Vertical Curvature of the Earth

Selected in MICRODEM:

In screen profiles the computer can include in its calculations curvature of the earth's surface along the profile. This can be seen on very long profiles through areas of low relief, where the ticks on both sides of the profile will be visibly at different levels (e.g. a 20 km profile through West Point will have a 50 m drop due to curvature of the earth with a 500 m vertical scale). The program will not allow curvature in very long profiles, such as those from SRTM30 where the curvature can be much greater than the actual relief.  

The algorithm choices are:

  • TM 5-441 (Feb 1970), p.2-12: the Army technical manual for topographic surveying. HP = HP - dē * 0.0676
  • Radio: radio line of sight. HP = HP - dē / (RadioK * 0.25 * 51).   This algorithm depends on the atmospheric conditions, but not the frequency/wavelength used. Frequency does impact Fresnel zone calculations.
    • For standard conditions RadioK is usually taken to be 1.33.  With this assumption, the formula becomes HP = HP - dē * 0.0590.
    • If you want other conditions, select an appropriate K value.
  • Yoeli: Yoeli (1985) gives a slightly different formula (HP = HP - 0.87 * dē /2R, where R is the radius of the earth, and the units are in kilometers) which differs slightly from the number calculated with the TM's formula.  With an earth radius of 6370 this becomes HP = HP - dē * 0.0683. ArcGIS uses this formula.
  • None.  Flat earth, appropriate for very long profiles which just show the terrain.

 
 

 

Vertical Earth Curvature (m)
Distance (m) TM5-441 Yoeli Radio, K=4/3
100 0.0 0.0 0.0
500 0.0 0.0 0.0
1000 0.1 0.1 0.1
2500 0.4 0.4 0.4
5000 1.7 1.7 1.5
10000 6.8 6.8 5.9
25000 42.3 42.7 36.9
50000 169.0 170.7 147.4
100000 676.0 682.9 589.7

 

The differences between Yoeli and TM5-441 are probably due to the low resolution of the constants in the equations, and should not be considered significant.

Earth curvature (over 3d shading from the DEM).

Create on Required antenna height of Calculate, Intervisibility menu. 

Provides an estimate of how good a flat earth approximation will be.

Graphs of the vertical earth curvature.

Horizontal earth curvature

Last revision 7/29/2011