Bill93 14 Posted November 9, 2016 Share Posted November 9, 2016 (edited) The current Wikipedia entry Geodetic Datum has a statement in a paragraph discussing NAD27: "The geoidal height at Meades Ranch was assumed to be zero." At first glance this makes no sense to me. I thought the horizontal datum was on the mathematical ellipsoid and would have no relationship to the geoid. Is there some small second order effect that causes an interaction of the vertical with NAD27 (or NAD83 either) that would need such an assumption at the time? I didn't find a data sheet for Meades Ranch, but look at the data sheet for KG0640 Meades Ranch Reset (NGS) (Geocaching, older data sheet) and note the NGVD29 elevation is within a meter of NAVD88, and the current geoid separation is more than 26 meters. Should that Wikipedia statement be deleted? Edited November 9, 2016 by Bill93 Quote Link to post

Bill93 14 Posted November 9, 2016 Author Share Posted November 9, 2016 I decided to post the question in the professional forum and got an authoritative answer there, that explained why that statement is true. Following the explanation really tests your understanding of geodesy. Quote Link to post

trmcconn 0 Posted November 10, 2016 Share Posted November 10, 2016 My understanding (as a mathematician, not a geodesist!) is that the ellipsoid is a simple surface chosen to approximate a complicated one (the geoid) over a limited area. A datum consists of a choice of shape and size for an ellipsoid as well as the location of its center and orientation of its principal axes relative to the celestial coordinate system. In the case of NAD27, the shape and size was that of the Clarke ellipsoid. The location and orientation was determined in part by requiring the two surfaces to cross at Meade's Ranch and also requiring them to osculate there, i.e. to have the same direction normal (=vertical) to both surfaces at the crossing point. That still leaves a degree of freedom for the ellipsoid to be rotated around the normal direction vector, and this was chosen to minimize the discrepancy (in least squares sense) between resulting geodetic and astronomic measurements at an existing network of stations. The current Wikipedia entry Geodetic Datum has a statement in a paragraph discussing NAD27: "The geoidal height at Meades Ranch was assumed to be zero." At first glance this makes no sense to me. I thought the horizontal datum was on the mathematical ellipsoid and would have no relationship to the geoid. Is there some small second order effect that causes an interaction of the vertical with NAD27 (or NAD83 either) that would need such an assumption at the time? I didn't find a data sheet for Meades Ranch, but look at the data sheet for KG0640 Meades Ranch Reset (NGS) (Geocaching, older data sheet) and note the NGVD29 elevation is within a meter of NAVD88, and the current geoid separation is more than 26 meters. Should that Wikipedia statement be deleted? Quote Link to post

Bill93 14 Posted November 10, 2016 Author Share Posted November 10, 2016 (edited) As I think I understand it, you can define the horizontal datum origin and orientation independently of the vertical, but in order to add any other points to your data base using that datum, you have to have the scale factor to convert surface measurements to distances on the ellipsoid model. I.e., if you are at lat-lon A,B and go some measured surface distance and direction then you need to convert that to distance on the ellipsoid before finding a new lat-lon. The conversion factor depends on elevation. They didn't have a very good geoid model at the time so in order to define the elevations they assumed the geoid was at the ellipsoid at Meades Ranch. That slightly inaccurate conversion of elevations introduced a significant distance (hence lat-lon) error as they got further away from that initial point toward the coasts. One of the benefits of NAD83 was fixing that problem, using a better geoid model. Hope I got that right. Edited November 10, 2016 by Bill93 Quote Link to post

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