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

▶️ Watch on 3Speak

---

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: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials
• Infinite Sequences and Series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

---

Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

MES Links: https://mes.fm/links

MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes

Email me: [email protected]

Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

---

▶️ 3Speak