An ideal linear meter dial maps the fraction of full-scale reading to the same fraction of angular sweep. Explore that pointer geometry and convert an entered percent-of-full-scale accuracy specification into absolute and relative error bands.
Linear Analog-Dial Worksheet
Enter a reading, full-scale value, dial sweep and data-sheet accuracy class. The worksheet maps the ideal pointer angle and translates full-scale accuracy into an absolute error band; it does not calibrate an instrument.
Equation Used
- The scale is linear from zero to full scale.
- Reading and full-scale value use the same arbitrary engineering unit.
- The entered class is a percent-of-full-scale specification for the exact instrument.
- Parallax, resolution, zero offset, hysteresis, calibration drift, waveform and loading effects are excluded.
Pointer position and instrument accuracy are separate quantities. The scale geometry sets the ideal angle, while the entered data-sheet accuracy class sets the displayed full-scale error band.
Pointer geometry and scale calibration
An analog indicating instrument turns a measured quantity into pointer motion over a graduated scale. For an ideal linear scale, the fraction of full-scale input equals the fraction of full-scale angular sweep.
That geometry does not establish accuracy. Accuracy, range, scale shape, orientation and operating conditions come from the exact instrument specification.
A scale-reading worksheet
Use the worksheet to compare ideal pointer position with the absolute error band implied by an entered percent-of-full-scale specification. It does not select, diagnose, repair or calibrate a meter.
Linear scale and full-scale error
When X is nonzero, 100 E_FS/X expresses that same absolute full-scale error band as a percentage of the reading. It becomes undefined at zero.
Entered-class example
For a reading of 60 on a 100-unit scale with a 250-degree sweep and an entered class of 2% FS, the ideal pointer angle is 150 degrees and the entered absolute error band is plus or minus 2 units. That band is 3.33% of the 60-unit reading.
Full-scale accuracy and low readings
Range, angular sweep and accuracy depend on the instrument specification. Calibration checks multiple readings and approach directions; pointer position alone cannot establish those properties.
A percent-of-full-scale specification does explain why relative uncertainty can grow at low readings, but it does not create universal green or red regions.
Analog-dial worksheet questions
Does the calculator know my meter's accuracy?
No. Accuracy class is an input from the exact data sheet.
Why is relative error undefined at zero?
The calculation divides the absolute error band by the indicated reading.
Does pointer angle prove calibration?
No. It is ideal linear geometry only.
Manufacturer and calibration references
- Fluke, ABCs of Digital Multimeters: analog specifications expressed as percentage of full scale and the resulting larger percentage-of-reading error low on the scale.
- Yokogawa, Switchboard Instruments: product-specific 250-degree scale and percent-of-full-scale accuracy examples.
- Yokogawa 2560A calibration application: multi-point analog-meter calibration and hysteresis checks from both approach directions.
- NIST, General Technique for Calibrating Indicating Instruments: calibration of direct-reading instruments.
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