Page 34 - Aeronautical Engineer Data Book

Fundamental dimensions and units 21
2.5 Foolproof conversions: using unity
brackets
When converting between units it is easy to
make mistakes by dividing by a conversion
factor instead of multiplying, or vice versa. The
best way to avoid this is by using the technique
of unity brackets.
A unity bracket is a term, consisting of a
numerator and denominator in different units,
which has a value of unity.
� 2.205 lb � � kg �
e.g. 3 or 3 are unity
kg
2.205 lb
brackets
as are
� 25.4 mm � � 25.4 mm � � 101 325 Pa �
in
atmosphere
33 or 33 or 33
in
Remember that, as the value of the term inside
the bracket is unity, it has no effect on any term
that it multiplies.

Example:
Convert the density of titanium 6 Al 4 V; # =
3
0.16 lb/in to kg/m 3
0.16 lb
Step 1: State the initial value: # = 3
in 3

Step 2: Apply the ‘weight’ unity bracket:
�
0.16 lb kg
# = 3 3 �
in 3 2.205 lb
Step 3: Then apply the ‘dimension’ unity
brackets (cubed):
�
0.16 lb kg 3 in 3
# = 3 3 � � �
33
in 3 2.205 lb 25.4 mm
� 1000 mm � 3
33
m