Videographic Recorders
SM1000 and SM2000
2 Math Configuration
IM/SM2000ADV
Issue 7
11
2.9 Standard Functions
The following examples, using preset functions available on the
Math Pad, are included for easier reference.
2.9.1 Trigonometric Functions
Three trigonometric functions, Sin(x), Cos(x) and Tan(x) return
the Sine, Cosine and tangent of the variable x.
2.9.2 Statistical Functions – Table 2.5 and Fig. 2.5
Statistical functions can be used to calculate the average, rolling
average and standard deviation of an analog variable.
2.9.3 Logarithmic Functions
The logarithmic functions Log(x), Ln(x) and e
x
can be used to
scale process inputs.
Example
– the output of vacuum gauges follow a logarithmic
curve and this must be linearized, therefore the antilog of the
input must be derived:
Linear Vacuum = k.10(Vacuum Gauge Output)
2.9.4 Relative Humidity – Fig. 2.6
Relative humidity is calculated using the following formula:
Where:
A relative humidity calculation requires two inputs, one from a
wet bulb sensor and one from a dry bulb sensor. Both of these
inputs are incorporated into the equation as analog.
RH tables are based on the use of an aspirated psychrometer
having an air velocity of at least 11.5 feet per second or 3.5
meters per second across the bulb sensors.
Inputs used for wet and dry bulb measurement must be in the
ranges 0 to 100°C or 32 to 212°F. The result must be set to 0 to
100.0% RH.
Note.
The variable x must be specified in Radians, where
1° =
π
/180 Radians.
For example, to find the Sine of 90°, first convert degrees to
radians:
90° = (90 x
π
) / 180 =
π
/2
≈
=1.571Radians
The equation is entered as Sin(1.571)
Instantaneous
Samples
Avg()Average
RAv()Rolling
Average
SD()
Standard
Deviation
No.
Value
Value Samples
Value Samples
1
40
–
–
–
–
–
2
80
–
–
–
–
–
3
70
–
–
–
–
–
4
50
–
–
–
–
–
5
60
60
1 to 5
60
1 to 5
20.8
6
30
58
2 to 6
18.3
7
40
50
3 to 7
12.9
8
100
56
4 to 8
17.1
9
120
70
5 to 9
12.9
10
110
80
6 to 10
80
6 to 10
31.0
Table 2.5 Sample Statistical Calculations
Fig. 2.5 Samples Included
Sample Number
°C
140
120
100
80
60
40
20
Average
and
Rolling Average
Samples 1 to 5
Rolling
Average
Samples
2 to 6
Rolling
Average
Samples
3 to 7
Average
and
Rolling Average
Samples 6 to 10
Standard
Devation
Samples
6 to 10
1
2
3
4
5
6
7
8
9
10
VPSw = Saturation Vapour Pressure at Wet Bulb
Temperature
VPSd = Saturation Vapour Pressure at Dry Bulb
Temperature
Td = Dry Bulb Temperature
Tc = Wet Bulb Temperature
P = Total Atmospheric Pressure (1000 mbar)
A = Psychometric Constant (6.66 x 10–4)
RH = % of Relative Humidity
RH
100
VPSw
AP
Td
Tw
)
–
(
×
–
VPSd
-------------------------------------------------------------
×
=
