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In general, passengers dislike turbulence. Avoiding all turbulence sometimes is not viable, as it would make the flight too long, too expensive (fuel consumed), or simply not having alternatives.

How does the pilot deal with turbulence? Does he or she keep the same altitude? The same speed (relative to the wind)? Increase power? AoA?

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Most of the time the turbulence we experience is termed "chop", which is akin to what you experience on a boat on the lake -- bumps but no real altitude deviations. With altitude deviations we'll call it "turbulence". Within these broad categories we'll qualify them with "light", "moderate", "severe" and "extreme" in reports to ATC and other aircraft. These reports do suffer from a fair bit of subjectivity with respect to aircraft type (wing stiffness) and pilot experience.

If it is light chop, I'll generally just ride it out and turn the seatbelt signs on.

The first thing I'll do if encountering moderate chop or turbulence is to query ATC and get ride reports from aircraft ahead of us and at different altitudes than us. From this information I'll make a determination to ride it out or to request a climb/descent. If the turbulence was particularly bad, slowing down was an option, but I only came across that need a few times. Our ability to descend would often be limited by route length and fuel and major lateral deviations also depended on contingency fuel, so in some cases we had no choice but to stay in the chop. If the turbulent areas were well forecast or had lots of PIREPS, our dispatchers would sometimes route us differently.

As for power adjustments, if we weren't slowing down due to aircraft limitations I would just adjust power so that maximum airspeed deviations stayed below Mmo.

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Some large aircraft (maybe all?) have a minimum and maximum turbulence penetration speed. For the 747-100 and -200 aircraft the minimum was 270 knots and the maximum 320 knots IAS. I forget the mach equivalents.

Those same aircraft had a turbulence mode on the autopilot that reduced the sensitivity to pitch and roll deviations. However, many pilots (including myself) would hand fly through heavy turbulence because the autopilot ride even in turbulence mode was worse than what we could get by hand.

There are situations in which changing altitude is not an option. For example, if you cannot descend because doing so would burn too much fuel, but you cannot climb because you are already as high as you can go. It also may not be possible to deviate much from your course because of fuel considerations.

Consider a Hajj flight from Jakarta to Jeddah. It's 10 hours and that's what you've got fuel for. Depending on the time of day, there is often (seemingly always) a line of thunderstorms too long to go around between Sumatra and India. You pick your way through the line using radar to avoid the intense echoes.

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The pilot can slow down the plane, or he can try flying at a different altitude. He also has the option of flying around it, although many times this is impractical.

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