I checked my spreadsheet again and the numbers do not seem right, neither mine or yours.
Given:
Earth radius R=6356766 m [ICAO Doc]
Earth's rotation 360 deg / 24 hrs
(angular velocity) 2*PI/ (24*60*60) rad/s
tang. spd v=2*PI*r[circumference] / (24*60*60) [time] m/s
crz alt h=11000 m
Formulas:
centripetal acceleration
a(c) = (v^2)/r
Calculated:
surface centripetal acceleration on equator
a(cS) = (v^2)/R = 0,33617737 m/s2
alt (height 11 km) centripetal acceleration over equator
a(cA) = ((2*pi*(R+11000)/(24*60*60))^2)/(R+11000) = 0,33617795 m/s2
crz eastbound centripetal acceleration (h=11km, trk=090, gs=1000 km/h=278 m/s) over EQ
a(cE) = ((2*pi*(R+11000)/(24*60*60)+278)^2)/(R+11000) = 0,08615724 m/s2
crz westbound centripetal acceleration (h=11km, trk=270, gs=1000 km/h=278 m/s) over EQ
a(cE) = ((2*pi*(R+11000)/(24*60*60)+278)^2)/(R+11000) = 0,00535496 m/s2
Assumption:
The ICAO sea level g = 9,8067 m/s2 includes the centripetal effect of earth's rotation.
The ICAO 11 km g = 9,7728 m/s2 neglectes the difference of centripetal effect which is calculated from above to be 0,000000058 m/s2.
The difference of centripetal effect with additional speed 1000 km/h
at altitude is compared to surface stationary is
0,052539503 m/s2.
This is the nubmer I believe we both got very incorrect the first time.
So, just as you summed up the difference between sea level stationary g and g required for FL360 equatorial westbound level flight with 550 kt GS is 0,0336 [ICAO alt difference] + 0,0525 [speed in crz difference] = delta g = 0,0861 m/s2 = compensating acceleration.
Until further mistakes are discovered, using your perfect example that gives:
With 10 sec reference V/S 170 fpm and altitude deviation 14 ft.
With 30 sec reference V/S 510 fpm and altitude deviation 127 ft.
With 1 min reference V/S 1015 fpm and altitude deviation 510 ft.
With 2 min reference V/S 2030 fpm and altitude deviation 2030 ft.
With 3 min reference V/S 3050 fpm and altitude deviation 4580 ft.
For a FCS that you were trained keeps level flight with free stick, that is a difference. Indeed, the FCOM says 'maintains 1 g compensated for pitch'.
FD (the un-real)