Lecture 1- May 14, 2002
Introduction to Performance
Flight Mechanics is the study of the motions of bodies (aircraft and rockets), through a fluid.
Stability and Control the science of designing for steady and controllable fight characteristics
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Aerodynamic Performance speed rate of climb range fuel consumption maneuverability runway length requirements
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
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Why Study Performance?
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Lecture 1- May 14, 2002
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The Anatomy of the Airplane
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Lecture 1- May 14, 2002
Airplane Configurations
Anhedral
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Source: Shevell, Fundamentals of Flight
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
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Airplane Configurations
Source: Shevell, Fundamentals of Flight
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
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Airplane Configurations
Source: Shevell, Fundamentals of Flight
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
The Standard Atmosphere
Why do we need to know about the atmosphere? The performance of aircraft, spacecraft, and engines depend on the atmosphere in which they operate, primarily density and viscosity. Density and viscosity, in turn, are functions of altitude. Density, ρ, varies with pressure, p, and temperature, T Viscosity, µ, varies only with temperature, T
The “standard atmosphere” is defined from the equation of state of a perfect gas:
p = ρ RT
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Perfect Gas Law
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
The Standard Atmosphere
p = pressure in lb/ft2 or N/m2 ρ = density in slugs/ft3 or kg/m3 T = absolute temperature in Rankine (R) or Kelvin (K) R = gas constant = 1718 ft-lb/slugR or 287.05 n-m/kgK Remember: R = F + 459.7 K = C + 273.15
For our purposes, the atmosphere can be regarded as a homogenous gas of uniform composition that satisfies the perfect gas law.
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Effect of Water Vapor on Atmosphere
When there is a significant amount of water vapor in the air, the density is changed, but by a very small amount.
ρ = 0.002243 slug/ft3
dry air
ρ = 0.002203 slug/ft3
100% humidity
Although the effect of water vapor on air density is very small, water vapor does have a significant effect on engine performance and supersonic aerodynamics.
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
International Standard Atmosphere
To allow for comparison of the performance of airplanes, as well as calibration of altimeters, “standard” properties of the atmosphere have been established by the International Civil Aviation Organization (ICAO). The ICAO and the U.S. Standard Atmosphere are identical below 65,617 feet. This standard atmosphere is representative of mid latitudes of the northern hemisphere. “Standard” sea level properties are: g0 = 32.17 ft/s2 = 9.806 m/s2 P0 = 29.92 in Hg = 2116.2 lb/ft2 = 1.013 x 105 N/m2 T0 = 59 F = 518.7 R = 15 C = 288.2 K r0 = 0.002377 slug/ft3 = 1.225 Kg/m3 AE 3310 Performance
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Regions of the Atmosphere Exosphere-rarefied Ionosphere Positive Temperature Gradient
300 ~ 600 mi
50 ~ 70 mi
Stratosphere Zero Temperature Gradient
Tropopause ( 36,089 ft)
5 ~ 10 mi
Troposphere Negative Temperature Gradient
In subsonic airplane aerodynamics, only the troposphere and stratosphere are important.
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Temperature Variation with Altitude
Below 36,089 ft, we assume there is a constant drop of temperature from sea level to altitude
T = T1 + a ( h - h1) a = “lapse rate” = -0.00356616 F/ft in the standard atmosphere T1 and h1 are reference temperatures. For sea level, T1 = T0 and h1 = 0 Above 36,089 ft in the stratosphere, the standard temperature is assumed constant and equal to -69.7 F.
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Below 36,089 ft
Pressure/Density Variation with Altitude (relative to standard sea level values)
T a =Θ=1+ h = 1 - 6.875 x 10-6 h T0 T0 p = δ = Θ 5.2561 p0 ρ ρ0
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= σ = Θ 4.2561
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Pressure/Density Variation with Altitude
Above 36,089 ft
(relative to standard sea level values)
T = constant = -69.7 F
p p0
ρ ρ0
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= 0.2234 exp
= 0.2971 exp
h-36,089 20806.7
h-36,089 20806.7
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Pressure/Density Variation with Altitude
So, now you can calculate the temperature, pressure, and density at any point in the troposphere or stratosphere …OR… You can use the nifty tables in the back of Anderson’s book (Appendices A, B)
Be careful which units you are using... AE 3310 Performance
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Viscosity
Viscosity varies primarily with temperature There is a strong relationship between air viscosity and boundary layer behavior. This will be discussed more when we review aerodynamics.
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ν = µ/ρ
Kinematic Viscosity
R = Vl ν
Reynold’s Number
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Lecture 1- May 14, 2002
Altimeters
Properties of the standard atmosphere can be used to calibrate altimeters. An altimeter translates barometric pressure into a display of elevation in feet.
known reference pressure inside As the airplane climbs and descends, the aneroids expand and contract, which is reflected by the altimeter reading AE 3310 Performance
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Altimeters
However, unfortunately, atmospheric pressure changes not only with altitude but also with fluctuations in the weather. To account for these changes, the altimeter must be set to the current altimeter setting, which is the current sea level barometric pressure, in inches of mercury. The adjustment knob is used to set the altimeter and this adjustment is shown in the Kollsman window. A change of 1 inch of mercury on the Kollsman window results in ~ 1000 foot change in altitude on the display needles. Pilots obtain current altimeter settings from an airplane control tower or a Flight Service Center. If this information is unavailable, the altimeter can be set to the field elevation of the airport.
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Lecture 1- May 14, 2002
Three point altimeter
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Altimeters
Drum altimeter
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Lecture 1- May 14, 2002
Errors in Altimeters
Scale error - at lower altitude, errors due to the aneroids not assuming the exact size corresponding to altitude is on the order of plus/minus 50 feet. At higher altitudes, these errors can be as much as plus/minus 200 feet. Friction error - due to friction of the mechanical parts. Usually the vibration of the airplane overcomes the friction, or the pilot can tap on the glass. Hysteresis - due to the imperfect elasticity of the wafers. After long flights at higher altitudes, the wafers can become “set”. Errors on the order of 100 feet are not uncommon. A few minutes at the new altitude will reset the altimeter
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Types of Altitude
Pressure Altitude - defined as the reading on an altimeter when the Kollsman window is set to 29.92 inches of mercury (standard sea level pressure). This is the altitude used in performance calculations and for flights above 18,000 feet (where pressure altitudes are called flight levels). True Altitude - is the true height above mean sea level (MSL). Sea level is assumed fixed, therefore MSL altitudes do NOT change with atmospheric conditions. Realize that a properly functioning altimeter will indicate true altitude ONLY if it is operating in a standard atmosphere, which rarely or never occurs. Indicated Altitude - is what the altimeter reads at any given time. Absolute Altitude - is altitude above ground level (AGL).
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Lecture 1- May 14, 2002
Types of Altitude
Pressure = 29.92 inches of mercury AE 3310 Performance
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Lecture 1- May 14, 2002
Weather and the Altimeter
If the pilot does not reset the Kollman window in flight, what happens? The pilot will be flying at a line of constant pressure. If s/he flies from high pressure weather to low pressure weather, the true altitude will show a descending flight path. To remember this phenomena, use the following rhyme: “from a high to a low, look out below from a low to a high, you’re high in the sky” This also works for temperature fluctuations
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Weather and the Altimeter
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Lecture 1- May 14, 2002
Pitot-Static Tube
Ram air, or pitot air, is captured in a hollow tube that projects from the aircraft. The pitot tube is placed in such a way as to capture impact air with minimal disturbance from the rest of the airframe. The static port measures local atmospheric pressure. The static port is usually placed perpendicular to the airstream so as to negate any pressure caused from motion.
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
The Airspeed Indicator
The airspeed indicator subtracts the static pressure from the total pressure supplied by the pitot tube. This difference is called dynamic pressure, and is a measure of the airplane’s forward speed. Recall Bernoulli’s Equation:
pt = p + 1/2 ρ V2 total pressure
static pressure dynamic pressure
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
The Airspeed Indicator
The chamber is flooded with static pressure. The diaphragm expands or contracts due to pitot (total) pressure. How much the needle deflects is an indication of the difference between the two pressures (dynamic pressure). AE 3310 Performance
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Lecture 1- May 14, 2002
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The Airspeed Indicator
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Lecture 1- May 14, 2002
Airspeed Indicator Limitations
The airspeed indicator may fail or reflect an incorrect speed primarily due to pitot tube blockage: the pilot forgets to remove the protective cover from the pitot before takeoff ice accumulation foreign object blockage such as dirt or insects
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Types of Airspeeds
Indicated Airspeed (IAS) - is the direct reading from the airspeed indicator. This represents the airplane’s speed through the air, NOT necessarily its speed across the ground. Calibrated Airspeed (CAS) - is the indicated airspeed corrected for instrument position and instrument error. This is a function of each unique aircraft and the position of its pitot tube. There is no direct reading of CAS in the cockpit! The pilot must refer to the Pilot’s Operating Handbook for a table corresponding to that particular aircraft. True Airspeed (TAS) - because an airspeed indicator is calibrated for standard sea level conditions, when the airplane is flying at altitude, the airspeed is not correctly reflected. The amount of error is a function of temperature and altitude. TAS can be approximated by increasing the indicated airspeed by 2% per thousand feet of altitude.
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Lecture 1- May 14, 2002
Vertical Speed Indicator
The vertical speed indicator, or VSI, registers the rate of change of static pressure and converts this to an indication in feet per minute.
airtight case
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Lecture 1- May 14, 2002
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The Pitot Static Instruments
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Lecture 1- May 14, 2002
The Magnetic Compass
Magnetic Compass - indicates the direction the airplane is heading with respect to magnetic north. The difference between this and true north is called variation.
magnets fixed to compass card liquid in the compass stabilizes and damps the motion AE 3310 Performance
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Gyroscopic Instruments
A gyroscope is a mass spinning rapidly about an axis. A spinning gyroscope exhibits two fundamental properties: Rigidity in space - a spinning gyroscope will tend to maintain its orientation in space an resist any forces that tend to displace it. Precession - when a gyroscope is displaced by a force, such as friction, the reaction generated by the gyroscope is called precession. This reaction acts 90 degrees from the applied force, in the direction of the rotation of the rotor. The instruments that depend on gyroscopic motion are powered instruments, using either electricity, air pressure, or vacuum.
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
The Attitude Indicator
The attitude indicator, also called the artificial horizon or gyro horizon, provides the pilot with a visual representation of the airplane’s flight attitude with respect to the horizon.
attitude sphere
The gyro is universally mounted on a vertical spin axis. It is attached to an attitude sphere, which remains rigid when the airplane manuevers. A miniature airplane is free to rotate with the airplane. AE 3310 Performance
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Lecture 1- May 14, 2002
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The Attitude Indicator
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Lecture 1- May 14, 2002
The Turn Coordinator
The turn coordinator actually contains two instruments. An airplane symbol indicates the airplane’s rate of turn once a constant bank angle is established. The ball in the tube, called the inclinometer, provides information about the quality of the turn. The gyroscope in the turn coordinator is installed with fore and aft axis of the mounting canted slightly with respect to the airplane’s longitudinal axis. The gyroscope senses motion about the roll and yaw axis. Any pitch related motion is restricted. The airplane symbol reacts directly with the aircraft. The inclinometer is a ball in a curved liquid filled tube. The position of the ball is determined by centrifugal and gravity forces of the turn.
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
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The Turn Coordinator
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Lecture 1- May 14, 2002
The Heading Indicator
The heading indicator is also called the directional gyro (DG). It displays the airplane’s heading from a gyroscopically rigid platform. It must be set prior to each flight or during straight and level flight to agree with the magnetic compass. Precession caused by friction in the bearings can cause the gyro to drift, so it must be periodically reset in flight (approx. every 15 minutes).
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Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
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Standard Instrument Panel Layout
Dr. Danielle Soban Georgia Institute of Technology
Lecture 1- May 14, 2002
Sources for Lecture 1
Shevell, Richard S., Fundamentals of Flight, 2nd Edition, Prentice Hall, NJ Lan, Chuan-Tau Edward and Roskam, Jan, Airplane Aerodynamics and Performance, Roskam Aviation and Engineering Corporation, KS Glaeser, Dennis et al, An Invitation to Fly- Basics for the Private Pilot, 4th Edition, Wadsworth Publishing, CA Kershner, William K., The Student Pilot’s Flight Manual, 7th Edition, Iowa State University Press, Iowa
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Dr. Danielle Soban Georgia Institute of Technology