Problem 4. (20 points) In a time interval of t = 0 through t = 60 s, an aircraft

Question

Problem 4. (20 points) In a time interval of t = 0 through t = 60 s, an aircraft's orientation remains (again, by sheer coincidence) perfectly aligned with its velocity vector. In this time interval, a strapdown 3-axis ac celerometer measures the aircraft's acceleration. After correcting for gravity, these measurements are provided in the attached .mat fi inertial acceleration, not proper acceleration. le, i.e. the measurements provided are of At time t 0, the position coordinates of the aircraft's center of mass (which is where the accelerometers are attached) in a tangent axis system (North-East-Down (NED) system) T are: p'(0)= | -2.5 | km. For this problem, the NED system is assumed to be inertial. At time t = 0, the airspeed is 75 m/s. The heading angle and the angle of climb are: (0) = 45°, 10) = 2. For the given time interval, plot the following: the airspeed, the heading angle, the angle of climb, and the three position coordinates. Write down the position coordinates of the aircraft's c.m. at time t = 60 s. Plot the two angles in degrees, not radians. Plot the position coordinates as a 3D trajectory using, say, the plot3 command in MATLAB®.

Explanation / Answer

An accelerometer is a compact device designed to measure non-gravitational acceleration. When the object it’s integrated into goes from a standstill to any velocity, the accelerometer is designed to respond to the vibrations associated with such movement. It uses microscopic crystals that go under stress when vibrations occur, and from that stress a voltage is generated to create a reading on any acceleration. Accelerometers are important components to devices that track fitness and other measurements in the quantified self movement.

Uses of a gyroscope or accelerometer

The main difference between the two devices is simple: one can sense rotation, whereas the other cannot. In a way, the accelerometer can gauge the orientation of a stationary item with relation to Earth’s surface. When accelerating in a particular direction, the accelerometer is unable to distinguish between that and the acceleration provided through Earth’s gravitational pull. If you were to consider this handicap when used in an aircraft, the accelerometer quickly loses much of its appeal.

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