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Auto Pilot and LPV Approach

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So you have an STEC 30 auto pilot with altitude hold with a GTN 650. GPS approaches are done with the STEC in Heading mode and a soft key switch between the GTN 650 and Auto pilot in GPSS mode. the switch has two settings GPPS mode where the auto pilot takes input from the GPS and Heading where the auto pilot will take input from the traditional heading bug.

You are coming into an airport and cleared for the RVAV GPS approach 35 which is an LPV approach. You load and activate the approach and the soft key is set to GPSS and of course the STEC remains in heading mode the entire time as it should. The approach is loaded to an IAF then an IF then the FAF. You are in Term mode of the GPS and not yet to the IAF when ATC starts giving you vectors away from the IAF telling you you are number two behind a regional jet. You switch the soft key switch to heading so that the STEC is now taking commands from the heading bug and you follow the vectors. After about 10 minutes these vectors have you lined up on a heading of 350 and you pass over the IF. You slow down and configure for the approach and you pass the final approach fix. GPS has transitioned from Term to LPV more and vertical and lateral is good according to the needles. You start managing your descent and monitoring lateral navigation that is being handled by the STEC.

You are busy and maybe not on your best game today and you forget to switch the soft key back to GPPS from Heading mode. So instead of following the GPS for lateral input on the LPV approach, the GPS is still following the heading bug which is set to approx 350 and you are on the GPS RNAV 35 approach.

What might you expect to see as you continue this approach, A drift away from the final approach course due to winds? Does not matter where the winds are coming from, the heading bug is set to 350 and this is GPS 35 approach so you will basically still track the final approach course? Other ideas or input welcome.

This is where some might say asking for a friend, but alas the friend is me.
 
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