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HSTA206 SURVEY TECHNIQUES MIDLANDS STATE UNIVERSITY FACULTY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF SURVEYING AND GEOMATICS BACHELOR OF SCIENCE HONOURS IN SURVEYING AND GEOMATICS HSTA206 SURVEY TECHNIQUES Assignment 1 Level 5.1 BY TINASHE MTANDA (R172759Z) Lecturer`s Comment 1. The phases of sample survey are often summarized into three categories namely design, implementation and reporting. Briefly outline the tasks which are required during the design phase using an example to illustrate your answer. SOLUTION: · The processes in the design phase, such as conducting a survey to determine the amount of persons who use muscle-building supplements at the MSU gym. · · choosing the sample frame; all the registered persons picking a sampling strategy; simple random sampling determining the sample size; and the number of people sufficient for the research n=100 executing the sampling process · · As a result, doing hypothesis testing and determining research estimates (b) Distinguish between sampling and non-sampling errors. SOLUTION: When working with representative samples, sampling errors occur when the sample's mean values diverge from the population's mean values. The term "sampling error" refers to an error that happens when the sample chosen for observation is not representative. Non-sampling error, on the other hand, is a statistical term that refers to an error that occurs during data collection, causing the data to differ from the true values. It can occur due to human error in problem identification, method or procedure used. A sampling error is not the same as a non-sampling error. 2. The department of Agricultural Research and Extension Services (AREX) desires to estimate the total maize yield for the year 2015 within Zimbabwe. a) Discuss the relative merits of using personal interviews as a method of data collection for the data. SOLUTION: -It allows interviewers to be more flexible. -The interview receives a higher response rate than sent questions, and persons who are unable to read or write can also participate. -The interviewer can assess the respondent's nonverbal conduct. - The response rate is the highest. - Allows for the use of a wide range of queries b) What is the target population for the survey? (2) SOLUTION: The farmers registered with AREX or all the registered maize Commercial farmers c) What could be used as the sampling frame for the survey? (2) SOLUTION: The map of the farming regions of Zimbabwe. The register of all commercial farms d) Describe any sampling technique that you think is suitable for use for this survey and how it can be used. (6) SOLUTION: Technique: Cluster sample design Definition: Cluster sampling is a sampling technique in which a researcher selects various clusters of persons from a population that share similar features and have an equal chance of being included in the sample. Method on how it can be used 1. Sample: Decide the target audience which is all the farmers and also the sample size. 2. Create and analyze sampling frames: Create a sampling frame by using existing natural agricultural regions or the agriculture officer's farming districts. Examine frameworks for coverage and clustering, and make changes as needed. These groupings will be diverse, taking into account the population, which can be both exclusive and inclusive. Individual members of a sample are chosen. 3. Assign people to groups:You can figure out how many groups there are by putting the same average members in each one. Make sure each of these groups is distinct from the others. 4. Select clusters: Using a random selection method, select clusters. Districts or provinces make up the clusters. 5. Create sub-types: The number of steps taken by researchers to build clusters is divided into two subtypes: two-stage and multi-stage. MIDLANDS STATE UNIVERSITY FACULTY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF SURVEYING AND GEOMATICS Geodesy ASSIGNMENT 2 STUDENT NAMES: STUDENT ID: LEVEL: 3:1 MODULE CODE: SVG306 LETURE NAME: DUE DATE: 30 May 2020 1. Using the following data for the ellipsoid: a = 6378160m, b= 6356774.71930860, f = 1/298.25000158005, e2 = 0.00669454 given data: ф1 = 30˚16´27.3ʺ, λ1 = 26˚14´16.2ʺ, s = 34 526.78m, α12 = 128˚12´57ʺ. Calculate ф 2, λ2 and α21 Bowring’s formula e'2 = = = 0.00673966 A = ) = = 1.001872823 B = = = 1.002510215 C = = = 1.003364172 σ = σ = σ = 0.005422251 σ = 00˚18´38.42ʺ λ2 = λ1 + λ2 = 26˚14´16.2ʺ + = 26˚31´09.174ʺ w = w = w = 00˚08´27.4354ʺ D = D = D = -0.096245677 φ2 = φ1 + 2D φ2 = 30˚16´27.3ʺ + 2 φ2 = 30˚04´52.05 ʺ α21 = α21 = α21 = 308˚21´27.67 ʺ Gauss Mid-Latitude Formula N = N = = 6 383 593.033 M = M = = 6 351 664.931 λ = λ2 - λ1 =26˚31´09.174ʺ - 26˚14´16.2ʺ = 00˚16´52.97ʺ λ = λ = = φ = φ = = = Approximation of the change in longitude of the second point λ2 = + λ2 = + Approximate change in longitude λ2 = λ1 + ∆λ = 26˚14´16.2ʺ + = α21 = α12 + ∆α ± 1800 = 128˚12´57ʺ + +180° = 2. Given data: ф A = 17˚36´37ʺ, λ1 = 31˚10´25ʺ, ф B = 17˚31´12ʺ, λB = 31˚05´14ʺ. Calculate S, α12 and α21 on the modified Clarke 1880 ellipsoid. Gauss Mid-Latitude Formula Inverse problems Mean latitude Фm = = =17˚33´54.5ʺ Approximate change in latitude Ф = (17˚31´12ʺ) - (17˚36´37ʺ) = -00˚05´25ʺ Approximate change in longitude ∆λ = λ2 + λ1 = (31˚05´14ʺ) – (31˚10´25)ʺ = -00˚05´11ʺ Find the radius curvature of the meridian M = M = = 6 340 747.420 Radius of curvature in the prime vertical N = N = N = 6 380 226.178 Mean azimuth Change in mean latitude Azimuth α21 = α12 + ∆α ± 1800 Distance S between two points b. Describe ways of determining global best fit ellipsoids. Determining Global best-fit Ellipsoids from Arcs of Meridian or Parallels The astronomical latitudes φp and φq at two point P and Q approximately on the same meridian are measured and a triangulation network connects P and Q. The network is approximately computed on any arbitrary ellipsoid to give geodetic coordinates for P and Q. The meridian distance PQ' is then computed from s and α, the computed distance and azimuth between P and Q. We put φm = = φp – φp Then the radius of curvature in the meridian = i.e. = Any triangulation network of about a few hundred km north-south extant can be used as long as the necessary astronomical observations have been made. The method is the classical geodetic way of determining the mean earth ellipsoid since the 17th century and many today's best known ellipsoids were computed in this way (Rainsford, 1955). If we have a predominantly east-west triangulation network, we can use the method of arcs of parallel in which we measure longitude at two points P and Q almost on the same arc of parallel. We have: = where, PQ' is the distance P and Q projected along the parallel through P and Δλ = λp –λq This method has not been used as much as meridian arcs because of the difficulties of measuring accurate longitude differences before the advent of radio time signals. Both methods are essentially finding the ellipsoid which makes deviation of the vertical as small as possible on average because the basic equation assumes the normal and the vertical to be the same. Determining Global best-fit Ellipsoids from Gravity Measurements The simplest way to use observed gravity to determine the mean ellipsoid is to use Clairaut's formula for the gravitational attraction of a rotating ellipsoid. This formula gives the gravity γφ, at a latitude φ in terms of the gravity at the equator, γε γφ = γε(1 + B2sin2φ) In the above equation, B2 is a function of the rate of rotation and flattening. This method works in such a way that, If there is a large number of gravity observations on the earth's surface and reduce them to the geoid level, there will be a large number of pairs of values of γφ and φ which can be used in Clairaut's formula. B2 can then be used with the known rate of rotation of the earth to give the flattening. A purely gravitational method such as this will give the shape of the earth but not its size. This method is not used today as it is very crude. We are more likely to compute gravity anomalies at all points and use a more complex geo-potential model. The latest solutions use the spherical harmonic model and a large number of harmonic coefficients are solved including the flattening. Because gravity data is still so sparse, especially over the oceans, gravity actually gives a better indication of local variations in the geoid rather the earth's overall shape. But it is possible to continue gravity and meridian arc measurements and this was done in the determination of some of the ellipsoids in later centuries There are also some other modern methods of determining Global Best-fit Ellipsoids and this may include the determination of the Cartesian coordinates of a large number of stations on the earth’s surface by reducing them to the geoid and fitting an ellipsoid in a geometrical way. The other method also includes the measuring of perturbations of orbits and computing spherical harmonic coefficients. Lastly by using satellite altimetry to give the sea surfaces directly and thus the geoid over the oceans. Surface height is the difference between the satellite’s positions on orbit with respect to an