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Where T is the thrust generated (force), is the rate of change of mass with respect to time (mass flow rate of exhaust), and v is the velocity of the exhaust gases measured relative to the rocket. For vertical launch of a rocket the initial thrust at liftoff must be more than the weight.
The various Euler angles relating the three reference frames are important to flight dynamics. Many Euler angle conventions exist, but all of the rotation sequences presented below use the z-y'-x" convention. This convention corresponds to a type of Tait-Bryan angles, which are commonly referred to as Euler angles. This convention is described ...
In fluid dynamics, angle of attack (AOA, α, or ) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is moving. [1] Angle of attack is the angle between the body's reference line and the oncoming flow.
To analyze thrust, we take a mathematical perspective. First, an aircraft takes off at some angle with respect to the ground. For a rocket traveling straight "up", this angle would be 90°, or at least close to 90°. For airplanes and most other aircraft, this angle will be much less, generally ranging from 0° to 60°.
The longitude of the ascending node Ω, measured in the fundamental plane counter-clockwise looking southward, from a reference direction (usually the vernal equinox) to the line where the spacecraft crosses this plane from south to north. (If inclination is zero, this angle is undefined and taken as 0.)
In straight, climbing flight at constant airspeed, thrust exceeds drag. In straight descending flight, lift is less than weight. [5] In addition, if the aircraft is not accelerating, thrust is less than drag. In turning flight, lift exceeds weight and produces a load factor greater than one, determined by the aircraft's angle of bank. [6]
The "M" indicates it is a measure of pitching moment changes. The indicates the changes are in response to changes in angle of attack. This stability derivative is pronounced "see-em-alpha". It is one measure of how strongly an aircraft wants to fly "nose first", which is clearly very important.
The angle of attack is the angle between the chord line of an airfoil and the oncoming airflow. A symmetrical airfoil generates zero lift at zero angle of attack. But as the angle of attack increases, the air is deflected through a larger angle and the vertical component of the airstream velocity increases, resulting in more lift.