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Formulas for Electrical Power Systems
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Signal Usage and AnalysisWeek 1: Role of sensors in Aviation + Pressure and temperature sensors
Theory
1. Sensor also called a transducer is a device that senses/detects specific physical
property (pressure, temperature, motion etc.) and transmits a resulting impulse for
measurements or control.
2. Pressure sensor —> application: altitude, velocity, fuel, tires, etc.
• Mechanical (manometer)
- liquid manometer (mercury)
- aneroid manometers (bellows, membrane manometers)
• Change in resistance = changes when force or pressure is applied
- load cells and strain gauges
• Separation of charge (Piezoelectric materials)
- Piezoelectric sensors
3. Temperature sensor —> temperature in engine
• mechanical (mercury thermometer)
• resistive (thermistors and RTD’s = Resistive Temperature Detectors)
o RTD
o Thermistors
• Seebeck effect (thermocouple)
4. Fiber optic strain sensing: Laser light, passing through the fiber, is used to measure
the elongation. ( 1microstrain resolution and complete immunity to electromagnetic
noise). → hoort bij pressure sensor
5. A computer-based instrumentation system → consists of sensors, signal
conditioning, a data-acquisition system, an analog-to-digital converter and one or
more general purpose computer(s).
6. Seebeck effect → is the direct conversion of a temperature difference between two
different metals or half conductors into an electrical voltage.
Formulas
Pressure sensors
- Pressure = force / area
- q= kx → with q charge in Coulomb, x displacement in meter, K sensitivity
(Coulombs/meter)
- C= q/V → with C the capacitance, so q = CV
- To determine pressure p: V = Kpp → with Kp sensitivity in V/(Nm^-2)
Temperature sensors
- Delta V= -S(T)delta T → with S(T) Seebeck coefficient
- SA, SB constant: V = SA(T1 – T2) – SB(T1 – T2) = ( SA – SB)(T1-T2) →
T1 = T2 + (V/(SA – SB))
, - SA, SB not constant: T1= T2 + alfa (0) + alfa (1) V + alfa (2) V^2 + etc.
Resistance Temperature Used very often below 600- T vs R almost linear at low
Detectors (RTD) 800 degrees temperature
Thermistors (ceramics) Used at lower temperatures T-R relationship negative at
(below 130 degrees) low temperature (formula)
Thermocouple Applicable in wide Formula
temperature range
Load cells and strain gauges
- Strain: delta L/L
- Delta R/R = K * Delta L/ L (K = 2)
- Rrtd = R0 ( 1 + alfa (T – T0))
Pitot tube
- Pt= Qc + Ps → Ps = static pressure, Pt is total pressure, Qc is dynamic pressure
- Qc= Ps0 ((1+0.2(Vc/Ao)^2)^3.5 -1) → Vc is indicated airspeed, A0 is the spead of
sound at sea level
- Vc= Mc * A → Mc is mach number
- F(x) = y0*((x-x1)/(x0-x1)) +y1*((x-x0)/(x1-x0))
- Vc = A0 wortel(5((Qc/Ps0) +1)^(1/3.5) -1)
, Week 2: linear accelerometers: laser gyroscopes, proximity sensors
1. Acceleration → linear and angular acceleration
2. Linear
• Mass spring system
• Piezoelectric crystals
3. Angular
• Classical gyroscope
- Mechanical device
- Important property: spinning motion preserved
- At least 3 gyro’s needed to preserve attitude
• Laser gyroscope (fiber optic or ring laser)
- Fiber optic gyroscope → Sagnac effect & phase difference
- Ring laser gyroscope → Sagnac effect & Frequency difference
4. Wheatstone bridge → determination of electrical resistance → electric circuit used
to measure an unknown electrical resistance by balancing two legs of a bridge circuit.
Configuration to measure small variations in resistance.
5. Capacitive proximity sensor & inductive proximity sensor
6. Galvanometer → analog device to measure current
• Draaispoelmeter
• Coil in combination with spring
• Needs to be build in an electrical circuit
• Internal resistance small
7. Ammeter → galvanometer with parallel resistance
• Variable shunt resistance Rsh in parallel
• Increased current range
8. Voltmeter using galvanometer
• Parallel with electrical circuit
• Internal resistance large
• Variable shunt resistance in series
9. Digital multimeters
• Current measurement: measure voltage across resistance
• Measurement of resistance, capacitance etc.: apply known current and
measure voltage
10. Accelerometers in Boeing 787
• Inertial navigation integration of linear acceleration
• 3 linear accelerators needed
• Gyroscopes are used to determine angular velocities
• Corrections made for earth’s rotation and attitude of aircraft
• Each IRU and AHRU has three ring laser gyros and three linear
accelerometers. Using these and air data from the flight control electronics
(FCE).
- IRU: Inertial Reference Unit
- AHRU: Attitude and Heading Reference Unit
- ERS: Earth Reference System
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