Pie diagrams and wind roses

Detail

What a pie diagram is

• Pie diagram (also called a divided circle diagram): a circle that stands for a whole total. The circle is cut into slices called sectors. Each sector's size matches the share of one part of the total.
• It answers one question: what share of the whole does each part make up?
• The whole circle is always 360°, and it always stands for 100% of the total.
• NCERT lists the pie diagram among the diagrams used to show data. It is also defined in the glossary of the next chapter.

Calculating the angles

• Formula 1: angle of a sector = (value of the part ÷ total) × 360°
• Formula 2 (when data are already in per cent): angle = percentage × 3.6

• Why 3.6? 100% = 360°, so 1% = 3.6°.

• Rounding rule: round each angle to a whole degree. Then check that all the angles add up to exactly 360°. If they do not, adjust the largest sector by 1°, because a 1° change there is hardest to see.

NCERT worked example: India's exports by region, 2010-11

• Data: Economic Survey 2011-12 (NCERT Tables 3.7a–b, Fig. 3.8).

Region	Share of exports, 2010-11 (%)	% × 3.6	Angle used
Asia and ASEAN	56.2	202.32	203°
Europe	20.2	72.72	73°
America	14.8	53.28	53°
Africa	6.5	23.40	23°
Others	2.3	8.28	8°
Total	100.0	360.00	360°

• Plain rounding gives Asia and ASEAN 202°, and the total comes to only 359°. So the largest sector is rounded up to 203° to close the circle at 360°.
• ASEAN (Association of Southeast Asian Nations): a group of 10 countries of South-East Asia.
• What the diagram shows: in 2010-11, more than half of India's exports (56.2%) went to Asia and ASEAN. Europe came second (20.2%), then America (14.8%), Africa (6.5%) and others (2.3%).

Construction steps

1. Choose a radius of 3–5 cm. The circle should be neither too big nor too small for the page.
2. Draw the circle and one radius line. A common choice is from the centre straight up to 12 o'clock. This is the starting line.

3. Measure the angles clockwise, starting with the smallest. Use a protractor. - For the export data the order is Others 8° → Africa 23° → America 53° → Europe 73° → Asia and ASEAN 203°. - The last sector is simply the space left over, so it checks your work.

4. Shade or colour each sector differently.

5. Add a title, a subtitle and a legend. The legend (also called the key) is a box that explains what each shade or colour means. - The steps in NCERT's text say "vehicles", but the data in the example are exports. This is a slip in the book.

Precautions (why start with the smallest angle)

• Plotting the biggest angle first causes errors to build up:
• every protractor reading has a small error, perhaps half a degree;
• after a big sector is drawn, these small errors pile up across the few degrees left;

• so tiny sectors such as 8° get squeezed, become hard to plot, and may look wrong.

• Starting small means the tiny sectors are drawn accurately while there is plenty of room. Any leftover error falls in the large last sector, where it cannot be seen.

• Do not make the circle too small, or sectors under about 10° cannot be read.

Beyond NCERT: comparing totals, and when pies fail

• Comparing two or more totals (for example, exports in two different years) needs circles of different size.
• The area of a circle should match the total. Area = πr², so the radius should be proportional to the square root of the total.
• Example: if total B is 4 times total A, B's radius is √4 = 2 times A's radius, not 4 times.

• If you scale the radius directly with the total, a total 4 times larger looks 16 times larger. That misleads the reader.

• Pies fail when:

• there are many small categories: thin slivers cannot be told apart or labelled. Group them under "Others" or use a bar diagram instead;
• the parts do not add up to one meaningful whole, or some values are negative;
• you need to compare exact sizes: the eye judges angles and areas less well than bar lengths.

Wind rose

• Wind rose: a diagram that sums up the wind at one place over a set period. It shows how often the wind blows from each direction and, often, how strongly.
• It is drawn as bars radiating from a centre (lines going out from the middle like spokes). Each bar points toward the direction the wind comes from.

• A wind is always named after the direction it blows from. A "south-west wind" blows from the south-west.

• How to read it:

• Bar length = how often (frequency, or % of time) the wind blew from that direction. A longer bar means that direction is more common [2][3].
• Wind strength is shown by the thickness of the bar, by "feathers" attached to it [2], or by colour bands along each spoke. Each colour stands for a range of wind speed [3].
• The calm percentage (time with no or almost no wind) is written as a number in the centre circle [2].

• The classic form has 8 lines, one for each main compass point [2]. Detailed versions use 16 directions.

• History: the earliest known wind roses appeared on navigation charts of the 13th century, used by Italian and Spanish sailors. The 8 points carried the initials of the main winds, and the north point was often marked with a fleur-de-lis (a lily-shaped symbol) [2]. This is where the compass rose on today's maps comes from.

• Data source today: wind roses are prepared for airport weather stations around the world from routine wind records [3]. In India, IMD (India Meteorological Department) surface observatories record wind direction and speed.
• NCERT names the wind rose under "Construction of Diagrams". The details above go beyond the chapter.

Star diagram

• Star diagram: a radial chart, like a wind rose, for data that have a direction or that repeat in a cycle.
• For monthly values (for example, rainfall or temperature) there are 12 radii, each 30° apart (360 ÷ 12). Each month's value is plotted along its radius, and the points are joined.
• The shape shows the season pattern at a glance. A station with monsoon rain gives a figure that bulges toward June–September.

Uses of wind roses

Use	Cause → what is done → result
Airport runway alignment	Aircraft take off and land safest into the wind (a headwind), and strong side winds (crosswinds) are risky → the runway is laid along the prevailing wind (the wind that blows most often) shown by the longest bars → safer take-offs and landings, used on more days of the year
Siting polluting industries	Smoke drifts with the prevailing wind → place factories and thermal power plants downwind of towns, meaning the wind carries smoke away from the town → less air pollution over homes
Reach of the monsoon	Wind roses for June–September at Indian stations show long south-westerly bars (the south-west monsoon: moist winds from the Indian Ocean); winter roses show north-easterly bars → this maps how far and how steadily the monsoon current reaches each place
Wind energy	The longest and strongest bars show the best direction to face turbines and where to place them, so they block each other less

Prelims Hooks

• Angle of a sector = percentage × 3.6, because 1% = 3.6°. A 25% share = 90°.
• NCERT, India's exports by region in 2010-11: Asia and ASEAN 203° (56.2%) > Europe 73° (20.2%) > America 53° (14.8%) > Africa 23° (6.5%) > Others 8° (2.3%).
• NCERT rule: measure the angles clockwise, starting with the smallest. "Start with the largest" is the trap option.
• Suggested pie radius in NCERT: 3–5 cm.
• To compare two totals with pies, the radius ∝ √total, not the total. A 4× total needs a 2× radius.
• Wind rose: bar length = frequency of wind from that direction. Calm % is written in the centre [2].
• Wind rose bars point toward the direction the wind comes from, not where it goes.
• The earliest wind roses were on 13th-century Italian and Spanish navigation charts [2].
• Star diagram for monthly data = 12 radii at 30° each.
• Runways are aligned with the prevailing wind. Polluting industries are placed downwind of towns.

Mains Points

• Choosing the right diagram: a pie diagram suits data that show parts of one whole, such as India's export destinations or land-use shares. Use bar diagrams when there are many small categories or when you compare over time. When comparing totals with pies, scale the radius by √total so the picture does not mislead.
• Wind roses in planning (GS-III): EIA (Environmental Impact Assessment, the study of a project's likely effects before it is approved) uses wind roses to place polluting units downwind of towns. This matters in industrial belts and cities with bad air, such as Delhi NCR and the coal-power cluster around Singrauli.
• Infrastructure: runway direction at new airports, and turbine layout at wind farms in Tamil Nadu and Gujarat, both depend on long-term station wind roses. Poor alignment causes crosswind risks and lost wind power.
• Climate geography (GS-I): seasonal wind roses show the monsoon's wind reversal, south-westerly in summer and north-easterly in winter. They are a simple map tool for explaining how far the monsoon reaches across India and how steady it is.