Is this true?

> "If I have a 3 second theodolite and I want to measure to 1 second I need to take 9 measurements...
I'm not sure about the exact number of reps quoted but I do know this. The "3 second" specification refers to pointings, not angles, and an angle measurement is composed of a minimum of 2 pointings. So the error in a minimally observed angle is twice the specification precision.

As you observe a pointing multiple times the mean of those observation approaches the theoretical true value (assuming no systematic error, which is a leap of faith). So the more times you observe an angle the better the precision of the mean of those many observations becomes.

My understanding is that if you observe an angle 2 complete FR sets (total of 4 observations on the BS and 4 on the FS) You would achieve a precision in the angle equal to the the instrument pointing specification.

I ordinary practice I'd expect enough stuff to happen while observing 25 sets to upset my plans of achieving precisions my instrument isn't designed for. Carrying mathematical concepts to extremes works on paper but rarely survives collision with the real world.

All other things considered. Such as optics quality. And, magnification. And, distortion, due to adding the EDM co axially. I think a genuine angle accurate to one second, does not happen very often. It is about 1/2 a hundredth, in 1000 feet. Or 0.05' in 10,000 feet. The heat waves, and other factors, such as refraction, and shadows, just makes such accuracy not very common.
N

Is this an instrument with a 3 second least count or 3 second DIN? Either way the number of sets quoted is an abuse of sound mathematical principles.

:good:
Yes, the spec is a probabilistic value based on pointings, so it takes 2 sets of direct and reverse face readings to average out an angle to the spec number. That assumes you use different parts of the internal circle for each set so that you aren't re-measuring the same errors. And of course, that all the systematic errors such as centering are negligible.

You have the mathematical rule correct in that accuracy statistically improves as the square root of the number of readings, until that remaining error becomes similar to the other effects.

Assuming a 3" repeating theodolite, i.e. with both upper & lower motions, I'd

1) set 0° on plate, clamp upper motion

2) Release lower motion, turn to BS, clamp lower, point BS w/ lower motion

3) release upper motion, turn to FS, clamp upper, point FS, (record 1st angle as a check on final result)

4) invert telescope, release lower, turn to BS, clamp lower, point BS w/ lower motion, clamp lower motion

5) release upper motion, turn to FS, clamp upper, point FS

At the end of 5) the reading on the plate should be 2x the subject angle. Repeating 2) - 5) and continuing to accumulate angles in this fashion, up to about 6-8 D& R, will further increase the precision, assuming an instrument in adjustment, carefully set up and no blunders.

See "Surveying: Theory & Practice", Davis, et al., 5th edition, p.293

SS

Nah, getting to one second in the real world is more a matter of faith and luck. And I speak from experience, turning many angles with one second and 3 and 5 second guns.

My T2 was far and away "better" turning angles than other guns I've used. But real one second accuracy.............

Achieving a one second 'true' angle' isn't a stretch, it's just time consuming. Number one error: never trust a tribrach.

Easy to remember: 2mm @ 200M is 2". That's .007ft at 660ft. It's not easy to have centering errors less than 0.005ft 95% of the time. So don't blame the instrument. Working under 500ft 1" is below noise. However, and it is do-able. Plumb your targets and gun using two transits 8ft away. And don't bother looking at a range pole. One second targets are a prize piece of kit too. Turn the angle 10-20 times. Consider an RMS of 1". Which is why you should have 20 angles to choose from. Don't average all of them, you need to reject a few. That's why all good calculators have a stats function. Slow down, speed kills. a one second angle is a statistics task as much as an observing task and dependent on centering error more than anything. If your observing targets a mile away, one second is not as hard, but 1" is 0.03'. Take enough sets to get an RMS of 1", then get another observer, different gun. But that's time consuming. Setup in a parking lot and look at some radio towers. Something that you can re-observe easily.

I have an array of points set up 100-500 ft apart. A triangle closure of 1" is common and that's not using forced centering, and observed over a several day period. It's time consuming. Also, if your looking for 1" at less than 500-600 ft, observe twice and reset the targets and gun. Then you'll see repeatability.

One second is so slight at even at 1000' that it's generally in the care of plumbing over the point, and four sets is just the first inning. And electronic guns might even do a lot of the arithmetic for you.

Easy to remember: 2mm @ 200M is 2". That's .007ft at 660ft. It's not easy to have centering errors less than 0.005ft 95% of the time. So don't blame the instrument. Working under 500ft 1" is below noise. However, and it is do-able. Plumb your targets and gun using two transits 8ft away. And don't bother looking at a range pole. One second targets are a prize piece of kit too. Turn the angle 10-20 times. Consider an RMS of 1". Which is why you should have 20 angles to choose from. Don't average all of them, you need to reject a few. That's why all good calculators have a stats function. Slow down, speed kills. a one second angle is a statistics task as much as an observing task and dependent on centering error more than anything. If your observing targets a mile away, one second is not as hard, but 1" is 0.03'.

Whew!!
Like I say luck and faith, and tighter than the eye can see.;-)

Also if you are truly going to try it, please do it at night, from my long experience it's the only way.

I guess that the quote wasn't clear enough.

The question that was really being debated was "can one achieve a higher accuracy than their instrument is specified to be, by simply repeating observations".

For example; can one achieve true sub-centimeter results with RTK by multiple observations or one second results with a five second instruments by multiple observations?

> ... can one achieve true sub-centimeter results with RTK by multiple observations or one second results with a five second instruments by multiple observations?
In theory, yes. In practice, beyond a certain degree (pun noted), not so much. I think that the practical limit is thought to be about 6 sets. Which would bring an angle with the 5" gun to a precision of about 3".

If you had a 30" transit, would you expect to get 1" precision by turning the angle 360 times? Not likely. But the math says you would.

A 3" gun will approach 3", ect......