Good afternoon, and thank you for your recent kind e-mail.
To take your points in order.
...Concorde makes its acceleration from M1.7 to 2.0 while in cruise climb...once the reheaters have been shut down...
...Isn't the altitude passed once the reheaters have been shut down in the order of FL400...
It will be nearer 43,200 ft on an ISA day, but in fact the re-heats are cancelled on achieving M1.7, rather than on passing a given altitude. Passing through FL400 the Mach number would be between M1.42 to M1.50, dependent on aircraft weight.
...Can she maintain level flight at say FL400...
Supersonic, yes, but only for a short time and highly undesirable. She would still be in a relatively high drag region, re-heats still required with their consequent very high fuel flows and with the clock running down against the time limit for the use of re-heat.
Subsonic, yes, but FL400 is far too high for an economical subsonic cruise at any weight.
…level flight……and get a quicker acceleration to 2.0…
No, and the reason is simply this.
Acceleration in level flight should not be possible, because Concorde should already be at the maximum speed allowed for that altitude.
Concorde flies at her (highly variable) VMO whenever possible, and when I say that, I mean it quite literally, to the knot. If she were to level off at any altitude, she should already be at her VMO, for that altitude, and to fly any faster, as an IAS, would generate an overspeed warning.
I know you will understand, but for the benefit of others who may possibly be interested, allow me to expand on this a little, and please forgive me the occasional simplification or generalisation as I do so!
In level flight, flying at the maximum IAS permitted at that altitude, there are only three ways for Concorde to increase her Mach number.
Firstly, if still below the tropopause, climb higher at a constant IAS and as the OAT falls, the Mach number will increase. Most subsonic aircraft do this anyway, climbing at a constant IAS (though not generally VMO!) until reaching their desired Mach number, when they will transition to a constant Mach number for the rest of the climb.
Secondly, if at FL400, as in your example, and now (probably) above the tropopause, the OAT will (in theory) remain constant at -56.5°C and won’t fall as she climbs, so this technique won’t work. In order to increase Mach number now, climb, and utilise the fact that Concorde’s VMO increases steadily by 10kts per 1,000 ft above the tropopause, and that by climbing she can now gradually increase her IAS, and thus her Mach number.
Thirdly, at around FL440, Concorde’s VMO stops increasing, and stays at 530 kts IAS for the rest of the cruise/climb. Now, with no further IAS increase possible, and no OAT decrease likely, the only way to increase Mach number still further is to climb at 530 kts IAS and utilise the fact that during a climb at fixed IAS, as the ambient air density decreases, her TAS, and hence her Mach number, will both rise.
There are also nose temperature limits (TMO) which, for the sake of simplicity, I haven’t gone into, but the common thread is that Concorde needs to climb in order to accelerate.