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Having a short sector to fly, it would not be convenient to climb all the way up to the best cruise altitude, since the time in climb would burn more fuel than that necessary for a flight at lower altitudes.
Having said that, what would be the minimum time spent at the best cruise altitude that will make it reasonable to climb to that pressure altitude with a medium range twin jet transport airplane (B737 or similar)?
Above is a simple model to break down the problem into its simplest form. Of course the model can be refined. Assuming for a short flight that the ground speed doesn't change much from after takeoff to before final approach, it becomes apparent that reaching the top and descending right away gives the shortest time burning fuel (blue line) and longest time with the engines idle during descent.
Operationally you need a few minutes in cruise for ATC purposes, approach briefing, etc. So the 5 minutes mentioned by @CptReynolds in a comment makes sense.
The same model should hold true for long haul flights, only if aerospace materials and propulsion would efficiently allow a sub-orbital flight from say London to LA, but alas that's not the case.
* Half-climb and half-descent.
Here the flight is divided into equal time segments (maintaining the 'same ground speed' assumption). I've taken into account the shallower descent rate, and the decreasing climb rate / thrust / fuel flow the higher the jet climbs. The numbers indicate the fuel flow (FF) ratios per time-segment.
With real FF figures, further refinements can be made.
(Click to view)
Here it is very clear that the longer the short flight (even by a little), the higher the cruise altitude. There is not a point where there is a cut-off. And from the right-hand side: the lighter the plane, the higher it should cruise.
Note regarding the cruise FF ratio being fixed at 1.25: looking at a 737 AFM, the FF doesn't change by much from FL250 to FL410 at the same weight (2374-2458 lb/hr/eng; the Mach number rises though). So, for short hops with lower cruise levels, I've maintained the cruise FF for that simple model.
In short-range flights: Ideally zero. Practically, a few minutes are sensible in order to transition between climb and descent. In longer-range flights there is initially no real difference between climb and cruise, because the aircraft climbs at or near its speed for best range until ATC or envelope limits forbid it to go any higher. Note that the Breguet range equation requires the aircraft to climb until the end of its flight.
Yes, a climb needs more fuel but will increase potential energy, too. This energy can be made good use of by flying at a lower thrust setting during descent. Now it is important at which speed the aircraft climbs: If its ground speed is not lower in a climb than in cruise, it will not lose anything by climbing.
Flying higher translates into a higher ground speed for a given indicated speed and an improved thermodynamic efficiency. Since the most efficient cruise speed is at a given lift coefficient and in most cases quite a bit lower than the maximum level speed at full throttle, flying fast at low altitude is very inefficient. Both, the best cruise speed and the maximum speed, converge with altitude until both fall together in the coffin corner.
If the aircraft flies at best range speed and full thrust, the excess power can be used for climbing. This short Gedankenexperiment makes it immediately attractive to climb - the aircraft covers the same ground while improving its ability to fly faster. In addition, applying full power will most likely improve engine efficiency a bit.
This will make climbing higher more attractive until you hit either of two limits:
Both cases require a lot of thrust, and in most practical cases the engines will run out of oomph with altitude before one of the two limits is reached. Also, in most practical cases the aircraft will fly a little slower than its optimum range speed in order to improve its climb rate, so it will spend more time at more attractive altitudes.
The maximum altitude in short flights is determined by the rate of climb and rate of descent: The aircraft will climb until it reaches the altitude and distance to the destination at which flight at idle power will bring it all the way to the destination. In longer flights it is engine performance which limits the climb speed, but ideally the aircraft should continue to climb as it sheds mass by burning off fuel.
