The cycle is such
Turn 0 - 5/8 Plane on ground at 0 Altitude and Velocity with engines on
Turn 1 - Plane takes off spending 2 Thrust in the process accelerating to Velocity 1 in the atmospheric hex
This is where things get weird because low-altitude vs high-altitude maps, first increasing Velocity or Altitude costs a straight 2 Thrust per Total Warfare regardless of which map you're on.
Presuming you 'must' go up the low altitude map there are 10 layers and you can only achieve a Max Safe Velocity of 2 and you lose half your Velocity each turn.
Turn 2 - Altitude 1 NOE, Spend 2 Thrust to maintain Velocity or fall out of the sky. Spend 2 more Thrust to increase Velocity to 2, 4 Thrust are spent to increase 2 Altitudes
Turn 3 - Altitude 3, Spend 2 Thrust to maintain Velocity at 2. Spend 6 Thrust to increase 3 Altitude
Turn 4 - Altitude 6, Spend 2 Thrust to maintain Velocity at 2, Spend 6 Thrust to increase 3 Altitude
Turn 5 - Altitude 9, Spend 2 Thrust to maintain Velocity at 2, Spend 2 Thrust increase to Low Altitude 10 where High Atmosphere Levels begin, then move to High Atmosphere level 2 then 3 using 4 Thrust.
Turn 6 - High Altitude 3 (54-71km), At High Altitude you only lose 1 Velocity not half so we still spend 2 Thrust to maintain Velocity 2, Spend 4 Thrust to reach Atmospheric Interface Layer (HA Row 5).
Total Cost - 6 Turns, 14 Thrust for Velocity, 26 for Altitude, 72 Fuel Points (due to afterburners)
If you don't need to transit the low altitude map first and can instead go straight to the High Altitude layers then it would be like this
Turn 2 - Ground Level, Spend 4 Thrust to increase Velocity to 2, 4 Thrust to increase Altitude to HA Layer 2 (36-53km)
Turn 3 - HA Layer 2, Spend 2 Thrust to maintain Velocity at 2, 6 Thrust to reach Atmospheric Interface Layer
Total Cost - 3 Turns, 8 Thrust for Velocity, 10 for Altitude, 32 Fuel Points (due to afterburners)
There are also further restrictions, propeller planes, airships, and VTOLs can only operate within low atmosphere (ground level at High Altitude). Conventional Fighters (ICE or Fusion) and non-propeller driven fixed wing support aircraft can reach High Altitude 1 but no further.
Spheroids don't do any of this because they don't typically have a horizonal velocity as they are going vertical (parabolic technically since the nose must point up and to the right or left) so only fight gravity.
Turn 0 - 3/5 Spheroid on landing pad ready to liftoff
Turn 1 - Spheroid spends 2 Thrust to take off, is hovering over the landing pad in atmospheric hex 1.
Turn 1 - Spheroid spends 2 Thrust to fight gravity, 2 more thrust to increase altitude to 2.
if you must transit the low altitude map repeat for 8 more turns
Turn 10 - Spheroid reaches high altitude layer 1.
Turn 15 - Spheroid finally reaches atmospheric interface layer.
Cost - 15 Turns, 32 to fight gravity, 30 to reach atmospheric interface, 122 Fuel Points
If you don't need to transit the low altitude map then
Turn 0 - 3/5 Spheroid on landing pad ready to lift off
Turn 1 - Spheroid spends 2 Thrust to take off, is on ground level map
Turn 2 - Spheroid spends 2 Thrust to fight gravity, 2 more to reach HA layer 1
repeat 4 more times
Costs - 6 Turns, 12 Thrust to fight gravity, 10 to reach space, 42 Fuel Points
Spheroids can Sideslip into adjacent hexes (effective horizonal movement) at the cost 2-3 Thrust (this one is weird) but do not acquire horizonal velocity in the process. Typically this would be either used as a weapon of mass destruction (Spheroid thrusters are devastating) or to adjust a landing zone.
Getting past the Space/Interface Layer and into orbit requires the expenditure of 4 Thrust.