SME
Mineralogy · Problem type
Grain size on the φ scale
Use this for “Convert a sand grain 0.2 mm across to the φ scale and name its Wentworth class.”
Chart
φ(d)
=
−
ln(d)
ln(2)
A log x-axis: each decade gets the same room.
This is an example. Type your own values to start a new problem.
φ
=
−log₂(
d (mm)
)
class
Wentworth class
worked out (not typed)
Formulas
φ
=
−log₂(
d
)
2.3219 = −log₂(0.2)
class
=
the
Wentworth
class
whose
φ
range
holds
φ
2 < 2.3219 ≤ 3, so fine sand
Assumptions
•
φ = −log₂ d with d in millimeters: each step of 1 φ halves the grain, so finer grains get bigger φ.
•
Wentworth classes: gravel below −1 φ (over 2 mm), sand from −1 to 4 φ (2 to 1/16 mm), silt to 8 φ, clay beyond.
•
A grain right on a class line goes to the coarser class, as it stays on that sieve.
Step-by-step
WE KNOW
d = 0.2 mm
FIND
phi size (φ), Wentworth class (class)
Step 1 · Find phi size (φ)
Use φ = −log₂(d)
Count how many times 1 mm halves to reach the grain: that power of 2, with its sign turned.
φ
=
−log₂(0.2)
φ
=
2.3219
Step 2 · Find Wentworth class (class)
Use class = the Wentworth class whose φ range holds φ
From −1 to 4 φ the grain is sand, split into five classes 1 φ wide.
2 < 2.3219 ≤ 3: fine sand
class
=
the
Wentworth
class
whose
φ
range
holds
2.3219
class = fine sand
Check
Put the numbers back in. Both sides should match.
2.3219 = −log₂(0.2) ✓
2 < 2.3219 ≤ 3, so fine sand ✓
Topic check
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