# Does an accelerating airplane also start climbing?

Assume that an airplane is flying level. If I understood correctly in this situations there are four forces acting on it: weight, thrust, drag and lift.

Lift depends on air density, airspeed, wing area and lift coefficient. In the situation described above all of these parameters are constant with the exception of airspeed which can be changed by pilot. So when increasing airspeed lift increases too which makes sense because that seems to be how planes take off.

However when you watch footage of airplanes accelerating (for instance when a fighter turns the afterburners on) they seem to be able maintain altitude.

At this point I see three possibilities:

1. The airplane doesn't climb or climbs very little because the pilot simultaneously compensates.
2. I have the wrong impression and the airplane does climb.
3. My reasoning above was wrong and there's actually no reason for the airplane to climb further.

So which one is it?

• Many pilots are taught by the concept that Throttle equals Height and Elevators equal Speed, as you've just discovered. Obviously it's all interlinked, but the way most people think of an aircraft climbing and descending with the elevator as an up/down control is wrong. – Dan Oct 12 '15 at 19:04
• Possible duplicate of Trim setting and constant airspeed? – fooot Oct 12 '15 at 19:13
• See also pitch vs. power. – fooot Oct 12 '15 at 19:13
• @Dan - I was taught that throttle equals energy, elevator equals AOA. The amount of energy you're adding into the equations for the four forces is directly related to throttle, and your lift and drag coefficients are directly related to your AOA. This is a mathy way to approach it which isn't for everyone, but I'd had experience with PC flight simulators growing up, and so was very familiar with the basic behaviors of stick and throttle and some of the fundamental physics of flight (like trading speed for altitude and vice versa, up to and including energy-management ACM theory). – KeithS Oct 12 '15 at 23:47
• What about this aircraft ? (I mean, induced AOA changes due to increasing thrust. Marginal, as the aircraft will pitch up soon enough, but yet, basically it does the opposite in the first few seconds, right ?) – Karl Stephen Oct 13 '15 at 19:19

You assume that three of the four forces are constant. This is not quite right: Only the mass is given, all the other forces are variable.

• Thrust $T$: Changes with throttle setting. Also, thrust can vary with flight speed $v$ in a way that can be expressed as $T \propto v^{n_v}$.
• Lift $L$: Depends on speed and on angle of attack $\alpha$, as in $L \propto v^2 \cdot (\alpha - \alpha_0)$. The accelerating airplane is held level by gradually reducing the angle of attack, such that lift exactly equals weight. The elevator is the instrument for controlling angle of attack.
• Drag $D$: Like lift, drag depends also on speed and angle of attack: $D \propto v^2\cdot (\alpha - \alpha_0)^2$

Your option a is the correct one: The pilot compensates by adjusting the angle of attack by gradually pushing the stick forward. If he would keep the stick (and consequently the elevator) unchanged, the airplane would climb.

Now it might be opportune to introduce the concept of specific excess power ($SEP$). This is the extra power available to the pilot, related to the aircraft weight to make it comparable between airplanes. $$SEP = \frac{P_{eff}-D\cdot v}{m\cdot g}$$ where $P_{eff}$ is the effective power: $P_{eff} = T\cdot v$. When the pilot commands more thrust than needed for level flight, the excess thrust can be either converted into kinetic energy (speed) or potential energy (altitude). If you look at the units, $SEP$ is a speed. It tuns out that it is the possible climb speed available if flight speed stays constant: $$SEP = v_z$$ In reality, the practical climb speed is smaller because the airplane needs to speed up when climbing to compensate for the decreasing air density.

The possible acceleration is almost as easy to calculate from the specific excess power: $$\ddot x = SEP\cdot\frac{g}{v}$$

Of course, a mixture of both is also possible, as is trading in one for the other. By adjusting the elevator and with it the flight path, the pilot decides what happens.

Your (a) assumption is correct -- the aircraft can accelerate without climbing because the pilot compensates. As the speed increases, an aircraft that was stable & in trim would naturally tend to climb to maintain airspeed, if the pilot didn't intervene. To counter this tendency, the pilot applies a slight nose-down input (i.e. elevator down, raises the tail & lowers the nose -- control stick forward).

• And if the plane uses a fly-by-wire system, this same pitch compensation can be applied by the flight director computer. Most Airbus airliners in service have such a system which compensates for this basic tendency, allowing a more "ideal" use of the sidestick and throttle by the pilots (though, after 1500 hours of flight time in aircraft with less sophisticated control setups, there's some unlearning to do when you sit in an Airbus for the first time). The latest Boeing widebodies and 747-8 have a FBW, but it's designed to be more similar to a pure mechanical system and doesn't compensate. – KeithS Oct 12 '15 at 23:34

A basic stability requirement for (most) a/c requires the plane to pitch down when speed decreases and pitch up when speed increases. It's called positive speed stability.

As you decelerate the nose of the plane will point down and the plane will pick up some speed as it begins to descend. It will do so until it picks up a little too much speed and the nose now starts to point a little up, in doing so slowing down a little bit and so on. It's called a phugoid oscillation.

The very same thing will happen when you floor the throttles: speed increases, airplane wants to point the nose towards the sky, plane slows down a little bit, that makes the aircraft want to point the nose a bit below. It wobbles a little bit and then it settles in a nice gentle climb at the very same speed you had before you have pushed the throttle.

It is not the increased lift that makes the a/c climb(in fact you will have less lift as you are climbing and a reduced AoA), it is the stability momentum that pitches the nose up and that makes that extra power from the engines point up. That is what makes you climb.

So how do pilots maintain level flight while accelerating? Pushing the control forward will instruct the tailplane to create less downlift, raising the tail, lowering the nose and counterbalancing the nose up intentions of the plane. You are now still flying level, a bit faster, and a bit more "nose down" mind you: because of the extra speed you now have a lower AoA than before, so your nose is a few minute degrees lower than before when you were slower.