# The Flight Computer

Updated on 29th March,2016

## Flight Computer

The flight computer is available in many formats and helps pilots complete navigation calculations. They come in both mechanical and electronic forms and are available as apps for most smartphones today. We are going to concentrate on the mechanical version today because most examiners will not permit you to use electronic versions. Mechanical versions are more reliable in that they do not require batteries. The common one used in the USA is the E6-B and in the UK and Ireland it is normally the CRP-1 (up to CRP-5).

The basic flight computer is an amazing tool for any pilot to have. With a little practice, it is extremely easy to use. It is essentially a circular slide rule. One important thing to remember about the Flight Computer is that, it does not know decimals. It is up to the user to determine where to place the decimal point after a calculation. There are a few little tricks and secrets that are often forgot about.

The Flight Computer can:

- Calculate Wind Correction Angle
- Calculate Ground Speed
- Calculate True Airspeed
- Calculate Density Altitude
- Calculate Time Enroute
- Calculate Fuel Consumption
- Do basic division
- Do basic multiplication
- Do unit conversions
- Much More!

## Flight Computer History

The flight computer was originally called the E-6B and it was made by Lt. Philip Dalton (US Navy) in the 1930s. He had a patent on the device and it became very popular with pilots all over the world (especially during World War II). More than 400,000 E-6Bs were made from plastic during WWII. It is sometimes called the E6-B and the CRP-1 (and other CRP models) are based on this.

The E-6B has two sides:

- The calculator side
- The wind side

# The Calculator Side of The Flight Computer

The calculator side is basically a slide rule that consists of two circles.

- A stationary circle
- A movable, rotating circle

*Refer to Figure 1 for location of important parts of the E6-B flight computer.*

The numbers printed on the outside of the stationary circle are referred to as the “**Outer**” scale. The outer scale is used to represent distance, fuel, ground-speed, true airspeed, or corrected (true) altitude, depending on the calculation being performed.

The numbers printed on the inside of the rotating circle are referred to as the “**Inner**” scale. The inner scale is used to represent time, calibrated or indicated airspeed, and calibrated or indicated altitude, depending on the calculation being performed.

You will notice that the number “60” on the inner scale is associated with a large triangle. The “60” normally refers to one minute (60 seconds) and it is used frequently when performing calculations involving time such as:

- Speed (knots) (nautical miles per hour)
- Fuel consumption (gallons/liters per hour)

In the center of the rotating portion are three windows and these are used to compute corrected (true) altitude, density altitude, and true airspeed.

Remember the following:

- Time is
**ALWAYS**on the**INNER**scale - Since Time is
**ALWAYS**on the**INNER**scale, Volume or distance must**ALWAYS**be on the**OUTER**scale for Speed/Distance problems or for Fuel Consumption/Volume problems. - When doing Speed or Fuel Consumption calculations
**ALWAYS put “60” (INNER scale**) under the Speed or Fuel Consumption. I.e. Nautical miles per**HOUR**(60min) or Gallons per**HOUR**(60min). - When asked to solve a problem,
**write down the relevant data**. Write down the fuel consumption, time, distance etc. and make sure you know what the question is asking you for. If you do not write the data down, you are more likely to make an error.

#### Scale Values

The numbers marked on the scales can represent different values.

For example, the number 10 can also represent the following numbers:

- 0.1
- 1.0
- 10
- 100
- 1000 etc

You should also be aware that the number of marks between the numbers on the scales can vary. Sometimes there are nine and sometimes there are four. Therefore it is very important that you take note of this.

Each mark may be valued differently. On the outer circle, each mark between 12 and 13 may be valued as 0.1 but when read between the numbers 17 and 18, each mark has a value of 0.2. Not reading the value of the marks correctly will have a serious effect on the answer you calculate.

The inner scale can be used to represent time. You will notice that the number 90 on the inner scale has the number 1:30 printed below it i.e. 90 minutes = 1 hour and 30 minutes. This makes it easier to convert minutes to hours and minutes. Notice that on the hour scale, each tick can represent either 5 minutes or 10 minutes.

#### Temperature Conversion

Below the number 30 on the outer scale, you will find a temperature conversion scale. This is very handy for converting degrees Celsius to degrees Fahrenheit or vice versa.

## Time – Speed – Distance

The inner and outer scales on the flight computer are like the scales of a slide rule. It can be seen that if you put 20 (outer scale) over 30 (inner scale), the following ratios hold good throughout the rest of the scale:

20 40 60

— = — = —

30 60 90

Problems are solved by using these ratios for distance, time and speed, or for gallons, time and fuel consumption rate.

The outer scale is used for distance and the inner scale represents time.

Because of the relationship of the scales of the flight computer; time, speed and distance problems are very easily calculated using the following equation.

. DISTANCE

SPEED = ———————

. TIME

**EXAMPLE 1**. Assume the speed to be 150 mph and time travelled is 36 minutes. What is the distance?

Solution: Place 150 mph over the one hour index (triangle). Find 36 minutes on the inner scale and read off a distance of 90 miles on the outer scale (distance scale for this type of question).

ANSWER: = 90 miles

**EXAMPLE 2.** Speed = 120 mph and distance = 200 miles. What is the time?

Solution: Set the index (60 on inner scale) under 120 (12 on outer scale). Opposite 200 (outer scale) read 100 minutes.

ANSWER: = 1 hour 40 minutes (100 minutes)

**EXAMPLE 3.** Time = 2 hours (120 minutes). Distance = 200 miles. What is the speed?

Solution: Set 200 (outer scale) over 120 minutes (inner scale). Locate the index (60 on inner scale) and read 100 mph (outer scale).

ANSWER: = 100 mph

**EXAMPLE 4**. Speed = 130 mph and time = 1 hour and 10 minutes (70 minutes). Find the distance.

Solution: Set index (inner scale) under 130 (13 on outer scale). Locate 70 minutes (inner scale) and read 152 on outer scale.

ANSWER: = 152 miles

**EXAMPLE 5**. Speed = 180 mph and distance = 330 miles. Find the time.

Solution: Set the index under 180. Opposite 330 (33 on outer scale) and read 110 minutes (inner scale).

ANSWER: = 110 minutes

## Fuel Consumption Problems

Fuel consumption problems are solved similarly to time, speed and distance problems except that volume is substituted for distance.

. Total Gallons

Gallons per Hour = ————————

. Total Time

**EXAMPLE 6. **Fuel consumption rate = 13 gallons/hour and time = 90 min. Find total fuel.

Solution: Place number 13 (outer scale) over the index (60 on the inner scale). Opposite 90 minutes on the inner scale, read 19.5 gallons.

ANSWER: 19.5 gallons

**EXAMPLE 7.** Fuel consumption rate = 9 gallons/hour. Total fuel = 22 gallons. Find flight time.

Solution: Place the index under 9. Opposite 22 (outer scale) read time of 147 minutes.

ANSWER: 2 hours 27 minutes (147 minutes)

**EXAMPLE 8. **Total fuel = 35 gallons. Time = 3 hours 10 minutes. Find fuel rate.

Solution: Place time of 3:10 under 35 (gallons). Read fuel rate of 11 gallons/hour opposite the index.

ANSWER: 11 gallons/hour

## Conversions

Indicated (or Calibrated) Airspeed and True Airspeed are equal at sea level under ISA conditions. As a helicopter climbs to a higher altitude, pressure and temperature will normally decrease. This change requires a correction to IAS to obtain TAS because TAS increases with altitude.

Pressure Altitude will be indicated on the altimeter when the sub-scale is set to 1013hPa.

### Conversion to TAS

**EXAMPLE 9: **Pressure altitude = 10,000 feet. Temperature = 0ºC. Calibrated Airspeed = 150 mph. Find True Airspeed and Density Altitude.

Solution: Using the Airspeed Correction Window, move the inner scale until the 10,000 feet pressure altitude is under 0ºC. Find 150 (inner scale) and read 176 (outer scale). In the Airspeed Correction Window, find the Density Altitude index arrow. Read a Density Altitude of 10,500.

ANSWER: TAS = 176 mph. Density Altitude = 10,500

Now use your flight computer to try and answer the following problems – Answers are listed below.

**EXAMPLE 10:** Pressure Altitude = 8000 ft. Temperature = -10ºC. IAS = 120 kt. Find TAS and Density Altitude.

**EXAMPLE 11:** Pressure Altitude = 9000 ft. Temperature = +10ºC. IAS = 140mph. Find TAS and Density Altitude.

**EXAMPLE 12:** Pressure Altitude = 5000ft. Temperature = +30ºC. IAS = 120mph. Find TAS and Density Altitude.

**EXAMPLE 13:** Pressure Altitude = 7000 ft. Temperature = -20ºC. IAS = 150 kt. Find TAS and Density Altitude.

**EXAMPLE 14:** Pressure Altitude = 12000ft. Temperature = -10ºC. IAS = 180mph. Find TAS and Density Altitude.

**ANSWER 10:** TAS = 133 kt. Density Altitude = 6900 ft

**ANSWER 11:** TAS = 164 mph. Density Altitude = 10500 ft

**ANSWER 12:** TAS = 135 mph. Density Altitude = 8000 ft

**ANSWER 13: **TAS = 160 kt. Density Altitude = 4500 ft

**ANSWER 14:** TAS = 216 mph. Density Altitude = 12000 ft

### Converting Miles to Kilometers

When any value of statute or nautical miles is set opposite the “stat” or “naut” index marks, the distance in kilometers may be read opposite the “Km” index mark (located on the outer scale).

### Converting US Gallons to Imperial Gallons

On the outer scale, locate the “U.S. gal.” and “imp. gal.” index marks.

When converting from US Gallons to Imperial Gallons, align the appropriate US Gallon number under the “U.S. gal.” index. The corresponding volume in Imperial Gallons can be read under the “imp. gal.” index.

When converting from Imperial Gallons to US Gallons, align the appropriate Imperial Gallon number under the “imp. gal.” index. The corresponding volume in US Gallons can be read under the “U.S. gal.” index.

### Converting Gallons to Liters

On the outer scale, locate the “U.S. gal.”, “imp. gal.” and “liters” index marks.

When converting from US Gallons or Imperial Gallons to Liters, align the appropriate US Gallon number under the “U.S. gal.” index or Imperial Gallon number under the “imp. gal.” index. The corresponding volume in Liters can be read under the “liters” index.

### Converting Nautical Miles to Statute Miles

On the outer scale, locate the “Naut” and “Stat” index marks.

When converting from Nautical miles to Statute miles, align the appropriate nautical mile number under the “Naut” index. The corresponding distance in Statute miles can be read under the “Stat” index.

When converting from Statute miles to Nautical miles, align the appropriate Statute mile number under the “Stat” index. The corresponding distance in Nautical miles can be read under the “Naut” index.

### Converting Pounds to Kilograms

On the outer scale, locate the “lb” and “kg” index marks.

When converting from Pounds to Kilograms, align the appropriate Pounds (weight) number under the “lb” index. The corresponding weight in Kilograms can be read under the “kg” index.

When converting from Kilograms to Pounds, align the appropriate Kilogram number under the “kg” index. The corresponding weight in Pounds can be read under the “lb” index.

### Converting Feet to Meters

When any value of feet is set under the “feet” or “ft” index mark on the outer scale, the distance in meters may be read opposite the “m” index mark (located on the outer scale).

## Multiplication

For multiplication use the number “10” on the inner scale as the index (not 60 [triangle]).

Use the following proportions:

. Multiplier Product

—————— = ———————

. 10 Other Factor

A sample problem would be:

2 x 4 = 8

On the flight computer, this problem would appear as:

2 x

— = — Therefore x = 8 (remember that the number 10 here represents 1 in the calculation)

10 4

## Division

Use the following proportions:

. Dividend Quotient

—————— = ——————

. Divisor 10

A sample problem would be:

8 ÷ 4 = 2

On the flight computer, this problem would appear as:

8 2

— = — (remember that the number 10 here represents 1 in the calculation)

4 10

Now use your flight computer to see if you can answer the following problems – Answers are listed below.

**EXAMPLE 15: **13 x 7 =

**EXAMPLE 16: **300 ÷ 15 =

**EXAMPLE 17: **19 x 5 =

**EXAMPLE 18: **345 ÷ 15 =

**EXAMPLE 19: **137 x 7 =

**ANSWER 15: ** 91

**ANSWER 16: ** 20

**ANSWER 17: ** 95

**ANSWER 18:** 23

**ANSWER 19: ** 959

# The Wind Side of The Flight Computer

The wind side of the flight computer is used mainly to calculate how much your aircraft is going to be blown of course by the wind and to help you calculate what course correction to make to compensate for this. It is possible to perform other calculation also and these will be covered below.

The three vectors in the triangle of velocities (see below) can be marked on the disc so that they appear in the same relationship to one another (as in flight) making it easier to visualise the situation and check that the vectors have been applied correctly.

The wind side of the flight computer is made up of the following components:

- A circular (rotatable) compass rose (or azimuth) that has an index marked on it.
- A transparent, plastic plotting disc with a centre dot (grommet).
- A sliding panel printed with concentric speed arcs and radial drift lines.

## The Triangle of Velocities

### The Wind Triangle

In dead-reckoning navigation many problems involving speed and direction have to be solved. Primarily, you are concerned with Ground Speed, True Heading, True Air Speed, Wind Direction, Wind Speed and True Course (or Track). Often you will know four of these six quantities and will need to determine the other two. For example, you may know True Heading, True Air Speed, Wind Direction and Wind Speed and need to know Track and Ground Speed. In order to solve such problems it is necessary to understand the relationship of these six quantities.

These quantities are represented by vectors. A vector is a quantity having both magnitude and direction. The vector quantity of most importance in navigation is velocity.

Velocity is speed in a specific direction. Wind velocity includes both Wind Speed and Wind Direction, not merely Wind Speed (WS) alone. Likewise, the velocity of an aircraft with relation to the earth’s surface includes both Track and Ground Speed. And the velocity of an aircraft with relation to the air in which it is flying includes both True Heading and True Air Speed.

The velocity of an aircraft over the earth’s surface depends on two quantities:

- The velocity of the aircraft through the air (True Heading and True Air Speed) and
- The velocity of the air over the earth (Wind Direction and Wind Speed)

A vector which thus results directly and entirely from two or more other vectors is said to be the **resultant** or vector sum of these other vectors. And two or more vectors whose sum or resultant is another vector are called **components** of this other vector. A change in any component will cause a change in the resultant.

### Vector Diagrams

A vector quantity, such as velocity, may be represented on paper by a straight line. The direction of the vector is shown by the line with reference to north. The vector usually is drawn like an arrow, with a head and a tail so that there can be no doubt as to its direction. The magnitude of the vector is shown by the length of the line in comparison with some arbitrary scale. For example, you may let 2.5 cm equal 20 nm. The a velocity of 50 kt in a certain direction is shown by a line 6.25 cm long [(50/20)x2.5] in that direction, *Figure 2*.

When two or more vectors are components of a third vector, this relationship may be shown by means of a vector diagram. If the components are drawn tail to head in any order, a line from the tail of the first component to the head of the last component represents the resultant. Consequently, if you know the components, you can find the resultant. And if you know the resultant, and all but one of the components, you can find the missing component, *Figure 3*.

A vector diagram showing the effects of the wind on the flight of an aircraft is called a wind triangle. One line is drawn to show the velocity of the aircraft through the air (True Heading and True Air Speed). This velocity is called the **true heading-true air speed vector** or **air vector**. Another line is drawn to the same scale and connected tail to head to show the velocity of the wind. This is the **wind vector**. A line connecting the tail of the first vector to the head of the second vector shows the resultant of these two velocities to the same scale; it shows the velocity of the aircraft over the earth (Track and Ground Speed). It is called the **track-ground speed vector** or **ground vector**. It does not matter which of the two components is drawn first; the resultant is the same, *Figure 4*.

Take care to remember that True Air Speed is always in the direction of True Heading and that Ground Speed is always in the direction of Track. Also remember that the track-ground speed vector is the resultant of the other two; hence the true heading-true air speed vector and the wind vector are always drawn head to tail.

An easy way to remember this is to recall that the wind always blows the aircraft from the True Heading to the Track (TR).

Consider just what the wind triangle in *Figure 5* above shows. An aircraft departs from point A on a True Heading of 360º at a True Air Speed of 150 kt. In one hour, if there were no wind, the aircraft would reach point B at a distance of 150 nm. The line AB shows the direction and distance the aircraft would have flown under no wind conditions. Therefore, the length of AB shows the True Air Speed of the aircraft. Thus, AB represents the velocity of the aircraft through the air and is the air vector.

Imagine that at the end of the first hour the aircraft stops flying forward and remains suspended in mid-air at point B. Suppose then that the wind starts blowing from 270º at 30 kt. At the end of the second hour the aircraft is at point C, 30 miles downwind from B. The line BC shows the direction and distance the aircraft has moved with the wind, or the direction and distance the air has moved in an hour. Therefore the length of BC represents the speed of the wind in the same scale as the True Air Speed. Thus, BC represents the wind velocity and is the wind vector.

As a result of the aircrafts forward motion and the effect of the wind during the same hour, the aircraft reaches C at the end of the first hour. It does not go to B and then to C. Instead, it goes directly by the line AC, since the wind carries it east at 30 kt at the same time that the engine forces it north at 150 kt. Therefore, the line AC shows the distance and direction the aircraft travels over the ground in one hour and the length of AC represents the Ground Speed in the same scale as the True Air Speed and Wind Speed. Thus AC, which is the resultant of AB and BC, represents the velocity of the aircraft over the ground and is the ground vector.

Measuring the length of AC, you find that the Ground Speed is about 153 kt. Measuring the drift angle BAC and applying it to the True Heading of 360º, you find that the track is 011, or 11º to the right.

### Work Only in Degrees True (or Totally in Degrees M)

It is most important that when working out the vector triangle, the directions are all related to the same datum. In Ireland it is common practice for PPL pilots to use degrees true. You can use degrees magnetic throughout and the result will be the same but it is vital to use the same units throughout your calculations.

### Choice of Method

The flight computer is such that each problem can be solved in a number of ways. Each method produces the same results. You must find a method that suits you. Initially, use the method recommended by your instructor. Once you have mastered this method, then feel free to try other methods.

Your flight computer will be mostly used during flight planning prior to flight. You will already know the following;

- Track (measured from the chart)
- Wind Velocity (obtained from weather forecasts and weather charts)
- True Air Speed (planned cruising speed)

You will then use the wind side of the flight computer to calculate the following:

- Heading
- Ground Speed

There are two commonly used methods for solving this type of calculation and I will refer to them as:

- Method A – Wind dot up method
- Method B – Wind dot down method

Either method will obtain the same results.

# Method A – Wind Dot Up

For this method I will use an E6-B flight computer. The process is the same for the CRP flight computers.

The graphical solution of a wind triangle is shown in *Figure 6* below. In the diagram, the centre line represents the true course of 30º. The wind is blowing from 100º at 30 kt. The ground speed (at the grommet) is at 150 kt and the True Air Speed at the wind dot is 163 kt. The heading is 10º right of centre, or 40º. The wind correction Angle is thus also 10º to the right.

All wind solutions can be graphically shown by a wind triangle similar to the one depicted in *Figure 6* above.

## Find Heading and Ground Speed Knowing TR, TAS and W/V

**EXAMPLE 20**

The planned Track (TR) = 340º

Reported wind = 035º at 30 kt

Planned True Air Speed = 140 kt

FIND:

- Ground Speed
- Wind Correction Angle
- True Heading

**Solution**

- As shown in
*Figure 7*above, set the wind direction of 35º at the True Index - Mark a wind speed dot at a value of 30 kt above the grommet.
- Rotate the centre disc to set 340º True Course at the True Index,
*Figure 8*. - Set the wind dot on the 140 kt air speed arc by adjusting the slide.
- The Ground Speed (120 kt) can be read under the grommet
- The Wind Correction Angle is 10º right or 350º

**EXAMPLE 21: **True Course = 360º. Wind Velocity = 040º@25 kt. TAS = 160. Find WCA, True Heading and Ground Speed.

**EXAMPLE 22: **True Course = 290º. Wind Velocity = 240º@30 kt. TAS = 130. Find WCA, True Heading and Ground Speed.

**EXAMPLE 23: **True Course = 050º. Wind Velocity = 190º@20 kt. TAS = 150. Find WCA, True Heading and Ground Speed.

**EXAMPLE 24: **True Course = 090º. Wind Velocity = 320º@30 kt. TAS = 145. Find WCA, True Heading and Ground Speed.

**EXAMPLE 25: **True Course = 120º. Wind Velocity = 120º@25 kt. TAS = 170. Find WCA, True Heading and Ground Speed.

**ANSWER 21: ** WCA = 6ºR True Heading = 006º Ground Speed = 140 kt

**ANSWER 22: **WCA = 10ºL True Heading = 280º Ground Speed = 109 kt

**ANSWER 23: **WCA = 5ºR True Heading = 055º Ground Speed = 165 kt

**ANSWER 24: **WCA = 9ºL True Heading = 081º Ground Speed = 163 kt

**ANSWER 25: **WCA = 0º True Heading = 120º Ground Speed = 145 kt

# Method B – Wind Dot Down

This is called the “Wind Dot Down” method for the following reasons:

- The centre dot is used as the starting point of the Wind Velocity vector
- The Wind Dot is marked beneath the centre dot (down from the centre dot)

Since the Wind Velocity blows the aircraft from its heading to its track and the heading vector ends where the Wind Velocity vector starts, the heading/TAS vector should be placed up the centre of the slide so that it ends at the centre dot.

## Find Heading and Ground Speed Knowing TR, TAS and W/V

This is the typical situation before flight.

Track is measured from the chart and wind velocity is obtained from meteorological information.

**EXAMPLE 26**

The planned Track = 295º

Reported wind = 320º at 25 kt

Planned True Air Speed = 97 kt

**Solution**

- Rotate the compass rose until the direction from which the wind is blowing is under the index, i.e. 320º.
- Mark the wind dot 25 kt down from the grommet,
*Figure 9*. - Move the slide until the True Air Speed (97 kt) is directly underneath the grommet,
*Figure 10*. - Turn the compass rose until the planned Track (295º) is aligned with the index.
- The Wind Dot will have moved over the 8º left drift line therefore the compass rose must be adjusted by rotating 8º anti-clockwise. 303º is now aligned under the index.
- The Wind Dot has moved again to the 6º drift line (not the original 8º). This means you must turn the compass rose 2º back (clockwise) to allow for this. 301º is now aligned with the index,
*Figure 11*. - Check the Wind Dot again and notice that there has been no further change in the drift angle.
- Read the Heading from the index (301º).
- The Ground Speed is read from under the Wind Dot (73 kt),
*Figure 12*.

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