DIMENSION

Real values have dimensionality such as length/time for velocity. Dimensionality is to be distinguished from the units such as km/h or ft/s. ASCEND takes care of mapping between units and dimensions. A value without units (this includes integer values) is taken to be dimensionless. Dimensionality is built up from the following base dimensions:

Symbol	definition	typical units	symbol
L	length	metre	m
M	mass	kilogram	kg
T	time	second	s
E	electric current	ampere	A
Q	quantity	mole	mol
TMP	temperature	kelvin	K
LUM	luminous intensity	candela	cd
P	plane angle	radian	rad
S	solid angle	steradian	srad
C	currency	US dollars	USD

The ATOM and CONSTANT definitions in the library illustrate the use of dimensionality. Dimensions may be any combination of these symbols along with rounded parentheses, (), and the operators *, ^ and /. Examples include M/T or M*L^2/T^2/TMP (this latter means (M*(L^2)/(T^2))/TMP). The second operand for the to-the-power-of operator, ^, must be an integer value (e.g., -2 or 3) because fractional powers of dimensional numbers are physically undefined in ASCEND. If the dimensionality for a real value is undefined, then ASCEND gives it a wildcard dimensionality. If ASCEND can later deduce its dimensionality from its use in a model definition it will do so. For example consider the real variable a, suppose a has wildcard dimensionality, b has dimensionality of L/T. Then the statement

a + b = 3 {ft/s};

requires that a have the same dimensionality as the other two terms, namely, L/T. ASCEND will assign this dimensionality to a. The user will be warned of dimensionally inconsistent equations.

See also

• Units
• ATOM
• CONSTANT