Units

LabRAD Units

Overview

One of the powerful convenience features provided by the LabRAD Manager is on-the-fly unit conversion. When registering an available setting, a server module can specify accepted units for incoming requests. The Manager will then seemlessly convert all (complex) values sent to this setting to match the requested units, or return an error if the given units can't be converted to the requested ones.

For a formal description, refer to the EBNF LabRAD Grammar.

Operation

The LabRAD Manager parses composite unit strings into their base components and respective fractional exponents. For example m/s^2 will get parsed into m with exponent 1 and s with exponent -2. This is done for the source unit string and the target unit string.

To find the conversion factor the Manager divides the source units by the target units. For this, the exponents of all base components in the target units are subtracted from the exponents in the source units. All base components that end up with exponent 0 are then dropped. Now, for the first time, the Manager tries to identify the base components and converts them to SI units. Therefore, you can specify units that the Manager does not know as long as they drop out during the division process above. The SI conversion factors then get raised to their corresponding exponents and multiplied together to yield the final conversion factor. The resulting quantity has to be unit-less for the conversion to succeed.

Example: TShirts/min to TShirts/hr

Parsing

Unit	Source Exponent	Target Exponent
TShirts	1	1
min	-1	0
hr	0	-1

Division by subtraction of exponents

Unit	Src - Tgt	New Exponent	Action
TShirts	1 - 1	0	drop
min	(-1) - 0	-1	keep
hr	0 - (-1)	1	keep

Conversion to SI

		Exponent of
Unit	Factor	m	kg	s	A	K	mol	cd	rad	sr
min	60	0	0	1	0	0	0	0	0	0
hr	3600	0	0	1	0	0	0	0	0	0

Exponentiation and multiplication

			New Exponent of
Unit	Exponent	New Factor	m	kg	s	A	K	mol	cd	rad	sr
min	-1	1/60	0	0	-1	0	0	0	0	0	0
hr	1	3600	0	0	1	0	0	0	0	0	0
Product		60
Sum			0	0	0	0	0	0	0	0	0

Since all exponents of the SI base units came out to be 0, the conversion succeeded and the conversion factor is 60, for example 5TShirts/min convert to 5 * 60 = 300TShirts/hr.

Notice that the conversion succeeded even though TShirts is not a unit that the Manager recognizes!

Linear units

The Manager knows the following units:

		Exponent of
Unit	Factor	m	kg	s	A	K	mol	cd	rad	sr	Prefixable
m	1	1	0	0	0	0	0	0	0	0	yes
g	0.001	0	1	0	0	0	0	0	0	0	yes
s	1	0	0	1	0	0	0	0	0	0	yes
A	1	0	0	0	1	0	0	0	0	0	yes
K	1	0	0	0	0	1	0	0	0	0	yes
mol	1	0	0	0	0	0	1	0	0	0	yes
cd	1	0	0	0	0	0	0	1	0	0	yes
rad	1	0	0	0	0	0	0	0	1	0	yes
sr	1	0	0	0	0	0	0	0	0	1	yes
Bq	1	0	0	-1	0	0	0	0	0	0	yes
Ci	3.7e10	0	0	-1	0	0	0	0	0	0	yes
acre	4046.9	2	0	0	0	0	0	0	0	0	no
a	100	2	0	0	0	0	0	0	0	0	yes
F	1	-2	-1	4	2	0	0	0	0	0	yes
C	1	0	0	1	1	0	0	0	0	0	yes
S	1	-2	-1	3	2	0	0	0	0	0	yes
V	1	2	1	-3	-1	0	0	0	0	0	yes
Ohm	1	2	1	-3	-2	0	0	0	0	0	yes
Btu	1055.1	2	1	-2	0	0	0	0	0	0	no
cal	4.1868	2	1	-2	0	0	0	0	0	0	yes
eV	1.6022e-19	2	1	-2	0	0	0	0	0	0	yes
erg	1e-7	2	1	-2	0	0	0	0	0	0	yes
J	1	2	1	-2	0	0	0	0	0	0	yes
dyn	0.00001	1	1	-2	0	0	0	0	0	0	yes
N	1	1	1	-2	0	0	0	0	0	0	yes
ozf	0.27801	1	1	-2	0	0	0	0	0	0	no
lbf	4.4482	1	1	-2	0	0	0	0	0	0	no
Hz	1	0	0	-1	0	0	0	0	0	0	yes
ft	0.3048	1	0	0	0	0	0	0	0	0	no
in	0.0254	1	0	0	0	0	0	0	0	0	no
mi	1609.3	1	0	0	0	0	0	0	0	0	no
nit	1	-2	0	0	0	0	0	1	0	0	yes
nits	1	-2	0	0	0	0	0	1	0	0	yes
sb	10000	-2	0	0	0	0	0	1	0	0	yes
fc	10.764	-2	0	0	0	0	0	1	0	1	no
lx	1	-2	0	0	0	0	0	1	0	1	yes
phot	10000	-2	0	0	0	0	0	1	0	1	yes
lm	1	0	0	0	0	0	0	1	0	1	yes
Mx	1e-8	2	1	-2	-1	0	0	0	0	0	yes
Wb	1	2	1	-2	-1	0	0	0	0	0	yes
G	0.0001	0	1	-2	-1	0	0	0	0	0	yes
T	1	0	1	-2	-1	0	0	0	0	0	yes
H	1	2	1	-2	-2	0	0	0	0	0	yes
u	1.6605e-27	0	1	0	0	0	0	0	0	0	yes
lb	0.45359	0	1	0	0	0	0	0	0	0	no
slug	14.594	0	1	0	0	0	0	0	0	0	no
º	0.017453	0	0	0	0	0	0	0	1	0	no
deg	0.017453	0	0	0	0	0	0	0	1	0	no
'	0.00029089	0	0	0	0	0	0	0	1	0	no
"	4.8481e-6	0	0	0	0	0	0	0	1	0	no
hp	745.7	2	1	-3	0	0	0	0	0	0	no
W	1	2	1	-3	0	0	0	0	0	0	yes
atm	1.0133e5	-1	1	-2	0	0	0	0	0	0	no
bar	1e5	-1	1	-2	0	0	0	0	0	0	yes
Pa	1	-1	1	-2	0	0	0	0	0	0	yes
torr	133.32	-1	1	-2	0	0	0	0	0	0	yes
mmHg	133.32	-1	1	-2	0	0	0	0	0	0	no
ºC	1	0	0	0	0	1	0	0	0	0	no
degC	1	0	0	0	0	1	0	0	0	0	no
ºF	5/9	0	0	0	0	1	0	0	0	0	no
degF	5/9	0	0	0	0	1	0	0	0	0	no
d	86400	0	0	1	0	0	0	0	0	0	no
h	3600	0	0	1	0	0	0	0	0	0	no
min	60	0	0	1	0	0	0	0	0	0	no
y	3.1557e7	0	0	1	0	0	0	0	0	0	yes
gal	0.0037854	3	0	0	0	0	0	0	0	0	no
l	0.001	3	0	0	0	0	0	0	0	0	yes
pint	0.00047318	3	0	0	0	0	0	0	0	0	no
qt	0.00094635	3	0	0	0	0	0	0	0	0	no

Remark:
If degF, ºF, degC, or ºC are part of composite units, like in m/degF, they simply contribute to the scaling factor of the conversion. If they, after the initial division process, end up alone, like in degF to degC, the unit conversion will also include the correct offset.

Non-linear units

The Manager supports the following non-linear units: dBW, dBm. If these units don't drop out during the initial division process, the conversion only succeeds if these units are not part of a composite unit string.

For example you CAN convert 15dBm to W, but you can NOT convert 15dBm/s to W/s.

SI prefixes

The Manager supports SI unit prefixing like km, MPa, etc. The prefixes get included when the SI conversion factor is calculated. The following prefixes are supported for all prefixable (see above) units:

Prefix	Factor
Y	1e24
Z	1e21
E	1e18
P	1e15
T	1e12
G	1e9
M	1e6
k	1000
h	100
da	10
d	0.1
c	0.01
m	0.001
µ	1e-6
u	1e-6
n	1e-9
p	1e-12
f	1e-15
a	1e-18
z	1e-21
y	1e-24

Note

Please post a bug report on this project's bug tracker if you find an error in the unit tables above or the way the Manager converts them.

You can test-run the unit conversion using the LabRAD Explorer as described in the LabRAD Quick Start Tutorial.

 

~ Markus Ansmann, Jan 25th, 2008