Time error
As time error in are astrometry and geodesy the random and systematic errors of the timing designated. They play a special role in measurements for celestial bodies and for earth satellites , because they - for example, when determining astronomical longitude - are fully included in the result.
In sport, the term can also mean the punishment of rule violations.
Measurement of star passages
Visual measurement and error influences
When visually measuring a star passage in the field of view of a telescope, the random portion of the time error depends on several factors, in particular:
- Experience and balance of the observer
- Measuring method ( eye-ear method , type of stopwatch or chronograph )
- Number of measuring threads on the reticle or the thread network
- Direction and speed of the star orbit
- Air turbulence and brightness of the star
- Magnification of the telescope.
The older specialist literature (Albrecht, Niethammer) differentiates between the ingress error (pure time error on a measuring thread) and a target error (which depends on the magnification). More recent analyzes (e.g. Ramsayer, Gerstbach) also show a transit error that cannot be reduced to below a certain amount per star transit even by averaging many individual times.
On geodetic measuring telescopes with 30 to 50 times magnification and with a digital stopwatch, a moderately trained observer can achieve about ± 0.2 seconds at the single thread, which can be reduced to about 0.06 to 0.10 seconds by averaging several times at the thread network. With a lot of experience, half of these values can be achieved.
The magnification of the telescope does not directly influence the time measurement, only the ability to detect the target. Their influence on the angle measurement in the eye is referred to as target error . On the Ni2 astrolabe (30x) it is about ± 0.5 ″, but it only drops insignificantly with increasing magnification (e.g. Wild T4 65x).
The above time errors averaging ± 0.1s are largely of a random nature, but contain small systematic components of around 0.03 to 0.05s. They therefore remain effective even if many individual times are averaged on the thread network ( throughput errors ). If, on the other hand, the next star pass of a measurement program has a different direction or speed, some of these errors become random and are compensated for in the course of further measurements. A suitable choice of such pairs or combinations of stars increases the accuracy of the final result approximately with the square root of the number of stars, so that a time or length determination with, for example, 20 star passes can have accuracies of ± 0.01 to 0.02 seconds.
Recording micrometer and automation
Like any manual time measurement, visual passage measurements are subject to the influence of the observer's reaction time . It is called the personal equation in astrometry and has amounts from 0.05 s to 0.20 s, which fluctuate by only about 0.03 s over longer periods of time. It can therefore be reliably determined by reference measurements and the end result corrected accordingly.
In terms of measurement technology, the personal equation can be significantly reduced using a recording micrometer . The star passages are no longer measured by individual times on the thread net, but by tracking a moving thread that automatically triggers electrical contacts. Until around 1970, the contact times were recorded on tape chronographs , today mostly electronically.
If the thread is adjusted manually , the systematic time error drops, depending on the observer, to values between 0.01 and 0.15 s and its fluctuation to less than 0.02 seconds. If the tracking is carried out by a motor and the observer only makes the necessary speed corrections, the personal equation is always less than 0.10 seconds and can be precisely applied to the end result. In the last few decades, accuracies better than 0.01 s have been achieved in this way, for example for the measurement of fundamental stars , precise astronomical longitude determinations or the monitoring of the earth's rotation .
Optoelectronic measuring methods such as photomultipliers or CCD sensors bring further improvement and automation . Modern meridian circles achieve time accuracies in the millisecond range, and the astrometry satellite Hipparcos was able to improve 120,000 star locations to ± 0.001 ″, which corresponds to a time measurement of 0.1 milliseconds.
Time error in satellite measurements
Visual and photographic observation
In the early days of satellite geodesy and up to around 1975, visual and photographic direction measurements for geodetic satellite networks and orbit determinations were carried out. The visual observations were made on the thread network of special telescopes - analogous to star passages - and had a time accuracy of ± 0.1 s. The typical direction measurement of around ± 0.01 °, on the other hand, would have required ten times the accuracy and complex time systems.
The first satellite cameras were able to record the times of the recordings to a few milliseconds, but were mostly limited to bright balloon satellites . At a track speed of 7 km / second, a time error of 0.001 s means that the position is already 7 meters. That is why the method of “ flash satellites” was used as early as the 1960s , which at least guaranteed the simultaneity of the tracks photographed by different ground stations.
A major step was the development of satellite lasers ( Satellite Laser Ranging SLR), the time of flight measurement of which soon penetrated into the nanosecond range (distance of 30 cm). Today's SLR systems already reach a few millimeters.
Time errors in GPS and GNSS systems
Even in modern satellite navigation with GNSS , time errors no longer play an essential role. The GPS time system (atomic clocks in the satellites) has a long-term stability of approximately 10 -14 and allowed by means of time stamps (codes) distance measurements in the cm range. Larger time differences can only occur in the receiver clock at the beginning of a measurement, but this is synchronized as soon as the signals from at least 4 satellites are received. With newer sensors, the time drifts are 0.1 ms per minute of signal loss.
Despite the high stability of the GPS system time, the atomic clocks show the satellites an individual drift, which is compensated for by so-called clock parameters . The synchronization error of the individual atomic clock is modeled with an accuracy of 0.1 nanoseconds using 3 terms: constant time error (bias), linear time drift and quadratic term (aging), while the random relative frequency error is averaged out when determining positions on earth.
Time mistakes in sport
For a trained timekeeper, a measurement error of a hand stop can be assumed to be about 0.1 to 0.2 seconds. Although electronic timekeeping (with a light barrier or other trigger) has been used in competitions for several decades , an additional manual stop is often required.
When crossing the finish line quickly - such as a 100 to 400 meter run or a slalom - the timekeeper usually combines the triggering of the stopwatch with a downward hand movement, which allows a certain control of his own reaction time. As a result, and with appropriate experience, until around 1968 - when the timekeeping of the 100-meter run was switched to electronic hundredths of a second - the measurement errors of several timekeepers were actually less than 0.1 seconds. As an example, the series of world records at that time: 1960 10.0 (Armin Hary) - 1968 9.9 and 9.95 (Jim Hines) - 1983 9.93 (Calvin Smith).
In sport, the term time error is used in two other meanings:
- As an error in the timing, e.g. B. in the handball rules
- as penalty points in seconds, e.g. B. in gymnastics , dog and horse races.
Time error (psychophysics)
Psychophysics and psychology know a perception error that occurs due to the sequence effects of two stimuli. One speaks of a positive timing error when the first of the stimuli is perceived more intensely and of a negative timing error when the second stimulus predominates. The difference thresholds change depending on the sequence of the stimuli.
Astrometrics literature
- Carl Theodor Albrecht : Formulas and auxiliary tables for geographic location determinations . 4th edition, 308 pages, Leipzig 1908.
- Walter Ehrnsperger: Models for the adjustment of satellite triangulations with special consideration of the time error . German Geodetic Commission Series C, Issue 218, Munich 1976.
- Theodor Niethammer : The exact methods of astronomical-geodetic location determination . 181 p., Basel 1947.
- W. Uhink: Contact and timing errors in passage observations with the impersonal micrometer . P. 321 ff., Journal of Surveying 1949.
- Karl Ramsayer : Geodetic Astronomy, Volume IIa of the Handbook of Surveying. 900 p., JBMetzler-Verlag, Stuttgart 1969.
- Karl Ramsayer: Automatic star tracking for astronomical theodolite . DGK series B, booklet 81, Munich 1962 (or K. Ruopp, series C / 100, 1966).
- Gottfried Gerstbach : Analysis of personal errors in passage observations of stars . Scientific med. Volume 7, pp. 51-102, TU Wien 1975.
- Gottfried Gerstbach: The external accuracy of astronomical location determinations with the Ni2 astrolabe and the personal equation . General Surveying news volume 84, issue 11/12, Karlsruhe 1977.
- Albert Schödlbauer : Geodetic Astronomy - Basics and Concepts . De Gruyter-Verlag Berlin / New York 2000.