DOW-UAP-D148, AAWSAP DIRD, Detection and High-Resolution Tracking of Vehicles at Hypersonic Velocities, November 2010
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This document is a Defense Intelligence Reference Document (DIRD), a technical reference format used by the Defense Intelligence Agency (DIA) to capture baseline knowledge on a specific topic for later analytic use. DIRDs are best understood as reference and synthesis products rather than as original research. It is one of 38 DIRDs produced under the Advanced Aerospace Weapon System Applications Program (AAWSAP) between 2009 and 2011. Because AAWSAP’s scope permitted a broad range of supporting topics, not every DIRD in the series directly concerns aerospace systems or future threat assessment. The following summary reflects the DIRD’s scope and framing at the time of writing and should not be read as implying current validation of the concepts discussed. This DIRD surveys how hypersonic vehicles may be detected and tracked by exploiting the physical effects they create in flight, especially shock waves, ionized gas, hot surfaces, and turbulent atmospheric wakes. The report reviews a broad set of detection methods, including radar, infrared sensing, optical imaging, LIDAR, passive radio reflection, infrasound, and seismic techniques, and argues that the most effective systems will likely combine multiple sensor types, because each captures different features of a high-speed vehicle’s passage through the atmosphere. It presents radar and infrared sensing as the strongest existing tools for operational detection, while giving particular attention to wake-based methods such as LIDAR and passive radio techniques for improving tracking, identification, and discrimination of future hypersonic aircraft. The paper identifies hypersonic vehicles as an evolving surveillance problem in which future progress will depend on better multi-sensor integration, improved wake characterization, and novel signature-exploitation techniques.
[번역 실패: TooManyRequests] (cid:14)(cid:10)(cid:3)(cid:9)(cid:2)(cid:13)(cid:13)(cid:8)(cid:7)(cid:8)(cid:6)(cid:5)(cid:1)(cid:1)(cid:7)(cid:11)(cid:12)(cid:16) (cid:11)(cid:7)(cid:7)(cid:8)(cid:4)(cid:8)(cid:2)(cid:9)(cid:16) (cid:14)(cid:13)(cid:6)(cid:16) (cid:15)(cid:16) (cid:1)(cid:10)(cid:11)(cid:10)(cid:18)(cid:22)(cid:10)(cid:27) (cid:3)(cid:18)(cid:23)(cid:10)(cid:16)(cid:16)(cid:14)(cid:12)(cid:10)(cid:18)(cid:8)(cid:10)(cid:27) (cid:4)(cid:10)(cid:11)(cid:10)(cid:21)(cid:10)(cid:18)(cid:8)(cid:10)(cid:27) (cid:1)(cid:19)(cid:8)(cid:25)(cid:17)(cid:10)(cid:18)(cid:23)(cid:27) (cid:1)(cid:3)(cid:5)(cid:4)(cid:6)(cid:8)(cid:3)(cid:11) (cid:2)(cid:10)(cid:9)(cid:10)(cid:7)(cid:3)(cid:8)(cid:11) (cid:5)(cid:3)(cid:26) (cid:14)(cid:20)(cid:25)(cid:17)(cid:19)(cid:16)(cid:17)(cid:21)(cid:26)(cid:5)(cid:3)(cid:4)(cid:3)(cid:26) (cid:1)(cid:11)(cid:15)(cid:12)(cid:8)(cid:26) (cid:6)(cid:3)(cid:26) (cid:9)(cid:24)(cid:18)(cid:24)(cid:22)(cid:23)(cid:26)(cid:5)(cid:3)(cid:4)(cid:3) (cid:2)(cid:3)(cid:7)(cid:2)(cid:4)(cid:3)(cid:4)(cid:5)(cid:2)(cid:3)(cid:3)(cid:4)(cid:26) (cid:1)(cid:10)(cid:24)(cid:10)(cid:8)(cid:23)(cid:14)(cid:19)(cid:18)(cid:27)(cid:7)(cid:18)(cid:9)(cid:27) (cid:2)(cid:14)(cid:12)(cid:13)(cid:27) (cid:4)(cid:10)(cid:22)(cid:19)(cid:16)(cid:25)(cid:23)(cid:14)(cid:19)(cid:18)(cid:27)(cid:5)(cid:21)(cid:7)(cid:8)(cid:15)(cid:14)(cid:18)(cid:12)(cid:27)(cid:19)(cid:11)(cid:27) (cid:6)(cid:10)(cid:13)(cid:14)(cid:8)(cid:16)(cid:10)(cid:22)(cid:27)(cid:7)(cid:23)(cid:27) (cid:2)(cid:26)(cid:20)(cid:10)(cid:21)(cid:22)(cid:19)(cid:18)(cid:14)(cid:8)(cid:27) (cid:6)(cid:10)(cid:16)(cid:19)(cid:8)(cid:14)(cid:24)(cid:14)(cid:10)(cid:22)(cid:27) (cid:14)(cid:10)(cid:3)(cid:9)(cid:2)(cid:13)(cid:13)(cid:8)(cid:7)(cid:8)(cid:6)(cid:5)(cid:1)(cid:1)(cid:7)(cid:11)(cid:12)(cid:16) (cid:11)(cid:7)(cid:7)(cid:8)(cid:4)(cid:8)(cid:2)(cid:9)(cid:16) (cid:14)(cid:13)(cid:6)(cid:16) (cid:15)(cid:16) UNCLASSIFIED//F8R: &FFIGl,liaL Mii QtPP X Detection and High Resolution Tracking of Vehicles at Hypersonic Velocities The Defense Intelligence Reference Document provides nonsubstantive but authoritative reference information related to iutelli ence to ics or methodolo ies. Prepared by: Technology Warning Division (DW0-4) Defense Warning Office Directorate for Analysis Defense Intelligence Agency Author: AAP Person 83 {U) COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one of a series of advanced technology reports produced in FY 2010 under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace Weapons System Applications (AAWSA) Program. Comments or questions pertaining to this document should be addressed to !AAP Person 1 f AWSA Program Manager, Defense Intelligence Agency, ATTN: JUIAF - 01/DWO-3, Bldg 6000, Washington D.C. 20340-5100 UNCLASSIFIED.'/FOR OliliiliGiliiliaL W&& 8HLV UNCLASSIFIED/fFOR. QFFIEl .t.L: Uii QD:I! X Contents Introduction ......................................... ............................ ...................... ................... 1 Chapter 1: Theory Governing Objects in Flight ............................................................... 3 Subsonic Flow and Drag ................................................................ .......................... 3 Supersonic Flow ............................................................................... ...................... 6 Chapter 2: Hypersonic Compressible Flow Theory .... ..................................................... 10 Chapter 3: Detection Technologies ............................................................................. 11 Electromagnetic Methods ....................... ................. ............................................... 13 RADAR (Reflected Energy) .................................................................................. 13 Doppler RADAR .............................. ................................................................... 14 Radio Reflection Detection .................................................................................. 15 Optical Methods ................................................................................................... 16 Sky Cameras and Photographic Methods ............................................................... 16 Infrared Detection ............................................................................................. 17 [번역 실패: TooManyRequests] LIDAR.............................................................................................................. 23 Acoustic and Seismic Methods ................................................................................ 25 Infrasound ....................................................................................................... 25 Seismic............................................................................................................ 27 Chapter 4: Vision of Progress Over the Next 30 Years ................................................... 28 Detectability of New Hypersonic Aircraft ................................................................... 29 Recommendation #1 - Build a Database of the Wake Characteristics for Existing Aircraft ...................................................................................................................... 29 Recommendation #2 - Exploit the Detectability of Hypersonic Aircraft Based on the Features That Allow Them To Fly Efficiently at High Speeds ..................................... 30 Recommendation #3 - Explore the Detection of Vehicles Designed To Be Undetectable30 Recommendation #4 - Explore the Development of Novel Detectors ......................... 31 Summary ............................................................................................................ 31 iii UNCLASSIFIED//EQA: QlililEl.t.L: W&&: O,.L'l UNCLASSIFIED/fFOR. QFFIEl.t.L: Uii QD:I! X Figures Figure 1. Boundary Layer Development in Subsonic Flow about a Projectile........................ 4 Figure 2. Subsonic Flow Past a Projectile....................................................................... 5 Figure 3. Strauhal Frequency as a Function of Reynolds Number for Flow over a Circular Cylinder ........................................................................................... 6 Figure 4. Supersonic Flow Past a Wedge-Shaped Body .................................................... 8 Figure 5. Supersonic Flow Past a Blunt Body (Spheroid) .................................................. 8 Figure 6. Ratios of Mach Number, Temperature, and Pressure Across a Normal Shock ....... 10 Figure 7. Hypersonic Vehicle Detection Techniques ....................................................... 11 Figure 8. Laser-Based Chronograph............................................................................ 12 Figure 9. Electromagnetic Spectrum as a Function of Wavelength................................... 13 Figure 10. Schematic of a RADAR System................................................................... 14 Figure 11. Radio Reflection Detector................ .. ......................................................... 16 Figure 12. Energy Spectrum of the Sun at 5,778 K....................................................... 19 Figure 13. Hypersonic Flow Past a Sphere................................................................... 20 Figure 14. Infrared Energy Spectra for Mach 3 and Mach 3.5......................................... 21 Figure 15. Peak Wavelength of the Infrared Radiation Emitted by Hypersonic Objects ........ 22 Figure 16. Peak Shock Layer Temperature for Hypersonic Objects .................................. 22 Figure 17. Schematic of a Pulsed LIDAR System ........................................................... 24 Figure 18. Mach Cone Generated by a Supersonic Object .............................................. 26 Figure 19. Comparison of Detection Technology for Hypersonic Objects ........................... 32 Tables Table 1: Normal Shock Values for Mach 3 Flow ...............................................................9 iv UNCLASSIFIED//EQA: QlililEl.t.L: W&&: O,.L'l UNCLASSIFIED/fFOR. QFFIEl.t.L: Uii QD:I! X Introduction An object is supersonic when its speed through the atmosphere is greater than the local speed of sound. The Mach number is defined as the speed of the object divided by the local speed of sound . For Mach numbers greater than 1 (supersonic flow), shock waves develop in the flowfield and near the surface of the object due to the air's compressibility. Traditionally, the lower Mach number limit for the so-called hypersonic speed regime is about Mach 5 (1. 7 km/sec). "Low hypersonic" values range between Mach 5 to about Mach 10, while "high hypersonic" values range between approximately Mach 10 to Mach 30 or above. Mach 30 [번역 실패: TooManyRequests] (10 km/s), for example, is close to Space Shuttle reentry velocity. Few objects can travel at hypersonic velocities. The most common object that we see moving at these speeds are meteors entering the Earth's atmosphere. As meteors fall to the Earth's surface, their velocities may reach 30 miles per second (48 km/s),1 and their corresponding Mach number as they enter the upper layers of the atmosphere will exceed 150. Meteors are preceded by a bow shockwave as they compress the air immediately in their path. Temperatures and pressures increase dramatically across the shockwave to a point where the gases in air ionize and disassociate, leading to the emission of visible light and radio waves. These conditions also lead to rapid heating of the meteor surface causing them to fracture and break up as they enter the atmosphere. Optical and RADAR-based surveillance systems are now used to scan outer space to detect asteroids and other objects with orbits that may lead them to collide with Earth. A second class of hypersonic objects includes reentry vehicles moving into the Earth's atmosphere from orbit. In the case of a reentry vehicle returning from low-Earth orbit at 100 km altitude, the velocity of the vehicle will reach 8 km/s (about 5 miles per second). The Mach number of this vehicle will exceed 26.5 in the upper atmosphere. As the vehicle moves through the atmosphere, flow-induced drag forces will slow down the vehicle; if the vehicle has sufficient thermal protection, it can survive reentry and be recovered. A third class of hypersonic vehicles includes the reentry payload used in ICBMs (intercontinental ballistic missiles). The payload in these missiles is launched using a rocket that boosts them above the atmosphere to a suborbital velocity. The payload velocity may exceed 7 km/s as they reenter the atmosphere, equating to M > 23. The coupled high velocity and high kinetic energy of these objects creates an ionized wake and shock wave that can be used to detect their position and to determine their velocity. This information, along with their ballistic trajectory, is used to locate their target and the time to impact. A fourth class of hypersonic vehicles includes manned and unmanned rockets and aircraft. The North American X-15, for example, exceeded a speed of 7,274 km/hr in 1964, equating to about M = 6.5. This aircraft also exceeded 100 km in altitude on two occasions, qualifying the X-15 as a spacecraft. The SR-71 Blackbird, an air-breathing strategic reconnaissance aircraft, has exceeded Mach 3.2 at 80,000-ft altitude, and its actual maximum speed may have reached into the hypersonic flow regime. Other real and conceptual aircraft capable of reaching hypersonic speeds include the alleged Aurora SR-91 (Mach 4 to 6), the Boeing X- 51, an unmanned Mach 6 scramjet, the HTV-2 from the DARPA Falcon project (designed for M=20 flight to low-Earth orbit), the HyperSoar (M = 12), the Russian Leninetz Ayaks, and the Skylon (designed for single-stage-to-orbit flights). Certain rockets are also designed to travel at hypersonic speeds. The Patriot missile, for example, travels at Mach 5, a high speed necessary for it to be able to intercept and destroy other missiles while they are in flight. 1 UNCLASSIFIED//EQA: QlililEl.t.L: W&&: O,.L'l UNCLASSIFIED/fFOR. QFFIEl.t.L: Uii QD:I! X There are a number of different techniques available to detect hypersonic objects and to determine their position, velocity, and trajectory. These detection methods can be broadly divided into electromagnetic, optical, and acoustic/seismic methods. Each method relies on the properties of the surface of the object to reflect incident radiation or upon the properties of the hot ionized gases caused by the bow shock and entrained into the object's wake. The theory of external fluid flow around objects in subsonic, supersonic, and hypersonic regimes will be reviewed and various detection methods will be compared in this report. 2 UNCLASSIFIED//EQA: QlililEl.t.L: W&&: O,.L'l UNCLASSIFIED/fFOR. QFFIEl.t.L: Uii QD:I! X Chapter 1: Theory Governing Objects in Flight Many of the detection technologies for hypersonic aircraft are based on the properties of the air flow around the object. The fluid mechanics affecting supersonic and hypersonic aircraft are well described in textbooks on compressible flow by J.D. Anderson;2•3 subsonic flow, including the affect of boundary layers, is covered in the textbook by F. M. White.4 [번역 실패: TooManyRequests] Hypersonic flow usually refers to the regime where objects are moving faster than Mach 5, but technically refers to the Mach range where pressure, temperature, and density ratios across shock waves reach constant values, and this does happen at about Mach 5. Fluid flow changes dramatically at Mach 1 defined at the point where the velocity of a projectile, V, equals the local speed of sound, a, in the atmosphere: M ='!_ (1) a Flow regimes are defined by the following: • M < 1, subsonic flow • M = 1, sonic flow • M > 1, supersonic flow • M > 5, hypersonic flow The speed of sound varies with temperature and with the type of gases in the atmosphere. A simple equation for the speed of sound includes the ratio of specific heats, y, the gas constant, R, and the temperature, T: a=.JyRT (2) For air at room temperature, y = 1.4, R = 287 J/kg -K, and T = 20° C or 293 K. The subsequent speed of sound is 343 m/s (1,125 ft/s or 767 mph). It is easier for a projectile to exceed the speed of sound at higher elevations since the temperature of the atmosphere is lower, reducing the speed of sound and the subsequent velocity necessary to break the sound barrier. The viscosity of the fluid flowing around an object induces drag and retards its forward motion. Supersonic flow has some of the viscous characteristics of subsonic flow, but adds in the complication of shock waves. To understand the nature of how a projectile affects the flow of fluid around it, consider the case of a subsonic projectile. SUBSONIC FLOW AND DRAG Subsonic flows, such as the flow shown in Figure 1, are heavily influenced by collisions between molecules of air and the surface of the proj
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UNCLASSIFIED//F8R: &FFIGl,liaL Mii QtPP X
Detection and High Resolution Tracking of Vehicles at
Hypersonic Velocities
The Defense Intelligence Reference Document provides nonsubstantive but
authoritative reference information related to iutelli ence to ics or methodolo ies.
Prepared by:
Technology Warning Division (DW0-4)
Defense Warning Office
Directorate for Analysis
Defense Intelligence Agency
Author:
AAP Person 83
{U) COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized.
This product is one of a series of advanced technology reports produced in FY 2010 under the
Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace Weapons System
Applications (AAWSA) Program. Comments or questions pertaining to this document should be
addressed to !AAP Person 1 f AWSA Program Manager, Defense Intelligence Agency,
ATTN: JUIAF - 01/DWO-3, Bldg 6000, Washington D.C. 20340-5100
UNCLASSIFIED.'/FOR OliliiliGiliiliaL W&& 8HLV
UNCLASSIFIED/fFOR. QFFIEl .t.L: Uii QD:I! X
Contents
Introduction ......................................... ............................ ...................... ................... 1
Chapter 1: Theory Governing Objects in Flight ............................................................... 3
Subsonic Flow and Drag ................................................................ .......................... 3
Supersonic Flow ............................................................................... ...................... 6
Chapter 2: Hypersonic Compressible Flow Theory .... ..................................................... 10
Chapter 3: Detection Technologies ............................................................................. 11
Electromagnetic Methods ....................... ................. ............................................... 13
RADAR (Reflected Energy) .................................................................................. 13
Doppler RADAR .............................. ................................................................... 14
Radio Reflection Detection .................................................................................. 15
Optical Methods ................................................................................................... 16
Sky Cameras and Photographic Methods ............................................................... 16
Infrared Detection ............................................................................................. 17
LIDAR.............................................................................................................. 23
Acoustic and Seismic Methods ................................................................................ 25
Infrasound ....................................................................................................... 25
Seismic............................................................................................................ 27
Chapter 4: Vision of Progress Over the Next 30 Years ................................................... 28
Detectability of New Hypersonic Aircraft ................................................................... 29
Recommendation #1 - Build a Database of the Wake Characteristics for Existing Aircraft
...................................................................................................................... 29
Recommendation #2 - Exploit the Detectability of Hypersonic Aircraft Based on the
Features That Allow Them To Fly Efficiently at High Speeds ..................................... 30
Recommendation #3 - Explore the Detection of Vehicles Designed To Be Undetectable30
Recommendation #4 - Explore the Development of Novel Detectors ......................... 31
Summary ............................................................................................................ 31
iii
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Figures
Figure 1. Boundary Layer Development in Subsonic Flow about a Projectile........................ 4
Figure 2. Subsonic Flow Past a Projectile....................................................................... 5
Figure 3. Strauhal Frequency as a Function of Reynolds Number for Flow over a
Circular Cylinder ........................................................................................... 6
Figure 4. Supersonic Flow Past a Wedge-Shaped Body .................................................... 8
Figure 5. Supersonic Flow Past a Blunt Body (Spheroid) .................................................. 8
Figure 6. Ratios of Mach Number, Temperature, and Pressure Across a Normal Shock ....... 10
Figure 7. Hypersonic Vehicle Detection Techniques ....................................................... 11
Figure 8. Laser-Based Chronograph............................................................................ 12
Figure 9. Electromagnetic Spectrum as a Function of Wavelength................................... 13
Figure 10. Schematic of a RADAR System................................................................... 14
Figure 11. Radio Reflection Detector................ .. ......................................................... 16
Figure 12. Energy Spectrum of the Sun at 5,778 K....................................................... 19
Figure 13. Hypersonic Flow Past a Sphere................................................................... 20
Figure 14. Infrared Energy Spectra for Mach 3 and Mach 3.5......................................... 21
Figure 15. Peak Wavelength of the Infrared Radiation Emitted by Hypersonic Objects ........ 22
Figure 16. Peak Shock Layer Temperature for Hypersonic Objects .................................. 22
Figure 17. Schematic of a Pulsed LIDAR System ........................................................... 24
Figure 18. Mach Cone Generated by a Supersonic Object .............................................. 26
Figure 19. Comparison of Detection Technology for Hypersonic Objects ........................... 32
Tables
Table 1: Normal Shock Values for Mach 3 Flow ...............................................................9
iv
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Introduction
An object is supersonic when its speed through the atmosphere is greater than the local
speed of sound. The Mach number is defined as the speed of the object divided by the local
speed of sound . For Mach numbers greater than 1 (supersonic flow), shock waves develop in
the flowfield and near the surface of the object due to the air's compressibility. Traditionally,
the lower Mach number limit for the so-called hypersonic speed regime is about Mach 5 (1. 7
km/sec). "Low hypersonic" values range between Mach 5 to about Mach 10, while "high
hypersonic" values range between approximately Mach 10 to Mach 30 or above. Mach 30
(10 km/s), for example, is close to Space Shuttle reentry velocity. Few objects can travel at
hypersonic velocities. The most common object that we see moving at these speeds are
meteors entering the Earth's atmosphere. As meteors fall to the Earth's surface, their
velocities may reach 30 miles per second (48 km/s),1 and their corresponding Mach number
as they enter the upper layers of the atmosphere will exceed 150. Meteors are preceded by
a bow shockwave as they compress the air immediately in their path. Temperatures and
pressures increase dramatically across the shockwave to a point where the gases in air ionize
and disassociate, leading to the emission of visible light and radio waves. These conditions
also lead to rapid heating of the meteor surface causing them to fracture and break up as
they enter the atmosphere. Optical and RADAR-based surveillance systems are now used to
scan outer space to detect asteroids and other objects with orbits that may lead them to
collide with Earth.
A second class of hypersonic objects includes reentry vehicles moving into the Earth's
atmosphere from orbit. In the case of a reentry vehicle returning from low-Earth orbit at
100 km altitude, the velocity of the vehicle will reach 8 km/s (about 5 miles per second).
The Mach number of this vehicle will exceed 26.5 in the upper atmosphere. As the vehicle
moves through the atmosphere, flow-induced drag forces will slow down the vehicle; if the
vehicle has sufficient thermal protection, it can survive reentry and be recovered.
A third class of hypersonic vehicles includes the reentry payload used in ICBMs
(intercontinental ballistic missiles). The payload in these missiles is launched using a rocket
that boosts them above the atmosphere to a suborbital velocity. The payload velocity may
exceed 7 km/s as they reenter the atmosphere, equating to M > 23. The coupled high
velocity and high kinetic energy of these objects creates an ionized wake and shock wave
that can be used to detect their position and to determine their velocity. This information,
along with their ballistic trajectory, is used to locate their target and the time to impact.
A fourth class of hypersonic vehicles includes manned and unmanned rockets and aircraft.
The North American X-15, for example, exceeded a speed of 7,274 km/hr in 1964, equating
to about M = 6.5. This aircraft also exceeded 100 km in altitude on two occasions, qualifying
the X-15 as a spacecraft. The SR-71 Blackbird, an air-breathing strategic reconnaissance
aircraft, has exceeded Mach 3.2 at 80,000-ft altitude, and its actual maximum speed may
have reached into the hypersonic flow regime. Other real and conceptual aircraft capable of
reaching hypersonic speeds include the alleged Aurora SR-91 (Mach 4 to 6), the Boeing X-
51, an unmanned Mach 6 scramjet, the HTV-2 from the DARPA Falcon project (designed for
M=20 flight to low-Earth orbit), the HyperSoar (M = 12), the Russian Leninetz Ayaks, and
the Skylon (designed for single-stage-to-orbit flights). Certain rockets are also designed to
travel at hypersonic speeds. The Patriot missile, for example, travels at Mach 5, a high
speed necessary for it to be able to intercept and destroy other missiles while they are in
flight.
1
UNCLASSIFIED//EQA: QlililEl.t.L: W&&: O,.L'l
UNCLASSIFIED/fFOR. QFFIEl.t.L: Uii QD:I! X
There are a number of different techniques available to detect hypersonic objects and to
determine their position, velocity, and trajectory. These detection methods can be broadly
divided into electromagnetic, optical, and acoustic/seismic methods. Each method relies on
the properties of the surface of the object to reflect incident radiation or upon the properties
of the hot ionized gases caused by the bow shock and entrained into the object's wake. The
theory of external fluid flow around objects in subsonic, supersonic, and hypersonic regimes
will be reviewed and various detection methods will be compared in this report.
2
UNCLASSIFIED//EQA: QlililEl.t.L: W&&: O,.L'l
UNCLASSIFIED/fFOR. QFFIEl.t.L: Uii QD:I! X
Chapter 1: Theory Governing Objects in Flight
Many of the detection technologies for hypersonic aircraft are based on the properties of the
air flow around the object. The fluid mechanics affecting supersonic and hypersonic aircraft
are well described in textbooks on compressible flow by J.D. Anderson;2•3 subsonic flow,
including the affect of boundary layers, is covered in the textbook by F. M. White.4
Hypersonic flow usually refers to the regime where objects are moving faster than Mach 5,
but technically refers to the Mach range where pressure, temperature, and density ratios
across shock waves reach constant values, and this does happen at about Mach 5. Fluid flow
changes dramatically at Mach 1 defined at the point where the velocity of a projectile, V,
equals the local speed of sound, a, in the atmosphere:
M ='!_ (1)
a
Flow regimes are defined by the following:
• M < 1, subsonic flow
• M = 1, sonic flow
• M > 1, supersonic flow
• M > 5, hypersonic flow
The speed of sound varies with temperature and with the type of gases in the atmosphere. A
simple equation for the speed of sound includes the ratio of specific heats, y, the gas
constant, R, and the temperature, T:
a=.JyRT (2)
For air at room temperature, y = 1.4, R = 287 J/kg -K, and T = 20° C or 293 K. The
subsequent speed of sound is 343 m/s (1,125 ft/s or 767 mph). It is easier for a projectile
to exceed the speed of sound at higher elevations since the temperature of the atmosphere
is lower, reducing the speed of sound and the subsequent velocity necessary to break the
sound barrier.
The viscosity of the fluid flowing around an object induces drag and retards its forward
motion. Supersonic flow has some of the viscous characteristics of subsonic flow, but adds in
the complication of shock waves. To understand the nature of how a projectile affects the
flow of fluid around it, consider the case of a subsonic projectile.
SUBSONIC FLOW AND DRAG
Subsonic flows, such as the flow shown in Figure 1, are heavily influenced by collisions
between molecules of air and the surface of the proj