Kitabı oku: «Introduction to Flight Testing», sayfa 5

2.2.6 Operationalizing the Standard Atmosphere

Applying the equations developed above, we can take one of several approaches to implementing the standard atmosphere for flight testing work. Most simply, these equations form the basis for tabulated values of the standard atmosphere, which are tabulated by NOAA et al. (1976) or ICAO (1993). In addition, a limited subset of the U.S. Standard Atmosphere (NOAA et al. 1976) is reproduced in Appendix A. Alternatively, pre‐written standard atmosphere computer codes may be downloaded and used in a straightforward manner. Popular examples include the MATLAB code by Sartorius (2018) or the Fortran code by Carmichael (2018). If these are not suitable for a particular purpose, then custom code can be written, as described below in a form that simplifies the coding.

In the troposphere where the temperature gradient is a = dT/dh =  − 6.5 K/km, the temperature distribution in Eq. (2.10) can be expressed as a linear function

(2.23)

where h is the geopotential altitude and k = 2.256 × 10⁻⁵ m⁻¹ = 6.876 × 10⁻⁶ ft⁻¹ is a decaying rate. According to Eqs. (2.19) and (2.20), the pressure ratio and density ratio in the troposphere (0 ≤ h ≤ 11 km) are given by

(2.24)

and

(2.25)

where n =  − g₀/aR = 5.2559.

Figure 2.4 The normalized temperature, pressure, and density distributions in the standard atmosphere.

In the lower stratosphere (11 km < h ≤ 20 km), the atmospheric temperature is constant at 216.65 K. If we define the critical altitude at the tropopause to be h_trop = 11 km, then the temperature and pressure ratios at the tropopause are θ_trop = 0.7518 and δ_trop = 0.2233, respectively. Recasting (2.16) in terms of these ratios, we obtain

(2.26)

for the pressure ratio in the lower stratosphere. Finally, the density ratio in the lower stratosphere is simply found by the ideal gas law,

(2.27)

Figure 2.4 shows the pressure, density, and temperature distributions normalized by the sea level conditions in the standard atmosphere.

2.2.7 Comparison with Experimental Data

The above equations describe the idealized atmosphere where the parameters are considered as the mean values of the measured quantities. However, as indicated in The U.S. Standard Atmosphere (NOAA et al. 1976), measurement data show considerable variations of the atmospheric parameters depending on time (day and season) and geographic location, which should be considered in flight testing.

Experimental measurements may be compared with the theoretical variation of pressure and temperature derived from the standard atmosphere. Atmospheric data can be collected by a weather balloon (Figure 2.5), which ascends through the atmosphere and measures pressure and temperature throughout the flight. For the case presented here, the balloon ascended to an altitude of 30.161 km (98,953 ft) before bursting and descending via parachute back to Earth. Data throughout the ascent and descent were collected and are presented in Figures 2.6 and 2.7. The temperature data shown in Figure 2.6 show similar trends to the standard temperature profile, but the agreement is not very good. This is not surprising, since the details of the temperature profile are strongly dependent on local weather, time of year, latitude, etc. However, some of the similarities are noteworthy: the experimental temperature lapse rate is approximately the same as the standard lapse rate, particularly at low altitudes. Also, the location of the tropopause, corresponding to a change to an isothermal temperature profile, is in good agreement. Finally, the slope of the high‐altitude lapse rate is also in fairly good agreement with the standard temperature profile. Pressure data, in Figure 2.7, show excellent agreement with the standard atmosphere. This is also expected since the hydrostatic equation is a good descriptor of the physics of pressure variation with altitude. The good agreement shown here underscores the utility of using pressure measurement for measuring altitude on aircraft (see Chapter 3 for further details on how altimeters operate).

Figure 2.5 Launch of a high‐altitude weather balloon from the oval of The Ohio State University.

Figure 2.6 Comparison of the standard atmosphere with temperature data measured by a weather balloon.

Figure 2.7 Comparison of the standard atmosphere with pressure data measured by a weather balloon.

2.3 Altitudes Used in Aviation

We will now conclude this chapter with a discussion of different altitude definitions used in aviation. We have already introduced several definitions of altitude for the preceding discussion on the standard atmosphere. To recap, these include absolute altitude, geometric altitude, and geopotential altitude. Absolute altitude, h_A, is measured from the center of the Earth and is only relevant when determining the value of gravitational acceleration at a particular altitude. Geometric altitude, h_G, is the height of an aircraft above mean sea level. And, geopotential altitude, h, is the height above sea level with the assumption of constant gravitational acceleration. Geopotential altitude is only relevant in the context of deriving the standard atmosphere, so should not be used elsewhere. For the remainder of this book, we will presume that the differences between geometric altitude and geopotential altitude are small and will simply refer to the geometric altitude as h.

However, these altitude definitions are limited to an engineering context. To make things interesting, we also have a set of altitudes that are defined for the aviation community. And, to make things more interesting, some of the aviation altitudes use the same terms but different definitions! The aviation set of altitudes include true altitude, indicated altitude, pressure altitude, density altitude, and absolute altitude. We will discuss each of these as follows.

True altitude is the height above mean sea level. In the aviation community, this altitude is often abbreviated as MSL. When an aircraft altimeter is referenced to the local barometric pressure reading, it indicates true altitude. (Details on altimeter operation are provided in Chapter 3.) Pilots around the world often refer to this setting of the altimeter as QNH. Note that the aviation definition of true altitude is identical to the engineering definition of geometric altitude.

Similarly, indicated altitude is a direct reading from the altimeter, no matter how the altimeter is set. This may or may not be the same as true altitude, depending on the reference pressure used on the altimeter. (The reference pressure essentially shifts the calibration of the altimeter to match local barometric pressure, instead of standard sea level pressure.)

Pressure altitude, in the aviation realm, is defined as the altitude read from the altimeter when it is set to a reference pressure of 29.92 inHg, which is the standard sea level pressure. In many locations around the world, barometric pressure readings are reported in millibars or hPa, where 1013 mbar (=1013 hPa) is equal to 29.92 inHg (both being standard sea level pressure). Pilots refer to this setting of the altimeter – to provide pressure altitude – as QNE. In engineering terms, pressure altitude has essentially the same meaning. An engineer would express pressure altitude as the altitude corresponding to a given pressure in the standard atmosphere. Both the engineering and aviation definitions for pressure altitude are equivalent, since the altimeter referenced to 29.92 inHg (1013 mbar) is calibrated based on the standard atmosphere.

Density altitude is defined, in aviation terms, as the pressure altitude corrected for non‐standard temperature. If the temperature on a given day at a particular altitude is hotter than the standard temperature, then the density altitude will be higher. In engineering terms, density altitude is defined as the altitude corresponding to a given density in the standard atmosphere. Aircraft performance depends significantly on local air density, so density altitude is a direct indication of aircraft performance. Higher density altitude (corresponding to lower density) will lead to longer takeoff ground roll, slower rates of climb, higher true airspeed for stall, etc.

Finally, pilots are also concerned with the height of the aircraft above the local terrain, which is termed absolute altitude. In the aviation realm, absolute altitude is often also termed height above ground level, so the acronym AGL is often used. On aviation charts, both true altitude (MSL) and absolute altitude (AGL) are reported for various obstacles. For example, the top of a 500‐ft tall radio tower mounted on ground that is 1500 ft above sea level will have a maximum height of 2000 ft MSL or 500 ft AGL. Thus, pilots pay close attention to the absolute altitude (also referred to as QFE) as well as the true altitude (QNH). Note that absolute altitude (AGL) in an aviation context is not the same as absolute altitude (h_A) in an engineering context. The engineering definition of absolute altitude is seldom used in aerospace or aviation, outside of discussions of the standard atmosphere.

A selection of the most significant of these altitudes is illustrated in Figure 2.8. The aircraft depicted in this figure is cruising at a true altitude of 5000 ft (MSL), but because its flight is over mountains rising 2000 ft above sea level, the aircraft is at an absolute altitude of only 3000 ft AGL. On this given day, the local barometric pressure reading is lower than standard, causing the pressure altitude to be higher than the true altitude. And, if the temperature on this day is higher than standard, then the density altitude will be even higher than pressure altitude or true altitude. Thus, we could easily have a situation where absolute altitude, true altitude, pressure altitude, and density altitude are all different. In Chapter 3, as we move into instrumentation used for flight testing, we will discuss the operation of the altimeter in greater detail.

Figure 2.8 Illustration of different altitudes used in aviation.

Nomenclature

a

temperature lapse rate,

dT

/

dh

c

chord

g

gravitational acceleration

g₀

gravitational acceleration at sea level

h

geopotential altitude

h_A

absolute altitude (height relative to the center of the Earth)

h_G

geometric altitude (height above mean sea level)

k

constant,

a

/

T

_SL

m

mass of air in the control volume

n

constant, −

g

₀

/

aR

p

pressure

R

gas constant for air

r_Earth

Earth's mean radius

Re_c

Reynolds number based on chord

S_visc

Sutherland's constant

T

temperature

U_∞

freestream velocity

W

weight of air in the control volume

x

length of control volume element

y

width of control volume element

β

constant used in Sutherland's Law

δ

pressure ratio,

p

/

p

_SL

μ

dynamic viscosity

ν

kinematic viscosity

ρ

density

σ

density ratio,

ρ

/

ρ

_SL

θ

temperature ratio,

T

/

T

_SL

Subscripts

ref

reference conditions at the base of a given atmospheric layer

SL

sea level

trop

tropopause

1

beginning of an atmospheric layer

2

end of an atmospheric layer

Acronyms and Abbreviations

AGL

height above ground level

ICAO

International Civil Aviation Organization

MSL

height above mean sea level

NOAA

National Oceanic and Atmospheric Administration

References

Anderson, J.D. Jr. (2016). Introduction to Flight, 8e. New York: McGraw‐Hill.

Carmichael, R. (2018). Public domain aeronautical software for the aeronautical engineer. http://www.pdas.com/atmos.html (accessed 28 December 2020).

ICAO (1993). Manual of the ICAO Standard Atmosphere (Extended to 80 Kilometres (262 500 Feet)), 3e, ICAO Document 7488. Montréal, QC: International Civil Aviation Organization.

NOAA, NASA, and USAF (1976). U.S. Standard Atmosphere, 1976, NOAA‐S/T‐76‐1562, NASA‐TM‐X‐74335. Washington, DC: U.S. Government Printing Office. http://hdl.handle.net/2060/19770009539.

Sartorius, S. (2018). Standard Atmosphere Functions, v. 2.1.0.0. MathWorks File Exchange. https://www.mathworks.com/matlabcentral/fileexchange/28135-standard-atmosphere-functions.

Sutherland, W. (1893). LII. The viscosity of gases and molecular force. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Series 5 36 (223): 507–531. https://doi.org/10.1080/14786449308620508.

3
Aircraft and Flight Test Instrumentation

This chapter fundamentally deals with how we will measure the various aircraft performance characteristics. We will cover common instruments used in the aircraft cockpit (both traditional and modern avionics systems), as well as instrumentation found in external data acquisition (DAQ) systems. This fundamental understanding is important for developing an appreciation of the capabilities and limitations of each instrument and sensor system. We will begin with a discussion of various sensors and instrumentation hardware used in flight testing (these instruments can be either the standard cockpit instrumentation or supplemental instrumentation dedicated for flight testing purposes).

A discussion of instrumentation and DAQ must begin by detailing what we wish to measure and how we will measure it. For aircraft flight testing, we essentially need to know the vehicle's state – we need to know the aircraft's position and orientation as a function of time. Practically speaking, this requires measurements of the vehicle's velocity, acceleration, orientation (pitch, roll, and yaw angle relative to a defined set of coordinate axes), altitude, and magnetic heading.

Aircraft instruments are generally calibrated to report quantities in the English unit system, sometimes using nonstandard units. Speed is most often reported in knots (nautical miles per hour), altitude is in feet, vertical speed is in feet per minute, distance is in nautical miles, angles are in degrees, and angular rates are in degrees per second. When analyzing flight test data from these measurements, it is critical to convert to standard consistent units before further analysis. All analysis must be done in a single, consistent unit system with standard units (e.g., English: ft/s, ft, deg, and deg/s, or SI: m/s, m, deg, and deg/s). After completion of the analysis, the results may be converted to any desired units for reporting. This section provides an orientation to the instruments installed in general aviation (GA) aircraft cockpits, including both classical “steam gauge” instruments and more modern glass panel instrument displays. We will first discuss the traditional instruments, followed by glass panel avionics systems.

3.1 Traditional Cockpit Instruments

In traditional flight testing methods at the university level, many of the desired parameters are hand‐recorded from cockpit indicators such as the airspeed indicator (ASI), attitude indicator, heading indicator, and altimeter, which are illustrated in Figures 3.1 and 3.2 for a traditional “steam gauge” cockpit. The traditional instruments are arranged in a “six pack” configuration (Figure 3.2): starting at the upper left and moving clockwise, the instruments are the ASI, attitude indicator, altimeter, vertical speed indicator (VSI), heading indicator (also known as the directional gyro), and turn/slip indicator (also known as the turn coordinator). We will group these instruments into two types. The first group, consisting of the attitude indicator, heading indicator, and the turn/slip indicator, is based on gyroscopes. The second group, consisting of the ASI, altimeter, and VSI, is based on physical measurements of pressure. We will discuss each group of instruments in more detail as follows. Interested readers can also consult various publications such as Chapter 7 of the Pilot's Handbook of Aeronautical Knowledge (2008), Chapter 5 of the Instrument Flying Handbook (2012), and the Advanced Avionics Handbook (2009) for more details.

Figure 3.1 Overview of aircraft cockpit instrumentation for traditional “steam gauge” instruments.

Source: https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Slingsby.t67c.panel.g-bocm.arp.jpg/1200px-Slingsby.t67c.panel.g-bocm.arp.jpg.

Figure 3.2 Detailed view of the six pack of key instruments in a traditional cockpit.

Source: Modified from photo by Mael Balland on Unsplash, https://unsplash.com/photos/V5hAryReZzo.

3.1.1 Gyroscopic‐Based Instruments

Before discussing the first group of instruments, it is helpful to briefly review the ideas behind gyroscopes. The operation of a gyroscope is based on the Newtonian principle of conservation of angular momentum. Due to conservation of angular momentum, the axis of rotation of a spinning object with a given angular momentum (L = Iω, where I is the moment of inertia and ω is the angular speed) will remain fixed unless acted upon by an external applied torque. (Think of how the axis of a child's spinning top remains upright as long as the top is spinning.) Over time, small external forces and moments that are present in any practical implementation of a physical gyro will lead to gyroscopic precession, which results in small changes in the axis of rotation that can grow over time.

The three gyroscopic instruments in a traditional six pack of instruments – the attitude indicator, heading indicator, and turn coordinator – all depend on gyroscopic principles. The rotational speed of the gyros in the attitude and heading indicators are traditionally powered by a vacuum system that flows air over a small turbine connected to the spinning disks in order to maintain rotation. The turn coordinator, on the other hand, is typically powered by the aircraft's electrical system. The attitude indicator provides an artificial horizon that provides an indication of the amount of bank and pitch that the aircraft has at a given moment. Essentially, the internal gyroscope (to which the artificial horizon is mounted) maintains its rigidity in space and the aircraft pitches and rolls about the internal gyro. Arcing along the top of the indicator, the first three white lines on either side of the centerline indicate increments of 10° bank angle (up to 30° bank). The next two lines on either side represent a 45° and 60° bank angles, respectively. The heading indicator is based on a geared gyro and simply indicates the magnetic heading of the aircraft (as long as the gyro has been set to match the magnetic compass). Both the attitude indicator and the heading indicator experience errors due to gyroscopic precession that must be occasionally corrected. For example, periodically in straight and level flight, the pilot may need to reset the heading indicator to match the indication on the magnetic compass. The turn coordinator, also based on a gyro, indicates the instantaneous rate of turn. The two white lines below the level lines each indicate a standard rate of turn of 3°/s to the right or left, which would require two minutes for the aircraft to complete a 360° turn.

3.1.2 Pressure‐Based Instruments

The second group of instruments is based on measurement of total pressure and static pressure on the aircraft. Total pressure is measured by a pitot probe, which is often mounted under the wing on GA aircraft (see Figure 3.3(a)). Static pressure is measured by flush‐mounted static pressure ports on the side of the aircraft fuselage (see Figure 3.3(b)). The pitot probe and static port are connected via tubing to the ASI, altimeter, and VSI mounted on the instrument panel (Figure 3.4).

Total pressure from the pitot tube and static pressure from the static port are fed into the ASI. The ASI is calibrated based on the assumption of standard sea‐level conditions with the isentropic Mach relation to convert a measured “impact pressure” (difference between total and static pressure) into indicated airspeed. For low‐speed, low‐altitude flight this is equivalent to converting a measured dynamic pressure to velocity by the Bernoulli equation. Further details on the functioning of the ASI are provided in Chapter 8 on calibration of the ASI.

Figure 3.3 Examples of the pitot tube (a) and static pressure port (b) on an aircraft.

The VSI, connected to the static pressure port, measures the time rate of change of pressure and converts this to a vertical speed. It is based on a mechanical comparison of the rate of change of static pressure with a known rate of change coming from a calibrated leak. Indications of vertical speed on the VSI tend to fluctuate so it is not as useful for measuring rate of climb or descent in a precise manner. Instead, for measurement of vertical speed in flight test, it is best to establish a steady rate and directly measure altitude from the altimeter and time with a stopwatch.

The altimeter (Figure 3.5) is based on a measurement of static pressure, which is converted into an indicated altitude. Altitude is displayed on the traditional altimeter by three hands, much like an analog clock displays time. The long, thin pointer with a triangle at the end indicates ten thousands of feet; the short, thick hand displays thousands of feet; and the medium length, slender hand displays hundreds of feet. So, the medium, slender hand makes a full revolution of the dial every 1000 ft; the short, thick pointer makes a complete revolution every 10,000 ft; and the long, slender pointer makes a full revolution every 100,000 ft. For example, the altimeter depicted in Figure 3.5 indicates an altitude of 10,180 ft.

Figure 3.4 Schematic of the pitot‐static system.

Source: Flight Instruments, Federal Aviation Administration.

Figure 3.5 Diagram of an aircraft altimeter. The reference pressure is set by the knob on the lower left side and indicated in the Kollsman window on the right side of the instrument.

Source: Bsayusd, A 3‐pointer pressure altimeter. Originally from en.wikipedia.

The calibration of the altimeter is based on the pressure lapse rate of the standard atmosphere (assuming standard temperature). As discussed in Chapter 2, the pressure lapse rate is extremely consistent, which enables the altimeter to provide a highly accurate measurement. However, the local barometric pressure can change significantly, which would have a first‐order impact on the indicated altitude provided by an altimeter. Thus, an altimeter must account for variations in local barometric pressure reading, which is done by setting a reference pressure. This reference pressure appears in a small window on the right side of the altimeter and is set by a knob on the lower left side of the instrument (see Figure 3.5). It is important to note that the reference pressure is not related in any way to the actual pressure at some arbitrary altitude. Instead, the reference pressure simply shifts the base of the calibration curve, providing an offset above or below standard sea level pressure in order to accommodate the actual local barometric pressure reading and providing a more accurate reading of altitude.

This type of altimeter – the so‐called sensitive altimeter – was first invented by Paul Kollsman, leading to the naming of the Kollsman window where the reference pressure is read on the altimeter (e.g., the reference pressure shown in Figure 3.5 is 29.92 inHg). The Kollsman setting essentially shifts the altimeter's calibration curve in order to account for local variations in sea level pressure, which is routinely encountered due to weather variations (e.g., low or high pressure regions moving through a geographical area). Since accurate measurement of altitude is critical in most flight testing work, we will devote some attention to the calibration and correct setting of the altimeter.

The most typical use of the altimeter under routine flight is to set the Kollsman reference pressure to the local barometric pressure, such that the indicated altitude is the aircraft's height above mean sea level (MSL). A pilot can easily obtain up‐to‐date readings of the local barometric pressure by listening to broadcasts from local weather stations (such as the Automated Weather Observing System, or AWOS, found at many airports). Alternatively, air traffic control (ATC) will often report the local barometric pressure setting, especially when aircraft are transitioning from one controller to another with responsibility for different geographical areas. Reporting of the local barometric pressure is an important function for ATC, since they aim to maintain consistent vertical separation between all aircraft. Thus, for a pilot to ensure an accurate reading of MSL altitude, the altimeter must be set to the correct local barometric pressure reading (viewed in the Kollsman window) by adjusting the Kollsman knob.

However, in flight testing, we often wish to know the pressure altitude, or the pressure at our flight altitude. This can be accomplished by setting the altimeter to a reference pressure of 29.92 inHg (1013 hPa) instead of the local barometric pressure reading. Under this situation, the altimeter will not provide an accurate indication of height above sea level; rather, it will indicate pressure altitude. A flight test engineer can readily take the measured pressure altitude and convert this to a value of the local freestream static pressure via the standard atmosphere, using the theory described in Chapter 2³.