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

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:

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[Imsparky]

When I completed my project at Testengeer Engineering, I worked with their survey team as temporary work between contracts. It was more Engineering than I perceived before the experience.

[SpellsOfTruth]

Have you asked a real life surveyor if they correct for curvature?

[jeffstewart]

Is this the same formula you use for tunnels

[pennyontrack]

How come the laser test people do make it look like there is no curvature ?