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Definition - is the art of measuring horizontal and vertical distances between objects, of measuring angles between lines, of determining the direction of lines, and of establishing points by predetermined angular and linear measurements. Plane Surveying - is that type of surveying in which the earth is considered to be a flat surface, and where distances and areas involved are of limited extent that the exact shape of the earth is disregarded.
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Surveying Theory Practice
A-1 Derivation of Pythagorean Theorem A-3 Chaining Formulas A-5 Units of Measurement A-7 Glossary of Terms A-9 Glossary of Abbreviations A Example Traverse Calculation Sheet B-1 Angle Measuring B-3 Bearings and Azimuths B-5 Coordinates B-7 Traverse B Differential Leveling B Trigonometric Leveling B Horizontal Curves B Spiral Curves B Vertical Curves C-1 Geometronics February It is the art of measuring horizontal and vertical distances between objects, of measuring angles between lines, of determining the direction of lines, and of establishing points by predetermined angular and linear measurements.
Along with the actual survey measurements are the mathematical calculations. Distances, angles, directions, locations, elevations, areas, and volumes are thus determined from the data of the survey.
Survey data is portrayed graphically by the construction of maps, profiles, cross sections, and diagrams. Types of Surveys: Geodetic Surveying: Plane Surveying: The type of surveying that takes into account the true shape of the earth. These surveys are of high precision and extend over large areas.
The type of surveying in which the mean surface of the earth is considered as a plane, or in which its spheroidal shape is neglected, with regard to horizontal distances and directions. Operations in Surveying: Control Survey: Boundary Survey: Topographic Survey: Made to establish the horizontal and vertical positions of arbitrary points. Made to determine the length and direction of land lines and to establish the position of these lines on the ground.
Made to gather data to produce a topographic map showing the configuration of the terrain and the location of natural and man-made objects.
Hydrographic Survey: The survey of bodies of water made for the purpose of navigation, water supply, or subaqueous construction. Mining Survey: Construction Survey: Made to control, locate and map underground and surface works related to mining operations. Made to lay out, locate and monitor public and private engineering works.
Geometronics February. Photogrammetric Survey: Made to utilize the principles of aerial photogrammetry, in which measurements made on photographs are used to determine the positions of photographed objects. For the derivation of the Pythagorean Theorem, see the appendix. A and B are the remaining sides. Since C is the unknown, we solve for C. This system uses angular notation in increments of 60 by dividing the circle into degrees; degrees into 60 minutes; and minutes into 60 seconds. Each unit has a corresponding symbol: degrees are indicated by ; minutes by ; and seconds by.
For example, , , and all represent the same magnitude of angle. However, in the last form, which is the preferred notation, notice that minutes and seconds equal to or greater than 60 are carried over to the next larger unit and that degrees and minutes do not have decimals.
Decimal seconds are acceptable. A radian is defined as the angle between radius lines from either end of an arc of radius length. Another unit is the grad or gon.
The grad is widely used in much of the world as part of the metric system, even though the radian is the primary unit. As a fraction, a ratio can be treated like any other fraction. The ratio is the quotient of the first value divided by the second value, and as such, can also be expressed as a decimal.
In our example above, the ratio of 2 to 5 is A proportion is a statement of equality between two ratios. Since the ratio of 2 to 5 is the same as the ratio of 4 to 10, we can say that the two ratios are a proportion. Find the value of x. The distinction between functions is which two sides are compared in the ratio. The figure below illustrates the side opposite from and the side adjacent to Angle A, and the hypotenuse the side opposite the right angle. In order for trig functions to be of significant value, there must be a known correlation between the magnitude of the angle and the magnitude of the trigonometric functions.
But if the lengths of the sides were altered and the 45 angle held, would the trig functions remain unchanged? Let s find out. Try developing the functions for the 45 angles in the following triangles. The right angle cannot be modified since trig functions are the ratios of one side to another side of a right triangle. If we maintain the length of the hypotenuse while decreasing the angle A, the figure at the right shows that the side opposite also decreases, while the side adjacent to angle A increases.
Let s decrease angle A until side a is shortened from to At this point, we don t know the size of angle A, except that it is less than Based on the above figure, what are the trig functions of 30? The co functions of sine, tangent, and secant are cosine, cotangent, and cosecant respectively.
Any function of an acute angle is equal to the cofunction of its complementary angle. Complementary angles are two angles whose sum is Since the two acute angles in any right triangle are complementary, the functions of one angle are equal to the cofunctions of the other.
We found this in our work with 30 and 60 angles. Angles outside of this range cannot be included in a right triangle as specified in the earlier definitions of the functions. The hypotenuse becomes r, or the radial distance from the origin.
The adjacent side becomes x, or the distance along the x-axis. The opposite side becomes y, or the right angle distance from the x-axis. The radial distance, r, is always considered positive in the 0 direction.
List the Sine, Cosine, and Tangent of each angle in both fractional and decimal form. Three are already done. Show the signs of the others in the chart below. One is equal to plus or minus the hypotenuse r and the other is equal to zero.
The tangent of 90 has an x value of 0 causing a division by zero. If we consider the tangent of an angle slightly less than 90, we have a y value very near to r and a very small x value, both positive. Dividing by a very small number yields a large function. The closer the angle gets to 90, the smaller the x value becomes, the closer the y value becomes to r, and the larger the tangent function becomes.
The first is long and involved and beyond the scope of this course. Both 1 and 2 have become obsolete due to 3. We will assume that our little electronic wonders will return the proper value when a function is calculated. Notice that only three functions exist on most electronic calculators, as the others can be expressed as reciprocals of those shown, or otherwise easily reached. While each angle has only one value for each of its trigonometric functions, exercise problems reveal that more than one angle can have the same trigonometric values.
It will be up to the individual to evaluate whether that is the correct value for the particular situation. Practice Problems: 40 Determine the missing side of a 30 right triangle with a hypotenuse of 6. On a wall in the tomb of Thebes and carved on a stone coffin are drawings of rope stretchers measuring a field of grain. The Great Pyramid of Gizeh B. This is an error of 1 in on each side.
English mathematician Edmund Gunter gave to the world not only the words cosine and cotangent, and the discovery of magnetic variation, but the measuring device called the Gunter s chain shown below.
Edmund also gave us the acre which is 10 square chains. It is composed of links, with a link being 0. Each link is a steel rod bent into a tight loop on each end and connected to the next link with a small steel ring.
Starting in the early s surveyors started using steel tapes to measure distances. These devices are still called chains to this day. The terms chaining and chainman are also legacies from the era of the Gunter s chain. This dictates that every field measurement taken be either measured horizontally or, if not, reduced to a horizontal distance mathematically.
In many instances, it is easiest to simply measure the horizontal distance by keeping both ends of the chain at the same elevation. This is not difficult if there is less than five feet or so of elevation change between points. A hand level or pea gun is very helpful for maintaining the horizontal position of the chain when level chaining. A pointed weight on the end of a string called a plumb bob is used to carry the location of the point on the ground up to the elevated chain by simply suspending the plumb bob from the chain such that the point of the plumb bob hangs directly above the point on the ground.
When the difference in elevation along the measurement becomes too great for level chaining, other methods are called for. One option, break chaining, involves simply breaking the measurement into two or more measurements that can be chained level.
Surveying Theory Practice
Definition - is the art of measuring horizontal and vertical distances between objects, of measuring angles between lines, of determining the direction of lines, and of establishing points by predetermined angular and linear measurements. Plane Surveying - is that type of surveying in which the earth is considered to be a flat surface, and where distances and areas involved are of limited extent that the exact shape of the earth is disregarded. Geodetic Surveying — are surveys of wide extent that takes into account the spheroidal shape of the earth. Measurement - is the process determining the extent, size, or dimensions of a particular quantity in comparison to a given standard. Direct Measurements — is a comparison of the measured quantity with a standard measuring unit.
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Surveying Theory and Practice (Compilation)
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A-1 Derivation of Pythagorean Theorem A-3 Chaining Formulas A-5 Units of Measurement A-7 Glossary of Terms
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Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required. This updated edition contains the same breadth and depth as previous editions with pertinent chapter topics divided into two parts. Part A covers elementary topics and Part B covers advanced topics. This innovative design, coupled with the most recent developments in technology, complements first- and second-level courses in surveying without losing its value as a reference textbook. Read more Read less. Previous page.
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Part A covers elementary topics and Part B covers advanced topics. This innovative design, coupled with the most recent developments in technology, complements first- and second-level courses in surveying without losing its value as a reference textbook. Download Surveying: Theory and Practice Users Review From reader reviews: Lori Hunt: Do you considered one of people who can't read pleasant if the sentence chained from the straightway, hold on guys this aren't like that. This Surveying: Theory and Practice book is readable simply by you who hate the straight word style.
ГЛАВА 114 - Обыщите их еще раз! - потребовал директор. В отчаянии он наблюдал за тем, как расплывчатые фигуры агентов обыскивают бездыханные тела в поисках листка бумаги с беспорядочным набором букв и цифр. - О мой Бог! - Лицо Джаббы мертвенно побледнело. - Они ничего не найдут. Мы погибли.
Сьюзан важно было ощущать свое старшинство. В ее обязанности в качестве главного криптографа входило поддерживать в шифровалке мирную атмосферу - воспитывать. Особенно таких, как Хейл, - зеленых и наивных. Сьюзан посмотрела на него и подумала о том, как жаль, что этот человек, талантливый и очень ценный для АНБ, не понимает важности дела, которым занимается агентство. - Грег, - сказала она, и голос ее зазвучал мягче, хотя далось ей это нелегко.
Я скажу вам, кто его сегодня сопровождает, и мы сможем прислать ее к вам завтра.
Она чувствовала, что здесь что-то не то, но не могла сообразить, что. Она достаточно хорошо знала Танкадо и знала, что он боготворил простоту. Его доказательства, его программы всегда отличали кристальная ясность и законченность. Необходимость убрать пробелы показалась ей странной. Это была мелочь, но все же изъян, отсутствие чистоты - не этого она ожидала от Танкадо, наносящего свой коронный удар.
Я еле добрел. - Он не предложил вам больницы поприличнее. - На этой его чертовой тарантайке. Нет уж, увольте.
Беккер легонько обнял. Девушка высвободилась из его рук, и тут он снова увидел ее локоть. Она проследила за его взглядом, прикованным к синеватой сыпи.
У вас испуганный вид, - сказала Сьюзан. - Настали не лучшие времена, - вздохнул Стратмор. Не сомневаюсь, - подумала. Сьюзан никогда еще не видела шефа столь подавленным. Его редеющие седые волосы спутались, и даже несмотря на прохладу, создаваемую мощным кондиционером, на лбу у него выступили капельки пота.
Да. Убийство азиата сегодня утром. В парке.
Невскрываемого алгоритма никогда не существовало, как не существовало и Цифровой крепости. Файл, который Танкадо разместил в Интернете, представлял собой зашифрованный вирус, вероятно, встроенный в шифровальный алгоритм массового использования, достаточно сильный, чтобы он не смог причинить вреда никому - никому, кроме АНБ.