We can use the GPS Data of some stations along the Erie Canal to measure the locations of the stations in Earth Centered Earth Fixed ECEF cartesian coordinates. With such coordinates we have the locations of the GPS stations in space with respect to the center of the earth, the origin of the ECEF coordinate system. This locations have nothing to do with the shape of the earth. They are pure vectors that can be used to get the shape of the ground they are placed on.
As each location is given as the coordinates of a vector, we can use vector algebra to calculate the drop of one station with respect to the horizontal plane of the other station. If the earth is flat then this drop will be zero and we get only the elevation difference between the stations.
In the following analysis I used the raw GPS Data of station P_{0} = AH9234 at Buffalo at one end of the canal and station P_{18} = MZ0796 at Troy at the other end of the canal. But we can use any pair of stations to do the same measurements and calculations.
PID  Location  Measured Drop  Expected Drop  ΔDrop 

AH9234  Buffalo  14,064.251 m  14,064.059 m  0.192 m 
MZ0796  Troy  14,387.343 m  14,387.364 m  −0.021 m 
The table above shows that the Measured Drop matches the Expected Drop of the WGS84 globe model to cm accuracy!
The earth is measurably not flat.
Below is a list of GPS Control Benchmarks along the Erie Canal that provide Geodetic data like the ECEF cartesian coordintes X,Y,Z, Elevation, Ellipsoid height and Geoid height. Using the Control Benchmarks coordinates it is possible to calculate the earth curvature drop and the various radii of the earth. A useful tool to calculate some ellipsoid radii is the WGS84 Distance, Azimuth and Radius Calculator.
Some Benchmarks are not located very near the water, so their elevation may be some meters above the water elevation. Such Benchmarks have the Name in parenthesis.
To make calculations like curvature drop and radii use the GeoData Visualisation and Calculator App. The Benchmark data are listet in the table at the bottom of the App. Because the Benchmarks are not located at the water surface, I measured the nearest water elevation in Google Earth. It is displayed in the table on the App page in the column labeled Additional Data.
PID  Name  USGS  State/County  Elev  H_{Ell}  H_{Geoid}  X Y Z  Data Sheet 

AH9234  906 3020 H  BUFFALO  NY/ERIE  176.5  141.322  35.146  902080.915 4593625.452 4317598.521  https://www.ngs.noaa.gov/ 
DE7803  (TOWN OF AMHERST MONUMENT 62)  CLARENCE CENTER  NY/ERIE  175.8  140.375  35.386  912110.030 4578411.782 4331533.017  https://www.ngs.noaa.gov/ 
AE2178  LOCKPORT  LOCKPORT  NY/NIAGARA  181.763  146.085  35.675  913179.466 4568967.492 4341212.269  https://www.ngs.noaa.gov/ 
OG0490  (MEDINA)  KNOWLESVILLE  NY/ORLEANS  196.456  160.890  35.571  939643.563 4560522.245 4344443.747  https://www.ngs.noaa.gov/ 
OF1042  L 129  ROCHESTER WEST  NY/MONROE  168.024  132.581  35.441  996723.410 4554321.684 4338223.528  https://www.ngs.noaa.gov/ 
DF5882  ROCHESTER OPS CNT CORS ARP  PITTSFORD  NY/MONROE  172.544*  137.142  35.402  1000295.368 4555059.500 4336643.828  https://www.ngs.noaa.gov/ 
DI0614  PITTSFORD CORS ARP  PITTSFORD  NY/MONROE  148.889  113.478  35.355  1007672.284 4554836.560 4335145.129  https://www.ngs.noaa.gov/ 
AE2168  LOCK 29  MACEDON  NY/WAYNE  136.200  101.098  35.106  1029955.952 4552039.040 4332843.226  https://www.ngs.noaa.gov/ 
DI0626  WATERLOO CORS ARP  SENECA FALLS  NY/SENECA  144.319^{1}  109.959  34.360  1064476.707 4557029.058 4319337.374  https://www.ngs.noaa.gov/ 
NB2147  (TT 40 R)  BURDETT  NY/SCHUYLER  225.727  192.564  33.171  1071592.861 4591438.100 4281348.164  https://www.ngs.noaa.gov/ 
AB3841  (LANSING)  LUDLOWVILLE  NY/TOMPKINS  118.6  85.324  33.357  1095086.670 4577565.021 4290031.370  https://www.ngs.noaa.gov/ 
AB3847  (WEEDSPORT)  WEEDSPORT  NY/CAYUGA  121.940  87.742  34.202  1083941.240 4541153.405 4331088.553  https://www.ngs.noaa.gov/ 
AB3840  LOCK 24  BALDWINSVILLE  NY/ONONDAGA  115.0  81.075  34.037  1100875.832 4528281.869 4340212.925  https://www.ngs.noaa.gov/ 
OF1307  (FULTON)  FULTON  NY/OSWEGO  134.995  100.575  34.415  1093018.104 4516439.598 4354447.421  https://www.ngs.noaa.gov/ 
AB3837  (CENTRAL SQ)  CENTRAL SQUARE  NY/OSWEGO  135.139  101.270  33.872  1115086.608 4514620.921 4350762.282  https://www.ngs.noaa.gov/ 
OE0979  (G 34 RESET)  CANASTOTA  NY/MADISON  131.867  98.937  32.929  1148304.377 4522709.112 4333799.143  https://www.ngs.noaa.gov/ 
OE1686  (U 465)  ROME  NY/ONEIDA  158.598  126.181  32.394  1175554.457 4507489.155 4342324.091  https://www.ngs.noaa.gov/ 
OE1692  (Z 465)  UTICA WEST  NY/ONEIDA  130.332  98.158  32.222  1183787.456 4510086.628 4337379.662  https://www.ngs.noaa.gov/ 
AA7945  UTICA  UTICA EAST  NY/ONEIDA  132.559  100.567  32.006  1192050.672 4509945.418 4335280.551  https://www.ngs.noaa.gov/ 
DI0464  HERKIMER CORS ARP  HERKIMER  NY/HERKIMER  126.896  95.284  31.600  1209173.580 4511392.211 4329062.840  https://www.ngs.noaa.gov/ 
AA7916  GPS 2G93020  RANDALL  NY/MONTGOMERY  89.351  58.419  30.939  1258876.263 4502846.227 4323770.294  https://www.ngs.noaa.gov/ 
NA1829  T 444  AMSTERDAM  NY/MONTGOMERY  84.663  53.753  30.908  1277707.613 4500143.208 4321071.065  https://www.ngs.noaa.gov/ 
MZ1442  (UNION RM 2)  SCHENECTADY  NY/SCHENECTADY  83.470  52.199  31.263  1296985.618 4502681.363 4312729.432  https://www.ngs.noaa.gov/ 
MZ0796^{3}  WATERFORD RM 2  TROY NORTH  NY/SARATOGA  10.855  20.441^{2}  31.296  1317679.236 4498882.876 4310328.535  https://www.ngs.noaa.gov/ 
1) Elevation is calculted using the following equation from the data in the data sheet. Elevations without superscript^{1} are taken from the data sheet (ORTHO HEIGHT).
(1) 
Elev = H_{Ell} − H_{Geoid} 
2) Ellipsoid height H_{Ell} is calculated from Elevation Elev and Geoid height H_{Geoid} as follows:
(2) 
H_{Ell} = Elev + H_{Geoid} 
3) Classic Horz and Vert Control used, where X,Y,Z are calculated using the WGS84 Calculator from Latitude, Longitude and Elevation. All other Controls used are GPS sites, which natively provide X,Y,Z coordinates.
In elevation profiles like the image above the curvature of the earth is straightened, because it is irrelevant for local elevation measurements. This does not mean that the earth is flat as the measurements on this page prove.
Erie Canal System KML.zip
Erie canal system SHP.zip
Given 2 location vectors we can use the following vector equation to calculate the measured drop
(3)  
where^{'} 

Note: due to the ellipsoidal shape of the earth the up vector
We can use the GeoData Visualisation and Calculator App to get the measured drops as calculated above. The drop values are displayed at Hlvl:
(4) 
 
(5) 

This are the measured geometrical drops of a far station from the plane that is tangent at the observer station using the raw GPS coordinates of the stations. The different drops at the 2 locations is due to the elevation differences of the GPS receivers and the ellipsoidal shape of the earth (rather than a perfect sphere).
I use the math of the WGS84 globe model to calculate the expected drop. This model uses a reference ellipsoid as the first approximation of the shape of the earth. To calculate the expected drop
(6)  
where^{'} 

The radius of curvature of an ellipsoid at a certain location depends on the direction it is measured. The radii
(7) 
 
(8) 
 
(9) 

To get the drop between the stations we have to take the ellipsoid heights
(10) 

Now I have all values to calculate the expected drops at each station using the equation (6):
(11) 
 
(12) 
