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Given that you use the same datum transformation, you should end up with the same coordinate regardless of how many times you convert between to datums. Is this a correct assumption? Is this applicable for both equation-based and grid-based transformations? For example: Convert NAD27 to NAD83 via NADCON then from those NAD83 to NAD27 via NADCON, and again, etc.

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    Theoretically yes but in a computer world with limited accuracy of floating point calculations not even if the formulas were perfect, and naturally they are not. – user30184 Feb 20 '18 at 21:33
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    There's almost always some rounding in a floating point calculation; a float, double or decimal can only store a finite number of digits and the rest are lost... it's in the order of nanometres usually but even a nanometre often enough can result in vertices (points) walking all over the place. It's best to only project when you absolutely have to. Note: this does not apply as much to project on the fly systems, the storage is in the datasets natural CRS and the display is in the screen CRS but really the projection is only done once: on edit/store, unmodified features are unchanged. – Michael Stimson Feb 20 '18 at 21:47
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Using NADCON as transformation method between Nad27<>Nad83 is accurate when the map scale is 1:1200 or smaller.

Accuracy and uncertainty [Reference1][Reference2]

The following statement is from the release notes of NADCON Version 2.1, October 1993:

“The accuracy of the transformation should be viewed with some caution. At the 67 percent confidence level, this method introduces approximately 0.15 m uncertainty within the coterminous United States, 0.50 m uncertainty within Alaska, 0.20 m uncertainty within Hawaii, and 0.50 m uncertainty within Puerto Rico and the Virgin Islands. In areas of sparse geodetic data coverage, NADCON may yield less accurate results but seldom in excess of 1.0 m. Transformations between NAD83 and the States/Regions with High Accuracy Reference Networks (HARN) introduce approximately 0.05 m uncertainty. Transformations between old datums (NAD27, Old Hawaiian, Puerto Rico, etc.) and HARN could combine uncertainties (that is, NAD27 to HARN equals 0.15 m + 0.05 m = 0.20 m). In near offshore regions, results will be less accurate but seldom in excess of 5.0 m. Farther offshore, NAD27 was undefined. Therefore, the NADCON computed transformations are extrapolations and no accuracy can be stated.”

Conclusion

In general, Any transformation procedure has an accuracy range and of course when transferring (to & back) many times you will have less accuracy as a result of the computations and the iterations. From the numbers above and from NADCON methodology, the accuracy is different.

If it's acceptable or not? that depends on how much accuracy you want? and depends on the area, and the scale.

  • I believe I am more interested in the relative accuracy of the converted point(s) back to the original point. Those should stay the same right, other that rounding and data precision problems others stated. – Rex Feb 21 '18 at 14:11
  • @Rex Technically yes, the values should be the same at least with three digits rounding – Moh Feb 21 '18 at 17:09

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