The Flight Computer: CRP-5 and E6B

The flight computer, also called a navigation computer and in the United States often simply the E6B, is the pilot's mechanical calculator. One face is a circular slide rule that solves any problem of proportion: time, speed and distance, fuel burn and endurance, unit conversions and, through its windows, true airspeed, density altitude and true altitude. The other face, the wind side, solves the triangle of velocities graphically to give the heading to steer and the groundspeed to expect. The CRP-5 is the model common in European training and the E6B the standard in FAA training. They differ in layout and in the method usually taught on the wind side, not in what they do.

GNSS receivers, electronic flight bags and flight management systems now do these sums, but the mechanical computer survives. EASA and FAA theory questions are written around it, it needs no power, and a pilot who can work a problem on it understands the arithmetic well enough to recognize a wrong answer from any machine. The arithmetic itself is set out in time, speed, distance and fuel calculations.

The flight computer and its scales

The calculator side has two scales around its edge: a fixed outer scale and a rotating inner scale, graduated identically and spaced logarithmically. On a logarithmic scale the distance between two numbers represents their ratio, so setting any value on one scale against any value on the other sets a ratio, and every other pair of numbers facing each other around the dial stands in the same ratio. That is all a proportion needs. With 105 set over 60, 84 also stands over 48, because 105 ÷ 60 and 84 ÷ 48 both equal 1.75.

The scales carry no decimal point. The figure 12 may mean 1.2, 12, 120 or 1,200, and the user places the decimal point from a rough estimate made first; a misplaced decimal point is a common slip on the computer.

Index marks and windows turn the slide rule into a navigation tool:

• The 60 index, an arrow or triangle on the inner scale, stands for 60 minutes. A speed or any rate per hour is set against it.
• The 10 index stands for one unit, and is used for rates per minute and plain multiplication.
• An hours scale inside the minutes scale prints times beyond 60 minutes as hours and minutes, such as 1:10 and 1:20 on the E6B.
• Conversion marks printed against the scales, such as NAUT, STATUTE and KM for distance, IMP GAL, U.S. GAL and LITERS for volume, and marks for pounds and meters.
• Windows in the inner disc, where the air temperature is set against the pressure altitude: one for true airspeed and density altitude, one for altitude computations. The E6B also has a scale for converting °C to °F.

Time, speed and distance

The basic setting puts the speed on the outer scale over the 60 index. The outer scale then reads distance and the inner scale time in minutes, for that speed:

• Time for a distance. At a groundspeed of 105 kt, with 105 over the 60 index, 84 NM on the outer scale stands over 48 minutes on the inner scale.
• Distance in a time. With the same setting, 20 minutes stands under 35 NM.
• Groundspeed from a timed run. Set the distance over the time and read the speed over the 60 index: 6 NM in 4 minutes puts 90 over the index, a groundspeed of 90 kt.

For long legs the hours scale saves a conversion: 210 NM at 140 kt stands over 90 minutes, printed 1:30.

Rates per minute use the 10 index as one minute. To descend from 9,000 ft to 3,000 ft within 20 NM at 150 kt, the 8 minutes available (20 NM at 2.5 NM a minute) need 6,000 ft in 8 minutes: with 60, standing for 6,000, set over 8, the outer scale shows 75 over the 10 index, so the rate is 750 ft/min. The estimate, 6,000 ft in roughly 10 minutes or about 600 ft/min, rules out 75 and 7,500.

Fuel consumption and conversions

Fuel problems use the same setting with the fuel flow in place of the speed: fuel flow on the outer scale over the 60 index, then fuel on the outer scale over time on the inner. The E6B prints the setting in a box: gallons per hour against the index, fuel burned against minutes or hours.

• Fuel for a leg. At 36 liters per hour, 90 minutes stands under 54 liters.
• Endurance. At 38 liters per hour, 133 liters stands over 210 minutes, 3:30 on the hours scale. Endurance is a time and does not change with the wind; the range does. Any reserve to be kept is subtracted first.
• Fuel flow from a check. 4.7 US gallons used in 35 minutes puts about 8 over the 60 index, a fuel flow of 8 gallons per hour.

Unit conversions use the marks. The known value is set against its own mark and the answer read against the other: 100 NM set against NAUT shows about 115 against STATUTE and 185 against KM. A knot is one nautical mile per hour, so the same marks convert knots to miles per hour: 20 kt is 23 mph. For the arithmetic behind the marks, 1 NM is 1,852 m, 1 km about 0.54 NM, 1 ft 0.3048 m, 1 US gallon 3.785 liters and 1 imperial gallon 4.546 liters.

Fuel mass needs one more step, because a liter of fuel weighs less than a liter of water. The mass is the volume multiplied by the specific gravity (SG), which on the slide rule is a single multiplication: 140 liters of avgas at an SG of 0.72 is about 101 kg, while dividing by mistake gives 194 kg. Jet A-1 is about 0.79 to 0.82, and FAA weight and balance uses 6 lb per US gallon for avgas. The E6B's temperature scale converts the other unit pilots meet: −20 °C is −4 °F, and +15 °C is 59 °F.

True airspeed and density altitude

The airspeed indicator is calibrated for sea-level air in the International Standard Atmosphere (ISA), so it under-reads the true airspeed whenever the air is less dense, at height or on a warm day. The computer makes the density correction in one setting. The indicated airspeed is first corrected to calibrated airspeed (CAS) with the airspeed calibration table for position and instrument error. At light airplane speeds CAS and equivalent airspeed are treated as equal, because compressibility is negligible below about 300 kt TAS.

In the airspeed window, the outside air temperature is set against the pressure altitude, and the true airspeed (TAS) is read on the outer scale opposite the CAS on the inner scale. At 6,000 ft pressure altitude in ISA conditions, 100 kt CAS gives about 109 kt TAS. The rule of thumb of 2 percent per 1,000 ft gives 112 kt, slightly high, so the computer's figure goes in the navigation log. Temperature matters on its own: if the air at the cruising level is 10 °C warmer than forecast, the same CAS gives a higher TAS than planned (see airspeed definitions).

The temperature must be the static, or outside, air temperature. At jet speeds the probe reading includes ram rise, roughly (TAS ÷ 100)² °C, or 16 °C at 400 kt. ATPL training material treats that formula as a quick mental check and expects the CRP-5 for exam answers. A jet's TAS also follows from its Mach number: TAS is the Mach number times the local speed of sound, about 38.95 × √T kt with T in kelvin. At FL380 in ISA, −56.5 °C or 216.5 K, the speed of sound is about 573 kt, so M 0.85 is about 487 kt TAS, one multiplication on the slide rule.

Density altitude comes from the same setting: with the temperature against the pressure altitude, it is read in its own window. At an aerodrome with a pressure altitude of 3,000 ft and +25 °C, 16 °C above ISA, the rule of 120 ft per degree gives about 4,900 ft: the airplane will take off and climb as if it were nearly 2,000 ft higher than it is (see density altitude).

The altitude window corrects an altimeter reading for a non-standard temperature. The air temperature is set against the pressure altitude, and the true altitude is read on the outer scale over the calibrated, or indicated, altitude on the inner scale. In air colder than ISA the altimeter over-reads and the aircraft is lower than indicated, by about 4 percent of its height above the source of the altimeter setting for every 10 °C below standard. That PANS-OPS rule of thumb is safe only above −15 °C; colder, procedure altitudes are corrected from the ICAO table (see pressure altimeter).

The wind side: heading and groundspeed

The wind side carries a rotating compass rose around a transparent plotting disc with a center dot, the grommet on the E6B, a true index at the top against which directions are set, and a drift scale either side of it. Behind the disc slides a grid printed with speed arcs and drift lines. The wind is drawn on the disc as a mark, the grid supplies the speeds and drift angles, and the rose the directions. All directions fed in must share one reference: forecast winds aloft are in degrees true, so the track is true and the answer is a true heading.

View full schematic

Wind down, the method usual with the CRP-5, sets the wind direction under the index and marks the wind speed downward from the center. With the TAS arc under the center and the track under the index, the drift read at the wind mark gives a first heading. The heading is then set under the index and adjusted until the drift read at the wind mark equals the difference between heading and track, and the groundspeed is read on the speed arc through the mark.

Wind dot, the method usual in FAA material for the E6B, also sets the wind direction under the index, but marks the wind speed upward from the grommet. The true course goes under the index, the grid slides until the wind dot lies on the TAS arc, and the wind correction angle is read at the dot and the groundspeed under the grommet.

The FAA's handbook uses a short VFR trip as its example: a true course of 031°, a TAS of 115 kt and a wind from 360° at 10 kt. The computer gives a wind correction angle of 3° left, a true heading of 028° and a groundspeed of 106 kt, so the 53 NM trip takes 30 minutes, 35 with 5 minutes added for the climb, and burns 4.7 gallons at 8 gallons per hour. The 1-in-60 rule agrees: the wind is 31° off the nose from the left, about 5 kt of crosswind, and 60 × 5 ÷ 115 is about 3°.

In flight the problem runs backward. Steering 090°T at a TAS of 140 kt, a pilot measures a track made good of 097°T and a groundspeed of 150 kt. With the wind-down method, the heading goes under the index and 140 under the center, and the wind mark is placed where the 7° right drift line meets the 150 kt arc. Turning the rose until the mark lies directly below the center then shows the wind direction under the index, and the mark's distance from the center gives the speed: about 334°/20 kt.

Electronic flight computers

Electronic flight computers do the same work from a keypad. The FAA's handbook describes the principle: enter the CAS, pressure altitude and temperature, and the computer calculates the TAS. The calculator it pictures has modes for time, speed and distance, altitude, airspeed, wind, weight and balance, a timer, and conversions of distance, volume and weight.

They are faster and cannot misread a scale, but they do exactly what they are told. A wind entered as the direction it blows toward, a temperature in the wrong unit or a volume entered as a mass gives a confident, wrong answer. The mental checks learned alongside the mechanical computer, about 2 percent TAS per 1,000 ft, 1-in-60 drift and groundspeed in nautical miles per minute, remain the gross-error check on any electronic result (see pilot rules of thumb).

Each authority sets which aids may be taken into its theory exams. The UAE GCAA, for example, allows candidates their own CRP-5 and a non-programmable calculator, with a protractor, dividers and a navigation ruler.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.