I have determined the geopotential difference between two stations. Now I want to compute the orthometric height difference between these two stations using Helmert's height formula. But I am confused with units of gravity, height, and geopotential difference. Can I get the calculation example where orthometric height difference is computed from geopotential difference.
Dear KC
If you have the geopotential number of each of the stations, you will be able to calculate the Orthometric Height using the following formula iteratively:
Hp = Cp/(g + 0.0424Hp)
where Cp, g, and Hp are the geopotential number, gravity acceleration, and Orthometric height, respectively. At first, you consider Hp = 0 and put the Cp and g values inside the formula. Then you will have Hp = Cp/g. Put the second approximation of Hp in the Helmert's equation and find the third one. This process iterates until the difference between the jth and the (j+1)th value be less than a threshold value. There is another method to solve the problem, which is transforming the Helmert's formula into a second-order equation. I mean:
0.0424Hp^2 + gHp - Cp = 0
now, the Hp value is simply determined if you know the Cp and g values.
The computed Hp is an approximated value of Orthometric height as the coefficient of 0.0424 is derived from the Poonakary-prey gradient. In order to compute the better approximation of the Orthometric height difference, it is better to use the following equation:
OC_AB = sum((g - gama0)/gama0)*deltan + ((mean(gA) - gama0)/gama0)*HA - ((mean(gB) - gama0)/gama0)*HB
where deltan and gama0 are the height difference of the leveling and the normal gravity acceleration in 45 degrees latitude. HA and HB are also the heights which are determined by the Helmert's equation.
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