Aeronautical Charts

Aeronautical Charts

        Aeronautical charts provide important information to the pilot. Sectional charts show topographic details, relief features and aeronautical information of the selected area and are updated regularly. Other types of charts display routes, airways and ground terminal locations.

 The direction and distance come from a map or chart. To navigate when driving a car one uses a map with printed routes, and you verify your position using landmarks and signs posted along the way. For air navigation your intended course is plotted on a map or chart and your position is verified along the way with any number of interesting methods. By the way, a chart is a map on which you plot a course. 

Anaeronautical chart provides pilots with a representation of a section of the Earth's surface (hence their name "Sectional Chart"). This section shows many of the same features on a road map. These emphasize landmarks and other special land features that would be easy for pilots to spot from the air. It delineates cities, tall structures, geographical features and major roads. It is also color-coded. Yellow areas depict cities, green areas indicate hills, brown is used to show mountains and magenta denotes roads. The intensity of the color corresponds to the object's height. The greater the intensity of the color, the higher or taller the object. These charts are updated and revised every six months. Pilots are encouraged to plot their course using the most recent and updated chart. 

The aeronautical chart is designed for convenient navigational use by pilots. It is intended to be written on and marked up as needed by the pilot to plot the course and/or solve navigational problems such as calculations of direction and distance.



	Sectional Chart         The scale of a "sectional" is 1/500,000 so one inch is about seven nautical miles. It usually gives enough detail to fly by ground reference or pilotage. A sectional shows highways and railroads, power transmission lines and television and radio towers. It shows lakes, quarries, race tracks and other landmarks. Sectionals also show information you cannot see on the ground such as Prohibited, Restricted, Warning, and Alert Areas that have their own special flight rules. Sectionals show Federal Airways commonly known as Victor Airways that are highways in the sky connecting Very High Frequency Omnirange Stations (VOR) stations. A sectional also shows topography or relief using contour intervals and color differentiation. Blue indicates the lowest elevations and brown indicates the highest. The highest obstruction in an area bounded by latitude and longitudes are shown with a numeral for thousands of feet with another numeral as a superscript for hundreds of feet. The highest terrain elevation is shown on the front of the chart. Isogonic lines showing Magnetic Variation are also shown on aeronautical charts.
	World Aeronautical Chart (WAC)         WAC charts scale is 1/1,000,000 making one inch about fourteen miles. Since WAC charts cover a larger area not as much detail is shown. WAC charts are used for flights of long distances.
	VFR Terminal Area Chart         If you plan to fly in or near a large metropolitan area a VFR Terminal Area Chart may be available. A VFR terminal Area Chart has everything asectional chart has but in greater detail. The scale is 1/250,00. Open circles with points at the top, bottom and both sides show VFR way points. Flags indicate a visual checkpoint. An air traffic controller may tell a VFR pilot to report over the golf course for instance. The golf course will be indicated on sectionals and VFR Terminal Area Charts with a flag icon. Small black squares indicate easily identified places on the ground.
	IFR Charts             If the flight will be flown under instrument meteorological conditions, there are two types of instrument charts. Pilots also have to file an IFR Flight Plan to fly in IMC conditions. En Route Low Altitude Charts are used for IFR flight planning by mostpropeller driven aircraft flying below the higher flying jet aircraft. Low altitude charts show Victor Airways, minimum altitudes, distances, magnetic courses, reporting points, and related data.
	En Route High Altitude Charts portray Jet routes, distances, time zones, special use airspace, radar jet advisory areas, and other data. IFR flight plans are necessary for all flights above 18,000 feet.

Calculations

Calculations

Air Speed / Ground Speed       Taking a 60 mile long road trip by car, the driver is fairly sure that if the average speed is 60 miles per hour (mph) for the trip, then it will probably take approximately one hour for the trip (60/60 = 1). This would not be as certain with an airplane because of wind. An airplane's speed can be greatly enhanced or diminished by the wind. This is the reason for the consideration of 2 speeds: ground speed and airspeed. Ground speed is the speed at which an airplane is moving with respect to the ground. Airspeed is the speed of an airplane in relation to the air. (Think of airspeed as the speed at which its propulsion system is set to move it along.) If an airplane is flying with the wind then its ground speed will be enhanced. That means its ground speed will be faster than its airspeed. If an airplane is flying against the wind then its ground speed will be reduced. That means its ground speed will be slower than its airspeed. If an airplane is flying through still air (air with no measurable wind), then its ground speed and airspeed will be the same. Look at the picture at left.

Vectors
       The term "vector" is used to describe a course flown by an aircraft. Pilots ask for and air traffic controllers issue a heading or a "vector". Avector quantity represents something that has magnitude and direction. Velocity is an example of a vector quantity. When flying, the pilot needs to know the aircraft's speed and direction. These combine to form a vector that represents velocity. Vectors are represented on a graph using a line segment drawn to scale to show the magnitude (in this case the aircraft's speed). An arrow is placed at the terminal point to indicate the direction of the course. The arrow also differentiates the initial point (starting point) from the opposite end (terminal point). Vectors represented on a graph with the same length and direction are considered to be equal.



Using vector addition you can compute the result of two forces that are applied at the same time to an object. Vector addition is used to solve navigation problems when airplanes fly through moving air. The result of vector addition depends on both the speed and direction of an aircraft's course as well as the wind vector. In the example below, we will consider the effects of the force of an airplane and the force of the wind. Vectors can be represented geometrically using a coordinate system. 


	For years, pilots have learned to solve wind correction problems graphically by plotting the vectors using paper, ruler, and protractor. Let's take a look at an example. Imagine an aircraft is flying with a heading of 45 degrees and a speed of 100 knots. A 20-knot wind is blowing due south. What will be the aircraft's groundspeed and course? We can plot the velocity through the air as a vector with the length of the vector indicating the airspeed and the angle of the vector (measured from north) as the heading.
	Now imagine that the aircraft is flying through a wind blowing due south at 20 knots. We can plot this as a vector with a length corresponding to 20 knots and pointing straight down. Since we want to add these two vectors together, plot the wind vector so that its tail is at the head of the heading vector.
	The sum of these two vectors will give the aircraft's direction and speed across the ground. You can simply draw the new vector running from the tail of the heading vector to the head of the wind vector. Its direction can be measured with a protractor, and the speed can be determined by measuring the length of the vector with a ruler. In this case, we measure a groundspeed of about 85 knots and course of about 55 degrees.
	If you know some trigonometry, you can quickly and accurately solve this problem without any drawing or measuring. We know that there is a 45-degree angle between our heading and the direction of the wind. We can combine this with the airspeed and windspeed and the law of cosines to find our groundspeed. If you know some trigonometry, you can quickly and accurately solve this problem without any drawing or measuring. We know that there is a 45-degree angle between our heading and the direction of the wind. We can combine this with the airspeed and windspeed and the law of cosines to find our groundspeed. c² = a² + b² - 2ab(cosC) c c² = 100² + 20² - 2(100)(20)(cos45) c = 87
Now that we know our groundspeed, we can use the law of sines to calculate how many degrees we will have to add to our headingto get our course across the ground. sin B = b (sin C)/ c sin B = 20 (sin 45)/ 87 B = 9.4 degrees Adding this angle to our heading gives a course of 54.4 degrees.

Flight Distance 
    Calculating flight distance on an aeronautical chart is perhaps simpler than planning a driving route on a road map. On the aeronautical chart locate your departure and destination airports. Using a series of straight lines, plot a course from the departure point to the destination point bearing in mind the following:

• Flight restrictions for your aircraft (altitude, fuel tank size)
• Physical obstructions (such as heights of buildings, towers, mountains, mountain passes)
• Other restrictions (such as restricted airspace, restricted airways, assigned airways)


Aeronautical charts usually use as a scale of 1:500,000 (or sometimes written 1/500,000). This means that 1 single unit on the chart (which could be inch, foot, yard, statute mile, nautical mile or kilometer) represents 500,000 of that same unit on the ground. So, if the aeronautical chart uses inches, then 1 inch on the chart equals 500,000 inches on the Earth. Check elsewhere on the chart to see the conversion scale of chart distance to statute or nautical miles. The smaller the scale of the chart, the less the detail can be shown on the chart. With chart measurements being equal, a 1:250,000 scale will provide greater detail than a chart with a scale of a 1:1,000,000 because the first chart will cover a smaller amount of area.

 Using the conversion scale as indicated on the aeronautical chart, calculate the total number of miles to be flown by multiplying the total number of inches measured by scale of miles to inches.




Flight Time

    Flight time indicates the actual time an aircraft is in the air flying from its departure point to its destination point. The computed flight time is a simple equation of T = D/S or Time equals Distance divided by Speed. Convert the decimal answer to our 60-minutes-to-an-hour and the flight time will be expressed in hours and minutes. 

Let's say for example, that a pilot will fly a small Cessna aircraft a distance of 560 miles. The airplane will have an average airspeed of 130 miles per hour moving with the wind which is blowing at 30 mph. How long will the flight take? Take the total number of miles and divide it by the ground speed (airspeed + or - wind speed). The quotient will give the pilot the flight time. Doing the calculation: 560 / (130 + 30) = 560 / 160 = 3.5. Since there are 60 minutes in an hour, the decimal .5 will need to be converted to our 60-minutes-to-an-hour clock. 
To do that, take the answer 3.5 and convert as shown below:

3.5 = 3 + (.5 x 60 minutes) = 3 + 30.0 = 3 hours and 30 minutes 

What if the pilot in the example above is flying against the wind? Calculating flight time would look like this:

560/ (130 - 30) = 560 / 100 = 5.6 

Then convert the answer to minutes:

5.6 = 5 + (.6 x 60 minutes) = 5 + 36.0 = 5 hours and 36 minutes.

View an animation that further explores the relationship between wind, course, and heading.

Fuel Requirements

    

The pilot of the aircraft makes the decision of how much fuel to carry based upon the following information:

• Aircraft operations handbook's specifications for fuel consumption, weight and balance
• Payload weight (cargo, baggage and passengers)
• Weight of fuel (number of gallons x 6 pounds = total weight of fuel in pounds)
• Weather and winds
• Total distance of flight
• Average flight speed
• Number of miles per gallon averaged by the aircraft carrying the weight for this flight

Typically there is a legal minimum fuel limit that all aircraft must follow when determining how much fuel to pump into the tanks. The minimum amount of fuel required needs to be able to fuel the following:

• the aircraft from its departure airport to its destination airport including
• being able to carry out an approach and go-around and
• flying to an alternate airport nearby (in case there is weather impediments at the scheduled destination airport)
• plus the ability to fly a 30-minute, holding pattern above the alternate airport
• land and taxi to the gate

To calculate the amount of fuel needed for a flight, the pilot uses the following equation: 

Fuel Flow (gallons per hour) x Time = Fuel Consumed

 The pilot uses charts found in the aircraft operation handbook that provides information about the miles per gallon of the aircraft at certain weights. The weight of the fuel is calculated by taking the total number of gallons and multiplying it by 6 pounds. One gallon of fuel weighs 6 pounds. This is usually figured into the charts found in the handbook. 

Once the pilot knows the aircraft's fuel consumption rate for the weight being flown and the flight time, the pilot can compute the fuel needed for the flight.

Look at the example below.

8.5 gph (fuel consumption rate) x 1:40 (flight time in hours/minutes) = 14.2 gallons

 The pilot of this aircraft will need to make sure that at least 14.2 gallons of fuel are pumped into the fuel tanks for this flight.

Fuel Consumption

        How much and how fast an aircraft uses fuel is known as fuel consumption. The same calculation used for determining a car's fuel consumption is also used for an aircraft with additional consideration for the weight of the payload (passengers and/or cargo). All aircraft have an operator's manual that gives specifications such as fuel consumption at different payload weights and fuel amounts. Remember the weight of the fuel also needs to figure into the equation! For example, let's say a small aircraft has a speed range of 120 - 170 mph and holds up to 40 gallons of fuel. Let's say that according to the aircraft's specifications at full payload and fuel weight the aircraft uses 10 gallons of fuel per hour. Take the total amount of fuel (40 gallons) and divide that by the number of gallons used per hour (10) and you will find that the aircraft could be flown for 4 hours. Remember that a good pilot will never fly on fumes, and would stop for re-fueling long before the 4 hours are up.

 Now let's say that the same aircraft is flying with a full tank of fuel, but only half its full payload weight. According to the fuel consumption specifications for this aircraft it will use 8 gallons of fuel per hour. How long will it be able to fly? Do the math: 40 gallons divided by 8 gallons per hour will provide a little over 5 hours of flight time.



True North / Magnetic North
          All aeronautical charts are drawn using True North. All airport runways, however, are marked by their magnetic compass directions to the nearest 10°. Runway 5-23 at an airport is a Northeast - Southwest runway. It means if an airplane lands from the SW heading NE on runway 5 the magnetic compass in the airplane would be showing about 050° for the heading. The difference between the magnetic direction and the true direction is called the magnetic variation. All aeronautical charts show the magnetic variation.

To convert from a true to magnetic direction many pilots use the saying "East is least, West is best." This serves as a reminder that one subtracts an eastward variation from the true course to get the magnetic course. Inversely, one adds a westward magnetic variation to the true course to get the magnetic course. For example, if the magnetic variation is 15 degrees 30 minutes East, after plotting one's true course, the magnetic course would be the true course minus 15 degrees 5 minutes. Pilots also use the saying "North lags and the south leads." This serves to remind pilots that if he or she turns the airplane from a northerly course the compass first indicates a turn in the opposite direction, then lags behind the actual compass heading. This means that when a pilot rolls out of a turn to a different heading, one must roll out before the compass reads that desired heading. Otherwise the new heading will be a few degrees more than desired (which would eventually lead one way off course). When turning from a southerly heading the compass leads initially, then shows the desired heading before actually reaching that heading.

Another compass error is caused when the airplane is accelerated. The compass indicates a turn to the north. When the airplane decelerates, the compass indicates a turn to the south. From this comes the pilot saying: "Accelerate north, decelerate south." Pilots and air traffic controllers need to be aware of such variations, so as to maintain a proper course at all times. 

At many airports the compass variation can be significant. In Anchorage, AK the variation is 25° East while in Dallas, TX the variation is 6° East. However, Nashville, TN the variation is only 1° West.

Measurement

Measurement

	Knots and Nautical Miles      Knots and Nautical Miles All navigation uses the Nautical Mile as the unit of distance. Traditionally a nautical mile is 6,080 feet but more precisely 6,076.11549 feet. In metric measurement it is 1,852 meters, which is one minute of arc of a great circle of the Earth. Even under the metric system, the unit of distance for navigation is still called the nautical mile. One knotconverted to miles per hour (mph) would be approximately 1.15 mph. One mile per hour would be 0.868 knots. A statute mile is the common "mile" with a length of 5,280 feet. Therefore a statute mile is not as long as a nautical mile. One nautical mile would equal approximately 1.15 statute miles. Making the conversion from nautical miles to statute mileswould be done as 120 nautical miles x 1.15 statute miles = 138 statute miles. Converting from statute to nautical miles would require dividing by 1.15. Therefore 200 statute miles would equal (200 / 1.15 = 174) 174 nautical miles. Many of the air navigational terms come from our heritage of sea navigation. In the days of wooden sailing vessels, the speed of a sailing ship was measured by unraveling a knotted rope into the water behind the moving ship. The number of knots in the rope that passed over the railing in a given amount of time would indicate how fast the ship was moving (its number of knots). It is this same term that is used inaeronautics and aviation to indicate flight speed, however without the knotted rope trailing behind the aircraft.
	Latitude / Longitude       A reference system is used with which an exact location on the Earth's surface can be pinpointed. This system uses designated lines of latitudeand longitude. Latitude measures north and south of the equator, andlongitude measures east and west of the prime meridian (located in Greenwich, England).The latitude of an exact location is expressed in terms of degrees, minutes and tenths of a minute. One minute of latitude equals 1/60th of a degree. The North Pole, for example, is 90 degrees north of the equator. This is written as N9000.0. The South Pole is located at 90 degrees south of the equator and is written as S9000.0. The longitude of an exact location is expressed in terms of degrees, minutes and tenths of a minute, also. One minute of longitude equals 1/60th of a degree. The longitude of the airport at Miami, Florida is located, for example, approximately 80 degrees west of the prime meridian. Precisely, this is written as W08016.6, and expressed as 80 degrees and 16.6 minutes west of the zero meridian. The airport at Perth, Australia is located approximately 115 degrees east of the zero meridian and is written as E11557.5. This is expressed as 115 degrees and 57.5 minutes east. Combining both latitude and longitude, the location of the airport in Miami, Florida is N2547.1 and W08016.6. This measure is used globally and communicates clearly to all pilots the same locations.
	Compass Directions       In navigation and surveying all measurement of direction is performed by using the numbers of a compass. A compass is a 360° circle where 0/360° is North, 90° is East, 180° is South, and 270° is West. Runways are laid out according to the numbers of a compass. A runway's compass direction is indicated by a large number painted at the end of each runway. A runway's number is not written in degrees, but is given a shorthand format. For example, a runway with a marking of "14" is actually close to (if not a direct heading of) 140 degrees. This is a southeast compass heading. A runway with a marking of "31" has a compass heading of 310 degrees, that is, a northwest direction. For simplicity, the FAA rounds off the precise heading to the nearest tens. For example, runway 7 might have a precise heading of 68 degrees, but is rounded off to 70 degrees. Move Cursor over Runway Designator and Observe Compass Heading
	Each runway has a different number on each end. Look at the diagram at left. One end of the runway is facing due west while the other end of the runway is facing due east. The compass direction for due west is 270 degrees ("27"). The compass direction for due east is 90 degrees ("9"). All runways follow this directional layout. This runway would be referred to as "Runway 9-27" because of its east-west orientation.
	Applying this to navigation means that pilots do not turn right or left, or fly east or south exactly. To fly east the pilot would take a heading of 90° . To fly south, the compass heading would be 180°. Look at the compass at left to note the compass headings for northeast, southwest and west.

Advanced Navigation

Advanced Navigation

       Advanced navigation equipment being developed by NASA gives pilots more information and freedom to fly in a more efficient manner thus saving fuel and lowering overall flight costs. These controls often combine several indicators into one for a more accurate display. Pilots now use satellite data from global positioning systems for navigation.



Inertial Navigation System (INS)
      An INS is very simple in theory, but complicated in practice. Put simply, it is a totally self-contained dead reckoning system. Given its starting position, INS keeps track of all movements in all directions so it calculates the aircraft's flight position in relation to that point. To detect movement, the INS uses three accelerometers, one north-south, one east-west, and one up-down mounted on a stable platform. An accelerometer is an electronic device that provides information similar to a gyroscope. Part of the accelerometer is in a fixed position and the other part is free to move with the aircraft. A magnetic field is produced by electricity between the two parts. Any change in movement by the free part will disturb the magnetic field. This disturbance will be recorded into the on-board computer which reads the data and calculates the amount of movement. The accelerometers use sliding shuttles and can detect accelerations up to a thousandth of a G force. The platform is stabilized using three gyros, one each for pitch, yaw and roll. This way the aircraft's movement is constantly monitored and helps the pilot keep the aircraft on course.



Newer Inertial Navigation Systems use ring laser gyros that are made up of a series of lasers aligned in the same plane and forming a ring. Interference patterns are generated as the aircraft accelerates indicating changes in the airplane's movement. These changes in movement are measured as nautical miles per hour (nmph) Accuracy is within 1.7 nmph. So after an hour the accuracy is 1.7 nm.



The INS must be initialized on the ramp prior to takeoff. The pilot merely enters the aircraft's coordinates and the system performs the calculations since it has an internal clock calendar. Warm-up time and the time it takes for the INS to "sense" north can take from 2.5 to 45 minutes.
 This system computes for the pilot the following flight data:

• Track
• Drift angle
• Cross track error
• Distance traveled
• Distance remaining
• Flight time remaining

Global Positioning System (GPS)        GPS receivers cost thousands of dollars in 1990, but are available now for under $100 for simple hand held units. Aircraft GPS units designed for IFR flight still cost thousands of dollars each, but many General Aviation (GA) pilots now fly with a low cost hand held GPS receiver. The GPS system uses a constellation of 24 or more satellites, 21 plus spares, at an altitude of 10,900 miles, moving 7,500 nmph. Two UHF frequencies, 1.57542 gHz and 1.22760 gHz are used. Ionospheric distortion is measured by the phase shift between the two frequencies. Two modes are available, the "P", or precise mode, and the "C/A" or Coarse/Acquisition Mode. The P mode used by the military transmits a pseudo-random pattern at a rate of 10,230,000 bits/sec and takes a week to repeat. The C/A code is 10 times slower and repeats every millisecond. The GPS receiver synchronizes itself with the satellite code and measures the elapsed time since transmission by comparing the difference between the satellite code and the receiver code. The greater the difference, the greater the time since transmission. Knowing the time and the speed of light/radio, the distance can be calculated.




The timing comes from four atomic clocks on each satellite. The clocks are accurate to within 0.003 seconds per thousand years. The GPS satellites correct for receiver error, by updating the GPS receiver clock. The GPS satellite also transmits its position, its ephemeris, to the GPS receiver so it knows where it is relative to the satellite. Using information from four or more satellites the GPS receiver calculates latitude, longitude, and altitude. (The math involves matrix algebra and the solution of simultaneous equations with four unknowns. Computers do that sort of computation very well.)

GPS receivers provide all needed navigational information including:

• Bearing
• Range
• Track
• Ground speed
• Estimated time en route (ETE)
• Cross track error
• Track angle error
• Desired track
• Winds & drift angle


Differential GPS or DGPS
 
DGPS uses a ground station to correct the code received from the satellites for 5 meter accuracy. DGPS could be used for Precision approaches to any airport.

Most people think that once they’re on the ground, the flight is over. Believe it or not, many pilots feel this is the most dangerous and stressful part of the route. NASA continues work on a project called the Taxiway Navigation and Situation Awareness System (T-NASA) that will speed up ground operations and aid flight safety.

T-NASA blends Global Positioning Satellite (GPS) abilities with virtual reality technology to create displays that help pilots move around the airport quickly and safely. GPS pinpoints the exact location of the aircraft on the ground, and the T-NASA system displays it on a real-time moving map and a heads-up-display (called a “HUD”) in the cockpit.

The map shows the pilot the aircraft’s exact position, a cleared route, and any other traffic on the taxiways. When looking through the HUD, the pilot sees a virtual representation of the airport surface. The image is projected on a piece of glass (the HUD), but it looks like it’s actually part of the world. The pilot follows virtual cones that are along the edge of the taxiway showing the route that he or she is cleared to follow.

So far, the results with this system are extremely exciting. After a flight test in Atlanta, researchers found that the workload for pilots and controllers goes way down. They also found that the pilots were much more aware of their exact position and the position of other traffic on the surface. Current additions to T-NASA are aimed at adding alerts, so that pilots know when there are other aircraft that need to be avoided. All this translates into significant performance benefits and improved safety.

Whether it’s seeing through fog or booming 1,600 nautical miles an hour, new technologies are giving pilots a clear view of what’s ahead.

The inside of an aircraft using T-NASA technology. The moving map is shown on the bottom right screen, while the HUD display is shown in the top of the image.

Radio Navigation

Radio Navigation

Radio navigation provides the pilot with position information from ground stations located worldwide. There are several systems offering various levels of capability with features such as course correction information, automatic direction finder and distance measuring.



Most aircraft now are equipped with some type of radio navigation equipment. Almost all flights whether cross-country or "around the patch" use radio navigation equipment in some way as a primary or secondary navigation aid.



Automatic Direction Finder (ADF)  ADF is the oldest radio navigation system still in use. ADF uses Non-Directional Beacons (NDBs) that are simply AM-radio transmitters operating in the Low and Middle Frequency (L/MF) Band from 190 to 535 kHz. These frequencies are below the standard broadcast band. All ADFs can also home in on AM broadcast stations. Pilots can listen to the radio and navigate also. The ADF indicator has a compass rose and an indicating needle. The needle automatically points to the station. "Homing" means following the needle. "Crabbing" to track to the station is more efficient. Crabbing is a method of flying in which the horizontal axis of the airplane is not parallel to the flight path. ADFs have a "HDG" knob where the pilot can dial in the aircraft heading.

Very High Frequency Omni-directional Range (VOR) The VOR station transmits two signals, one is constant in all directions, and the other varies the phase relative to the first signal. The VOR receiver senses the phase difference between the two frequencies and the difference identifies 360 different directions or "radials" from the VOR. The aircraft is on one, and only one, radial from the station. The system does not provide distance information. When the appropriate VORfrequency is entered into a navigation radio, the VOR indicator connected to that radio is used to find where the aircraft is relative to the VOR station. The vertical needle called a Course Deviation Indicator (CDI) on the VOR indicator shows whether the aircraft is right or left of the chosen course. A "To/From/Off" indicator indicates whether the aircraft is on the "to" or "from" side. If the aircraft is "abeam the station", an "off" indication is given. To fly toward the station, the Omni Bearing Selector (OBS) is turned until the CDI is centered with a "to" indication. The pilot then flies that heading. To find out where the aircraft is located from that station, center the needle with a "from" indication. If a radial is dialed into the VOR indicator, the CDI will be right or left of the center and either a "to" or a "from" indication will be seen. The heading of the aircraft does not matter.

Distance Measuring Equipment (DME)
DME as its name states is an electronic device that measures "slant range" from the DME station. Slant range is a measure of an aircraft's position relative to the DME station that incorporates the height of the aircraft, its angle from the ground station and its unknown ground range based upon a 90° angle. The farther the aircraft is from the station and the lower the aircraft's altitude, the more accurate the distance reading. An aircraft could be directly over the DME station at an altitude of 10,500 feet above ground level (AGL) and the DME would correctly indicate the aircraft is two miles from the station.

	Instrument Landing System (ILS) An aircraft on an instrument landing approach has a cockpit with computerized instrument landing equipment that receives and interprets signals being from strategically placed stations on the ground near the runway. This system includes a "Localizer" beam that uses the VOR indicator with only one radial aligned with the runway. The Localizer beam's width is from 3° to 6°. It also uses a second beam called a "glide slope" beam that gives vertical information to the pilot. The glide slope is usually 3° wide with a height of 1.4°. A horizontal needle on the VOR/ILS head indicates the aircraft's vertical position. Three marker beacons (outer, middle and inner) are located in front of the landing runway and indicate their distances from the runway threshold. The Outer Marker (OM) is 4 to 7 miles from the runway. The Middle Marker (MM) is located about 3,000 feet from the landing threshold, and the Inner Marker (IM) is located between the middle marker and the runway threshold where the landing aircraft would be 100 feet above the runway.
The VOR indicator for an ILS system uses a horizontal needle in addition to the vertical needle. When the appropriate ILS frequency is entered into the navigation radio, the horizontal needle indicates where the aircraft is in relation to the glide slope. If the needle is above the center mark on the dial, the aircraft is below the glide slope. If the needle is below the center mark on the dial, the aircraft is above the glide slope. LORAN-C LORAN-C stations across the contiguous United States Originally just a marine navigation system, LORAN-C determines present position by the intersection of Lines of Position (LOPs) that are hyperbolic curves. At least three stations, (a Master and two Secondaries) are needed. Accuracy is plus or minus 2.5 miles. The LORAN-C uses triangulation to measure the location of an aircraft or boat.
	LORAN-C provides Range (RGE) Track (TRK) Ground speed (GS) Estimated time en route (ETE) Cross track error (XTD) Track angle error (TKE) Desired track (DTK) Winds and drift angle (DA)

Basic Navigation

Basic Navigation


Pilotage 

      For a non-instrument rated, private pilot planning to fly VFR (Visual Flight Rules) in a small, single engine airplane around the local area on a clear day, the navigation is simple. The navigation process for such a local trip would be pilotage. (Bear in mind, however that the flight planning and preflight for such a trip should be as thorough as if the pilot is preparing to fly cross-country.)


The pilotage method of navigation developed naturally through time as aircraft evolved with the ability to travel increasingly longer distances. Flying at low altitudes, pilots used rivers, railroad tracks and other visual references to guide them from place to place. This method called pilotage is still in use today. Pilotage is mainly used by pilots of small, low speed aircraft who compare symbols on aeronautical charts with surface features on the ground in order to navigate. This method has some obvious disadvantages. Poor visibility caused by inclement weather can prevent a pilot from seeing the needed landmarks and cause the pilot to become disoriented and navigate off course. A lack of landmarks when flying over the more remote areas can also cause a pilot to get lost. Using pilotage for navigation can be as easy as following an interstate highway. It would be difficult to get lost flying VFR from Oklahoma City to Albuquerque on a clear day because all a pilot need do is follow Interstate 40 west. Flying from Washington, DC to Florida years ago was accomplished by flying the "great iron compass" also called the railroad tracks.

Dead Reckoning
     
"Dead" Reckoning (or "Ded" for Deductive Reckoning) is another basic navigational method used by low speed, small airplane pilots. It is based on mathematical calculations to plot a course using the elements of a course line, airspeed, course, heading and elapsed time. During this process pilots make use of a flight computer. Manual or electronic flight computers are used to calculate time-speed-distance measurements, fuel consumption, density altitude and many other en route data necessary for navigation. 


The estimated time en route (ETE) can be calculated using the flight distance, the airspeed and direction to be flown. If the route is flown at the airspeed planned, when the planned flight time is up, the destination should be visible from the cockpit. Navigating using known measured and recorded times, distances, directions and speeds makes it possible for positions or "fixes" to be calculated or solved graphically. A "fix" is a position in the sky reached by an aircraft following a specific route. Pilots flying the exact same route regularly can compute the flight time needed to fly from one fix to the next. If the pilot reaches that fix at the calculated time, then the pilot knows the aircraft is on course. The positions or "fixes" are based on the latest known or calculated positions. Direction is measured by a compass or gyro-compass. Time is measured on-board by the best means possible. And speed is either calculated or measured using on-board equipment. Navigating now by dead reckoning would be used only as a last resort, or to check whether another means of navigation is functioning properly. There are navigation problems associated with dead reckoning. For example, errors build upon errors. So if wind velocity and direction are unknown or incorrectly known, then the aircraft will slowly be blown off course. This means that the next fix is only as good as the last fix.

Aviation Navigation

Introduction

       Navigation is the art and science of getting from point "A" to point "B" in the least possible time without losing your way. In the early days of aviation, navigation was mostly an art. The simplest instruments of flight had not been invented, so pilots flew "by the seat of their pants". Today, navigation is a science with sophisticated equipment being standard on most aircraft.




The type of navigation used by pilots depends on many factors. The navigation method used depends on where the pilot is going, how long the flight will take, when the flight is to take off, the type of aircraft being flown, the on-board navigation equipment, the ratings and currency of the pilot and especially the expected weather.

 To navigate a pilot needs to know the following:

• Starting point (point of departure)
• Ending point (final destination)
• Direction of travel
• Distance to travel
• Aircraft speed
• Aircraft fuel capacity
• Aircraft weight & balance information

With this information flight planning can commence and the proper method of navigation can be put to use.


Aeronautical Calculations: What’s with All Those Coefficients Anyway?

Aeronautical Calculations: What’s with All Those Coefficients Anyway? 

         When aircraft designers decide on the design specifications for a new aircraft, they develop a model that is tested in a wind tunnel. The data collected from wind tunnel tests are used to develop a comparison to how the aircraft will fly at full scale. They make these and other comparisons by using proven aeronautical equations using dimensionless coefficients. 

In the previous sections you saw that thrust, lift, weight, and drag are forces and are usually expressed in pounds or newtons. You also saw that pitch, yaw and roll are moments and are expressed in inch-pounds, foot-pounds or newton-meters. So when we talk about our test data we may say, "The wing generated 12 pounds of lift," or "The engine generated 3000 pounds of thrust." That will work fine as long as we are willing to talk only about one specific wing, or one specific engine. What do we do when we want to compare a wing that was tested at one scale and set of conditions, and apply it to another scale and a different set of conditions? Suppose we tested a scale model of a jet transport Model X in the wind tunnel, and now we want to know if the full-scale airplane based on this model will be able to fly from San Francisco to London. The following scenario will show how dimensionless coefficients can help address this problem.

The wind tunnel tests run on the model gave us the following data:

wind tunnel tests run on the model gave us the following data." border=1 cellspacing=0 cellpadding=0>

Model X Data	Test 1	Test 2	Test 3	Test 4	Test 5	Test 6	Test 7	Test 8
Angle of Attack (deg)	0.0	0.5	1.0	1.5	2.0	3.0	5.0	10.0
Lift (pounds)	11.9	238.0	476.4	714.1	952.5	1785.9	2381.4	4048.3
Drag (pounds)	2.5	23.8	42.9	59.6	78.4	118.8	238.1	476.4

The model tested is 5% of full-scale, and the wind tunnel was operated at sea level pressure and a velocity of 300 knots. It is anticipated that the real airplane will fly at 35,000 feet at a velocity of 550 knots. The actual airplane is anticipated to weigh about 550,000 pounds (without fuel) and have a wing area of about 4,800 square feet. The aircraft designers believe that the airplane will have about 200,000 pounds of fuel available for the cruise portion of the flight. The weight of the aircraft (550,000 pounds) plus the weight of the fuel (200,000 pounds) equals a total weight of 750,000 pounds. Engineers anticipate using 2 engines that together, burn about 25,000 lbs of fuel each hour while creating 50,000 pounds of thrust. Does the wind tunnel data show that the airplane would make the 5,300-nautical mile trip?

This is exactly the kind of problem that aerospace engineers evaluate every day. How can we take data from a wind tunnel test and apply it to the real vehicle, especially if that vehicle has yet to be built? Fortunately, we have a hundred years of aeronautical experimentation to back us up. We will use the non-dimensional coefficients that were implemented over those one hundred years to solve the problem.

Over the years the engineers have determined that much of the data can be non-dimensionalized into coefficient form. This means that coefficients will not have units of pounds or foot-pounds like the original data; they will have no units attached. So what this means is that a quantity that was measured in pounds will be divided by something else that has units of pounds, and since pounds divided by pounds results in '1' the units effectively disappear. For example:
3 pound / 1 pound = 3

Treat 'pound' as you would any other number. Now the '3' is a non-dimensional or 'dimensionless' coefficient. Now we just need to find something that has units of 'pounds' to divide by. However, we can't just divide by any old 'pounds' since we are really looking for a way to account for scale, pressure, and velocity effects so we can use our wind tunnel data to predict how the actual airplane will perform.

Instead of proving to ourselves the statement below, this time we will take advantage of the hundred years of aeronautical data that came before us and accept the following statement as fact:

The dynamic pressure "q" and wing area "S" put together will give us the necessary quantity that will "non-dimensionalize" the force measurements, and permit them to be scaled (Think: "Cancel out the units."). The unit part is easy to verify. See the calculations below.

q = pound / foot2
S = foot2
so q * S = pound

There are literally hundreds of reports and research papers that put the scaling effect under scrutiny, so let us just say, that for the most part, and especially for what we are trying to show, non-dimensionalizing forces by dynamic pressure and wing area give the appropriate coefficients. (There are instances and conditions where this may not be true, but those are beyond the scope of this web site.) Similarly, moments are non-dimensionalized by dynamic pressure, wing area, and mean aerodynamic chord. "C" which is usually expressed in feet.

Let’s take another look at the table:

The wind tunnel tests run on the model gave us the following data with the appropriate coefficients added. 

wind tunnel tests run on the model gave us the following data with the appropriate coefficients added." border=1 cellspacing=0 cellpadding=0 >

The wind tunnel tests run on the model gave us the following data with the appropriate coefficients added.

Model X Data	Test 1	Test 2	Test 3	Test 4	Test 5	Test 6	Test 7	Test 8
Angle of Attack (deg)	0.0	0.5	1.0	1.5	2.0	3.0	5.0	10.0
Lift (pounds)	11.9	238.0	476.4	714.1	952.5	1785.9	2381.4	4048.3
Drag (pounds)	2.5	23.8	42.9	59.6	78.4	118.8	238.1	476.4
Dynamic Pressure 'q' in pounds/ft^2 at 300 knots and0 ft alt.	301	301	301	301	301	301	301	301
Wing Area ft^2	12	12	12	12	12	12	12	12
Coefficient of Lift CL	.0033	.0659	.1319	.1977	.2637	.4944	.6593	1.1208
Coefficient of Drag CD	.0007	.0066	.0119	.0165	.0217	.0329	.06593	.1319

We have added some more data, and have expressed the lift and drag in coefficient form. We will now use those coefficients to compute and create some predicted values for lift and drag on the actual airplane.

We will now use those coefficients to compute and create some predicted values for lift and drag on the actual airplane.

We will now use those coefficients to compute and create some predicted values for lift and drag on the actual airplane.

Aircraft X Data	Test 1	Test 2	Test 3	Test 4	Test 5	Test 6	Test 7	Test 8
Angle of Attack (deg)	0.0	0.5	1.0	1.5	2.0	3.0	5.0	10.0
Coefficient of Lift CL	.0033	.0659	.1319	.1977	.2637	.4944	.6593	1.1208
Coefficient of Drag CD	.0007	.0066	.0119	.0165	.0217	.0329	.06593	.1319
Dynamic Pressure 'q' in pound/ft^2 at 550 knots and 35K ft alt.	316	316	316	316	316	316	316	316
Wing Area ft^2	4800	4800	4800	4800	4800	4800	4800	4800
Lift (pounds)	5,000	100,000	200,000	300,000	400,000	750,000	1,000,000	1,700,000
Drag (pounds)	1,000	10,000	18,000	25,000	33,000	50,000	100,000	200,000

We can see within the column marked "Test 6" that the airplane needs to maintain an angle of attack of at least 3 degrees to hold its own weight in the air. We can also see that it generates 50,000 pounds of drag at that condition which matches those engines our designers pick out. We are now very close to determining whether our airplane can fly from San Francisco to London.

We need one more equation: the Breguet Range. This equation is used to calculate the range of an aircraft given a specific flight plan or profile. A typical flight profile includes taxi and takeoff, steep initial climb, climb, cruise, descent, approach and landing. The changing weight of the aircraft as it burns fuel is also taken into consideration. Furthermore, reserves are also calculated as part of a contingency plan for when an approach is missed, which would require additional maneuvers and flight time.

To find the range is much more complex than simply dividing the total fuel by the average hourly fuel consumption and then multiplying by the velocity. That's why we need the Breguet Range equation to predict how far an airplane will fly accounting for flight performance and the change in weight of the airplane as it burns or uses its fuel.

The Breguet Range equation is given below.

Range = (V/C) * (L/D) * ln(Wi/Wf)

V= Velocity in knots

C= Specific fuel consumption in pounds fuel per pounds thrust per hour

L= Lift in pounds

D= Drag in pounds

ln= Natural logarithm, or loge

Wi= Weight of aircraft at start of cruise in pounds

Wf= Weight of aircraft at end of cruise in pounds

The Breguet Range equation will give the flying range of our actual aircraft in nautical miles. For our aircraft we hope the range will be greater than 5,300 nautical miles for our hypothetical trip.

Specific fuel consumption was alluded to earlier, even though it was not specifically named. It was mentioned in the line: "using 2 engines that together, burn about 25,000 pounds of fuel each hour while creating 50,000 pounds of thrust." That comes out to a specific fuel consumption of 0.5.

C = Fuelflow/Thrust
C = (25000 pounds/hour)/(50000 pounds) = 0.5/hour 

Notice that "C" isn't quite a non-dimensional coefficient, since it has units of "per hour." We can also see that L/D could be replaced with CL/CD since we could divide both the numerator and denominator by q * S and not change the equation since (q*S)/(q*S) is like multiplying by 1.0. We can now solve the Breguet range equation. See the solution below.

The aircraft will not make the 5,300 nm trip. Using the Breguet equation range with the data collected from the wind tunnel tests on the model, it appears we need to either land in Scotland or make some changes to our airplane. From the Breguet equation we know that we can increase range by increasing the values of V, L or Wf, and by reducing the values of C, D, and Wi. Changing these values will affect other design aspects of the aircraft that have problems and complications associated with them in real life. Since Wi and Wf are manipulated by the ln function, the impact of changing these parameters is less dramatic. This is referred to as modifying the "fuel fraction." This will involve reducing the structural weight so a larger percentage of the total weight is fuel. This can be very tricky and expensive since it has the potential to affect just about everything on the aircraft. For example, we really cannot increase the lift on our actual aircraft since we want to maintain a steady altitude. To increase the lift in this case it would mean a change in the structural weightof the airplane. We could increase the speed, but that might also increase the drag if we go too fast.

Our best choices for improvement really come with specific fuel consumption and drag. If we can refine our design a bit more, we may get a reduction in drag. If we can get some help from the engine manufacturer, they might be able to reduce the amount of fuel needed to generate the same amount of thrust. We only need 3.4% improvement in either one or in a combination of both to meet our goal. Of course, that may not sound like a lot, but it is enough to financially make or break an aircraft company.