Undergrad Does an airplane have to nose down in order to follow a curve?

[OmCheeto]

Mea culpa too.
But any answer you came up with would have been just as irrelevant to the price of fish and most of the rest of this thread. The whole topic could be dealt with in a single paragraph, imo.

Well, that all depends on if you mean a paragraph of maths, or a paragraph of words.

No amount of words can answer this, IMHO.

ps. When Greg asks for upgrade ideas to the forum next time, please remind me to post that such problems should be sent to the "homework" section, where I'm pretty sure it would have died a quick, and merciful death.

 

[olivermsun]

i think the question has morphed into two, maybe 3 , unintentionally.
1. does a properly trimmed and conditionally stable aircraft require additional control inputs to follow the Earth's curve at a set altitude and speed.
2. does this properly trimmed aircraft , also fly on a flat Earth with no changes to the control settings from the round earth.
2a. above but with the aircraft being conditionally unstable.

“Properly trimmed” includes everything that affects the (desired) flight characteristics of the plane: the speed and weight balance of the plane, the pressure and density of the air outside, the wind, etc. If the pilot notices the plane slowly gaining pitch and altitude, whether because of the earth’s curvature or some other reason, the trim can be corrected. In principle the same plane would then seem to be out of trim for flight in the exact same conditions except over a flat earth. That should answer 1 & 2. 2b shouldn’t change anything except that being out of trim is self-reinforcing.

 

[rcgldr]

“Properly trimmed” includes everything that affects the (desired) flight characteristics of the plane: the speed and weight balance of the plane, the pressure and density of the air outside, the wind, etc. If the pilot notices the plane slowly gaining pitch and altitude, whether because of the earth’s curvature or some other reason, the trim can be corrected. In principle the same plane would then seem to be out of trim for flight in the exact same conditions except over a flat earth. That should answer 1 & 2. 2b shouldn’t change anything except that being out of trim is self-reinforcing.

As mentioned in post #116, assume a normal plane with a center of mass slightly in front of the center of lift, and some up elevator (this is the elevator "trim") to generate aerodynamic downforce at the tail which compensates for the center of gravitational force being in front of the aerodynamic lift force. If "properly trimmed", the plane self corrects. If the plane pitches up, it slows down, reducing the downforce at the elevator, and the plane will pitch down and speed up. If the plane pitches down, it will speed up, increasing the downforce at the elevator, and the plane will pitch up and slow down. If due to curvature of the atmosphere about the earth, the plane travels into lower density air due to the curved atmosphere, the lift on the main wing decreases (and typically power from the engine also decreases), so the plane will tend to follow the curvature of the atmosphere around the Earth since the plane is trimmed to fly "level" at a certain speed and air density.