(英文原版)超音速飞机空气动力学
航空发动机专业英语之空气动力学
Introduced how to reduce the impact of emissions on aircraft performance and meet environmental regulations by optimizing exhaust emission design and control technologies.
With the continuous improvement of aircraft performance, the aerodynamic design of aircraft engines is affecting more string requirements, including higher take off and landing speeds, longer flight distances, and more complex flight conditions
Detailed description
Definition and Concepts
Understanding the characteristics and classification of fluids helps to gain a deeper understanding of the working principles of aircraft engines.
Air inlet aerodynamics
Explored the effects of aerodynamic phenomena in combustion chambers on combustion efficiency and emissions, including flame propagation speed, combustion stability, and combustion chamber outlet temperature distribution.
航空专英1教案第1,2章 Low speed aerodynamics
专英一教案1、2章Ch.1 Low speed aerodynamicsDivision of AerodynamicSubsonic aerodynamics 亚音速空气动力学M<0.8 Transonic aerodynamics 跨音速空气动力学0.8<M<1.2 Supersonic aerodynamics 超音速空气动力学1.2<M<5 Hypersonic aerodynamics 高超音速空气动力学M>5 1.1 The atmosphereComposition of air (See tab.)Layer of atmosphereTroposphere 对流层Stratosphere 同温层Mesosphere 散逸层Thermosphere 热电离层Ionosphere 离子层,电离层Ozone layer 臭氧层专业名词ISA International Standard Atmosphere 国际标准大气pressure 压强Ptemperature 温度Tdensity 密度ρaltitude 高度H,hspeed,velocity 速度vattitude 姿态viscosity 粘度μcompressibility 压缩性compressible 可压缩的,可压的(density changes with pressure)incompressible 不可压缩的,不可压的(density does not changewith pressure)English system(英制):Fundamental units 基本单位force(力)pounds(lb)磅distance(距离)feet(ft)英尺time(时间)seconds(sec)秒Derived units 导出单位速度:velocity(distance/time)V,ft/sec(fps),knots=1.69(fps),节=1海里/小时面积:area(distance squared)S or A,squared ft(ft2)压强:pressure(force/unit area)P,lb/ft2加速度:acceleration(change in velocity)a,ft/sec/sec(fps2),ft/sec2质量:mass(weight/ acceleration of gravity)m,lb-sec2/ft(slug)m=w/g=lb/ft/sec2位能:potential energy(force× height)p,ft-lb功:work(force ×distance)W,ft-lb海里:nautical miles,(nmi),浬nmi=6076ft=1853.2m英里:statute miles,mile,(stmi),法定里,stmi=5280ft=1609m每分钟转速:revolution per minute,RPM,密度:density(mass/unit volume)ρ,slug/ft3,(lb-sec2/ft4)温度:temperature 。
空气动力学英文PPT(Chapter_02)
an infinitesimally small fluid element in the flow, with a differential volume.
It contains huge large amount of molecules Fixed and moving infinitesimal fluid element. Focus of our investigation for fluid flow.
Fixed control volume and moving control volume. Focus of our investigation for fluid flow.
中英文日报导航站
中英文日报导航站
2.3.2 Infinitesimal fluid element approach
中英文日报导航站
2.3.3 Molecule approach
Definition of molecule approach:
The fluid properties are defined with the use of suitable statistical averaging in the microscope wherein the fundamental laws of nature are applied directly to atoms and molecules. In summary, although many variations on the theme can be found in different texts for the derivation of the general equations of the fluid flow, the flow model can be usually be categorized under one of the approach described above.
空气动力学的名词解释
空气动力学的名词解释空气动力学是研究气体与固体的相互作用及其对物体运动的影响的学科。
它在航空航天领域中起着至关重要的作用,不仅可以帮助我们理解飞机和火箭的飞行原理,还可以用来优化设计、提高效率和安全性。
在本文中,我们将介绍一些与空气动力学相关的关键术语,以帮助读者更好地理解这个领域。
1. 空气动力学(Aerodynamics)空气动力学是研究气体在运动物体表面产生的力学效应的科学。
它涉及流体力学、力学和热力学等领域的知识。
通过分析气体流动规律,可以预测物体的运动、阻力和升力等参数。
2. 流场(Flow Field)流场是指空气或气体在物体周围的流动状态。
空气动力学中的流场可以通过数学模型和实验来描述和分析。
了解流场可以帮助我们研究物体受力和运动的规律。
3. 阻力(Drag)阻力是指物体在运动中受到的与速度方向相反的力。
当物体在空气中移动时,面对气体的粘性和惯性影响,会产生阻力。
阻力的大小取决于物体的形状、速度和流场状况。
4. 升力(Lift)升力是指垂直于运动方向的力,也是飞行器保持浮空或升起的关键力量。
升力的产生源于空气动力学中的贴面效应和伯努利定律。
飞行器通常利用翼面的形状和倾角,通过改变气流的速度和压力分布,获得升力。
5. 翼效(Wing Efficiency)翼效是指在产生升力的同时,减小阻力的能力。
一个高效的翼面设计可以使飞行器在给定的马赫数下获得更大的升力,同时降低阻力,提高燃烧效率和航程。
6. 翼面(Airfoil)翼面是拥有空气动力学特性的平面或曲面。
常见的翼面形状有对称翼和非对称翼,它们的流场效应和升力系数有所不同。
飞机、直升机和风力发电机等设备都采用翼面来实现升力或减小阻力。
7. 空气动力学系数(Aerodynamic Coefficients)空气动力学系数是用来描述物体在特定运动状态下受到的气流作用的参数。
常见的系数有升力系数、阻力系数和升阻比等。
它们的计算和实验测定可以精确地预测和分析物体在不同飞行状态下的性能。
飞机空气动力学 第五章 超声速机翼绕流气动特性
Cplu
2 cos
M
2
c
os2
1
利用 m B 的关系进行变换,可得:
K
C plu
B
2m
m2 1
在三维区流动参数与翼型和机翼平面形状都有关。
Folie 24
5.3.4 有限翼展薄机翼的超声速绕流特性
有限翼展薄机翼的超声速绕流特性与其前后缘性质有很 大关系,后掠机翼随来流马赫数不同可以是亚声速前 (后)缘,亚声速前缘超声速后缘或超声速前(后)缘, 如图:
Folie 21
5.3.2 前缘后缘和侧缘
根据上述几何关系引入参数 m 表示前缘半角与前缘马
赫角的比较:
tg( )
m 2
M
2
1
tg
tg
令 B
M
2
1,
K tg
则: m B
K
综上,可用如下三法判断是否超声速前(后)缘:
1.M∞n>1 或 V∞n> a∞ 2.几何上马赫线位于前(后)缘之后
3. m>1 (取“=” 号和 “<” 号时分别对应音速和亚声速 前(后)缘)
解法思路是: 1.由满足超声速线化方程的基本解确定超声速源(汇)的 表达,并利用翼面斜率规定的边界条件确定超声速源 (汇)的强度; 2.将超声速点源(汇)分布在机翼部分,积分求出由分布 源(汇)形成的扰动位函数,以及相应的压强系数(压 强系数与扰动速度有关); 3.通过对前述压强系数积分可得升力系数等气动特性;
Folie 6
5.2 无限翼展斜置翼的超声速气动特性
超声速流中任一扰源发出的扰动只能对它后马赫锥内的 流场产生影响,所以对于有限翼展机翼的超声速绕流, 机翼上某些部分就有可能不受翼尖或翼根的影响,例如 下图两种机翼的ABCD区域。
空气动力学英文PPT(chapter9(1))精品文档26页
the pressure, density, and
density, and temperature
temperature discontinuously
continuously decrease.
increase.
中英文日报导航站 anydaily
Hence, an expansion wave is the direct antithesis of a shock wave. 因此,膨胀波是激波的一个正相反的对应物。
M
中英文日报导航站 anydaily
On the other hand, if the upstream flow is supersonic, as shown in
Fig.9.2b, the disturbances cannot work their way upstream; rather, at
some finite distances from the body, the disturbance waves pile up and
The information is propagated upstream at approximately the local speed of sound. 物体存在的信息以近似等于 当地音速的速度传播到上游 去。
If the upstream flow is subsonic , as shown in Fig.9.2a, the disturbances have no problem working their way upstream, thus giving the incoming flow plenty of time to move out of the way of the body. 如图9.2a所示,如果上游是亚音速的, 扰动可以毫不困难地传播 到远前方上游,因此,给中了英文来日流报导足航站够an的ydai时ly 间以绕过物体。
超音速飞行器空气动力学特性解析
超音速飞行器空气动力学特性解析随着科学技术的不断发展,超音速飞行器已成为航空航天领域的研究热点。
而研究超音速飞行器的空气动力学特性对于提高其性能和安全性具有重要意义。
本文将从空气动力学的角度,对超音速飞行器的特性进行解析。
首先,我们需要明确超音速飞行器与亚音速飞行器的区别。
亚音速飞行器的飞行速度较低,飞行速度小于音速(即马赫数小于1)。
而超音速飞行器的飞行速度超过音速,即马赫数大于1。
由于超音速飞行器在飞行过程中会遭受到更高的空气阻力和压力差,因此其空气动力学特性与亚音速飞行器有所不同。
在超音速飞行器的空气动力学特性中,最重要的因素之一是震波的生成与传播。
当飞行器的速度超过音速时,会产生一系列的震波,这些震波由于其超音速的传播速度而导致了飞行器周围流场的复杂变化。
特别是当超音速飞行器突破音障时,会产生一条由多个菲涅耳-朗之万(Fanno-Mach)波和波尔坎-朗之万(Prandtl-Meyer)波组成的复杂震波系统。
这些震波系统对超音速飞行器的气动力和热力特性产生了重要影响。
除了震波的生成和传播,超音速飞行器还面临着较大的阻力和压力差。
由于超音速飞行的特殊性,空气动力学设计中需要克服更大的阻力。
阻力的大小直接影响飞行器的能耗和速度性能。
因此,在超音速飞行器的设计中,需要采取各种措施来减小阻力的产生,如采用流线型的外形和优化翼型等。
此外,超音速飞行器还需要面对较大的压力差。
由于超音速飞行器在朝向气流中运动时,面对的气体压强比非运动状态下要大得多。
这个差异导致了飞行器表面所承受的压力差也较大。
在设计超音速飞行器时,需要采用合适的材料和结构来增强飞行器的结构强度和耐压性能,确保其在超音速飞行过程中能够承受较大的压力差。
最后,超音速飞行器的空气动力学特性还包括其机翼和尾翼的特性。
在超音速飞行器中,机翼和尾翼的设计对于保持飞行器的稳定性和操纵性至关重要。
由于超音速飞行器在飞行过程中会遭受到更大的空气动力负载和压力差,机翼和尾翼的结构设计需要考虑更多的因素。
直升机空气动力学介绍(英文版)
Thrust
Shock Waves
Aeroelastic Response
Unsteady Aerodynamics
0
Main Rotor / Tail Rotor / Fuselage Flow Interference
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Tip Vortices
Blade-Tip Vortex interactions
Hinges
Only the lifts were transferred to the fuselage, not unwanted moments. In later models, lead-lag hinges were also used to Alleviate root stresses from Coriolis forces
V
180
270
Dynamic Stall on Retreating Blade
© L. Sankar Helicopter Aerodynamics
2
A systematic Approach is necessary
• • A variety of tools are needed to understand, and predict these phenomena. Tools needed include
© L. Sankar Helicopter Aerodynamics 7
Earliest Helicopter.. Chinese Top
© L. Sankar Helicopter Aerodynamics
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© L. Sankar Helicopter Aerodynamics
高超1
2 M ∞ / Re⋅ x
µ ↑→ 粘性变大 → δ ↑
附面层内法向压力恒定 P = ρ RT, ρ ↓ 边界层变厚 质量守恒 V ↑→ δ ↑
一、高超声速流的基本特征
5、激波层内高温和真实气体效应:
P 强烈压缩导致温度剧增: = ρ RT 不成立 C p,Cv,γ 不为常数
T > 2000 K,O2 → 2O
C p1
⇒
tan β ≈ sin β ≈ β
tan θ ≈ θ
tan( β − θ ) ≈ β − θ
2 4 2 1 C py γ + 1 4 C py = β − ⇒ C p1 = 2θβ ⇒ 2 = 1+ 1+ 2 γ +1 M∞ 2 θ ( γ + 1) M ∞θ ⇒ θ 2 = γ + 1
C p1 = P − P∞ 1 1 ρ ∞V∞ 2 2
a2 = γ
ρ∞
P∞
4 2 1 2 P 1 sin β − ⇒ C p1 = − 1 = 2 M ∞2 γ M ∞ P∞ γ + 1
一、激波(续)
M ∞ >> 1 ⇒ β ↓
若θ ↓
高超声速空气动力学 内容:研究和确定高超声速飞行器气动力、热环 境和其它物理现象。 目标:气动设计和防热设计。
一、高超声速流的基本特征
1、流场非线性性质:
dp dV = −γ M 2 p V
dρ
ρ
= −M 2
dV V
dT dV = −(γ − 1) M 2 T V
M >> 1
扰动速度小的变化会引起参数剧烈变化,从而流 场参数不再是小扰动线化理论了
超声速飞机空气动力学和飞行力学
超声速飞机空气动力学和飞行力学超声速飞机是一种可以飞行速度超过音速的飞行器,它的出现对航空工业和航空运输领域产生了深远的影响。
要理解超声速飞机的空气动力学和飞行力学,需要从机翼设计、气动外形、飞行控制等方面进行全面评估。
在本文中,我们将深入探讨超声速飞机的空气动力学和飞行力学,并共享个人的观点和理解。
一、机翼设计超声速飞机的机翼设计是空气动力学和飞行力学中的关键问题。
在超声速飞行条件下,机翼需要具有较小的厚度和较大的横截面积,以减小飞机的阻力和提高升力。
机翼的前缘通常采用锥形或凸出的设计,以减小激波对机翼表面的影响,提高飞行效率。
二、气动外形超声速飞机的气动外形对其空气动力学性能有着重要影响。
通常情况下,超声速飞机采用尖嘴和尾巴翼的设计,以减小阻力和增大升力。
在设计中,还需要考虑到激波的影响,合理设计激波的位置和强度,以减小激波对飞机的阻力和干扰。
三、飞行控制超声速飞机的飞行控制是飞行力学中的重要问题。
在超声速飞行条件下,飞机需要具有较强的稳定性和操纵性,以保证飞行安全和飞行品质。
飞机的操纵面需要具有较大的偏转角度和灵活的控制系统,以满足超声速飞行时的飞行需要。
在总结回顾本文所述内容时,超声速飞机的空气动力学和飞行力学对飞机的设计和飞行性能有着重要影响。
合理的机翼设计、气动外形和飞行控制是超声速飞机能够安全、高效地进行超音速飞行的关键。
个人认为,超声速飞机的空气动力学和飞行力学是航空工程领域中的重要课题,需要不断进行研究和探索,以推动航空工业和航空运输的发展。
通过本文的探讨,相信读者能够对超声速飞机的空气动力学和飞行力学有更全面、深入的理解。
在未来的研究和实践中,希望能够更加注重这一领域的发展,推动超声速飞机技术的不断创新和进步。
以上就是本文关于超声速飞机空气动力学和飞行力学的论述,希望对读者有所启发。
超音速飞机是一种能够飞行速度超过音速的飞行器,通常指的是飞行速度在1.2至5马赫之间的飞行器。
Aerodynamics_of_Flight-1_教材[1]
第2页
飞行空气动力学 Aerodynamics of Flight 作用在飞机上的力 Forces Acting on the Aircraft
• 推力 Thrust • 阻力 Drag • 重力 Weight • 升力 Lift
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飞行空气动力学 Aerodynamics of Flight
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飞行空气动力学 Aerodynamics of Flight
作用在飞机上的力 Forces Acting on the Aircraft
• 作用于不加速、直线平飞的飞机上的四个力为推力、阻 力、升力和重力。 • The four forces acting on an aircraft in straight-and-level, unaccelerated flight are thrust, drag, lift, and weighmics of Flight
作用在飞机上的力 Forces Acting on the Aircraft
• 升力——抵抗向下的重力,由作用于机翼上的空气的动 力效应产生,作用方向垂直于飞行轨迹,且通过升力中 心。
• Lift - opposes the downward force of weight, is produced by the dynamic effect of the air acting on the airfoil, and acts perpendicular to the flightpath through the center of lift.
作用在飞机上的力 Forces Acting on the Aircraft
• 飞行中的所有飞机都会受到推力、阻力、升力和重力。 理解这些力如何起作用、了解如何使用动力和飞行操纵 来控制它们对飞行很重要。
超音速客机设计与空气动力学
超音速客机设计与空气动力学超音速客机是一种能够以超音速(即速度超过音速)飞行的飞机。
它是航空工程领域的重要研究领域之一,设计与空气动力学是其中最为重要的方面之一。
本文将对超音速客机设计与空气动力学进行探讨。
超音速客机设计包括多个关键要素,如机身形状、机翼设计、引擎选型等。
首先,在机身形状设计中,考虑到超音速飞行时的空气动力学性能,需要选择符合流线型的机身形状。
这种形状能够减小飞机在超音速状态下的空气阻力,提高飞机的速度和效率。
同时,合适的机身形状还可以减小气动噪声,提高客舱的舒适性和飞机的环境友好性。
其次,机翼设计对超音速客机的性能和操纵特性具有重要影响。
在超音速飞行时,压缩震波是一个重要的现象。
合理的机翼设计可以减弱或消除压缩震波,减小阻力和气动噪声。
此外,机翼的扰流板和襟翼等辅助设备的设计也是必不可少的。
这些设备可以提供超音速客机在起飞、爬升、巡航和着陆等各个飞行阶段所需的升力和操纵性。
引擎是超音速客机设计中的另一个重要组成部分。
超音速客机通常采用涡轮风扇发动机或喷气发动机。
这些发动机需要具备足够的推力和燃料效率,以满足超音速飞行时的需求。
此外,在超音速飞行时,考虑到热力学效应和气密性,发动机的外部结构也需要进行特殊优化设计。
空气动力学在超音速客机设计中起着至关重要的作用。
空气动力学是研究飞行器与空气相互作用的学科。
超音速飞行时,空气动力学性能的优化对飞机的速度、操纵性和燃油效率等方面都有重要影响。
因此,在超音速客机设计中,空气动力学原理的研究和应用是不可或缺的。
超音速飞行时,流场的压力、温度和密度分布会发生剧烈变化。
这对飞机的气动稳定性和操纵特性提出了挑战。
为了保证飞机的稳定性和操纵性,需要进行严格的空气动力学分析和模拟,确定合适的控制系统和操纵面的设计方案。
此外,超音速客机在进入超音速飞行状态时会形成剧烈的震波,产生较大的气动噪声。
这对飞行的安全性和乘客的舒适性都是一种挑战。
因此,在超音速客机设计中,需要考虑减小气动噪声的措施,如优化飞机的外形、减少尖峰噪声、采用吸声材料等。
空气动力学进展英文版
空气动力学进展英文版The field of aerodynamics, also known as air or fluid dynamics, has seen significant progress and advancements in recent years. These developments have been driven by a combination of theoretical research, computational methods, and experimental techniques.One notable area of progress is the use of computational fluid dynamics (CFD) to model and simulate the behavior of air around various objects, such as aircraft, automobiles, and even buildings. CFD has become increasingly sophisticated, allowing for more accurate predictions of aerodynamic performance and behavior.Additionally, advancements in experimental techniques, such as wind tunnel testing and high-speed imaging, have provided valuable insights into the complex flow patterns and phenomena associated with aerodynamics. These experimental methods have contributed to a deeper understanding of aerodynamic principles and have helpedvalidate and refine theoretical and computational models.Furthermore, the development of new materials and manufacturing techniques has also had a significant impact on aerodynamics. Lightweight and durable materials, such as carbon fiber composites, have enabled the design and construction of more aerodynamically efficient structures and vehicles.In the realm of aerospace, the design of more efficient and environmentally friendly aircraft has been a major focus of aerodynamic research and development. Concepts such as laminar flow control, winglet design, and advanced propulsion systems have all contributed to improvements in aerodynamic efficiency and reduced fuel consumption.In summary, the field of aerodynamics has experienced considerable progress in recent years, driven by advancements in computational methods, experimental techniques, and materials science. These developments have led to more efficient and environmentally friendly designs in aerospace, automotive, and other industries.。
空气动力学英文PPT
Aerodynamics is considered with the force acting on objects as they move through the air, such as lift, drag, and thrust, as well as the pressure force acting on the surface of objects It also deals with the flow of gases around objects, including the flow patterns and turbulence
Aerodynamics is also important in the design of cars, trucks, trains, and other vehicles that move through the air It is used to understand the flow of air around these vehicles and to optimize their design for better performance, fuel efficiency, and reduced drag
Friction between the air and the surface of an object moving through it. It is caused by the visibility of air and depends on the surface roughness of the object
Aerodynamics English
目录
Introduction to aerodynamics Basic Theory Principles of aerodynamics Aerodynamic applications Future development and challenges Aerodynamics English terminology
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The only undergraduate from the Virginia Tech Aerospace Engineering program to earn astronaut status was Jack McKay, who flew the X-15 as a NASA test pilot, and reached 295,000 feet in September of 1965. 5/8/09
11. Hypersonic Aerodynamics
11.1 Introduction Hypersonic vehicles are commonplace. There are more of them than the true supersonic aircraft discussed in the last chapter. Applications include missiles, launch vehicles and entry bodies. Nevertheless, there is no exact definition defining the start of the hypersonic flow regime. Possibilities are: a) Mach numbers at which supersonic linear theory fails b) Where γ is no longer constant, and we must consider temperature effects on fluid properties. c) Mach numbers from 3 - 5, where Mach 3 might be required for blunt bodies causing large disturbances to the flow, and Mach 5 might be the starting point for more highly streamlined bodies. In this section we will provide a brief outline of the key distinguishing concepts. The book by Anderson1 provides a starting point for further study. Essentially there are five key points to be made: 1. 2. 3. 4. 5. Temperature and aerodynamic heating become critically important In many cases pressure can be estimated fairly easily Blunt shapes are commonplace Control and stability issues lead to different shapes Engine-airframe Integration is critical
Figure 11-1. X-15 (NASA Dryden photo archives photo) In case the issue of aerodynamic heating seems academic, consider the M = 6.7 flight of the X-15. It turned out to be the last flight of that plane. A dummy ramjet installation was
5/8/ቤተ መጻሕፍቲ ባይዱ9
11-1
11-2 Configuration Aerodynamics airplane aerodynamics, hypersonic vehicles fly at very high altitudes, and the Reynolds number may be so low that the flow is laminar. Thus laminar flows are often of interest. This is important because the heat transfer is much lower when the flow is laminar. In fact, being able to estimate the transition location with certainty is a critical requirement in hypersonic vehicle design, and is the subject of current research.2 The X-15, shown in Figure 11-1, is the only real manned hypersonic airplane flown to date. It was rocket powered, and started flight by being dropped from a B-52, so it was purely a research airplane. The first flight was by Scott Crossfield in June of 1959. The X-15 reached 314,750 feet in July of 1962. An improved version reached a Mach number of 6.7 and an altitude of 102,100 feet in October of 1967 with Pete Knight at the controls. The X-15 program flew 199 flights, with the last one being in October of 1968.* Milt Thompson’s book3 describes the X-15 program, including the crackling sounds in the airframe as it heated up!
T0 γ −1 2 =1 + M∞ T 2
Or the wall temperature
(11-1)
γ −1 2 Tadiabatic = 1 + r M∞ T e 2 wall
(11-2)
where r is the recovery factor. With these relations, the limit for aluminum structure is around Mach 2, which was the Concorde’s cruise Mach number. The SR-71 is made of titanium, and temperature limits the speed to slightly over Mach 3. Note that some sources indicate that this limit is actually the temperature limit on the wiring in the airplane, and that is the condition that limited the speed. Thus hypersonic aerodynamic configuration design means that you must always deal with heating. In general, at sustained high speeds surfaces must be cooled, and since heating is a critical concern, this means that viscous effects are crucial immediately. Also, unlike normal
W.H. Mason
Hypersonic Aerodynamics 11-3
tested by placing the ramjet mockup below the airplane. The shocks from the front of the ramjet inlet spike impinged on the pylon supporting the scramjet. The shock interference heating was so severe that the shocks acted as a blowtorch, cutting through the structure, and effectively slicing off the scramjet. The internal damage to the airplane from the heating led to the scrapping of this high-speed version of the airplane. Figure 11-2 below shows the scramjet hanging below the airplane.
C p = 2sin θ
2
(11-4)
where θ is the angle between the flow vector and the surface. Thus you only need to know the geometry of the body locally to estimate the local surface pressure. Also, particles impact only the portion of the body facing the flow, as shown in Figure 11-3. The rest of the body is in a “shadow”, and the Cp is zero. See Anderson1 for the derivation of this and other pressureslope rules. Two key observations come from the Newtonian rule. First, the Mach number does not appear! Second, the pressure is related to the square of the inclination angle and not linearly as it is in the supersonic formula. This illustrates how the situation in hypersonic flow is significantly different than the linearized flow models at lower speed.