time difference between these two areas can be calculated by the following equation:
DT = (a1-a2)*24/360
where the positive value means area 1 has the day staring DT hours earlier than area 2.
First, it integrates the concepts of geodetic points, line sections, areas and regions and generates a unified form to represent all these geodetic units.
Second, it generates extremely short coordinates for all these geodetic units to save storage size, for examples:
For a geodetic point, the following are equivalent:
NAC: 2CHD Q87M
Longitude West 151.3947, Latitude North 43.6508
For a line section, the following are equivalent:
NAC: 2C Q87M
Piont 1: Longitude West 151.5902, Latitude North 43.6508
Point 2: Longitude West 151.1902, Latitude North 43.6508
For an area, the following are equivalent:
NAC: 2C Q8
Northwest corner: Longitude West 151.5902, Latitude North 43.8033
Southwest corner: Longitude West 151.5902, Latitude North 43.6033
Northeast corner: Longitude West 151.1902, Latitude North 43.8033
Southeast corner: Longitude West 151.1902, Latitude North 43.6033
For a three-dimensional region, the following are equivalent:
NAC: 2C Q8 H000
In WGS-84, it is expressed by
The bottom surface has the height = 0 meter above the geoid
surface and four corners on the surface are:
Northwest corner: Longitude West 151.5902, Latitude North 43.8033
Southwest corner: Longitude West 151.5902, Latitude North 43.6033
Northeast corner: Longitude West 151.1902, Latitude North 43.8033
Southeast corner: Longitude West 151.1902, Latitude North 43.6033
The upper surface has the height = 25 meters above the geoid
surface and four corners on the surface are:
Northwest corner: Longitude West 151.5902, Latitude North 43.8033
Southwest corner: Longitude West 151.5902, Latitude North 43.6033
Northeast corner: Longitude West 151.1902, Latitude North 43.8033
Southeast corner: Longitude West 151.1902, Latitude North 43.6033
The efficiency of the Natural Area Coding System is so significant that
it can save 50% of memory for geodetic points, 75% for line sections,
87% for NAC areas and 94% for NAC regions. Third, the simple NAC can be used to a represent map both in digital and hardcopy forms. If the NAC is used for digital map then all the geodetic coordinates of the map can be save by the relative NAC to save another 50% memory and make the database of maps extremely efficient in retrieving and storing maps. If the NAC is used to name a hardcopy map, then the maps will be very well shelved which will be very conveniently retrieved and placed.
Fourth, an eight-character NAC is an ideal universal address for postal services, delivery services, emergency services and taxi services because it can specify an area less than 25 by 50 meters anywhere in the world.
Five, a ten-character NAC is a perfect property identity code for each property in the world, which specify a reference area less than 0.8 by 1.6 meters on a property anywhere in the world.
Many countries presently utilize postal codes for simplifying mail sorting process to increase efficiencies. However, these codes have many disadvantages. Since each country has created its unique postal code system which differs from those of other countries, international mail can not be sorted and transported in the most efficient manner. Based on the distribution structure of postal corporations, postal codes have to change frequently as postal corporations adapt to continually increased urbanization. These resulting changes have inconvenienced both the public and postal corporations. For example, the public has had to remember new postal codes, to inform their friends of changes, and some of their mail has been lost or delayed. Postal corporations have had to cancel and assign codes, to inform all people within the area of changes, to convert old codes on mail to new codes, and to compensate for the loss of mail. Due to the frequent changes, postal corporations have had to update postal code databases, to revise and publish postal code books and postal zone atlases periodically. Many marketing companies have had to buy these books and atlases to update their mailing lists, and risk losing their customers, letters and parcels due to postal code changes. The rapid increase in the amount of mail has forced postal corporations to introduce longer postal codes to expand the capacity of postal code systems. These long meaningless and single-use codes have become more and more difficult for the public to remember and use.
Current emergency services use common addresses to find their locations. Since all the names of countries, provinces, cities, streets and street numbers are not developed systematically but historically, using common addresses to find their locations is always inefficient. Therefore, emergency address dispatching centers in many developed countries have introduced powerful computers and large address-geocode databases for dispatching addresses, which has really increased the address dispatching efficiency. But this is still far from the maximum efficiency these systems should have. For example, these systems need to get the common address of an emergency call from the telephone company, input the address into a computer to search a street name in a street name alphabetic list and find out the coordinates of two street intersections between which the street number is located. The location of the address have to be interpolated from the coordinates of these two street intersections using the street number. Since the street numbers are not uniformly distributed, the interpolation has a poor accuracy. If the street is new and not included in the database, the dispatching will fail. Since the database is so large, mistakes are inevitable, and sometimes the dispatched results may completely wrong. If the correct location of an address has been obtained in the address dispatching center, it is still inconvenient to communicate it with the local emergency station. An emergency vehicle always need be guided by the address dispatching center. Therefore, these systems are not really efficient and reliable in spite of lot of money being invested.
Currently, map grid systems on different maps are always different, which gives people many inconveniences in correlating the information obtained from different maps. Since most map grid systems are artificial, the grid coordinates of a map has always a use limited to this specific map and does not have any other uses, and nobody would like to include these coordinates as part of an address. Therefore, locating a street or an address on such a map is always a time wasting process. Furthermore, since the grid systems are different, people may feel difficult to link a street or highway between maps for two neighboring cities or maps of a city and its province. It is even more difficult for people to calculate distance and determine relative locations between two addresses located on two maps.
Computerized Geographic Information Systems (GIS) have greatly improved the efficiency of using maps and geographic databases, which have been widely used in managing natural resources, planning and constructions, statistics, transportation, environment protection, weather and earthquake analysis, agriculture, fishing, mining and exploring, tourism, education and research, etc. Since everybody lives in the world, the potential users may cover the whole population of the world.
However, these GIS's have not been very efficient due to the lack of a language to describe geodetic points, areas on the earth and three-dimensional regions systematically and efficiently. The coordinates of a geodetic point in all current geodetic systems are always unnecessary long character strings. The description of an area on the earth or an underground three-dimensional region always needs a paragraph of words if it does not coincide with a political identity. Therefore, using current geodetic coordinates to store geodetic points, areas and regions in a GIS wastes huge amount memory. Storing geographic information related to specific areas or three-dimensional region not only wastes memory but also becomes poor structured, which inconveniences users to retrieve and use the information.
Navigation systems have been greatly improved since navigation satellites were launched. Now a hand-held Global Positioning System (GPS) unit can tell the coordinates of its location to the accuracy within 100 meters. These cheap and convenient units have greatly increased their uses outside its military services. Mountain hikers, truck drivers, fishing boats, taxi and emergency vehicles start to use GPS units to navigate. If the price and volume of a GPS is continuously decreasing, everybody will use it in the daily life for finding locations and addresses like a watch to tell the time. However, there is still a great potential to increase the use of a GPS unit significantly. A GPS unit can not tell the common addresses but simply tell the geographic coordinates of a location. It is still difficult to relate the geocodes to the common addresses because a common address with its postal code does not include any information of its absolute geographic coordinates. If the NAC global postal code is used as part of an address, the application of a GPS unit for daily life can be greatly increased since a NAC global postal code has included very accurate geographic coordinates of an address. Therefore, equipped with a GPS unit, a person will never have trouble to find any address anywhere in the world.
As the computer science develops rapidly, telecommunication is undergoing a revolution. Telephone, fax, cellular phone, electronic mail, world wide web and file transfer protocol are entering more and more homes. It is an exciting time and people can notice changes everyday. At the same time, you may also feel the burden to remember and use continually introduced address codes for new communication services and the codes of continually increased length for existing services. In fact, all these codes serve the same purpose: to represent an address. Why should we introduce so many single-use codes? Why don't we unify them to be one code for all the services? Furthermore, the unification of codes can also help the unification of the telecommunication network and optimize its capacity and efficiency.
There are many geodetic reference systems in the world and nobody can remember exactly how all these systems are defined and how the coordinates of these systems can be converted. For example, the longitude/latitude system has more than 20 different variations in different countries and different times. The longitude/latitude coordinates of a geodetic point can be written in many different ways: to put either latitude or longitude first, to use units like: degree.decimals, degree:minute.decimals, degree:minute:second.decimals, and to mark either latitude south or latitude north, either longitude west or longitude east by adding "-" in front of the numbers or to put characters "N", "S", "W" or "E" either in front of the numbers or at the end of the numbers. The differences of the geographic and geodetic systems and their writing conventions create serious problems for people to use, interpret and communicate geographic information. Huge amount of time and money have been continuously wasting in all these unnecessary work.
It has been a great demand to introduce an official universal geodetic reference system to eliminate all these problems. Many people have made great efforts to unify the systems but not very successful because no one has convinced other people that one specific system is super and should be adopted as the universal geodetic reference system. Therefore, we have to create a geodetic system with more uses than all current systems and many advantages over all current systems to realize this ambition.
There area many many codes created for one address or one property such as a property identity number, postal code, geocodes for emergency services, telephone number, codes for cable TV, electricity distribution, water supply, etc. Most of these codes are created by specific services and are not related. There information databases are independent. A lot of duplicated work is wasted in all these codes and the exchange of the information is seriously blocked.
As discussed above, the world requires a universal geodetic reference system which should have all the uses of all current systems. The system should be able to be directly used for global postal services, emergency services, taxi and delivery services, and all telecommunication services. The system should unify all map grid systems, create efficient geodetic coordinates, represent areas and three-dimensional regions efficiently and link addresses with geocodes. The Natural Area Coding System is such a system which have all these uses and advantages.