Page 14 - Petrology of Sedimentary Rocks

where Vp is the actual volume of the particle (measured by immersion in water) and
Vcsis the volume of the circumscribing sphere (the smallest sphere that will just enclose
the particle); actually the diameter of this sphere is considered as equal to the longest
dimension of the particle. A sphere has a sphericity of I .OO; most pebbles or sand
grains have a sphericity of about 0.6-0.7 when measured by this system. One can get an
approximation of this measure by the formula,

where L, I and S represent the long, intermediate and short dimensions respectively
(Krumbein).

The above formula, although in common use today, does not indicate how the
particle behaves upon settling in a fluid medium and is thus rather unsatisfactory.
Actually, a rod settles faster than a disk of the same volume, but Waddell’s formula
would have us believe the opposite. A sphericity value which shows better the behavior
of a particle during transport is the Maximum Projection Sphericity (Sneed and Folk, J.
Geol. 19581, given by the formula
3 s2 .
LI
Jr-

Particles tend to settle with the maximum projection area (the plane of the L and I
axes) perpendicular to the direction of motion and hence resisting the movement of the
particle. This formula compares the maximum projection area of a given particle with
the maximum projection area of a sphere of the same volume; thus if a pebble has a
sphericity of 0.6 it means that a sphere of the same volume would have a maximum
projection area only 0.6 as large as that of the pebble. Consequently the pebble would
settle about 0.6 as fast as the sphere because of the increased surface area resisting
downward motion. The derivation follows: assuming the particle to be a triaxial
ellipsoid, the maximum projection area of the particle is IT/~ (LI). The volume of the
particle is IT/~ (LIS). Hence the volume of the equivalent sphere will also be
n/6 (LIS). The general formula for the volume of a sphere is IT/~ d3. Therefore, in
11s
this example, d3 = LIS and the diameter of the equivalent sphere, d, will equal
v- .
3

The maximum projection area of this sphere will equal
n 3 LIS 2

4 P-> *

The maximum projection sphericity then equals

8