Can you predict a tree's height from its trunk?

AI SLAI HLAA SL Solid Also in: Geometry & Voronoi, Environment, Statistics

Research question

Is the height of trees in my local park related to trunk diameter by a power law, and does the exponent agree with the value predicted by the theory of elastic similarity (about ⅔)?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Foresters estimate height from diameter all the time, and biologists argue about the exponent. You measure heights with trigonometry and a clinometer, then test a published scientific claim with your own data.

The mathematics you'll need

Trigonometry (right-angled triangles) to measure heights
Power models and log-log regression
Correlation and residuals
Measurement uncertainty

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Measure 30+ trees of one species: circumference at 1.3 m and height using a clinometer app and pacing the distance.

phyphox (RWTH Aachen) — Free app that turns your phone's accelerometer, microphone, barometer and gyroscope into data loggers with CSV export.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain the clinometer method and its error.
Collect and tabulate data for one species.
Fit a power model via logs; compare the exponent with ⅔.
Examine outliers (damaged or crowded trees).
Reflect on species, age and environment.

Pitfalls that cost marks

Mixing species, which have different shapes.
Not adding eye height to the trigonometric height.
Measuring height from too close, where small angle errors explode.

Showing personal engagement

Choose trees you know — your school grounds or a local park.
Calculate how your height error depends on your distance from the tree and choose the best distance.
Compare two species.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Use your model to estimate the height of a tree you cannot measure and assess the prediction interval.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).