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1/ "How works fcu speed/mach, heading/track, and altitude knobs : Have they three positions : Selected (pulled) Managed (pushed) and the inactive position(disengage selected or managed mode). Or are they only used to engage a selected or managed mode. In this case, how disengage them ?"
ANS... It has a neutral position and you engage/activate eitheir mode by pulling or pushing. After the action it will return to neutral. To disengage a mode just activate a different one.. i.e. if you have selected a speed then just PUSH it and it will reverte to Managed and vice versa
2/ What exactly is Vls ? when is it represents 1.13 Vs or 1.23 Vs ? is it depends on load factor like Vs, Alpha protection and alpha max spd ?
ANS... VLS is the minimum selectable clean speed. 1.13 (V2) as far as I remember is on departure where as 1.23 (Vapp) on approach. They are multiples of Vs1g. Alfa prot is a high angle of attach protection..... too long to explain all the protections. As for Alfa Max...well this is the min speed/angle of attack the A/C will fly at depending on config... it really onlys gives you enough speed so as to give you enough air flow to give a roll rate. Level flight may not be achivable.
3/ About the Engine rating limit control : FLEX power can be used for takeoff if a FLX temperature has been entered via the MCDU. When Flex power becomes inactive ? Is it replaced by maximum continuous thrust ?
ANS..Engine rating limit... basically it is like a govener... it wont let you over boost the engine... Flex..no you firstly get an ECAM warning to tell you to select toga but it should give you climb power... a bit vague at this hour I'm afraid