animal flight

 

Bird, bat and insect wings are complex structures that are moved in stereotypical ways to generate lift and thrust.  It was once thought that animal flight could simply be understood by assuming that animals were no different from aeroplanes.  The claim that "bumblebees can't fly" is based on this assumption.  Clearly bumblebees can fly. The truth is that bats, birds, and especially insects, use unconventional aerodynamic mechanisms for generating the forces necessary for flight.  We have recently begun to visualize and understand the aerodynamic tricks that these animals use to generate lift and thrust.   This research is valuable not only in terms of our understanding of animal flight mechanics, but also for the development of new technologies, such as micro-air vehicles and improved propeller designs, which have significant engineering applications.

In this essay, we will briefly explain how animal flight is different from aeroplane flight, how animal flight is typically studied, and present some of the emerging theories and applications of this work.  The complexities of biological wings and wing motions present many technical challenges for studying flight.  Here, we use the term "flight" broadly and note that it applies to many behaviours including gliding, soaring, hovering, parachuting, manoeuvring, and even take- off and landing.  This essay is not limited to the work of our own research group, but hopefully will convince the reader why it is valuable, and necessary, to look to animals for aerodynamic insight.

Conventional aerodynamic theory

Let us begin with aeroplane wings and a basic understanding of how they generate lift.  Structurally, aeroplane wings are rounded at the leading edge, sharp at the trailing edge and are often cambered, meaning they have a slight curvature when viewed in cross section.  An aeroplane wing generates lift when the airflow becomes separated at the leading edge, and the air moves faster over the upper wing surface than along the lower surface.  This causes a pressure difference to develop between the upper and lower wing surfaces because, in accordance with Bernoulli's principle, fast-moving fluid has a lower pressure than slow-moving fluid.  It is the pressure difference above and below the wing that causes lift.

The amount lift .

ادامه نوشته

دیوار صوتی

دیوار صوتی

تصاویری از لحظه ی شکسته شدن دیوار صوتی

 

  در این مقاله، تمامی مطالب مربوط به دیوار صوتی و چگونگی شکست آن و موارد مرتبط بررسی و مطالعه خواهند شد.

در اعصار آغازین دوران هوانوردی ابتدایی، هواپیما ها بیشتر با سرعت های بسیار پایین نسبت به هواپیما های امروزی پرواز می کردند که حتی به بیشتر از ۳۰۰ کیلومتر در ساعت نمی رسید؛ در حالی که چنین سرعتی، سرعت مطلوب برای تیک آف یا برخاست یک هواپیمای جنگنده امروزی است و رسیدن به چنین سرعتی، ابداً مستلزم تلاش بسیار و فشار آوردن بیش از حد به موتور نمی باشد.

اما رفته رفته، سرعت هواپیما ها حتی با موتورهای پیستونی به گاه بالای ۶۵۰ کیلومتر بر ساعت رسیده و از آن زمان بود که دانشمندان علوم آیرودینامیک دریافتند که با افزایش سرعت، به تدریج میزان پسا افزایش پیدا کرده و در سرعت معینی، دیگر هواپیما قادر به سرعت گرفتن نبوده، گاه نیز استال می شوند.

در آن زمان، علت این موضوع بدین گونه بیان شد که با افزایش سرعت، به تدریج سرعت گردش انتها یا نوک پره های پروانه ی موتور، به سرعت صوت نزدیک شده و سرانجام در حداکثر سرعت یک هواپیمای پیستونی که حدود ۹۵۰ کیلومتر می باشد، سرعت انتهای پره ها از سرعت صوت گذشته و پسا یا درگ بسیاری ایجاد می شود که خود مانع سرعت گرفتن بیشتر هواپیماست.

در چنین سرعت هایی، پروانه موتور هواپیماهای پیستونی، نه تنها تراست یا نیروی کشش تولید نمی کند، بلکه در اثر سرعت بسیار زیاد، تبدیل به یک دیسک یا دایره توپر چرخنده می شود که جز ایجاد درگ و پسا، کار دیگری انجام نمی دهد.

آیرودینامیست های آن زمان این حد را یک محدوده سرعت یا همان دیوار صوتی در نظر گرفته و بسیاری از آنان نیز بر این عقیده بودند که گذشتن از دیوار صوتی و پشت سر گذاشتن آن، کاریست غیر ممکن؛ اما با ورود به عصر جت و پیشرفت علم آیرودینامیک، همه ما شاهد هستیم که این کار برای جنگنده های امروزی کاری بس سهل و آسان است.

حال، پس بررسی تاریخچه آن، بهتر است به اصل موضوع بپردازیم و نخست، ببینیم که خصوصیات صوت و دیوار صوتی چیست و چرا گذر از آن نیازمند قدرت و کشش و توانایی زیادی است.

صوت، در شرایط عادی (دما، فشار و … معمولی) در سطح دریا دارای سرعتی معادل ۳۳۲ متر بر ثانیه یا ۱,۱۹۵ کیلومتر بر ساعت می باشد که این سرعت، با افزایش ارتفاع و کاهش فشار و تراکم هوا، کاهش یافته و در ارتفاعات بالاتر، صوت فواصل را با سرعت کمتری می پیماید.

این مسئله بدین صورت است که صوت همانطور که می دانیم، از طریق ضربات ملکول های هوا به یکدیگر و انتقال انرژی آن ها فضا را طی می کند و هرچه تعداد مولکول ها در یک حجم معین بیشتر باشند، انتقال انرژی زودتر صورت پذیرفته و صوت با سرعت بیشتری انتقال می یابد؛ چنانکه سرعت صوت در مایعات بیشتر از هوا و در جامدات بسیار بیشتر از مایعات و هوا و معادل ۶۰۰۰ کیلومتر بر ساعت است. پس در نتیجه افزایش ارتفاع، تعداد ملکول ها در یک حجم معین کاهش یافته و صوت با سرعت کمتری فضا را می پیماید.

دیوار صوتی، شیئی فیزیکی و قابل  

ادامه نوشته

normal shock wave

As an object moves through a gas, the gas molecules are deflected around the object. If the speed of the object is much less than the speed of sound of the gas, the density of the gas remains constant and the flow of gas can be described by conserving momentum and energy. As the speed of the object increases towards the speed of sound, we must consider compressibility effects on the gas. The density of the gas varies locally as the gas is compressed by the object.

For compressible flows with little or small flow turning, the flow process is reversible and the entropy is constant. The change in flow properties are then given by the isentropic relations (isentropic means "constant entropy"). But when an object moves faster than the speed of sound, and there is an abrupt decrease in the flow area, the flow process is irreversible and the entropy increases. Shock waves are generated which are very small regions in the gas where the gas properties change by a large amount. Across a shock wave, the static pressure, temperature, and gas density increases almost instantaneously. Because a shock wave does no work, and there is no heat addition, the total enthalpy and the total temperature are constant. But because the flow is non-isentropic, the total pressure downstream of the shock is always less than the total pressure upstream of the shock; there is a loss of total pressure associated with a shock wave. The ratio of the total pressure is shown on the slide. Because total pressure changes across the shock, we can not use the usual (incompressible) form of Bernoulli's equation across the shock. The Mach number and speed of the flow also decrease across a shock wave.

If the shock wave is perpendicular to the flow direction it is called a normal shock. On this slide we have listed the equations which describe the change in flow variables for flow across a normal shock. The equations presented here were derived by considering the conservation of mass, momentum, and energy. for a compressible gas while ignoring viscous effects. The equations have been further specialized for a one-dimensional flow without heat addition.

The equations can be applied to the two dimensional flow past a wedge for the following combination of free stream Mach number M and wedge angle a :

a > (4 / ( 3 * sqrt(3) * (gam + 1)) * {[M^2 -1]^3/2} / M^2

where gam is the ratio of specific heats. If the wedge angle is less than this detachment angle, an attached oblique shock occurs and the equations are slightly modified.

Across the normal shock wave the Mach number decreases to a value specified as M1:

M1^2 = [(gam - 1) * M^2 + 2] / [2 * gam * M^2 - (gam - 1)]

The total temperature Tt across the shock is constant,

Tt1 / Tt0 = 1

The static temperature T increases in zone 1 to become:

T1 / T0 = [2 * gam * M^2 - (gam - 1)] * [(gam - 1) * M^2 + 2] / [(gam + 1)^2 * M^2]

The static pressure p increases to:

p1 / p0 = [2* gam * M^2 - (gam - 1)] / (gam + 1)

And the density r changes by:

r1 / r0 = [(gam + 1) * M^2 ] / [(gam -1 ) * M^2 + 2]

The total pressure pt decreases according to:

pt1 / pt0 = {[(gam + 1) * M^2 ] / [(gam - 1) *M^2 + 2]}^[gam/(gam-1)] * {(gam + 1) /[2 * gam * M^2 - (gam - 1)]}^[1/(gam - 1)]

The right hand side of all these equations depend only on the free stream Mach number. So knowing the Mach number, we can determine all the conditions associated with the normal shock. The equations describing normal shocks were published in a NACA report (NACA-1135) in 1951

speed of sound

Air is a gas, and a very important property of any gas is the speed of sound through the gas. Why are we interested in the speed of sound? The speed of "sound" is actually the speed of transmission of a small disturbance through a medium. Sound itself is a sensation created in the human brain in response to sensory inputs from the inner ear. (We won't comment on the old "tree falling in a forest" discussion!)

Disturbances are transmitted through a gas as a result of collisions between the randomly moving molecules in the gas. The transmission of a small disturbance through a gas is an isentropic process. The conditions in the gas are the same before and after the disturbance passes through. Because the speed of transmission depends on molecular collisions, the speed of sound depends on the state of the gas. The speed of sound is a constant within a given gas and the value of the constant depends on the type of gas (air, pure oxygen, carbon dioxide, etc.) and the temperature of the gas. An analysis based on conservation of mass and momentum shows that the speed of sound a is equal to the square root of the ratio of specific heats g times the gas constant R times the temperature T.

a = sqrt [g * R * T]

Notice that the temperature must be specified on an absolute scale (Kelvin or Rankine). The dependence on the type of gas is included in the gas constant R. which equals the universal gas constant divided by the molecular weight of the gas, and the ratio of specific heats.

The speed of sound in air depends on the type of gas and the temperature of the gas. On Earth, the atmosphere is composed of mostly diatomic nitrogen and oxygen, and the temperature depends on the altitude in a rather complex way. Scientists and engineers have created a mathematical model of the atmosphere to help them account for the changing effects of temperature with altitude. Mars also has an atmosphere composed of mostly carbon dioxide. There is a similar mathematical model of the Martian atmosphere. We have created an atmospheric calculator to let you study the variation of sound speed with planet and altitude.

mach angle

As an object moves through a gas, the gas molecules are deflected around the object. If the speed of the object is much less than the speed of sound of the gas, the density of the gas remains constant and the flow of gas can be described by conserving momentum, and energy in the flow. As the speed of the object increases towards the speed of sound, we must consider compressibility effects on the gas. The density of the gas varies locally as the gas is compressed by the object. Near and beyond the speed of sound (about 330 m/s or 700 mph on Earth at sea level), small disturbances in the flow are transmitted to other locations isentropically (with constant entropy) as sound waves.

For supersonic and hypersonic flows, small disturbances are transmitted downstream within a cone. The edge of the cone is depicted two-dimensionally by the blue lines on the figure at the top of this page. The sound waves strike the edge of the cone at a right angle and the speed of the sound wave is denoted by the letter a. The flow is moving at velocity v which is greater than a. From trigonometry, the sine of the cone angle mu is equal to the ratio of a and v:

sin(mu) = a / v

But the ratio of v to a is the Mach number of the flow.

M = v / a

With a little algebra, we can determine that the cone angle mu is equal to the inverse sin of one over the Mach number.

sin(mu) = 1 / M

mu = asin(1 / M)

where asin is the trigonometric inverse sine function. It is also written as shown on the slide sin^-1. Mu is an angle which depends only on the Mach number and is therefore called the Mach angle of the flow.

We are interested in determining the Mach angle because small disturbances in a supersonic flow are confined to the cone formed by the Mach angle. There is no upstream influence in a supersonic flow; disturbances are only transmitted downstream within the cone.

mach number

 

As an aircraft moves through the air, the air molecules near the aircraft are disturbed and move around the aircraft. If the aircraft passes at a low speed, typically less than 250 mph, the density of the air remains constant. But for higher speeds, some of the energy of the aircraft goes into compressing the air and locally changing the density of the air. This compressibility effect alters the amount of resulting force on the aircraft. The effect becomes more important as speed increases. Near and beyond the speed of sound, about 330 m/s or 760 mph, small disturbances in the flow are transmitted to other locations isentropically or with constant entropy. But a sharp disturbance generates a shock wave that affects both the lift and drag of an aircraft.

The ratio of the speed of the aircraft to the speed of sound in the gas determines the magnitude of many of the compressibility effects. Because of the importance of this speed ratio, aerodynamicists have designated it with a special parameter called the Mach number in honor of Ernst Mach, a late 19th century physicist who studied gas dynamics. The Mach number M allows us to define flight regimes in which compressibility effects vary.

1. Subsonic conditions occur for Mach numbers less than one, M < 1 . For the lowest subsonic conditions, compressibility can be ignored.
2. As the speed of the object approaches the speed of sound, the flight Mach number is nearly equal to one, M = 1, and the flow is said to be transonic. At some places on the object, the local speed exceeds the speed of sound. Compressibility effects are most important in transonic flows and lead to the early belief in a sound barrier. Flight faster than sound was thought to be impossible. In fact, the sound barrier was only an increase in the drag near sonic conditions because of compressibility effects. Because of the high drag associated with compressibility effects, aircraft do not cruise near Mach 1.
3. Supersonic conditions occur for Mach numbers greater than one, 1 < M < 3. Compressibility effects are important for supersonic aircraft, and shock waves are generated by the surface of the object. For high supersonic speeds, 3 < M < 5, aerodynamic heating also becomes very important for aircraft design.
4. For speeds greater than five times the speed of sound, M > 5, the flow is said to be hypersonic. At these speeds, some of the energy of the object now goes into exciting the chemical bonds which hold together the nitrogen and oxygen molecules of the air. At hypersonic speeds, the chemistry of the air must be considered when determining forces on the object. The Space Shuttle re-enters the atmosphere at high hypersonic speeds, M ~ 25. Under these conditions, the heated air becomes an ionized plasma of gas and the spacecraft must be insulated from the high temperatures.

For supersonic and hypersonic flows, small disturbances are transmitted downstream within a cone. The trigonometric sine of the cone angle b is equal to the inverse of the Mach number M and the angle is therefore called the Mach angle.

sin(b) = 1 / M

There is no upstream influence in a supersonic flow; disturbances are only transmitted downstream.

The Mach number depends on the speed of sound in the gas and the speed of sound depends on the type of gas and the temperature of the gas. The speed of sound varies from planet to planet. On Earth, the atmosphere is composed of mostly diatomic nitrogen and oxygen, and the temperature depends on the altitude in a rather complex way. Scientists and engineers have created a mathematical model of the atmosphere to help them account for the changing effects of temperature with altitude. Mars also has an atmosphere composed of mostly carbon dioxide. There is a similar mathematical model of the Martian atmosphere. We have created an atmospheric calculator to let you study the variation of sound speed with planet and altitude.