thunderbird
Airman
- 74
- Jul 8, 2009
just to be a jonnie come lately.
i use this formula for autocrossing. knowing i can sustain 1.2 gs of acceleration in a corner, given a corner radius defined by three nonlinearly located cones, how fast can i go reasonably enter the corner? for say a sixty foot radius, my corner speed should be about 58 mph. Now all this acceleration is lateral, or perpendicular simultaneously to the velocity vector and the ground.
Of course the ground is holding the car up and there is no meaningful acceleration in the vertical axis.
For a plane, this is too simple of a model. One normally wants to keep flying against the force of gravity, lest the ground come up and smite thee. so an airplane flying with one gee needs all of that to counter the pull of gravity. There is nothing left to cause the airplane to turn. Lift mst balance gravity.
Say one wants to turn with one gee of lateral acceleration, both once again simultaneously perpendicular to the direction of flight and diection of velocity, one still would need one gee t act against the force of gravity. The turn is accomplished only by the unbalanced forces, (and knowing f=ma), the acceleration not balancing gravity. The plane would fly at a 45 degree bank angle, and the pilot would feel the squaroot of 2 gees, about 1.4 gees. the acceleration used in your simple formula and one gee then gets the radius of turn answer in your original post.
Lets say for some curious reason your pilot wants to use all of that one gee for turning. so he banks 90 degrees and pulls one gee. One's turn radius would, momentarily at least, match your calculations. But what force is balancing gravity? None, of course. And the plane will fall like a rock out of the sky. Unheeded, the plane and pilot will sadly be discumbombulated as the ground "rises up" and smites thee.
Of course there is the curious case where the pilot uses the aircraft body to generate enough lift to fend off gravity. Just the right amount of rudder, plus aileron input to keep the plane flying at 90 degrees to both the ground and the direction of flight. The pilot will still feel the force of gravity pulling him towards the ground, but it will be to his side, from his point of view, and the one gee of lift that is generating the turn.
i use this formula for autocrossing. knowing i can sustain 1.2 gs of acceleration in a corner, given a corner radius defined by three nonlinearly located cones, how fast can i go reasonably enter the corner? for say a sixty foot radius, my corner speed should be about 58 mph. Now all this acceleration is lateral, or perpendicular simultaneously to the velocity vector and the ground.
Of course the ground is holding the car up and there is no meaningful acceleration in the vertical axis.
For a plane, this is too simple of a model. One normally wants to keep flying against the force of gravity, lest the ground come up and smite thee. so an airplane flying with one gee needs all of that to counter the pull of gravity. There is nothing left to cause the airplane to turn. Lift mst balance gravity.
Say one wants to turn with one gee of lateral acceleration, both once again simultaneously perpendicular to the direction of flight and diection of velocity, one still would need one gee t act against the force of gravity. The turn is accomplished only by the unbalanced forces, (and knowing f=ma), the acceleration not balancing gravity. The plane would fly at a 45 degree bank angle, and the pilot would feel the squaroot of 2 gees, about 1.4 gees. the acceleration used in your simple formula and one gee then gets the radius of turn answer in your original post.
Lets say for some curious reason your pilot wants to use all of that one gee for turning. so he banks 90 degrees and pulls one gee. One's turn radius would, momentarily at least, match your calculations. But what force is balancing gravity? None, of course. And the plane will fall like a rock out of the sky. Unheeded, the plane and pilot will sadly be discumbombulated as the ground "rises up" and smites thee.
Of course there is the curious case where the pilot uses the aircraft body to generate enough lift to fend off gravity. Just the right amount of rudder, plus aileron input to keep the plane flying at 90 degrees to both the ground and the direction of flight. The pilot will still feel the force of gravity pulling him towards the ground, but it will be to his side, from his point of view, and the one gee of lift that is generating the turn.
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