# Hypersonic flight

Artist's impression of a waverider by the Chinese National Science and Technology Major Project 0901 Flying Vehicle.

Hypersonic flight is flight through the atmosphere below about 90km at speeds above Mach 5, a speed where dissociation of air begins to become significant and high heat loads exist. In such a regime the aerodynamic flow around a flight body is described by similarity parameters such as its Mach number and its Reynolds number.[1]

## History

The first manufactured object to achieve hypersonic flight was the two-stage Bumper rocket, consisting of a WAC Corporal second stage set on top of a V-2 first stage. On February 1949, at White Sands, the rocket reached a speed of 5,150 miles per hour, or approximately Mach 6.7.[2] The vehicle, however, burned on atmospheric re-entry, and only charred remnants were found. In April 1961, Russian Major Yuri Gagarin became the first human to travel at hypersonic speed, during the world's first piloted orbital flight. Soon after, in May 1961, Alan Shepard became the first American and second person to achieve hypersonic flight when his capsule reentered the atmosphere at a speed above Mach 5 at the end of his suborbital flight over the Atlantic Ocean.

In November, 1961, Air Force Major Robert White flew the X-15 research airplane at speeds over Mach 6.[3][4]

The reentry problem of a space vehicle was extensively studied.[1] The hypersonic regime has since become the subject for further study during the 21st century, and strategic competition between the US, Russia, and China.

The NASA X-43A flew on scramjet for 10 seconds, and then glided for 10 minutes on its last flight in 2004. The Boeing X-51 Waverider flew on scramjet for 210 seconds in 2013, finally reaching Mach 5.1 on its fourth flight test.

## Physics

The stagnation point of air flowing around a body is a point where its local velocity is zero.[1] At this point the air flows around this location. A shock wave forms, which deflects the air from the stagnation point and insulates the flight body from the atmosphere.[1] This can affect the lifting ability of a flight surface to counteract its drag and subsequent free fall.[5] Ning describes a method for interrelating Reynolds number with Mach number.[6]

In order to maneuver in the atmosphere at faster speeds than supersonic, the forms of propulsion can still be airbreathing systems, but a ramjet no longer suffices for a system to attain Mach 5, as a ramjet slows down the airflow to subsonic.[7] Some systems (waveriders) use a first stage rocket to boost a body into the hypersonic regime. Other systems (boost-glide vehicles) use scramjets after their initial boost, in which the speed of the air passing through the scramjet remains supersonic. Other systems (munitions) use a cannon for their initial boost.

### High Temperature Effect

Hypersonic flow is a high energy flow.[8] The ratio of kinetic energy to the gas internal energy increases as the square of the Mach number. When this flow enters a boundary layer, there are high viscous effects due to the friction between air and the high-speed object. In this case, the high kinetic energy is converted in part to internal energy and gas energy is proportional to the internal energy. Therefore, hypersonic boundary layers are high temperature regions due to the viscous dissipation of the flow’s kinetic energy. Another region of high temperature flow is the shock layer behind the strong bow shock wave. In the case of the shock layer, the flows velocity decreases discontinuously as it passes through the shock wave. This results in a loss of kinetic energy and a gain of internal energy behind the shock wave. Due to high temperatures behind the shock wave, atoms in the air will begin to dissociate. For example, in air when T > 2000 K, diatomic oxygen will dissociate: O2 → 2O

For T > 4000 K, diatomic nitrogen will dissociate: N2 → 2N In this temperature range, nitric oxide will form: N2 + O2 → 2NO And will ionize: N + O → NO+ + e-

Measuring the high temperature effect of hypersonic vehicles is not possible by attaching a thermocouple, this would ruin the airflow over the wing. However, a real-time method exists to locate transient, concentrated heating sources when location cannot be directly measured, as explained by Dr. Mike Myers in his defense dissertation "Parameter Estimation using the Extended Kalman Filter and Ultrasonic Pulse Time of Flight to Locate Transient, Concentrated Heating Sources."

### Low Density Flow

At standard sea-level condition for air, the mean free path of air molecules is about ${\displaystyle \lambda =68\mathrm {nm} }$. Low density air is much thinner. At an altitude of 342,000 feet or 104 km the mean free path is ${\displaystyle \lambda =1ft=0.305m}$. Because of this large free mean path aerodynamic concepts, equations, and results based on the assumption of a continuum begin to break down, therefore aerodynamics must be considered from kinetic theory. This regime of aerodynamics is called low-density flow. For a given aerodynamic condition low-density effects depends on the value of a nondimensional parameter called the Knudsen number Kn, defined as K_n=λ/l where l is the typical length scale of the object considered. The value of the Knudsen number based on nose radius, Kn = λ/R, can be near one.

Hypersonic vehicles frequently fly at very high altitudes and therefore encounter low-density conditions. Hence, the design and analysis of hypersonic vehicles sometimes require consideration of low-density flow. New generations of hypersonic airplanes may spend a considerable portion of their mission at high altitudes, and for these vehicles, low-density effects will become more significant.[8]

### Thin Shock Layer

The flow field between the shock wave and the body surface is called the shock layer. As the Mach number M increases, the angle of the resulting shock wave decreases. This Mach angle is described by the equation ${\displaystyle \mu =\sin ^{-1}(a/v)}$ where a is the speed of the sound wave and v is the flow velocity. Since M=v/a, the equation becomes ${\displaystyle \mu =\sin ^{-1}(1/M)}$. Smaller Mach numbers position the shock wave closer to the body surface, thus at hypersonic speeds, the shock wave lies extremely close to the body surface, resulting in a thin shock layer. At low Reynolds number, the boundary layer grows quite thick and merges with the shock wave, leading to a fully viscous shock layer.[9]

### Viscous Interaction

The compressible flow boundary layer increases proportionately to the square of the Mach number, and inversely to the square root of the Reynolds number.

At hypersonic speeds, this effect becomes much more pronounced, due to the exponential reliance on the Mach number. Since the boundary layer becomes so large, it interacts more viscously with the surrounding flow. The overall effect of this interaction is to create a much higher skin friction than normal, causing greater surface heat flow. Additionally, the surface pressure spikes, which results in a much larger aerodynamic drag coefficient. This effect is extreme at the leading edge and decreases as a function of length along the surface.[8]

### Entropy Layer

The entropy layer is a region of large velocity gradients caused by the strong curvature of the shock wave. The entropy layer begins at the nose of the aircraft and extends downstream close to the body surface. Downstream of the nose, the entropy interacts with the boundary layer which causes an increase in aerodynamic heating at the body surface. Although the shock wave at the nose at supersonic speeds is also curved, the entropy layer is only observed at hypersonic speeds because the magnitude of the curve is far greater at hypersonic speeds.[8]

## Hypersonic weapons development

In the last year, China has tested more hypersonic weapons than we have in a decade. We've got to fix that.

— Michael Griffin, US Undersecretary of Defense for Research and Engineering, Flightglobal (2018)[10]

Hypersonic weapons, by definition, travel five or more times the speed of sound. Hypersonic cruise missiles which are powered by scramjet are restricted below 100,000 feet; hypersonic glide vehicles can travel higher. Compared to a ballistic (parabolic) trajectory, a hypersonic vehicle would be capable of large-angle deviations from a parabolic trajectory.[7] According to CNBC, Russia and China lead in hypersonic weapon development, trailed by the United States. France, India, and Australia may also be pursuing the technology.[7]

Waverider hypersonic weapons delivery is an avenue of development. China's XingKong-2 (星空二号, Starry-sky-2), a waverider, had its first flight 3 August 2018.[11] [12] [13]

In 2016, Russia is believed to have conducted multiple successful tests of Avangard, a hypersonic glide vehicle.[14] In 2018, an Avangard was launched at the Dombarovskiy missile base, reaching its target at the Kura shooting range, a distance of 3700 miles.[15] Avangard uses a scramjet engine.[16] Avangard uses new composite materials which are to withstand temperatures of up to 2,000 degrees Celsius (3,632 degrees Fahrenheit).[17] The Avangard's environment at hypersonic speeds reaches such temperatures.[17] Russia considers its current carbon fiber solution to be unreliable.[18]

These tests have prompted US responses in weapons development[19][20][21] per John Hyten's USSTRATCOM statement 05:03, 8 August 2018 (UTC).[22] At least one vendor is developing ceramics to handle the temperatures of hypersonics systems.[16] There are over a dozen US hypersonics projects as of 2018, notes the commander of USSTRATCOM.[22] [23]

According to Air Force Chief Scientist, Dr. Greg Zacharias, the US anticipates having hypersonic weapons by the 2020s, hypersonic drones by the 2030s and recoverable hypersonic drone aircraft by the 2040s.[24] The focus of DoD development will be on air-breathing boost-glide hypersonics systems.[25] Countering hypersonic weapons during their cruise phase will require radar with longer range, as well as space-based sensors, and systems for tracking and fire control.[25]

Rand Corporation (28 September 2017) estimates there is less than a decade to prevent Hypersonic Missile proliferation.[26] In the same way that anti-ballistic missiles were developed as countermeasures to ballistic missiles, counter-countermeasures to hypersonics systems are not yet in development. [7] [27] [18] [28] Both the US and Russia withdrew from the Intermediate-Range Nuclear Forces (INF) Treaty in February 2019. This will spur arms development, including hypersonic weapons.[29]

## References

1. ^ a b c d Alfred J. Eggers, H. Julian Allen, Stanford Neice. (10 December 1954) NACA report 1382 "A comparative analysis of the performance of long-range hypervelocity vehicles" pp. 1141-1160
2. ^ Winter, Frank (2000-08-03). "V-2 missile". Smithsonian National Air and Space Museum. airandspace.si.edu. Retrieved 2018-08-16.
3. ^ White, Robert. "Across the Hypersonic Divide". HistoryNet. HistoryNet LLC. Retrieved 11 October 2015.
4. ^ "Hypersonic plane passes latest test - Just In - ABC News (Australian Broadcasting Corporation)". Abc.net.au. 2010-03-22. Retrieved 2014-02-18.
5. ^ MIT "Fluids" 1. Effects of Reynolds Number 2. Effects of Mach Number
6. ^ Andrew Ning "Matching Mach and Reynolds Number"
7. ^ a b c d Amanda Macias (21 March 2018; Updated 22 March 2018) Russia and China are 'aggressively developing' hypersonic weapons — here's what they are and why the US can't defend against them: America's top nuclear commander said the U.S. doesn't have defenses against hypersonic weapons. Russia and China are leading the way in developing hypersonic weapons.
8. ^ a b c d Anderson, John (2016). Introduction to Flight (Eighth ed.) McGraw-Hill Education
9. ^ https://www.grc.nasa.gov/WWW/K-12/airplane/machang.html
10. ^ Garrett Reim (14 DECEMBER, 2018) Counter hypersonic weapon possible by mid-2020s: DoD
11. ^ 3 August 2018 China tests waverider hypersonic aircraft Starry Sky-2
12. ^ China successfully tests first hypersonic aircraft that can ..
13. ^ Youtube clip XingKong-2 hypersonic aircraft (Starry Sky-2)
14. ^ Macias, Amanda (26 December 2018). "The Kremlin says it conducted another successful test of a hypersonic weapon". www.cnbc.com. Retrieved 27 December 2018.
15. ^ (26 December 2018) Putin crows as he oversees Russian hypersonic weapons test
16. ^ a b Nick Stockton (27 Dec 2018) Rotating Detonation Engines Could Propel Hypersonic Flight
17. ^ a b (27 December 2018) Putin Says ‘Invulnerable’ New Hypersonic Nuclear Missile Is Ready For Deployment
18. ^ a b Amanda Macias (FRI, OCT 12 2018 • 1:43 PM EDT | UPDATED FRI, OCT 12 2018 • 6:37 PM EDT) Russia hits a snag in developing a hypersonic weapon after Putin said it was already in production
19. ^ Lockheed Martin Hypersonic Conventional Strike Weapon (HCSW) Missile for US Air Force
20. ^ Joseph Trevithick (6 September 2018) DARPA Starts Work On "Glide Breaker" Hypersonic Weapons Defense Project
21. ^ (14 August 2018) Lockheed Martin gets a second hypersonic weapons contract, this time for \$480 million, as the US tries to keep pace with Russia and China
22. ^ a b
23. ^ Sydney Freedberg (March 13, 2019) Hypersonics Won’t Repeat Mistakes Of F-35
24. ^ Osborn, Kris. "Get Ready, Russia and China: America's Next Fighter Jet Will Dominate the Skies". The National Interest. Retrieved 2 March 2018.
25. ^ a b David Vergun (December 14, 2018) DOD scaling up effort to develop hypersonics
26. ^
27. ^ a b "Putin unveils new nuclear missile, says 'listen to us now'". nbcnews.com. Retrieved 2 March 2018.
28. ^ Sydney Freedberg (1 Feb 2019) Pentagon Studies Post-INF Weapons, Shooting Down Hypersonics
29. ^ Linda Givetash and Reuters (2 Feb 2019) Putin says Russia also suspending key nuclear arms treaty after U.S. move to withdraw
30. ^ Cui, et. al.(Feb 2019) Hypersonic I-shaped aerodynamic configurations Science China Physics, Mechanics & Astronomy 61:024722 Wind tunnel proposal
31. ^ http://aviationweek.com/commercial-aviation/boeing-unveils-hypersonic-airliner-concept
32. ^ https://www.popularmechanics.com/flight/a21948533/boeing-hypersonic-passenger-plane-concept/
33. ^ D. Preller and P. M. Smart, "Abstract: SPARTAN: Scramjet Powered Accelerator for Reusable Technology AdvaNcement," 2014. http://rispace.org/wp-content/uploads/2015/03/33_preller.pdf
34. ^ http://www.esa.int/Our_Activities/Space_Engineering_Technology/High-Speed_Experimental_Fly_Vehicles_-_INTernational