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Let an aircraft in a steady level flight be trimmed at certain speed. A level and steady flight at a higher speed can be achieved by changing throttle and elevator together ( and not just by changing elevator or throttle alone). How?

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From a purely practical standpoint, let's say you're in a Cessna 172 (a common light aircraft often used for training) and you're in economy cruise at 2400 rpm at 6,000 feet on a standard day. According to the cruise performance chart I have here, you would be using 60% power, burning 6.8 gph, and have a true airspeed of 109 kts. You're hand flying the airplane as it has no autopilot.

Now the cute gal that you've talked into taking this trip with you mentions that she's beginning to need a bathroom. You neglected to bring along a urinal (and maybe more than a urinal is needed), so you decide to speed up to the maximum cruise speed for 6,000 feet. You consult the cruise performance chart and see that you can get 75% power at 2600 rpm. That will increase your cruise speed to 120 kts at the cost of burning 8.4 gph.

You would smoothly increase the rpm to 2600. As the power came up, you would have to hold a little forward pressure on the elevator to keep from climbing. If you're used to the airplane, you might unconsciously reach down to the trim wheel and roll in a little down elevator. In any event, you will eventually want to trim out the down elevator force you're holding on the control wheel.

If you set 2600 rpm to start the speed up, you'll notice that the rpm goes a little above 2600 as your speed increases (this is a fixed pitch propeller), so you monitor and adjust the rpm as necessary to settle on 2600 rpm with elevator forces trimmed.

If you have an autopilot with an altitude hold function but that doesn't control the power, all you'll have to do is control the power.

If you have an autopilot with FADEC, just set what you want and it will do all the work from there.

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I'm not sure if the question is how or why.

Assume that the throttle is changed (let's say increased) in level flight. The following things happen:

  1. The speed increases.
  2. The increase in speed increases the lift produced by the wing and the aircraft attitude changes (it pitches up) and the aircraft is no longer in level flight.
  3. In order to trim this, the elevator correction has to be applied.

On the other hand, assume that the elevator is used to pitch the aircraft down. Then the following things happen:

  1. The lift (and drag) decreases and the speed increases.
  2. In order to maintain the speed, the engine power has to be reduced.

So, its not possible to maintain level flight at a set speed at a given altitude using only throttle or elevator.

Of course, at different altitudes the aircraft will be trimmed for different power settings for fixed elevator setting.

One way to understand this is that the energy is conserved and if the kinetic energy is changed (by changing the speed), the potential energy (altitude) should also be changed for level flight. Otherwise the aircraft will trim itself at another stable altitude.

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