two real life stories with significant and least significant figures:
My friend, Pete Estes, Orange County Virginia surveyor (deceased), told the story about surveying a 5 acre rural tract for a church.?ÿ He surveyed the property and came up with 4.8 acres.?ÿ The church committee wanted to know where the other .2 acres was and after spending much time trying to educate the group and frustrated, he confessed he hid it in the traffic circle in Gordonsville along with all the other properties he stole.?ÿ I always think about Pete when I pass through Gordonsville.?ÿ
Another maybe more relevant story to this post was a survey of a 5 acre parcel in a rapidly changing urban area.?ÿ The rectangular parcel was platted at 5 acres and met zoning requirements for minimum 5 acre lot size.?ÿ Along comes a subsequent survey for development with 499.99 vs 500.00 feet measurements and the 5 acre parcel ended up with 4.99999 acres.?ÿ Guess what, the county said they had a non-conforming parcel and refused the development as it did not meet zoning minimum lot size.?ÿ The owner sued, went to court and lost.?ÿ ?ÿThe monuments at each corner were 3/4" iron pinch pipes.?ÿ?ÿ
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Remember Pete when?ÿ
Witnessed a mechanical engineering professor make a VERY powerful statement about significant figures.?ÿ The graduate level class in Environmental Engineering focused on heating, air-conditioning, ventilation, feels like effects on humans, etc.?ÿ ?ÿWe were all provided a very complex problem of determining the cooling load for a very well described house over a period of a certain number of days.?ÿ All sorts of data was provided from which we had to calculate numerous impacts adding or subtracting from the final number of BTUS's.?ÿ Everything from building and insulating materials and thicknesses to types and sizes of windows on each side of the house located at a?ÿ precise lat/long?ÿ (for solar insolation calculations) and oriented in a precise position.
The day arrived for us to turn in our work.?ÿ The professor went into quite a spiel of the processes we should have applied, then turned to Mr. Perfecto in the front row of desks and asked for him to?ÿ tell us his answer.?ÿ He very proudly announced something like:?ÿ 168,341,246.877 BTU's.?ÿ The professor asked him to hand over his paperwork.?ÿ The professor then promptly dropped the papers to the floor and stomped on them for quite a few seconds as Mr. Perfecto almost died of shock while the rest of us gasped or laughed.
The lecture that followed was very clear about significant figures and "magic numbers".?ÿ ?ÿ One key figure we all had used for a portion of our work was a multiplier of 0.4.?ÿ Another was 0.24.?ÿ Simplifying assumptions had to be made in numerous portions of our work that would also be somewhat crude.?ÿ Mr. Perfecto's parents had purchased for him the top of the line HP handheld scientific calculator with far more digits being carried along than were ever needed or realistic.
I look at it this way.?ÿ A 3/8" rebar at 200' away is 6 seconds wide.?ÿ One second at a 1 mile distance is 0.03' of a foot.?ÿ But yet, Surveyors are signing and sealing a set of field notes certifying they measured a property to thousandths or even ten-thousandths of a foot??ÿ
Local Attorneys and Title Companies run our work thru Deed Checkers and when the closure is not near perfect, they bounce it back to us and want it better or they won't use our Property Descriptions.
Relaying the information of our Professional Land Surveying Practices Act and General Rules of Procedures and Practices that the State BOR requires that the positional tolerances of our monuments to be within 1:5,000 in rural areas, 1:7,500 in extraterritorial areas adjacent to cities or 1:10,000 in any city bounces off of them because they don't understand the specifics.
I was asked to change the statement "45.03 acre tract of land" to "45.03 acres tract of land" last week to satisfy the newest spelling nazi in town. The Grammarly spell checker on my computer wanted it to be "a 45.03-acre tract of land".
On some days it is necessary to reply to them that "they can not make requirements beyond what is a State law". And yes, that does get them in a testy mood.
About 2 months ago, one Title Agent blasted me with "I don't know if you will ever get another survey approved at this company" because I had to ask them to make a new payment check out in my "actual name" rather than "Harris Surveying" as they call my business. All of which is stated on every invoice sent out by the statement "Make all payments by check or money order to may actual name".?ÿ That took them about 10 days to accomplish.
0.02
So you only call out distances to the nearest 0.05'??ÿ
Calling out a distance to the 0.01' is not any different in practice (to calling out too many digits in an area), if you are considering the 3/8" to be your tolerance.
BTW, yesterday a field crew under my direction measured between two monuments that I measured in '09. They matched to 0.01'. I was pleasantly surprised.?ÿ
My point is that this is something that is a reality in our profession, we all know about it, but the realities of interacting with others means that we publish numbers outside of significant digits all the time. Everyone does. There should be something done about it, there is no doubt.
I lose zero sleep at night worrying about significant digits. I just report what is typical standard practice. I'm not a theoretical physicist.
To get a survey recorded in the Virgin Islands, the precision isn't the issue as much as the word "Acres" which is not acceptable. "Acres U.S." is required as opposed to Danish Acres, used before the 1917 transfer from Denmark to U.S. The difference is much less that the accuracy of any Danish survey so it makes no sense to me. And we're not required to say "U.S. Feet" as opposed to "Danish Feet" or "International Feet".?ÿ I don't think there are Danish degrees, minutes or seconds.
Exactly. Significant digits gets messy when you mix with CAD and other types of software, because there is no fuzziness there. It snaps to the next line.
A standard issue is having a line that ends in an odd number, such as 1330.03 feet.?ÿ Hit the midpoint to connect to something else.?ÿ Boom.?ÿ You now have what appears to be a line 1330.04 feet long with two 665.02 feet halves.
But 1330.03 feet has six significant digits. And 665.015 has six significant digits. So, from a significant digits viewpoint, 665.015 feet is ok for the midpoint, but if you can measure only to the nearest hundredth of a foot, you could never find it.
This is a common problem when annotating tiers of lots on subdivision maps. You have to manually edit some of the sublengths (& curve deltas) generated by your drafting software. From an annotation drafting manual I wrote 25+ years ago:
"The sum of the sublengths of lines must exactly equal the overall length of the line, the sum of the sublengths of curves must exactly equal the overall length of the curve and the sum of the central angles of the sublengths of curves must exactly equal the overall central angle of the curve. No sublength can be changed by more than 0.01' and no sublength central angle can be changed by more than 1" to satisfy this rule."
Your example is more subtle than it appears. The line could actually be 1330.026xxx' long, when split the sublengths would be 665.013' and reported as 665.01'
The "rounding" effect is sometimes quite noticeable; consider a ten lot tier with a back lot line 1000.04' long. Divided equally each back lot line would be 100.004' long and reported as 100.00' Where did the 0.04' go? Rather than arbitrarily report 4 lots as 100.01' it might be wiser to move the sidelines so 9 of the lots are exactly 100.00' and the last lot is 100.04'
The Devil's in the details.
Oh, I agree.?ÿ Where it drives people nuts is when the draftsman shows the full length and the two half lengths and they, of course, do not add perfectly.?ÿ Somebody, then, wants to know where the missing 0.01 came from or went to.?ÿ I do prefer to do as you suggested with lots but it doesn't work out when you are splitting things equally.
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An easy fix that many abhor is altering the reported total length.?ÿ Shortening or lengthening a half mile by 0.01 is insignificant, but it's a manual fix.
We were working on a survey that would reference a survey I had worked on as a crew chief/draftsman in the late 90's. I had called off a field stone (8"x12" that doesn't have much of a defined point) by 0.20' and someone who I consider a very good surveyor signed the plat. I don't know what caused him to overlook a boneheaded move like that but there it is recorded.
Or...you could simply let the numbers tell the story
Each lot could be 100.00 AND be 1000.04 overall...these can both be true. This is not incorrect.?ÿ
Is it harder to calculate, sure, but everyone should know how to make that work such that each lot in your CAD software is 100.004.
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The rest of the world wants to know where the 0.04 went. Especially if you added that into your area calculation and then showed area to the nearest 10000th of a square foot.
When we are showing accuracy to the nearest 100th of a foot on our plat, we need to get all figures shown to add up to what we are showing for a total.
