Standard Functions; Trigonometric Functions; Statistical Functions; Logarithmic Functions - ABB SM2000 User Manual Supplement

Videographic Recorders
SM1000 and SM2000

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.
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
The equation is entered as Sin(1.571)
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.
Instantaneous
Avg()Average
Samples
No. Value Value Samples
1 40 –
2 80 –
3 70 –
4 50 –
5 60
6 30
7 40 60 1 to 5
8 100
9 120
10 110 80 6 to 10
Table 2.5 Sample Statistical Calculations
Average Rolling Average
Rolling Rolling
Average Average
1 2 3 4
Fig. 2.5 Samples Included
IM/SM2000ADV Issue 7
≈
=1.571Radians
RAv()Rolling
SD()
Average
Standard
Deviation
Value Samples
– – –
– – –
– – –
– – –
60 1 to 5 20.8
58 2 to 6 18.3
50 3 to 7 12.9
56 4 to 8 17.1
70 5 to 9 12.9
80 6 to 10 31.0
Average
Rolling Average
Standard
Devation
5 6 7 8 9

2.9.3 Logarithmic Functions

The logarithmic functions Log(x), Ln(x) and e
scale process inputs.
– the output of vacuum gauges follow a logarithmic
Example
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:
VPSw AP
×
------------------------------------------------------------ -
RH = 100
Where:
VPSw = Saturation Vapour Pressure at Wet Bulb
VPSd = Saturation Vapour Pressure at Dry Bulb
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
–
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.
10
2 Math Configuration
× ( Td Tw )
– –
VPSd
Temperature
Temperature
x
can be used to
11