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Angle and Direction MeasurementHorizontaland vertical angles are fundamental measurements in surveying.It is necessary to be familiar withthe meanings of certain basic terms before describing angle and direction measurement. The terms discussed here have reference to the actual figure of the earth. Basic TermsA vertical line at any point on the earths surface is the line that follows the direction of gravity at that point. It is the direction that a string will assume if a weight is attached at that point and the string is suspended freely at the point. At a given point there is only one vertical line.A horizontal line at a point is any line that is perpendicular to the vertical line at the point. At any point there are an unlimited number of horizontal lines.A horizontal plane at a point is the plane that is perpendicular to the vertical line at the point.There is only one horizontal plane through a given point. A vertical plane at a point is any plane that contains the vertical line at the point. There are an unlimited number of vertical planes at a given point. Horizontal Angle and Vertical AngleA horizontal angle is the angle formed in a horizontal plane by two intersecting vertical planes, or a horizontal angle between two lines is the angle between the projections of the lines onto a horizontal plane. For example, observations to different elevation points B and C from A will give the horizontal angle bac which is the angle between the projections of two lines (AB and AC) onto the horizontal plane. It follows that,although the points observed are at different elevations, it is always the horizontal angle and not the space angle that is measured .The horizontal angle is used primarily to obtain relative direction to a survey control point, or topographic detail points, or points to be set out. A vertical angle is an angle measured in a vertical plane which is referenced to a horizontal line by plus (up) or minus (down) angles, or to a vertical line from the zenith direction. Plus and minus vertical angles are sometimes referred to as elevation or depression angles respectively. A vertical angle thus lies between 0 and 90.Zenith is the term describing points on a celestial sphere that is a sphere of infinitely large radius with its center at the center of the earth. The zenith is an angle measured in a vertical plane downward from an upward directed vertical line through the instrument. It is thus between 0 and 180. Obviously the zenith angle is equal to 90 minus the vertical angles. Vertical angles or zeniths are used in the correction of slope distance to the horizontal or in height determined. For the most part, the instrument used in the measurement of angles is called a transit or theodolite, although angles can be measured with clinometers, sextants (hydrographic surveys), or compasses. The theodolite contains a horizontal and vertical circles of either glass or silver. The horizontal and vertical circles of theodolite can be linked to circular protractors graduated from 0 to 360 in a clockwise manner set in horizontal and vertical plane. The horizontal circle is used when measuring or laying off horizontal angles and the vertical circle is used to measure or lay off vertical angles or zenith angles. Usually the units of angular measurement employed in practice are degrees, minutes, and seconds, the sexagesimal system. Angle Measurement A horizontal angle in surveying has a direction or sense; that is, it is measured or designed to the right or to the left, or it is considered clockwise or counterclockwise. In the above figure, the angle at A from B to C is clockwise and the angle from C to B is counterclockwise. With the theodolite set up, centered, and leveled over at station A, then a simple horizontal angle measurement between surveying point B, A and C would be taken as follows: Commencing on , say, “face left”, the target set at survey point B is carefully bisected and the reading on horizontal scale is 25. The upper plate clamp is released and telescope is turned clockwise to survey point C. The reading on horizontal circle is 75The horizontal angle is then the difference of the two directions, i.e. (75-25) =50Change face and observe point C on “face right”, and note the reading=255Release upper plate and swing counterclockwise to point B and note the reading =205The reading or the direction must be subtracted in the same order as 255-205=50The mean of two values would be accepted if they are in acceptable agreement. Modern electronic digital theodolites contain circular encoders that sense the rotations of the spindles and the telescope, convert these rotations into horizontal and vertical (or zenith) angles electronically, and display the value of the angles on liquid crystal displays (LCDs) or light-emitting diode displays (LEDs). These readouts can be recorded in a conventional field book or can be stored in a data collector for future printout or computation. The instrument contains a pendulum compensator or some other provision for indexing the vertical circle readings to an absolute vertical direction.The circle can be set to zero readings by a simple press of a button or initialized to any value on the instrument. Azimuth is the horizontal angle measured in a clockwise direction from the plane of the meridian, which is a line on the mean surface of the earth joining the north and south poles. Azimuth ranges in magnitude from 0 to 360, values in excess of 360, which are sometimes encountered in computations, are simply reduced by 360 before final listing. Bearing is the traditional way of stating the orientation of the line. It is actually the angle measured from the north or south.The bearing, which can be measured clockwise or counterclockwise from the north or south end of the meridian, is always accompanied by letters that locate the quadrant in which the line falls. For example, bearing N32W indicates a line trending 32 west of the north.It is equal to an azimuth of 328. Bearing S12W indicates a line trending 12 west of the south. It is equal to an azimuth of 192. It is important to state that the bearing and azimuth are respect to true north.角度和方向测量水平角和竖直角是测量的基本测量工作,在描述角度和方向测量之前,有必要熟悉几个基本术语的含义,这里讨论的这些术语与地球的真实形状有关.基本术语地球表面任一点的垂线是指这点上沿着重力的方向的线,如果在这点上用线悬挂一个重物,当线自由静止时,这条线所呈现的方向即重力方向。在给定的一个点上只有一条垂线。一点上的水平线是垂直于过该点的垂线的直线。过任一点的水平线有无数条。过一点的水平面是垂直于过该点的垂线的平面,过给定的一个点只有一个水平面.过一点的竖直面是包含过该点的垂线的任一平面过给定的一点有无数个竖直面.水平角和竖直角水平角是指在一个水平面内由两相交的竖直面形成的角,或者说,两条线之间的水平角是这两条线在水平面上的投影线的夹角.例如,在A点观测不同高度的B和C点,其水平角bac是由AB和AC两条线在水平面上的投影构成的.由此得出结论结论,虽然被观测的点在不同的高度上,测出的总是水平角而不是空间角。水平角主要用来由联测控制点获得相对方向,或者地形测量碎部点、或者放样点,竖直角是在一个竖直面内参考于水平线的正(仰)角或负(俯)角,或者相对于一个天顶方向的垂线的角.正负竖直角有时分别被称为仰角或俯角.竖直角位于090度之间.天顶方向是一个术语,用来描述在天球上的点,天球是一个半径无限大的球,其中心在地球中心。天顶距是一个在竖直面内从一个过仪器的被定向为向上的竖直方向线向下测量的角。它的范围是从0到180度。显然,天顶距等于90度减去竖直角.竖直角或天顶距用于斜距化平距的改正或者高程的测量.在极大程度上,用来测角的工具被称为经纬仪,虽然角度可以用倾斜仪、六分仪、或罗盘仪来测,经纬仪有一个玻璃的或镀银的水平度盘和竖直度盘.经纬仪的水平度盘和竖直度盘与顺时针刻了0到360度刻划的圆分度器相连。测或拨水平角时用水平度盘,测或拨竖直角或天顶距时用竖直度盘,通常角度测量法

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