Exercise 6: Surveying: Elevation Correction due to Earth's Curvature using Taylor Polynomials

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In this video I derive the elevation correction required when surveying long distances across a highway due to Earth's curvature, and also derive a Taylor polynomial approximation for the correction. For an 100 km long highway, the Taylor polynomial is accurate to within an amazing 0.00808 mm!

Timestamps:

• Exercise 6: Surveying: 0:00
• Solution to (a): Deriving the correction due to Earth's curvature: 1:41
• Solution to (b): Taylor polynomial approximation for the correction: 6:07
  • Derivatives of secant for the Taylor series: 7:38
  • 4th degree Taylor polynomial for sec(x): 22:45
  • Plugging in our Taylor polynomial into the correction formula: 24:52
  • Correction approximation formula: 27:38
• Solution to (c): Comparing corrections for a 100 km long highway: 28:19
  • Approximation has an accuracy of 0.00808 mm: 31:10

Full video, notes, and playlists:

• Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0F76sIU8xm09oqBTq1mlry3
• HIVE notes: @mes/infinite-sequences-and-series-applications-of-taylor-polynomials
• Infinite Sequences and Series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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