Maybe I’m misunderstanding something, but I’m still not sure how you fly the LDA in MSFS. Even flying raw data, without the GPS, the LOC is simply wrong.
Here’s the LDA Z Rwy 19
At position BESSE (under the aircraft symbol) in the sim shows full scale deflection to the left.
Yet when you fly an inbound course of 185 (rwy hdg), instead of the correct course 147, the LOC indicates centered.
This brings you over downtown DC, to the east of the White House/Washington Monument.
This problem is more than just an issue on the map screen and with the GPS path. The actual LOC’s in game are aligned incorrectly.



