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

mes (67)in DTube • 2 months ago

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

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