How does the shape of the daylight curve change with latitude?

AA SLAI SLAA HLAI HL Accessible Also in: Modelling, Geometry & Voronoi

Research question

When daylight hours through the year are modelled with sinusoids for cities at different latitudes, how does the amplitude depend on latitude, and is the sinusoidal model equally good everywhere?

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

Why it makes a good exploration

Modelling daylight with a sine curve is common; comparing many latitudes and modelling the amplitude itself as a function of latitude makes it original.

The mathematics you'll need

Sinusoidal models: amplitude, period, phase, vertical shift
Fitting with technology
Modelling amplitude against latitude
Residuals near the poles

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

Day lengths on the 1st and 15th of each month for 6–8 cities from timeanddate.com.

timeanddate.com sun calculator — Sunrise, sunset and day length for any city and date.

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 why day length varies.
Fit sinusoids for each city.
Plot amplitude against latitude and model it.
Test where the sinusoid fails (high latitudes).
Reflect on the astronomy behind the shape.

Pitfalls that cost marks

Only one city (too common).
Mixing time zones and daylight saving time.
Wrong period (use 365.25 days).

Showing personal engagement

Include your home city and relatives' cities.
Predict the amplitude for an unseen city.
Explain polar day and night with your model.

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

Taking it further

Compare your amplitude–latitude model with the astronomical formula using the sunrise equation.

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).