In 1890, Surveyor A measures a network with metric invar tapes standardized to Clarke's determination of 1866 with a conversion to inches of 39.370432. The average elevation is 2000 feet above sea level and feet coordinates are computed using plane trigonometry with ground distances. He chooses station "O" as origin.
In the 1920s, Surveyor B adds onto network A with metric invar wires standardized to Clarkes determination of 1873 with a conversion to feet of 0.30479947. The average elevation is 2000 feet and plane trigonometry is used to generate feet coordinates with ground distances.
In the 1960s, Surveyor C adds onto B network with a metric EDM, but knowing he is now too far from the origin, adds a projection using Clarkes 1866 spheroid with a conversion to feet of 0.304799433. In a "eureka moment" of dubious value, he realizes he can save time and effort in computation if he simply adds 2000 feet to the 'a' radius and holds the flattening, instead of reducing to sea level, computing and then raising back to the coordinate datum and re-computing.
There is then an implied assumption that the geoid and computational surfaces are tangent at the origin, in addition, the gravity and spheroidal normals are implied as coincident.
It gets better.
In using the Clarke 1866 spheroid, surveyor C didn't realize the 'a' radius is in Clarke feet with a conversion of 0.3047972656.
By adding 2000 feet to the 'a' radius he has produced a modified spheroid that is not parallel to the
original spheroid surface, and in fact, approaches the original surface as the modified spheroid
approaches the poles.
In the 1970s, Surveyor D extends the C network and adjusts feet coordinates using the Clarke spheroid of 1866 using international feet in the radii and a conversion to feet of 0.3048.
In 2016, Surveyor E phones Surveyor Z and asks for help with a transformation of preceding ABCD coordinates into NAD83.
Surveyor Z, knowing the back story, pretends to be late for a meeting and goes to lunch.
Real story.
lol, sounds like lots of fun Scott, don't you know you just need to push a button and it fixes it all;)
My brain hurts.
N
Throw some money at it; that'll fix it.
That poster: RADAR, sure is a swell guy
Excuse me but; "The average elevation is 2000 feet above sea level", has nothing to do with any spheroid that I know of.
We would have to know the what and when of these sea level valuations.
All in all it doesn't really matter as original monuments hold.
Paul in PA
"Surveyor Z, knowing the back story, pretends to be late for a meeting and goes to lunch."
Easily the best way to go...
I wonder who surveyor Z could be? 🙂
Even if the math can be worked out, finding some existing monuments and re-measuring would be the best way to either avoid the headache, or check the translation.
How big are these networks?
I once heard of a preacher, who had a horse. Named "visitation".
Phone would ring... His wife would tell folks "he's out on visitation".
I could suggest a boat named "work".
🙂
Ha!