Question

explain consideration of earth's rotation in designing and launching missiles and also explain angular velocity vector.

explain fiber optic methods of pressure sensing, piezoelectric, magnetostrictive and hall-effect sensors, smoke and fire detectors.

Answer 1

1)The effects of structural deflections (aeroelasticity) and of the dynamics of the relative motion of the control surfaces on overall missile dynamics are neglected, such that missile dynamics is based on the equations of motion for a single rigid body.

The rotation of the Earth is neglected, with the curved surface (longitude/latitude grid) of the fixed Earth unwrapped into a flat plane tangential to the launch point. This is the so called stationary and flat-Earth Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011 9588 approach applicable to in-atmosphere, Earth-bound flights, valid for vehicles flying in the atmosphere with speeds less than Mach 5 (below hypersonic speed).

The air is assumed to be at rest, neglecting any effect caused by wind.

Gravity is assumed to be acting through the center of mass of the missile, so that missile center of mass (CM) coincides with missile center of gravity (CG).

For modeling the motion of a rigid-body flight vehicle under consideration 1, two reference frames are introduced. They are the fixed-Earth frame F_E( O_E; i_E , j_E , k_E ) and the missile body-fixed frame F_B( O_B; i​​​​​​​_B , j_B , k_B ) , whose triad of unit base vectors are orthonormal and right-handed by convention. The axes of the coordinate systems associated with each of the frames F_E and F_B are aligned with their respective triads.  as by the second consideration, the fixed-Earth frame F_E is declared as an inertial (Newtonian) reference frame. Its origin O_E is defined as the launch point of the missile, with X_E-axis pointing North, Y_E-axis pointing East, and the positive Z_E -axis pointing downward in the direction of the local gravity vector. The body-fixed frame F_B has its origin O_B located at the instantaneous CM of the missile, the X_B - axis is parallel with the body longitudinal center line and points toward the nose of the missile, the Y_B-axis is directed to the right when viewed from the rear, and the Z_B -axis points in a direction below the horizontal. The three Euler angles φ , θ and ψ in roll, pitch and yaw, respectively, then describe the instantaneous angular orientation of the body coordinate system relative to the Earth coordinate system.

In the sequel, 6-DOF rigid-body nonlinear equations of motion will be derived, and then resolved in the body reference frame, such that all components of forces and moments acting on the missile will be modeled in the missile body-fixed axes.The six projections of the linear and angular velocity vectors on the moving body coordinate axes are the six degrees of freedom.

As the vehicle moves through the air mass, it experiences a relative wind over its body, which gives rise to aerodynamic forces. Introducing the wind frame F_W , such that its X_W coordinate axis lies along the velocity vector V of the vehicle CM w.r.t. the air mass gives rise to the Cartesian incidence angles (also called wind angles), which are the pitch-plane angle of attack α and yaw-plane sideslip angle β. The wind frame relates “the velocity vector of the CM w.r.t. the air mass” to the body frame. In order to relate the “ground (inertial) velocity vector of the CM w.r.t. the Earth” to the inertial fixed-Earth frame, an additional frame is introduced, called the velocity frame F_V (also known as the flight path frame). Since air is at rest by consideration 3, the two velocity vectors are in fact one and the same, so that the X_V coordinate axis also lies along the total velocity vector V of the vehicle CM. Two angles γ and χ then describe the instantaneous angular orientation of the velocity coordinates relative to the Earth coordinate system. The horizontal flight path angle (or heading angle) χ is measured from North to the projection of V into the local tangent plane X_EY_E (positive clockwise about downward vertical Z_E ), such that North and East are expressed by 0 and π/2 rad, respectively. The vertical flight path angle γ takes this projection vertically up to V . The wind and velocity coordinates are then related through μ about the velocity vector, such that the velocity frame FV is obtained by rotating F_W about the X_W axis so that the Y_V axis of F_V becomes parallel to the horizontal plane of F_E .

Fixed-Earth and body-fixed reference frames showing vector components resolved in Cartesian body coordinates Nomenclature for vector components resolved in F_b

Vector Description units roll axis pitch axis yaw axis

symbol O_B X_B O_BY_BO_BZ_B

F Total Force N F_XB   F_YB F_ZB

M Total Moment   Nm L M N

V Linear Velocity m/s   u v w

ω_BlX    Angular Velocity rad/s   p q r

a Total Acceleration   m/s² a_XB   a_YB a_ZB

​​​​​​​

2 fiber optics

This form of optical sensor uses an optical glass fiber as the sensing element. Multimode fibers with large core diameters (>10 μm) are used for sensor applications. Optical fibers can be coated with materials that respond to changes in strain, temperature, or humidity. The most commonly used fiber-optic sensor types include:

• Strain sensing: Mechanical strain in the fiber changes the geometric properties of the fiber, which changes the refraction of the light passing through it. These changes can be correlated to the applied strain.

• Temperature sensing: Strain in the fiber is caused by thermal expansion or contraction of the fiber. A strain measurement can be correlated directly with changes in temperature.

• Pressure sensing: Fiber-optic pressure sensors can be of two types—intensity and interferometric. In intensity-sensing fiber-optic sensors, the magnitude of light intensity reflected from a thin diaphragm changes with applied pressure (Udd, 2011). Interferometric pressure sensors work on the principle that pressure changes introduce perturbations into the sensor, which generate path-length changes in a fiber. This in turn causes the light/dark bands of an interference pattern to shift. By measuring the shift of the wavelength spectrum, the pressure applied on it can be quantitatively obtained (Lee, et al., 2012).

• Humidity sensing: A broad range of principles have been applied to optical fiber-based humidity sensors, including (i) luminescent systems with fluorescent dyes that are humidity-sensitive (ii) refractive index changes due to absorption in a hygroscopic (moisture absorbing) fiber coating such as polyimide; and (iii) reflective thin film-coated fibers made from tin dioxide (SiO₂) and titanium dioxide (TiO₂), which change the refractive index, resulting in a shift in resonance frequency (Morendo-Bondi, et al., 2004).

Interferometers

An interferometer is a device used to measure changes in a propagating light beam, such as path length or wavelength along the path of propagation. Generally, the sensor uses a light source such as a laser LED and two single fibers. The light is split and coupled into both of the fibers. The quantity being measured modulates the phase of the optical signal, which can be detected by comparison with a reference optical signal. There are four types of interferometric configuration: Fabry-Perot, Mach-Zehnder, Michelson, and Sagnac. This form of sensor is commonly used for measuring physical quantities, such as temperature, velocity, vibration, pressure, and displacement (Baldini, et al., 2002).

Because optical sensors use light either directly or indirectly for measurements, they have a number of advantages over other forms of sensing. However, these advantages are application-specific, as are the associated disadvantages. Table 2-2 presents the general advantages and disadvantages of optical sensors.Table 2-2.

Advantages and Disadvantages of Optical Sensors

Advantages	Disadvantages
High sensitivity	Susceptible to interference from environmental effects
Chemically inert	Can be costly
Small and lightweight	Susceptible to physical damage
Suitable for remote sensing
Immunity to electromagnetic interference
Wide dynamic range
Capable of monitoring a wide range of chemical and physical parameters
Reliable operation

Gas Sensors

Semiconductor sensors are commonly used to detect hydrogen, oxygen (O₂), alcohol, and harmful gases, such as carbon monoxide (CO). Domestic CO detectors are one of the most popular applications of gas-monitoring semiconductors. A typical gas sensor has a sensing layer and a sensor base, and is housed in a porous enclosure. The sensing layer is composed of a porous, thick-film metal oxide semiconductor (MOS) layer, such as SnO₂ or tungsten trioxide (WO₃). This is deposited onto a micro-sensor layer containing electrodes that measure the resistance of the sensing layer and a heater that heats the sensing layer to 200°C to 400°C. When the metal oxide is heated to a high temperature in air, oxygen is absorbed on the crystal surface with a negative charge, and donor electrons in the crystal surface are transferred to the absorbed oxygen, leaving positive charges in a space-charge layer. This creates a potential barrier against electron flow. In the presence of reducing gases, such as CO or (Hydrogen) H₂, catalytic reduction at the pre-absorbed oxygen layer decreases the resistance of the sensor. Oxidizing gases, such as nitrogen dioxide (NO₂) and ozone (O₃), have the opposite effect, resulting in an increase in resistance. The magnitude of resistance change can be correlated to the concentration of the gas species. The magnitude of the change depends on the microstructure and composition/doping of the base material; on the morphology and geometrical characteristics of the sensing layer and substrate; as well as on the temperature at which the sensing takes place (AppliedSensor, 2008). These parameters can be altered to tune the sensitivity toward different gases or classes of gases.

Despite many advantages, including low cost, relatively low maintenance, and long operational lifespan, semiconductor gas sensors can lack specificity in mixed gas environments. Thus, gases that are not of interest contribute to the overall signal response, resulting in an inaccurate elevated reading or false positives. To increase the selectivity of the gas sensors, chemical filters can be placed before the sensing material to remove the interfering components in the sample. These filters can be either passive or active, depending on whether a physical (passive) or chemical (active) mechanism is used. Filters can also be classified according to their location in the sensor, that is, internal (directly on the sensing element) or external (in a separate block). External filters such as charcoal are commonly used in commercial gas sensors.

Temperature Sensors

Semiconductor temperature sensors are based on the change of voltage across a p-n junction, which exhibits strong thermal dependence. The simplest form of temperature sensor is a silicon diode where the forward bias across the diode has a temperature coefficient of approximately 2.0–2.3mV/°C. Measurements are made by holding the bias current constant and measuring voltage changes. For accurate readings, the sensor needs to be calibrated (two-point calibration is sufficient due to good linearity) as significant inter-device variations can occur in the ±30 °C range. For more accurate measurements, diode-connected bipolar transistors are used. Again, a constant current is applied through the base-emitter junction, generating a voltage that is a linear function of the temperature. An offset may be applied to convert the signal from absolute temperature to Celsius or Fahrenheit. Typically, operating ranges are −55°C to +150°C. Semiconductor temperature sensors are often categorized by their output signal type, which can be analog (voltage and current), logic, or digital (Gyorki, 2009). The key advantages of this sensor type are ease of integration into a circuit, general ruggedness, and low cost. Their primary disadvantages are limitations of accuracy and stability, often poor thermal chip design, and slow response time (CAPGO, 2010)(Fraden, 2010).

Magnetic Sensors

Semiconductor magnetic sensors detect changes or disturbances in magnetic fields and convert these changes into a measureable electrical signal. They can produce information on properties, such as directional movement, position, rotation, angle, or electrical currents in machines or devices. They are used in medical devices such as ventilators to control the extent of movement; in enclosures for consumer electronic devices to detect opening and shutting of a device; and in renewable-energy scenarios, such as solar installations. For example, in domestic solar installations, magnetic sensors are used in power invertors that convert the electricity generated by the solar panels into usable electrical current for the home. They can also be used to monitor the charge level of batteries used in conjunction with solar panels for energy storage (Racz, 2011). The most common semiconductor magnetic integrated circuits apply the Hall effect (discovered by Edwin Hall in 1879) or magnetoresistive principles (ansiotropic, giant, or tunnel magnetoresistivity).

Hall-effect sensors comprise a thin layer of p-type (or n-type) semiconductor material that carries a continuous current. When the device is placed within a magnetic field, the measured voltage difference across the semiconductor depends on the intensity of the magnetic field applied perpendicular to the direction of the current flow. Charge carriers (electrons) moving through the magnetic field are subjected to Lorentz force (the force experienced by a charged particle as it moves through an electromagnetic field) at right angles to the direction of motion and the direction of the field. A voltage called the Hall voltage is generated in response to Lorentz force on the electrons. This voltage is directly proportional to the strength of the magnetic field passing through the semiconductor material. Semiconductor materials that have high electron mobility, such as indium (In), indium antimonide (InSb), indium arsenide (InAs), or gallium arsenide (GaAs) are commonly used in Hall-effect sensors (Eren, 2001). The output voltage is often relatively small—no more than a couple of microvolts—which requires amplification and signal conditioning to improve sensitivity and compensate for hysteresis (the difference in output between the rising and falling output values for a given input). In commercial sensors, sensing, signal amplification, voltage regulation, and signal conditioning are contained in a single package.

Hall-effect sensors demonstrate good environmental immunity to problems such as dust, vibration, and moisture. However, they can be affected by other sources of magnetic flux that are in close proximity, such as those generated by electrical wires. They are robust, having no mechanical contacts for sensing. They are, however, effective only over a limited distance and do not work at distances great than 10cm unless the magnetic field strength is very high.