Ordnance Survey
The height of every point on a British map is measured relative to Ordnance Datum Newlyn, a single reference point on the Cornish coast established in the 19th century. Investigate the trigonometry surveyors used to carry that height across the country.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Before satellite positioning, surveyors measured height and distance across an entire country using a network of triangles: from two known points, the angles to a third point (a hilltop, a church spire) are measured, and the sine and cosine rules give its position and height. Ordnance Survey's original triangulation network carried height data from Ordnance Datum Newlyn, on the Cornish coast, across all of Great Britain this way, one triangle at a time. This exploration works through the trigonometry of a real triangulation problem, then considers how small measurement errors in one triangle compound as they are carried through a long chain of them.
Guiding Questions
- How can you find the height of a hill using only angles measured from two points?
- Use the sine and cosine rules to solve a real triangulation problem with your own measurements.
- How did surveyors carry height across the country from one datum point? Model a chain of triangles.
- How do small angle errors grow along the chain? Quantify it with your model.