[notlefthanded]

I think we're interpreting op differently. No, not all the energy added to a heavier than air aircraft (thrust) in straight-n-level flight* is used to counteract drag. Yes, where there is lift, there is induced drag. But the kinetic energy being added to maintain velocity is also being used for lift.

Imagine if the airfoil on an aeroplane were replaced with a symmetrical airfoil mounted with no angle of incidence. Thrust could be reduced because there's less drag from no lift. No lift, no induced drag, only parasitic drag, and the plane starts to lose altitude. Would you agree that not all the energy added to straight and level flight goes towards counteracting drag?

*where a' and v' are zero, and where for argument's sake, the thrust vector is perfectly horizontal

edit: by a' I mean change in vertical airspeed, by v' i mean change in true airspeed.

[teraflop]

No, that's a non sequitur. An aircraft that doesn't produce lift requires less energy input, but that's not because lift requires energy -- it's because when there is no lift, the aircraft is gaining kinetic energy by losing potential energy.

If lift requires energy, then where would that energy go?

[notlefthanded]

I think ppl are equating energy with force. Airspeed, altitude, and fuel are forms of energy, kinetic, potential, and chemical, respectively. Lift, drag, thrust, and weight are forces. We're talking about a heavier than air aircraft in cruise right now, and the contention is over whether all the energy added to the aircraft if used to counter drag.

Simple example: consider a helicopter in cruise. Fuel is burned to produce thrust. There is an insignificant component of that thrust vector pointed orthogonal to the vector of velocity. Since drag by definition acts along the same vector as velocity, not all the energy is being used to counteract drag.

Back to an aeroplane in straight and level, since that's a more interesting example. Let's assume that the direction of travel of the aircraft is normal to the plane of the propeller, so thrust is acting on the same plane as drag, in this idealized situation. Energy is added to the system in the form of thrust created by the prop. Said thrust is used to maintain the amount of kinetic energy of the aircraft. At the same time, this kinetic energy is being transformed into both lift and drag by the wings (and elevators, depending on how far aft the cog is) ergo not all the energy added to the system is used to counteract drag.

[iliis]

To explain it in yet another way: As long as you maintain your height no energy is used for lift, as energy is equal to force integrated over distance. Like as standing on a table requires no energy ;) However, an airplaine isn't standing on anything and the lift force is generated by pushing air downwards and this is what consumes energy.

A car or a train that drives with a constant velocity has constant kinetic and potential energy (assuming level ground). Therefore all energy that is consumed to maintain the status quo is spent to counteract drag.

A plane however pushes down on air instead of solid ground and accelerates it downwards. So not only does the fuel heat up the system due to drag, some of the energy accelerates quite a chunk of air.

Now you can argue that 'moving air' is nothing else than turbulence that takes a bit longer to dissipate and is therefore just another form of drag ;)

[htns]

This is a bit like the debate on whether it's the current or the voltage that kills, with lift-to-drag ratio being resistance. You are right in the physics sense in that drag alone is enough to calculate instantaneous fuel consumption, but to calculate range you already need to consider mass ratios and lift.

[notlefthanded]

Interesting point, sfc (specific fuel consumption) is only really density altitude and humidity dependant, since it's only calculated on a per engine basis, but a fixed wing aeroplane's range can be greatly affected by the weight and balance of the plane, ie whether the elevators need to be adding upward or downward pressure to the tail section to maintain a cruise attitude