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The Physics of Flight ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Lift Lift is achieved through the cross-sectional shape (airfoil design) of the wing. As the wing moves through the air, the airfoil's shape causes the air moving  over  the wing to travel faster than the air moving  under  the wing. The slower airflow beneath the wing generates more pressure, while the faster airflow above generates less. This difference in pressure results in  lift . Lift  will vary dynamically depending on the speed an aircraft is traveling at.
Angle of Attack ,[object Object],[object Object],[object Object],[object Object]
Thrust When the propeller on the aircraft engine rotates, it pulls in air from in front of the aircraft and pushes it back towards the tail. The force generated by this is  thrust . Thrust gives the aircraft forward momentum, and in turn, creates lift on the lifting surfaces (mainly the wings). Generally, the greater the thrust, the greater the airspeed. Thrust is controlled by raising or lowering the revolutions-per-minute (rpm) of the engine by using the throttle. Drag As an aircraft is propelled forward by thrust, an undesirable effect is also created: resistance. When the aircraft travels through the air, its frontal area pushes against the air in front of it, and air flowing over the aircraft causes friction. This is known as  drag . For any given aircraft, drag can be increased and decreased depending on the conditions. For example, a more streamlined aircraft will reduce drag, while other factors may increase drag. These include increased AoA, lowering flaps and/or landing gear, and carrying external stores, such as bombs and rockets Altitude Air density varies with altitude; at lower altitudes, it is thicker, while higher up, the air is thinner. The density of the air directly affects drag and thrust. For example, at lower altitudes the thicker air increases thrust by supplying the propeller with more mass to move. However, that mass also increases drag. The lesser amount of oxygen associated with the thinner atmosphere of higher altitudes reduces the power output of the engine, thereby reducing thrust. However one benefit of thinner atmosphere is that it creates less drag. G-Forces Gravity effects all objects within the Earth's gravitational field -  G-force . When a person is standing still on the earth, they are experiencing  One G  (one times the force of gravity). When a pilot in an airplane changes its orientation rapidly (tight turns, loops, etc.), the aircraft will undergo additional G-forces. These may be  positive  or  negative  G-forces.
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Aircraft Control Surfaces ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Primary Control Surface Function Ailerons (Roll) The  Ailerons , located on the outer part of the trailing edge of the wings, control the  roll  or bank of the airplane. The two ailerons (one on each wing), work in opposite directions to each other. When the left one is raised, the right one is lowered. The roll/bank of the aircraft is controlled by the side to side movement of the joystick Elevator (Pitch) The   pitch , or the up and down movement of the aircraft is controlled by the  Elevator . It is located on the trailing edge of the horizontal tail assembly and is controlled by the forward and backward movement of the joystick. Pulling the joystick back will move the elevator up, causing the nose of the aircraft to point up. Similarly, pushing the joystick forward will move the elevator down and pitch the nose down.
Control Surface Function ,[object Object],[object Object],Flaps The   Flaps   are located on the underside of the trailing edge of the wings, inboard of the ailerons. This set of control surfaces, when lowered, changes the cross sectional shape (airfoil) of the wing. By lowering the flaps, more surface area on the wing is created, thus increasing lift. This enables you to lower your  stall  speed and increase your  Angle-of-Attack  (AoA). However, the flaps also increase the drag on the aircraft, which reduces speed. Flaps are most commonly used for take off and landing.
Un conventional Control surfaces FLAPERON:  is a type of control surface that combines aspects of both flaps and ailerons. In addition to controlling the roll or bank of an aircraft like conventional ailerons, both flaperons can be lowered together to function much the same as a dedicated set of flaps would. Both ailerons could also be raised, which would give spoilerons. The pilot has separate controls for ailerons and flaps. A mixer is used to combine the separate pilot input into this single set of control surfaces called flaperons. The use of flaperons instead of separate ailerons and flaps can reduce the weight of an aircraft. The complexity is transferred from having a double set of control surfaces (flaps and ailerons) to the mixer. Certain aircraft use different kinds of surfaces, such as a V-tail/ruddervator, flaperons, or elevons, to avoid pilot confusion the aircraft will still normally be designed so that the yoke or stick controls pitch and roll in the conventional way, as will the rudder pedals for yaw. V-TAIL/RUDDERVATOR:   In aircraft, a  V-tail  (sometimes called a  Butterfly tail ) is an unconventional arrangement of the tail control surfaces that replaces the traditional fin and horizontal surfaces with two surfaces set in a V-shaped configuration when viewed from the front or rear of the aircraft. The rear of each surface is hinged, and these movable sections, sometimes called ruddervators, combine the tasks of the elevators and rudder. Advantages:  With fewer surfaces than a conventional three-aerofoil tail or a T-tail, the V-tail is lighter, has less wetted surface area, and thus produces less drag (disputed). In modern day light jet general aviation aircraft such as unmanned aerial drone Global Hawk .the power plant is often placed outside the aircraft to protect the passengers and make certification easier. In such cases V-tails are used to avoid placing the vertical stabilizer in the exhaust of the engine Disadvantages:  Combining the pitch and yaw controls is difficult and requires a more complex control system. The V-tail arrangement also places greater stress on the rear fuselage when pitching and yawing ELEVONS:  On an aeroplane, elevons are a single control surface which combines the function of the elevators and ailerons in one. They are usually seen on delta-wing aircraft
In addition to the primary flight controls for roll, pitch, and yaw, there are often secondary controls available to give the pilot finer control over flight or to ease the workload. The most commonly-available control is a wheel or other device to control. A few of the most common Secondary control Surfaces are as follows ,[object Object],Secondary control Surfaces SPOILER  : (sometimes called a  lift dumper ) is a device intended to reduce lift in an aircraft. Spoilers are plates on the top surface of a wing which can be extended upward into the airflow and  spoil  it. By doing so, the spoiler creates a carefully controlled stall over the portion of the wing behind it, greatly reducing the lift of that wing section. Spoilers differ from airbrakes in that airbrakes are designed to increase drag while making little change to lift, while spoilers greatly reduce lift while making only a moderate increase in drag. Spoilers are sometimes used when descending from cruise altitudes to assist the aircraft in descending to lower altitudes without picking up speed. the real gain comes as the spoilers cause a dramatic loss of lift and hence the weight of the aircraft is transferred from the wings to the undercarriage, allowing the wheels to be mechanically braked with much less chance of skidding. Reverse thrust is also often further used to help slow the aircraft on landing. AIR BRAKES:  In  aeronautics,  air brakes  are a type of flight control used on an aircraft to reduce speed during landing. Air brakes differ from spoilers in that air brakes are designed to increase drag while making little change to lift, whereas spoilers greatly reduce the lift-to-drag ratio and a higher angle of attack required to maintain lift, resulting in a higher stall speed.
Secondary control Surfaces Elevator trim:  The most commonly-available control is a wheel or other device to control elevator trim, so that the pilot does not have to maintain constant backward or forward pressure to hold a specific pitch attitude (other types of trim, for rudder and ailerons, are common on larger aircraft but may also appear on smaller ones) Trim tabs are small surfaces connected to the trailing edge of a larger control surface on aircraft. The angle of the tab relative to the larger surface can be adjusted to null out hydro- or aero-dynamic forces and stabilize the boat or aircraft in a particular desired attitude without the need for the pilot to constantly apply a control force. Many airplanes also have rudder and/or aileron trim systems. When a trim tab is employed, it is moved into the slipstream opposite to the control surface's desired deflection.
Major Systems/Parts of Aircraft Fuselage  : The fuselage is that portion of the aircraft that usually contains the crew and payload, either passengers, cargo, or weapons. Most fuselages are long, cylindrical tubes or sometimes rectangular box shapes. All of the other major components of the aircraft are attached to the fuselage.  Empennage  is another term sometimes used to refer to the aft portion of the fuselage plus the horizontal and vertical tails.  Landing Gear : The Under Carriage/ landing gear is used during takeoff, landing, and to taxi on the ground. Most planes today use what is called a tricycle landing gear arrangement. This system has two large main gear units located near the middle of the plane and a single smaller nose gear unit near the nose of the aircraft.  They are either  retractable  or  fixed .
The wing is the most important part of an aircraft since it produces the lift that allows a plane to fly. The wing is made up of two halves, left and right, when viewed from behind. These halves are connected to each other by means of the fuselage. A wing  produces lift  because of its special shape, a shape called an airfoil. If we were to cut through a wing and look at its cross-section, as illustrated below, we would see that a traditional airfoil has a rounded leading edge and a sharp trailing edge.  Top View The top view shows a simple wing geometry, like that found on a light general aviation aircraft. The front of the wing (at the bottom) is called the  leading edge ; the back of the wing (at the top) is called the  trailing edge . The distance from the leading edge to the trailing edge is called the  chord , denoted by the symbol  c . The ends of the wing are called the  wing tips , and the distance from one wing tip to the other is called the  span , given the symbol  s . The shape of the wing, when viewed from above looking down onto the wing, is called a  plan form . In this figure, the plan form is a rectangle. For a rectangular wing, the chord length at every location along the span is the same. For most other plan form ,  the chord length varies along the span. The  wing area, A,  is the projected area of the plan form and is bounded by the leading and trailing edges and the wing tips.  Note:   The wing area is NOT the total surface area of the wing. The  total surface area  includes both upper and lower surfaces. The wing area is a projected area and is almost half of the total surface area. Aspect ratio  is a measure of how long and slender a wing is from tip to tip. The  Aspect Ratio  of a wing is defined to be the square of the span divided by the wing area and is given the symbol  AR . For a rectangular wing, this reduces to the ratio of the span to the chord length as shown at the upper right of the figure.  AR = s^2 / A = s^2 / (s * c) = s / c  High aspect ratio wings have long spans (like high performance gliders), while low aspect ratio wings have either short spans (like the F-16 fighter) or thick chords (like the Space Shuttle). There is a component of the drag of an aircraft called induced drag which depends inversely on the aspect ratio. A higher aspect ratio wing has a lower drag and a slightly higher lift than a lower aspect ratio wing. Because the glide angle of a glider depends on the ratio of the lift to the drag, a glider is usually designed with a very high aspect ratio. The Space Shuttle has a low aspect ratio because of high speed effects, and therefore is a very poor glider. The F-14 and F-111 have the best of both worlds. They can change the aspect ratio in flight by pivoting the wings--large span for low speed, small span for high speed. wing Continue
Engine :  The other key component that makes an airplane go is its engine, or engines. Aircraft use several different kinds of engines, but they can all be classified in two major categories. Early aircraft from the Wright Flyer until World War II used propeller-driven piston engines, and these are still common today on light general aviation planes. But most modern aircraft now use some form of a jet engine. Many aircraft house the engine(s) within the fuselage itself. Most larger planes, however, have their engines mounted in separate pods hanging below the wing or sometimes attached to the fuselage. These pods are called  nacelles .  PROPULSION The key to making a jet engine work is the compression of the incoming air. If uncompressed, the air-fuel mixture won't burn and the engine can't generate any thrust. Most members of the jet family employ a section of compressors, consisting of rotating blades, that slow the incoming air to create a high pressure. This compressed air is then forced into a combustion section where it is mixed with fuel and burned. As the high-pressure gases are exhausted, they are passed through a turbine section consisting of more rotating blades. In this region, the exhausting gases turn the turbine blades which are connected by a shaft to the compressor blades at the front of the engine. Thus, the exhaust turns the turbines which turn the compressors to bring in more air and keep the engine going. The combustion gases then continue to expand out through the nozzle creating a forward thrust. The above explanation describes a simple turbojet, as illustrated Here Diagram of an axial-flow turbojet The term "jet engine" is often used as a generic name for a variety of engines, including the turbojet, turbofan, turboprop, and ramjet. These engines all operate by the same basic principles, but each has its own distinct advantages and disadvantages. All jet engines operate by forcing incoming air into a tube where the air is compressed, mixed with fuel, burned, and exhausted at high speed to generate thrust.
The turbojet (and the turbofan) can also be fitted with an  afterburner . An afterburner is simply a long tube placed in between the turbine and the nozzle in which additional fuel is added and burned to provide a significant boost in thrust. However, afterburners greatly increase fuel consumption, so aircraft can only use them for brief periods. Turbofan  : A further variation on the turbojet is the turbofan. Although most components remain the same, the turbofan introduces a fan section in front of the compressors. The fan, another rotating series of blades, is also driven by the turbine, but its primary purpose is to force a large volume of air through outer ducts that go around the engine core. Although this "bypassed" air flow travels at much lower speeds, the large mass of air that is accelerated by the fan produces a significant thrust (in addition to that created by the turbojet core) without burning any additional fuel. Thus, the turbofan is much more fuel efficient than the turbojet. In addition, the low-speed air helps to cushion the noise of the jet core making the engine much quieter. Turbofans are typically broken into one of two categories--low-bypass ratio and high-bypass ratio--as illustrated.  The bypass ratio refers to the ratio of incoming air that passes through the fan ducts compared to the incoming air passing through the jet core.  In a low-bypass turbofan, only a small amount of air passes through the fan ducts and the fan is of very small diameter. The fan in a high-bypass turbofan is much larger to force a large volume of air through the ducts. The low-bypass turbofan is more compact, but the high-bypass turbofan can produce much greater thrust, is more fuel efficient, and is much quieter.  Turboprop  : A concept similar to the turbofan is the turboprop. However, instead of the turbine driving a ducted fan, it drives a completely external propeller. Turboprops are commonly used on commuter aircraft and long-range planes that require great endurance. The turboprop is attractive in these applications because of its high fuel efficiency, even greater than the turbofan. However, the noise and vibration produced by the propeller is a significant drawback, and the turboprop is limited to subsonic flight only. In a typical turboprop, the jet core produces about 15% of the thrust while the propeller generates the remaining 85%.
Ramjet  : Another noteworthy variation on the turbojet is the ramjet. The idea behind this type of engine is to remove all the rotary components of the engine (i.e. fans, compressors, and turbines) and allow the motion of the engine itself to compress incoming air for combustion. However, the price of this simplicity is that the ramjet can only produce thrust when it is already in motion. Instead of using a compressor to draw in air and compress it for combustion, the ramjet relies on the motion of the aircraft to ram air into the engine at high enough speed that it is already sufficiently compressed for combustion to occur. Since ramjets typically cannot function until reaching about 300 mph (485 km/h) at sea level, they have been rarely used on manned aircraft. However, the ramjet is more fuel efficient than turbojets or turbofans starting at about Mach 3 making them very attractive for use on missiles. Such missiles are typically launched using rocket motors that accelerate the vehicle to high-subsonic or low-supersonic speeds where the ramjet is engaged. CONCLUSION :  ( Interactive) Classification of Aircraft ,  Discuss What are the control surfaces used for Take off and Landing of an Aircraft ? Sequence of operation ?  Discuss
GLOBAL NAVIGATION SYSTEM ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
LAAS/GBAS :  Local Area Augmentation System is the ICAO definition ground based augmentation for Satellite Navigation. Ground Based Augmentation System is the European application of LAAS.   SBAS:  SBAS is a generic term for GPS and GLONASS augmentations such as WAAS, EGNOS and MSAS, which use geostationary satellites to broadcast information to users over a large Geographical service. SBAS uses the transmission of a GPS look-alike signal from the SBAS geostationary satellite to further augment the GPS system performance. WAAS   :  WAAS consists of two basic elements. The first is a network of differential ground-stations that receive the GPS signals and calculate differential correction signals. 35 ground stations are required to cover the USA. These differential corrections are then transmitted to the second element of the system, which are WAAS transponders on a number of Inmarsat geostationary communications satellites. The differential signals are then transmitted from the communication satellites to the aircraft. In addition, the communication satellites also transmit integrity information about the performance of the GPS satellites and a signal similar to a GPS satellite. This GPS type signal is used for navigation and gives the appearance of an additional GPS satellite being present.  This situation highlights the importance of the GNSS receiver in the aircraft being able to detect   faulty satellites and discard them from the position calculation .   MSAS:  Japan is implementing the Multi Satellite-based Augmentation System (MSAS  –  Japanese   Definition) that will provide correction to GPS only. The SBAS system planned by Japan. Differential Global Positioning System  (DGPS) is an enhancement to GPS that uses a network of fixed, ground-based reference stations to broadcast the difference between the positions indicated by the satellite systems and the known fixed positions. These stations broadcast the difference between the measured satellite pseudo ranges and actual (internally computed) pseudo ranges, and receiver stations may correct their pseudo ranges by the same amount. Correction signal is typically broadcasted with in-build UHF band radio modem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
ABAS : Aircraft-based augmentation system (ABAS-ICAO definition) augments and/or integrates the information obtained from the GNSS elements with other information available on board the aircraft. The aim is to enhance the overall performance of the GPS equipment on board in terms of integrity, (continuity), availability and (accuracy)   Frequency spectrum VHF datalink appear  “ better than ”  satellite communications Switching between ground-based VHF and satellite-derived datalink for CNS/ATM operations can   be a seamless procedure, according to tests carried out by the Dutch National Laboratory NLR   and ARINC. In general, the ground-based system proved faster and broader than the satellite link.  EGNOS:  The space-borne segment of EGNOS will initially be composed of navigation transponders carried on two satellites owned by the International Maritime Satellite Organization (Inmarsat).These are Inmarsat-3 series satellites that are positioned above the Indian Ocean at 64° East, and over the Atlantic Ocean at 15.5° West. The Inmarsat-3 satellites operate from geostationary orbits at 36,000km above the Equator. Since their orbit speed matches that of the Earth’s rotation, the spacecraft appear to be stationary above the same area of Earth at all times. The EGNOS ground network will provide the backbone for three navigation services: ranging, integrity monitoring and wide-area differential corrections. The ranging service will enable the EGNOS transponders to broadcast GPS-like navigation signals. As a result, these satellites become two more sources of space-based navigation data for users. This is important because neither the GPS or GLONASS systems can guarantee that the minimum number of six satellites required for safety-critical applications, like aircraft navigation, is in view at all times and all locations world-wide. The EGNOS integrity service will enable users to know within 10 seconds (or 6 secs?) whether a navigation satellite signal is out of tolerance, allowing action to be taken before any critical situation arises. The third function of EGNOS is known as the wide-area differential service, which broadcasts correction signals to improve the precision of satellite navigation. With the wide-area differential service, the satellite navigation precision will dramatically increase to 5 or 10 metres – well above the approximately 100 metres for the currently available non-encrypted signals from GPS
Current global navigation systems GPS The United States' Global Positioning System (GPS), which as of 2007 is the only fully functional, fully available global navigation satellite system. It consists of up to 32 medium Earth orbit satellites in six different orbital planes, with the exact number of satellites varying as older satellites are retired and replaced. Operational since 1978 and globally available since 1994, GPS is currently the world's most utilized satellite navigation system. GLONASS The formerly Soviet, and now Russian,  GLObal'naya NAvigatsionnaya Sputnikovaya Sistema , or GLONASS, was a fully functional navigation constellation but since the collapse of the Soviet Union has fallen into disrepair, leading to gaps in coverage and only partial availability. The Russian Federation has pledged to restore it to full global availability by 2010 with the help of India, who is participating in the restoration project. Compass China has indicated they intend to expand their regional navigation system, called  Beidou  or  Big Dipper , into a global navigation system; a program that has been called  Compass  in China's official news agency Xinhua. The Compass system is proposed to utilize 30 medium Earth orbit satellites and five geostationary satellites. Having announced they are willing to cooperate with other countries in Compass's creation, it is unclear how this proposed program impacts China's commitment to the international  Galileo  position system Galileo The European Union and European Space Agency agreed on March 2002 to introduce their own alternative to GPS, called the Galileo positioning system. the system is scheduled to be working from 2012. The first experimental satellite was launched on 28 December 2005. Galileo is expected to be compatible with the modernized GPS system. The receivers will be able to combine the signals from both Galileo and GPS satellites to greatly increase the accuracy. Other regional navigation systems Beidou navigation system Chinese regional network to be expanded into the global COMPASS Navigation System. Till 2007, the resolution of Beidou navigation system already reached as high as 0.5m, thus China became the second country after USA which achieved <1m resolution. DORIS Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) is a French precision navigation system. QZSS The Quasi-Zenith Satellite System (QZSS), is a proposed three-satellite regional time transfer system and enhancement for GPS covering Japan. The first demonstration satellite is scheduled to be launched in 2009.
IRNSS   The  Indian Regional Navigational Satellite System (IRNSS)  is an autonomous regional satellite navigation system being developed by Indian Space Research Organization which would be under the total control of Indian government. The government approved the project in May 2006, with the intention of the system to be completed and implemented by 2012. It will consist of a constellation of 7 navigational satellites by 2012. All the 7 satellites will be placed in the Geostationary orbit (GEO) to have a larger signal footprint and lower number of satellites to map the region. It is intended to provide an absolute position accuracy of better than 20 meters throughout India and within a region extending approximately 2,000 km around it. A goal of complete Indian control has been stated, with the space segment, ground segment and user receivers all being built in India frequency allocation of  GPS ,  Galileo , and Compass; the light red color of E1 band indicates that the transmission in this band has not yet been detected
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AVIATION TERMINOLOGY Shortest distance between two points on  Earth If you assume that Earth is a round sphere with a flat surface, you can use basic spherical trigonometry equations to calculate the &quot;great circle&quot; distance along Earth's surface between any two points. If the sites are not just at different longitudes and latitudes, but also at different elevations, this adds a variable that the smooth spherical Earth model ignores. However, in most cases this won't be a serious problem. (The accuracy of this calculation depends on the accuracy of the longitude and latitude coordinates. Earth's circumference is about 40,000 km. So 1° of longitude at the equator, or 1° of latitude, is about 40,000/360 = 110 km. So, if you know a site's latitude to only the nearest degree, you know its north-south location only to within about 100 km. If you know latitude to the nearest one-thousandth of a degree, xx.xxx, you know its north-south distance to within about 100 m; for the nearest one-ten-thousandth of a degree, xx.xxxx, to within about 10 m. Longitude and latitude coordinates from modern GPS receivers (but not necessarily the elevation) should always be accurate to at least 10 m). The distance between two points at different longitudes but the same latitude decreases as the cosine of the latitude. 1° is 110 km at the equator, but at a latitude of 60°, 1° of longitude corresponds to about 110•cos(60°) = 110•0.5 = 55 km.  The shape of our planet is irregular and changing (due to the tides caused by the  Moon  and  Sun ). Its daily rotation causes the equator to bulge. Earth can be considered a rigid sphere at first approximation. A better description would be a rigid ellipsoid of revolution ( oblate spheroid ), having an  equatorial radius  of 6378.1365 km (3963.1903 mi) and  polar radius  (its axis of revolution) of 6356.7517 km (3949.9024 mi). The average radius for a spherical approximation of the figure of the Earth is approximately 6371.01 km (3958.76 statute miles, 3440.07 nautical miles). (For  nautical miles , divide km by 1.852, For  miles , divide km by 1.609344) The  great-circle distance (orthodromic distance)  is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere's interior). Because spherical geometry is rather different from ordinary Euclidean geometry, the equations for distance take on a different form. The distance between two points in Euclidean space is the length of a straight line from one point to the other. On the sphere, however, there are no straight lines. In non-Euclidean geometry, straight lines are replaced with Geodesics. Geodesics on the sphere are the  great circles  (circles on the sphere whose centers are coincident with the center of the sphere). Between any two points on a sphere which are not directly opposite each other, there is a unique great circle. The two points separate the great circle into two arcs. The length of the shorter arc is the great-circle distance between the points. A great circle endowed with such a distance is the Riemannian circle.
Let be the geographical latitude and longitude of two points (a base &quot;standpoint&quot; and the destination &quot;forepoint&quot;), respectively, and their differences and the (spherical) angular difference/distance, or central angle, which can be constituted from the spherical law of cosines . The distance  d , i.e. the arc length, for a sphere of radius  r  and given in radians, is then: This arccosine formula above can have large rounding errors for the common case where the distance is small, however, so it is not normally used. Instead, an equation known historically as the haversine formula was preferred, which is much more accurate for small distances: Historically, the use of this formula was simplified by the availability of tables for the haversine function: hav(θ) = sin 2 (θ/2). Although this formula is accurate for most distances, it too suffers from rounding errors for the special (and somewhat unusual) case of antipodal points (on opposite ends of the sphere). A more complicated formula that is accurate for all distances is the following special case of the Vincenty formula (which more generally is a method to compute distances on ellipsoids) When programming a computer, one should use the atan2() function rather than the ordinary arctangent function (atan()), in order to simplify handling of the case where the denominator is zero. If  r  is the great-circle radius of the sphere, then the great-circle distance is . Note:  above, accuracy refers to rounding errors only; all formulas themselves are exact (for a sphere). Formulas
TRUE AIRSPEED True airspeed  is the vector difference of the velocity vectors of the aircraft and the air mass, both with reference to the earth's surface. When determining the true airspeed of an aircraft under zero wind conditions and in horizontal flight, the true airspeed of the aircraft is equal to the speed of the aircraft relative to the earth's surface. When determining the true airspeed of an aircraft under non-zero wind conditions an estimation of the wind speed vector is used. To maintain a desired ground track whilst flying in the moving air mass, the pilot of an aircraft must use knowledge of wind speed, wind direction, and true air speed to determine the required heading. Indicated airspeed  (IAS) is the airspeed read directly from the airspeed indicator on an aircraft, driven by the pitot-static system. IAS is directly related to calibrated airspeed (CAS), but includes instrument errors and position error. Aircraft display an indicated airspeed on an instrument called an airspeed indicator. Indicated airspeed will differ from true airspeed whenever the aircraft is flying in air whose density differs from the density at sea level and 15 degrees Celsius. Air density is affected by temperature, moisture content, and altitude. Indicated airspeed is used in aircraft  operation  as the aircraft stalling speed and structural limiting speeds are dependent on indicated airspeed, irrespective of true airspeed. However, proper navigation via dead reckoning (without constant ground reference) requires the use of true airspeed and wind corrections. Calculating true airspeed Low-speed flight True airspeed (TAS) can be calculated as a function of indicated airspeed (or equivalent airspeed) and air density: [ where  TAS  is true airspeed V I  is indicated (or equivalent) airspeed  ρ 0  is 1.225 kg/m 3 , the air density at sea level and 15 degrees Celsius  ρ is the density of the air in which the aircraft is flying. High-speed flight TAS can be calculated as a function of Mach number and static air temperature: Where  TAS  = true airspeed a sl  is the standard speed of sound at 15 °C (661.47 knots)  M a  is Mach number,  T  is static air temperature in Kelvin's,  T sl  is standard sea level temperature (288.15 K)
Combining the above with the expression for Mach number under subsonic compressible flow gives an expression for TAS as a function of impact pressure (pitot tube), static pressure and static air temperature: Where   q c  is impact pressure P  is static pressure  Electronic Flight Instrument Systems  (EFIS) contain an air data computer with inputs of impact pressure, static pressure and total air temperature. In order to compute TAS the air data computer must convert total air temperature to static air temperature. This is a function of Mach number: Mach   number (Ma or  M ) is the speed of an object moving through air, or any fluid substance, divided by the speed of sound as it is in that substance. It is commonly used to represent an object's (such as an aircraft or missile) speed,when it is travelling at (or at multiples of) the speed of sound. Where  T t  = total air temperature For manual calculation of TAS in knots where Mach number and static air temperature are known the expression may be simplified to: remembering that temperature is in Kelvin's. In simple aircraft, without an air data computer or Mach meter,  true airspeed can be calculated as a function of calibrated airspeed and local air density (or static air temperature and pressure altitude which determine density). Some airspeed indicators incorporate a slide rule mechanism to perform this calculation. V speeds In aviation,  V-speeds  or  Velocity-speeds  are standard terms used to define airspeeds important or useful to the operation of aircraft, such as airplanes, gliders, autogiros, helicopters, blimps, and dirigibles. These speeds are derived from data obtained by aircraft designers and manufacturers during flight testing and verified in most countries by government flight inspectors during aircraft type-certification testing. Using them is considered a best practice to maximize aviation safety, aircraft performance or both. The actual speeds represented by these designators are true airspeeds specific to a particular model of aircraft, and are expressed in terms of the aircraft's indicated airspeed, so that pilots may use them directly, without having to apply correction factors.
In general aviation aircraft, the most commonly-used and most safety-critical airspeeds are displayed as color-coded arcs and lines located on the face of an aircraft's airspeed indicator. The lower ends of the green arc and the white arc are the stalling speed with wing flaps retracted, and stalling speed with wing flaps fully extended, respectively. These are the stalling speeds for the aircraft at its  maximum weigh.  Having V speeds properly displayed is an airworthiness requirement for type-certificated aircraft in most parts of the world. Regulatory V-speeds V-speed designator Description V 1 Maximum speed during takeoff at which a pilot can safely stop the aircraft without leaving the runway. This is also the minimum speed that allows the pilot to safely continue (to V2 takeoff) even if a critical engine failure occurs (between V1 and V2) V 2 Takeoff safety speed V 2min Minimum takeoff safety speed. V 3 Flap retraction speed V A Design maneuvering speed, also known as the &quot;Speed for maximum control deflection.&quot; This is the speed above which it is unwise to make full application of any single flight control (or &quot;pull to the stops&quot;) as it may generate a force greater than the aircraft's structural limitations . V B Design speed for maximum gust intensity V C Design cruising speed, also known as the optimum cruise speed, is the most efficient speed in terms of distance, speed and fuel usage. V-speed designator Description V NE Never exceed speed V S Stall speed or minimum steady flight speed for which the aircraft is still controllable V S0 Stall speed or minimum flight speed in landing configuration. V NO Maximum structural cruising speed or maximum speed for normal operations V FE Maximum flap extended speed V FC Maximum speed for stability characteristics. V F Designed flap speed
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Flight Basics

  • 1.
  • 2.
  • 3. Thrust When the propeller on the aircraft engine rotates, it pulls in air from in front of the aircraft and pushes it back towards the tail. The force generated by this is thrust . Thrust gives the aircraft forward momentum, and in turn, creates lift on the lifting surfaces (mainly the wings). Generally, the greater the thrust, the greater the airspeed. Thrust is controlled by raising or lowering the revolutions-per-minute (rpm) of the engine by using the throttle. Drag As an aircraft is propelled forward by thrust, an undesirable effect is also created: resistance. When the aircraft travels through the air, its frontal area pushes against the air in front of it, and air flowing over the aircraft causes friction. This is known as drag . For any given aircraft, drag can be increased and decreased depending on the conditions. For example, a more streamlined aircraft will reduce drag, while other factors may increase drag. These include increased AoA, lowering flaps and/or landing gear, and carrying external stores, such as bombs and rockets Altitude Air density varies with altitude; at lower altitudes, it is thicker, while higher up, the air is thinner. The density of the air directly affects drag and thrust. For example, at lower altitudes the thicker air increases thrust by supplying the propeller with more mass to move. However, that mass also increases drag. The lesser amount of oxygen associated with the thinner atmosphere of higher altitudes reduces the power output of the engine, thereby reducing thrust. However one benefit of thinner atmosphere is that it creates less drag. G-Forces Gravity effects all objects within the Earth's gravitational field - G-force . When a person is standing still on the earth, they are experiencing One G (one times the force of gravity). When a pilot in an airplane changes its orientation rapidly (tight turns, loops, etc.), the aircraft will undergo additional G-forces. These may be positive or negative G-forces.
  • 4.
  • 5.
  • 6. Primary Control Surface Function Ailerons (Roll) The Ailerons , located on the outer part of the trailing edge of the wings, control the roll or bank of the airplane. The two ailerons (one on each wing), work in opposite directions to each other. When the left one is raised, the right one is lowered. The roll/bank of the aircraft is controlled by the side to side movement of the joystick Elevator (Pitch) The pitch , or the up and down movement of the aircraft is controlled by the Elevator . It is located on the trailing edge of the horizontal tail assembly and is controlled by the forward and backward movement of the joystick. Pulling the joystick back will move the elevator up, causing the nose of the aircraft to point up. Similarly, pushing the joystick forward will move the elevator down and pitch the nose down.
  • 7.
  • 8. Un conventional Control surfaces FLAPERON: is a type of control surface that combines aspects of both flaps and ailerons. In addition to controlling the roll or bank of an aircraft like conventional ailerons, both flaperons can be lowered together to function much the same as a dedicated set of flaps would. Both ailerons could also be raised, which would give spoilerons. The pilot has separate controls for ailerons and flaps. A mixer is used to combine the separate pilot input into this single set of control surfaces called flaperons. The use of flaperons instead of separate ailerons and flaps can reduce the weight of an aircraft. The complexity is transferred from having a double set of control surfaces (flaps and ailerons) to the mixer. Certain aircraft use different kinds of surfaces, such as a V-tail/ruddervator, flaperons, or elevons, to avoid pilot confusion the aircraft will still normally be designed so that the yoke or stick controls pitch and roll in the conventional way, as will the rudder pedals for yaw. V-TAIL/RUDDERVATOR: In aircraft, a V-tail (sometimes called a Butterfly tail ) is an unconventional arrangement of the tail control surfaces that replaces the traditional fin and horizontal surfaces with two surfaces set in a V-shaped configuration when viewed from the front or rear of the aircraft. The rear of each surface is hinged, and these movable sections, sometimes called ruddervators, combine the tasks of the elevators and rudder. Advantages: With fewer surfaces than a conventional three-aerofoil tail or a T-tail, the V-tail is lighter, has less wetted surface area, and thus produces less drag (disputed). In modern day light jet general aviation aircraft such as unmanned aerial drone Global Hawk .the power plant is often placed outside the aircraft to protect the passengers and make certification easier. In such cases V-tails are used to avoid placing the vertical stabilizer in the exhaust of the engine Disadvantages: Combining the pitch and yaw controls is difficult and requires a more complex control system. The V-tail arrangement also places greater stress on the rear fuselage when pitching and yawing ELEVONS: On an aeroplane, elevons are a single control surface which combines the function of the elevators and ailerons in one. They are usually seen on delta-wing aircraft
  • 9.
  • 10. Secondary control Surfaces Elevator trim: The most commonly-available control is a wheel or other device to control elevator trim, so that the pilot does not have to maintain constant backward or forward pressure to hold a specific pitch attitude (other types of trim, for rudder and ailerons, are common on larger aircraft but may also appear on smaller ones) Trim tabs are small surfaces connected to the trailing edge of a larger control surface on aircraft. The angle of the tab relative to the larger surface can be adjusted to null out hydro- or aero-dynamic forces and stabilize the boat or aircraft in a particular desired attitude without the need for the pilot to constantly apply a control force. Many airplanes also have rudder and/or aileron trim systems. When a trim tab is employed, it is moved into the slipstream opposite to the control surface's desired deflection.
  • 11. Major Systems/Parts of Aircraft Fuselage : The fuselage is that portion of the aircraft that usually contains the crew and payload, either passengers, cargo, or weapons. Most fuselages are long, cylindrical tubes or sometimes rectangular box shapes. All of the other major components of the aircraft are attached to the fuselage. Empennage is another term sometimes used to refer to the aft portion of the fuselage plus the horizontal and vertical tails. Landing Gear : The Under Carriage/ landing gear is used during takeoff, landing, and to taxi on the ground. Most planes today use what is called a tricycle landing gear arrangement. This system has two large main gear units located near the middle of the plane and a single smaller nose gear unit near the nose of the aircraft. They are either retractable or fixed .
  • 12. The wing is the most important part of an aircraft since it produces the lift that allows a plane to fly. The wing is made up of two halves, left and right, when viewed from behind. These halves are connected to each other by means of the fuselage. A wing produces lift because of its special shape, a shape called an airfoil. If we were to cut through a wing and look at its cross-section, as illustrated below, we would see that a traditional airfoil has a rounded leading edge and a sharp trailing edge. Top View The top view shows a simple wing geometry, like that found on a light general aviation aircraft. The front of the wing (at the bottom) is called the leading edge ; the back of the wing (at the top) is called the trailing edge . The distance from the leading edge to the trailing edge is called the chord , denoted by the symbol c . The ends of the wing are called the wing tips , and the distance from one wing tip to the other is called the span , given the symbol s . The shape of the wing, when viewed from above looking down onto the wing, is called a plan form . In this figure, the plan form is a rectangle. For a rectangular wing, the chord length at every location along the span is the same. For most other plan form , the chord length varies along the span. The wing area, A, is the projected area of the plan form and is bounded by the leading and trailing edges and the wing tips. Note: The wing area is NOT the total surface area of the wing. The total surface area includes both upper and lower surfaces. The wing area is a projected area and is almost half of the total surface area. Aspect ratio is a measure of how long and slender a wing is from tip to tip. The Aspect Ratio of a wing is defined to be the square of the span divided by the wing area and is given the symbol AR . For a rectangular wing, this reduces to the ratio of the span to the chord length as shown at the upper right of the figure. AR = s^2 / A = s^2 / (s * c) = s / c High aspect ratio wings have long spans (like high performance gliders), while low aspect ratio wings have either short spans (like the F-16 fighter) or thick chords (like the Space Shuttle). There is a component of the drag of an aircraft called induced drag which depends inversely on the aspect ratio. A higher aspect ratio wing has a lower drag and a slightly higher lift than a lower aspect ratio wing. Because the glide angle of a glider depends on the ratio of the lift to the drag, a glider is usually designed with a very high aspect ratio. The Space Shuttle has a low aspect ratio because of high speed effects, and therefore is a very poor glider. The F-14 and F-111 have the best of both worlds. They can change the aspect ratio in flight by pivoting the wings--large span for low speed, small span for high speed. wing Continue
  • 13. Engine : The other key component that makes an airplane go is its engine, or engines. Aircraft use several different kinds of engines, but they can all be classified in two major categories. Early aircraft from the Wright Flyer until World War II used propeller-driven piston engines, and these are still common today on light general aviation planes. But most modern aircraft now use some form of a jet engine. Many aircraft house the engine(s) within the fuselage itself. Most larger planes, however, have their engines mounted in separate pods hanging below the wing or sometimes attached to the fuselage. These pods are called nacelles . PROPULSION The key to making a jet engine work is the compression of the incoming air. If uncompressed, the air-fuel mixture won't burn and the engine can't generate any thrust. Most members of the jet family employ a section of compressors, consisting of rotating blades, that slow the incoming air to create a high pressure. This compressed air is then forced into a combustion section where it is mixed with fuel and burned. As the high-pressure gases are exhausted, they are passed through a turbine section consisting of more rotating blades. In this region, the exhausting gases turn the turbine blades which are connected by a shaft to the compressor blades at the front of the engine. Thus, the exhaust turns the turbines which turn the compressors to bring in more air and keep the engine going. The combustion gases then continue to expand out through the nozzle creating a forward thrust. The above explanation describes a simple turbojet, as illustrated Here Diagram of an axial-flow turbojet The term &quot;jet engine&quot; is often used as a generic name for a variety of engines, including the turbojet, turbofan, turboprop, and ramjet. These engines all operate by the same basic principles, but each has its own distinct advantages and disadvantages. All jet engines operate by forcing incoming air into a tube where the air is compressed, mixed with fuel, burned, and exhausted at high speed to generate thrust.
  • 14. The turbojet (and the turbofan) can also be fitted with an afterburner . An afterburner is simply a long tube placed in between the turbine and the nozzle in which additional fuel is added and burned to provide a significant boost in thrust. However, afterburners greatly increase fuel consumption, so aircraft can only use them for brief periods. Turbofan : A further variation on the turbojet is the turbofan. Although most components remain the same, the turbofan introduces a fan section in front of the compressors. The fan, another rotating series of blades, is also driven by the turbine, but its primary purpose is to force a large volume of air through outer ducts that go around the engine core. Although this &quot;bypassed&quot; air flow travels at much lower speeds, the large mass of air that is accelerated by the fan produces a significant thrust (in addition to that created by the turbojet core) without burning any additional fuel. Thus, the turbofan is much more fuel efficient than the turbojet. In addition, the low-speed air helps to cushion the noise of the jet core making the engine much quieter. Turbofans are typically broken into one of two categories--low-bypass ratio and high-bypass ratio--as illustrated. The bypass ratio refers to the ratio of incoming air that passes through the fan ducts compared to the incoming air passing through the jet core. In a low-bypass turbofan, only a small amount of air passes through the fan ducts and the fan is of very small diameter. The fan in a high-bypass turbofan is much larger to force a large volume of air through the ducts. The low-bypass turbofan is more compact, but the high-bypass turbofan can produce much greater thrust, is more fuel efficient, and is much quieter. Turboprop : A concept similar to the turbofan is the turboprop. However, instead of the turbine driving a ducted fan, it drives a completely external propeller. Turboprops are commonly used on commuter aircraft and long-range planes that require great endurance. The turboprop is attractive in these applications because of its high fuel efficiency, even greater than the turbofan. However, the noise and vibration produced by the propeller is a significant drawback, and the turboprop is limited to subsonic flight only. In a typical turboprop, the jet core produces about 15% of the thrust while the propeller generates the remaining 85%.
  • 15. Ramjet : Another noteworthy variation on the turbojet is the ramjet. The idea behind this type of engine is to remove all the rotary components of the engine (i.e. fans, compressors, and turbines) and allow the motion of the engine itself to compress incoming air for combustion. However, the price of this simplicity is that the ramjet can only produce thrust when it is already in motion. Instead of using a compressor to draw in air and compress it for combustion, the ramjet relies on the motion of the aircraft to ram air into the engine at high enough speed that it is already sufficiently compressed for combustion to occur. Since ramjets typically cannot function until reaching about 300 mph (485 km/h) at sea level, they have been rarely used on manned aircraft. However, the ramjet is more fuel efficient than turbojets or turbofans starting at about Mach 3 making them very attractive for use on missiles. Such missiles are typically launched using rocket motors that accelerate the vehicle to high-subsonic or low-supersonic speeds where the ramjet is engaged. CONCLUSION : ( Interactive) Classification of Aircraft , Discuss What are the control surfaces used for Take off and Landing of an Aircraft ? Sequence of operation ? Discuss
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  • 18. ABAS : Aircraft-based augmentation system (ABAS-ICAO definition) augments and/or integrates the information obtained from the GNSS elements with other information available on board the aircraft. The aim is to enhance the overall performance of the GPS equipment on board in terms of integrity, (continuity), availability and (accuracy) Frequency spectrum VHF datalink appear “ better than ” satellite communications Switching between ground-based VHF and satellite-derived datalink for CNS/ATM operations can be a seamless procedure, according to tests carried out by the Dutch National Laboratory NLR and ARINC. In general, the ground-based system proved faster and broader than the satellite link. EGNOS: The space-borne segment of EGNOS will initially be composed of navigation transponders carried on two satellites owned by the International Maritime Satellite Organization (Inmarsat).These are Inmarsat-3 series satellites that are positioned above the Indian Ocean at 64° East, and over the Atlantic Ocean at 15.5° West. The Inmarsat-3 satellites operate from geostationary orbits at 36,000km above the Equator. Since their orbit speed matches that of the Earth’s rotation, the spacecraft appear to be stationary above the same area of Earth at all times. The EGNOS ground network will provide the backbone for three navigation services: ranging, integrity monitoring and wide-area differential corrections. The ranging service will enable the EGNOS transponders to broadcast GPS-like navigation signals. As a result, these satellites become two more sources of space-based navigation data for users. This is important because neither the GPS or GLONASS systems can guarantee that the minimum number of six satellites required for safety-critical applications, like aircraft navigation, is in view at all times and all locations world-wide. The EGNOS integrity service will enable users to know within 10 seconds (or 6 secs?) whether a navigation satellite signal is out of tolerance, allowing action to be taken before any critical situation arises. The third function of EGNOS is known as the wide-area differential service, which broadcasts correction signals to improve the precision of satellite navigation. With the wide-area differential service, the satellite navigation precision will dramatically increase to 5 or 10 metres – well above the approximately 100 metres for the currently available non-encrypted signals from GPS
  • 19. Current global navigation systems GPS The United States' Global Positioning System (GPS), which as of 2007 is the only fully functional, fully available global navigation satellite system. It consists of up to 32 medium Earth orbit satellites in six different orbital planes, with the exact number of satellites varying as older satellites are retired and replaced. Operational since 1978 and globally available since 1994, GPS is currently the world's most utilized satellite navigation system. GLONASS The formerly Soviet, and now Russian, GLObal'naya NAvigatsionnaya Sputnikovaya Sistema , or GLONASS, was a fully functional navigation constellation but since the collapse of the Soviet Union has fallen into disrepair, leading to gaps in coverage and only partial availability. The Russian Federation has pledged to restore it to full global availability by 2010 with the help of India, who is participating in the restoration project. Compass China has indicated they intend to expand their regional navigation system, called Beidou or Big Dipper , into a global navigation system; a program that has been called Compass in China's official news agency Xinhua. The Compass system is proposed to utilize 30 medium Earth orbit satellites and five geostationary satellites. Having announced they are willing to cooperate with other countries in Compass's creation, it is unclear how this proposed program impacts China's commitment to the international Galileo position system Galileo The European Union and European Space Agency agreed on March 2002 to introduce their own alternative to GPS, called the Galileo positioning system. the system is scheduled to be working from 2012. The first experimental satellite was launched on 28 December 2005. Galileo is expected to be compatible with the modernized GPS system. The receivers will be able to combine the signals from both Galileo and GPS satellites to greatly increase the accuracy. Other regional navigation systems Beidou navigation system Chinese regional network to be expanded into the global COMPASS Navigation System. Till 2007, the resolution of Beidou navigation system already reached as high as 0.5m, thus China became the second country after USA which achieved <1m resolution. DORIS Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) is a French precision navigation system. QZSS The Quasi-Zenith Satellite System (QZSS), is a proposed three-satellite regional time transfer system and enhancement for GPS covering Japan. The first demonstration satellite is scheduled to be launched in 2009.
  • 20. IRNSS The Indian Regional Navigational Satellite System (IRNSS) is an autonomous regional satellite navigation system being developed by Indian Space Research Organization which would be under the total control of Indian government. The government approved the project in May 2006, with the intention of the system to be completed and implemented by 2012. It will consist of a constellation of 7 navigational satellites by 2012. All the 7 satellites will be placed in the Geostationary orbit (GEO) to have a larger signal footprint and lower number of satellites to map the region. It is intended to provide an absolute position accuracy of better than 20 meters throughout India and within a region extending approximately 2,000 km around it. A goal of complete Indian control has been stated, with the space segment, ground segment and user receivers all being built in India frequency allocation of GPS , Galileo , and Compass; the light red color of E1 band indicates that the transmission in this band has not yet been detected
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  • 22. AVIATION TERMINOLOGY Shortest distance between two points on Earth If you assume that Earth is a round sphere with a flat surface, you can use basic spherical trigonometry equations to calculate the &quot;great circle&quot; distance along Earth's surface between any two points. If the sites are not just at different longitudes and latitudes, but also at different elevations, this adds a variable that the smooth spherical Earth model ignores. However, in most cases this won't be a serious problem. (The accuracy of this calculation depends on the accuracy of the longitude and latitude coordinates. Earth's circumference is about 40,000 km. So 1° of longitude at the equator, or 1° of latitude, is about 40,000/360 = 110 km. So, if you know a site's latitude to only the nearest degree, you know its north-south location only to within about 100 km. If you know latitude to the nearest one-thousandth of a degree, xx.xxx, you know its north-south distance to within about 100 m; for the nearest one-ten-thousandth of a degree, xx.xxxx, to within about 10 m. Longitude and latitude coordinates from modern GPS receivers (but not necessarily the elevation) should always be accurate to at least 10 m). The distance between two points at different longitudes but the same latitude decreases as the cosine of the latitude. 1° is 110 km at the equator, but at a latitude of 60°, 1° of longitude corresponds to about 110•cos(60°) = 110•0.5 = 55 km. The shape of our planet is irregular and changing (due to the tides caused by the Moon and Sun ). Its daily rotation causes the equator to bulge. Earth can be considered a rigid sphere at first approximation. A better description would be a rigid ellipsoid of revolution ( oblate spheroid ), having an equatorial radius of 6378.1365 km (3963.1903 mi) and polar radius (its axis of revolution) of 6356.7517 km (3949.9024 mi). The average radius for a spherical approximation of the figure of the Earth is approximately 6371.01 km (3958.76 statute miles, 3440.07 nautical miles). (For nautical miles , divide km by 1.852, For miles , divide km by 1.609344) The great-circle distance (orthodromic distance) is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere's interior). Because spherical geometry is rather different from ordinary Euclidean geometry, the equations for distance take on a different form. The distance between two points in Euclidean space is the length of a straight line from one point to the other. On the sphere, however, there are no straight lines. In non-Euclidean geometry, straight lines are replaced with Geodesics. Geodesics on the sphere are the great circles (circles on the sphere whose centers are coincident with the center of the sphere). Between any two points on a sphere which are not directly opposite each other, there is a unique great circle. The two points separate the great circle into two arcs. The length of the shorter arc is the great-circle distance between the points. A great circle endowed with such a distance is the Riemannian circle.
  • 23. Let be the geographical latitude and longitude of two points (a base &quot;standpoint&quot; and the destination &quot;forepoint&quot;), respectively, and their differences and the (spherical) angular difference/distance, or central angle, which can be constituted from the spherical law of cosines . The distance d , i.e. the arc length, for a sphere of radius r and given in radians, is then: This arccosine formula above can have large rounding errors for the common case where the distance is small, however, so it is not normally used. Instead, an equation known historically as the haversine formula was preferred, which is much more accurate for small distances: Historically, the use of this formula was simplified by the availability of tables for the haversine function: hav(θ) = sin 2 (θ/2). Although this formula is accurate for most distances, it too suffers from rounding errors for the special (and somewhat unusual) case of antipodal points (on opposite ends of the sphere). A more complicated formula that is accurate for all distances is the following special case of the Vincenty formula (which more generally is a method to compute distances on ellipsoids) When programming a computer, one should use the atan2() function rather than the ordinary arctangent function (atan()), in order to simplify handling of the case where the denominator is zero. If r is the great-circle radius of the sphere, then the great-circle distance is . Note: above, accuracy refers to rounding errors only; all formulas themselves are exact (for a sphere). Formulas
  • 24. TRUE AIRSPEED True airspeed is the vector difference of the velocity vectors of the aircraft and the air mass, both with reference to the earth's surface. When determining the true airspeed of an aircraft under zero wind conditions and in horizontal flight, the true airspeed of the aircraft is equal to the speed of the aircraft relative to the earth's surface. When determining the true airspeed of an aircraft under non-zero wind conditions an estimation of the wind speed vector is used. To maintain a desired ground track whilst flying in the moving air mass, the pilot of an aircraft must use knowledge of wind speed, wind direction, and true air speed to determine the required heading. Indicated airspeed (IAS) is the airspeed read directly from the airspeed indicator on an aircraft, driven by the pitot-static system. IAS is directly related to calibrated airspeed (CAS), but includes instrument errors and position error. Aircraft display an indicated airspeed on an instrument called an airspeed indicator. Indicated airspeed will differ from true airspeed whenever the aircraft is flying in air whose density differs from the density at sea level and 15 degrees Celsius. Air density is affected by temperature, moisture content, and altitude. Indicated airspeed is used in aircraft operation as the aircraft stalling speed and structural limiting speeds are dependent on indicated airspeed, irrespective of true airspeed. However, proper navigation via dead reckoning (without constant ground reference) requires the use of true airspeed and wind corrections. Calculating true airspeed Low-speed flight True airspeed (TAS) can be calculated as a function of indicated airspeed (or equivalent airspeed) and air density: [ where TAS is true airspeed V I is indicated (or equivalent) airspeed ρ 0 is 1.225 kg/m 3 , the air density at sea level and 15 degrees Celsius ρ is the density of the air in which the aircraft is flying. High-speed flight TAS can be calculated as a function of Mach number and static air temperature: Where TAS = true airspeed a sl is the standard speed of sound at 15 °C (661.47 knots) M a is Mach number, T is static air temperature in Kelvin's, T sl is standard sea level temperature (288.15 K)
  • 25. Combining the above with the expression for Mach number under subsonic compressible flow gives an expression for TAS as a function of impact pressure (pitot tube), static pressure and static air temperature: Where  q c is impact pressure P is static pressure Electronic Flight Instrument Systems (EFIS) contain an air data computer with inputs of impact pressure, static pressure and total air temperature. In order to compute TAS the air data computer must convert total air temperature to static air temperature. This is a function of Mach number: Mach number (Ma or M ) is the speed of an object moving through air, or any fluid substance, divided by the speed of sound as it is in that substance. It is commonly used to represent an object's (such as an aircraft or missile) speed,when it is travelling at (or at multiples of) the speed of sound. Where T t = total air temperature For manual calculation of TAS in knots where Mach number and static air temperature are known the expression may be simplified to: remembering that temperature is in Kelvin's. In simple aircraft, without an air data computer or Mach meter, true airspeed can be calculated as a function of calibrated airspeed and local air density (or static air temperature and pressure altitude which determine density). Some airspeed indicators incorporate a slide rule mechanism to perform this calculation. V speeds In aviation, V-speeds or Velocity-speeds are standard terms used to define airspeeds important or useful to the operation of aircraft, such as airplanes, gliders, autogiros, helicopters, blimps, and dirigibles. These speeds are derived from data obtained by aircraft designers and manufacturers during flight testing and verified in most countries by government flight inspectors during aircraft type-certification testing. Using them is considered a best practice to maximize aviation safety, aircraft performance or both. The actual speeds represented by these designators are true airspeeds specific to a particular model of aircraft, and are expressed in terms of the aircraft's indicated airspeed, so that pilots may use them directly, without having to apply correction factors.
  • 26. In general aviation aircraft, the most commonly-used and most safety-critical airspeeds are displayed as color-coded arcs and lines located on the face of an aircraft's airspeed indicator. The lower ends of the green arc and the white arc are the stalling speed with wing flaps retracted, and stalling speed with wing flaps fully extended, respectively. These are the stalling speeds for the aircraft at its maximum weigh. Having V speeds properly displayed is an airworthiness requirement for type-certificated aircraft in most parts of the world. Regulatory V-speeds V-speed designator Description V 1 Maximum speed during takeoff at which a pilot can safely stop the aircraft without leaving the runway. This is also the minimum speed that allows the pilot to safely continue (to V2 takeoff) even if a critical engine failure occurs (between V1 and V2) V 2 Takeoff safety speed V 2min Minimum takeoff safety speed. V 3 Flap retraction speed V A Design maneuvering speed, also known as the &quot;Speed for maximum control deflection.&quot; This is the speed above which it is unwise to make full application of any single flight control (or &quot;pull to the stops&quot;) as it may generate a force greater than the aircraft's structural limitations . V B Design speed for maximum gust intensity V C Design cruising speed, also known as the optimum cruise speed, is the most efficient speed in terms of distance, speed and fuel usage. V-speed designator Description V NE Never exceed speed V S Stall speed or minimum steady flight speed for which the aircraft is still controllable V S0 Stall speed or minimum flight speed in landing configuration. V NO Maximum structural cruising speed or maximum speed for normal operations V FE Maximum flap extended speed V FC Maximum speed for stability characteristics. V F Designed flap speed
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