Flight: Basic Calculations and Pilotage

Before a cross-country flight, a pilot should make common calculations for time, speed, and distance, and the amount of fuel required.

Converting Minutes to Equivalent Hours 

Frequently, it is necessary to convert minutes into equivalent hours when solving speed, time, and distance problems. To convert minutes to hours, divide by 60 (60 minutes = 1 hour). Thus, 30 minutes is 30/60 = 0.5 hour. To convert hours to minutes, multiply by 60. Thus, 0.75 hour equals 0.75 × 60 = 45 minutes.   

Time T = D/GS 

To find the time (T) in flight, divide the distance (D) by the GS. The time to fly 210 NM at a GS of 140 knots is 210 ÷ 140 or 1.5 hours. (The 0.5 hour multiplied by 60 minutes equals 30 minutes.) Answer: 1:30.

Distance D = GS X T 

To find the distance flown in a given time, multiply GS by time. The distance flown in 1 hour 45 minutes at a GS of 120 knots is 120 × 1.75 or 210 NM.

GS GS = D/T 

To find the GS, divide the distance flown by the time required. If an aircraft flies 270 NM in 3 hours, the GS is 270 ÷ 3 = 90 knots. 

Converting Knots to Miles Per Hour 

Another conversion is that of changing knots to miles per hour (mph). The aviation industry is using knots more frequently than mph, but is important to understand the conversion for those that use mph when working with speed problems. The NWS rep

A knot is 1 nautical mile per hour (NMPH). Because there are 6,076.1 feet in 1 NM and 5,280 feet in 1 SM, the conversion factor is 1.15. To convert knots to mph, multiply speed in knots by 1.15. For example: a wind speed of 20 knots is equivalent to 23 mph.

Most flight computers or electronic calculators have a means of making this conversion. Another quick method of conversion is to use the scales of NM and SM at the bottom of aeronautical charts. 

Fuel Consumption 

To ensure that sufficient fuel is available for your intended flight, you must be able to accurately compute aircraft fuel consumption during preflight planning. Typically, fuel consumption in gasoline-fueled aircraft is measured in gallons per hour. Since turbine engines consume much more fuel than reciprocating engines, turbine-powered aircraft require much more fuel, and thus much larger fuel tanks. When determining these large fuel quantities, using a volume measurement such as gallons presents a problem because the volume of fuel varies greatly in relation to temperature. In contrast, density (weight) is less affected by temperature and therefore, provides a more uniform and repeatable measurement. For this reason, jet fuel is generally quantified by its density and volume. 

This standard industry convention yields a pounds-of-fuelper-hour value which, when divided into the nautical miles (NM) per hour of travel (TAS ± winds) value, results in a specific range value. The typical label for specific range is NM per pound of fuel, or often NM per 1,000 pounds of fuel. Preflight planning should be supported by proper monitoring of past fuel consumption as well as use of specified fuel management and mixture adjustment procedures in flight.

When planning a flight, you must determine how much fuel is needed to reach your destination by calculating the distance the aircraft can travel (with winds considered) at a known rate of fuel consumption (gal/hr or lbs/hr) for the expected groundspeed (GS) and ensure this amount, plus an adequate reserve, is available on board. GS determines the time the flight will take. The amount of fuel needed for a given flight can be calculated by multiplying the estimated flight time by the rate of consumption. For example, a flight of 400 NM at 100 knots GS takes 4 hours to complete. If an aircraft consumes 5 gallons of fuel per hour, the total fuel consumption is 20 gallons (4 hours times 5 gallons). In this example, there is no wind; therefore, true airspeed (TAS) is also 100 knots, the same as GS. Since the rate of fuel consumption remains relatively constant at a given TAS, you must use GS to calculate fuel consumption when wind is present. Specific range (NM/lb or NM/gal) is also useful in calculating fuel consumption when wind is a factor. 

You should always plan to be on the surface before any of the following occur: 

• Your flight time exceeds the amount of flight time you calculated for the consumption of your preflight fuel amount 

• Your fuel gauge indicates low fuel level  

The rate of fuel consumption depends on many factors: condition of the engine, propeller/rotor pitch, propeller/ rotor revolutions per minute (rpm), richness of the mixture, and the percentage of horsepower used for flight at cruising speed. The pilot should know the approximate consumption rate from cruise performance charts or from experience. In addition to the amount of fuel required for the flight, there should be sufficient fuel for reserve. When estimating consumption you must plan for cruise flight as well as startup and taxi, and higher fuel burn during climb. Remember that ground speed during climb is less than during cruise flight at the same airspeed. Additional fuel for adequate reserve should also be added as a safety measure.

Flight Computers 

Up to this point, only mathematical formulas have been used to determine such items as time, distance, speed, and fuel consumption. In reality, most pilots use a mechanical flight computer called an E6B or electronic flight calculator. These devices can compute numerous problems associated with flight planning and navigation. The mechanical or electronic computer has an instruction book that probably includes sample problems so the pilot can become familiar with its functions and operation.

Plotter 

Another aid in flight planning is a plotter, which is a protractor and ruler. The pilot can use this when determining TC and measuring distance. Most plotters have a ruler that measures in both NM and SM and has a scale for a sectional chart on one side and a world aeronautical chart on the other.

Dead Reckoning

Dead reckoning is navigation solely by means of computations based on time, airspeed, distance, and direction. The products derived from these variables, when adjusted by wind speed and velocity, are heading and GS. The predicted heading takes the aircraft along the intended path and the GS establishes the time to arrive at each checkpoint and the destination. Except for flights over water, dead reckoning is usually used with pilotage for cross-country flying. The heading and GS, as calculated, is constantly monitored and corrected by pilotage as observed from checkpoints.

Wind Triangle or Vector Analysis 

If there is no wind, the aircraft’s ground track is the same as the heading and the GS is the same as the true airspeed. This condition rarely exists. A wind triangle, the pilot’s version of vector analysis, is the basis of dead reckoning.  

The wind triangle is a graphic explanation of the effect of wind upon flight. GS, heading, and time for any flight can be determined by using the wind triangle. It can be applied to the simplest kind of cross-country flight, as well as the most complicated instrument flight. The experienced pilot becomes so familiar with the fundamental principles that estimates can be made that are adequate for visual flight without actually drawing the diagrams. The beginning student, however, needs to develop skill in constructing these diagrams as an aid to the complete understanding of wind effect. Either consciously or unconsciously, every good pilot thinks of the flight in terms of wind triangle. 

Pilotage

Pilotage is navigation by reference to landmarks or checkpoints. It is a method of navigation that can be used on any course that has adequate checkpoints, but it is more commonly used in conjunction with dead reckoning and VFR radio navigation.

The checkpoints selected should be prominent features common to the area of the flight. Choose checkpoints that can be readily identified by other features, such as roads, rivers, railroad tracks, lakes, and power lines. If possible, select features that make useful boundaries or brackets on each side of the course, such as highways, rivers, railroads, and mountains. A pilot can keep from drifting too far off course by referring to and not crossing the selected brackets. Never place complete reliance on any single checkpoint. Choose ample checkpoints. If one is missed, look for the next one while maintaining the heading. When determining position from checkpoints, remember that the scale of a sectional chart is 1 inch = 8 SM or 6.86 NM. For example, if a checkpoint selected was approximately one-half inch from the course line on the chart, it is 4 SM or 3.43 NM from the course on the ground. In the more congested areas, some of the smaller features are not included on the chart. If confused, hold the heading. If a turn is made away from the heading, it is easy to become lost. 

Roads shown on the chart are primarily the well-traveled roads or those most apparent when viewed from the air. New roads and structures are constantly being built and may not be shown on the chart until the next chart is issued. Some structures, such as antennas, may be difficult to see. Sometimes TV antennas are grouped together in an area near a town. They are supported by almost invisible guy wires. Never approach an area of antennas less than 500 feet above the tallest one. Most of the taller structures are marked with strobe lights to make them more visible to pilots. However, some weather conditions or background lighting may make them difficult to see. Aeronautical charts display the best information available at the time of printing, but a pilot should be cautious for new structures or changes that have occurred since the chart was printed.