From above calculations, it can be derived that RM increases with increased latitude. At equator, the curvature radius of prime meridian reach its minimum, which is less than the length of semi-minor axis, b, while in the poles, the curvature radius of prime meridian reach its maximum, which is greater than the length of semi-major axis, a.
Example: 得到子午面内一点（纬度?）的曲率半径RM后，可以从载体的北向速度vN求出载体相对地球沿东向的转动角速度?E（即纬度的变化率）:
???vN/RM ?E???The curvature radius of Prime Vertical RN:
可以从数学上证明，卯酉圈曲率半径的端点总是落在短轴上。于是有：
r?RNcos? RN??a(1?e2sin2?)1/2
when ??0, RN0?a when ??90, RN90??a(1?e2)1/2?a?a?RM90 bFrom calculations, it can be derived that RN increases as well with increased latitude. At equator, the curvature radius of Prime Vertical reach its minimum, which is equal to the length of semi-major axis, a, while in the poles, the curvature radius of Prime Vertical reach its maximum, which is greater than the length
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of semi-major axis, a. And
aRNe2cos2?(1?e2sin2?)1/21?e2sin2????1? 222RMa(1?e)1?e1?e(1?e2sin2?)3/2We can know that RN>RM at any latitude unless at ??90, where RN=RM.
Example: 载体以东向速度vE沿纬度圈航行，产生极轴方向的角速度?e:
????e??vE rvEvcos??E rRN北向角速度是极轴方向角速度的分量，即：
?N??e?cos??1.5.6 The arc length of 1’ on meridian
Assuming S is the arc length of 1‘ on meridian, we can derive from the following equation:
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S?RM?1'?a(1?e2)22(1?esin?)
3?a(1?e2)(1?e2sin2?)?1'2?1852.2?9.3cos2?S increases with increased latitude.(赤道最短，两极最长) At
?1'??0?, S=1842.9m. At ??45?, S=1852.2m. At ??90?, the
length of S reach its maximum, S=1861.5m.
1 nautical mile (nm) = 1852 m. The errors of S at equator and poles are 9.1m and 9.5m, respectively. （1929年国际水文物理学会制定）
1 cable (cab) = 0.1 n mile = 185m 1 foot (ft) = 0.3048 m 1 yard = 3ft =0.9144 m
1 fathom (fm，拓) = 6 ft = 1.8288 m 1.6 Distance On The Earth
Distance, as used by the navigator, is the length of rhumb lineconnecting two places. This is a line making the same angle with all meridians. Meridians and parallels which also maintain constant true directions may be considered special cases of rhumb line. Any other rhumb line spirals toward the pole, forming a loxodromic curve or loxodrome.( A line which makes the same angle with all meridians. Theoretically not the shortest route, but a
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handy straight line on a Mercator chart.)
Speed (S) is rate of motion, or distance per unit of time. A knot (kn.), the unit of speed commonly used in navigation, is a rate of 1 nautical mile per hour.
The expression speed of advance (SOA) is used to indicate the speed to be made along the intended track.
Speed over the ground (SOG) is the actual speed of vessel over the surface of the earth at any given time.
To calculate the speed made good (SMG) between two positions, divide the distance between two positions by the time elapsed between the two positions.
S (nm) = V (kn) ? T (hr) S (nm) = V (kn) ? T (min) / 60 1.7 Direction On the Earth
Direction is the position of one point relative to another. Navigators express direction as the angular difference in degrees from a reference direction, usually north or the ship‘s head. True North: intersection of Observer True Horizon and Observer Meridian. The North, East, South and West are called Cardinal Directions.
The directions can be expressed in several methods: (1) Circle method（圆周法）: 000?-360?: 005?.0, 085?.7
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(2) Semi-Circle method（半圆法）:0?-180?：150?.0NE, 125?.0SW
(3) Quadrant method(象限法): 0?-90?：N60?.0E, S35?.0W (4) Compass method(罗经点法): 32等分圆周，每一等分称作一个罗经点（point of the compass）.1 point of compass = 360??32=11?.25
N, N/E, NNE, NE/N, NE, NE/E, ENE, E/N, E, E/S ESE, SE/E, SE, SE/S, SSE, S/E, S, ………….
Course (C, Cn) is the horizontal direction in which a vessel is steered or intended to be steered, expressed as angular distance from north clockwise through 360?.
The course is often designated as true, magnetic, or compass, according to the reference direction.
Track made good (TMG) is the single resultant direction from the point of departure to point of arrival at any given time. Course of advance (COA) is the direction intended to be made good over the ground.
Course over ground (COG) is the direction between a vessel‘s last fix and an EP(Estimated Position).
Course line is a line drawn on a chart extending in the direction of a course.
Track (TR) is the intended horizontal direction of travel with respect to the earth.
Fore and Aft Line (艏艉线)
Heading(Hdg., SH) is the direction in which a vessel is
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