1 / 14

Observed Angles and Spherical Excess

Observed Angles and Spherical Excess. Learning Objectives. After completing this lecture you will be able to: Illustrate concept of spherical excess with the aid of a suitable diagram Apply spherical excess to geodetic figures. Lecture Outline. Introduction Normal Sections

kasen
Download Presentation

Observed Angles and Spherical Excess

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Observed Angles and Spherical Excess

  2. Learning Objectives After completing this lecture you will be able to: • Illustrate concept of spherical excess with the aid of a suitable diagram • Apply spherical excess to geodetic figures

  3. Lecture Outline • Introduction • Normal Sections • Curve of Alignment • Observed Angles • Spherical Excess • Conclusion

  4. Introduction • Want to read an angle and calculate forward azimuth from known back azimuth • But what line do we measure angles to? • If you said straight line between points, what is this? • Remember normal sections

  5. M Plane Sections (Normal Sections) • Instrument set at B Rotation axis is normal BN • Vertical plane containing A = ABN. • Instrument set at A Rotation axis is normal AM • Vertical plane containing B = BAM • Line A ® B ¹ Line B ® A A B N

  6. A B Curve of Alignment Curve of Alignment • Locus of all points where Bearing to A = bearing to B + 180° is called Curve of Alignment. • Marked on ground - A surveyor sets up between A and B such that A and B are in same vertical plane • Horizontal angles are angles between curves of alignment • But can assume normal sections because start off same • Spheroidal triangles are figures formed by 3 curves of alignment joining the 3 points Normal Section B to A Normal Section A to B

  7. Observed Angles and Azimuth

  8. Observed Angles Note that a geodesic is not a line of sight and therefore we can’t measure angles to it!

  9. Spherical Triangle Spherical Triangle Spherical Excess

  10. Spherical Excess

  11. Practical Implication • All geodetic figures will have spherical excess • Apportion evenly throughout angles.

  12. Conclusion You can now: • Illustrate what spherical excess with the aid of a suitable diagram • Apply spherical excess to geodetic figures

  13. Self Study • Read relevant module in study materials • Follow numerical example

  14. Review Questions

More Related