Aircraft Operations. Volume II - Construction of Visual and Instrument ...

Appendix B to Chapter 4
ALGORITHM FOR CALCULATING THE HEIGHT OF SURFACE
DEFINED BY FOUR POINTS IN SPACE
The height (Z) of a point in the OAS side surface located at (X, Y), between the origin of the FAS at threshold level
(XFAS) and the origin of the Zi surface (XZi) at threshold level, could be calculated using the four vertices of the surface
(X1, Y1, Z1), (X2, Y2, Z2), (X3, Y3, Z3), (X4, Y4, Z4) and the following formulae (see Figure III-3-4-App B-1):
Calculation of Z at (X,Y):
X5 = X
Y5 = Y1 + (Y2 - Y1) × ((X1 - X) / (X1 - X2))
Z5=Z1+(Z2-Z1)×((X1-X)/(X1-X2))
X6 = X
Y6 = Y3 + (Y4 - Y3) × ((X3 - X) / (X3 - X4))
Z6=Z3+(Z4-Z3)×((X3-X)/(X3-X4))
Finally, calculate the required height Z as follows:
Z=Z5+(Z6-Z5)×((Y-Y5)/(Y6-Y5))
Definitions of vertices
X1= X3 = XFAS
X2 = X4 = XZi
Y1 and Y2 = distance of edge of primary area at XFAS and XZi respectively
Y3 and Y4 = distance of edge of secondary area at XFAS and XZi respectively
Z1 = Z2 = 0
Z3 = MOCapp
Z4 = 30m
III-3-4-App B-1 23/11/06