SRV-32

Geoid undulation

N = h − H. Ellipsoidal height minus orthometric (levelled) height.

Reading speed

Geodesyh = H + N

Governing equation

N=h-H

$h \in \left[-100, 4000\right]$

where

h: Ellipsoidal height (m)
H: Orthometric height (m)
N: Undulation (m)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

N=h-H

$h \in \left[-100, 4000\right]$

$h = -100$ $N = -118.7$

Along the curve

②

Domain of the variable — blue

h_{\min} = -100,\quad h_{\max} = 4000

$h \in \left[-100, 4000\right]$

$h = -100$ $h = -100$

Along the curve

③

Response curve — green

N=h-H

$h \in \left[-100, 4000\right]$

$h = -100$ $N = -118.7$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}N}{\mathrm{d}h}

$h \in \left[-100, 4000\right]$

$h = -74.21$ $N^{\prime} = 1$

Along the curve

Lecture brief

Historical brief

From chain and theodolite through Bowditch’s compass-rule (1802) to GPS PDOP, surveying is the propagation of small errors across a network. These sheets close traverses, reduce stadia and state map scale. This sheet (SRV-32 — Geoid undulation) is the form associated with h = H + N. Working symbols: $h$ , $H$ $\rightarrow$ $N$ . The geoid is the equipotential that best fits mean sea level. GPS gives h; levelling gives H; a geoid model supplies N.

Purpose

Purpose: compute

N

from

h

H

in Surveying via

N=h-H

N = h − H. Ellipsoidal height minus orthometric (levelled) height. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

h = 52.400\,\mathrm{m}

H = 18.700\,\mathrm{m}

, the governing relation

N=h-H

yields

N = 33.700\,\mathrm{m}

. An ellipsoid, a geoid, a separation N. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Ellipsoidal height h52.4 mOrthometric height H18.7 m

Outputs

Undulation N33.700 m

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

An ellipsoid, a geoid, a separation N.

The geoid is the equipotential that best fits mean sea level. GPS gives h; levelling gives H; a geoid model supplies N.

Reading speed

Watch on YouTube