E6B

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The front of a metal E6B.

An E6B flight computer commonly used by student pilots.

The E6B Flight Computer, also known as the "whiz wheel", is a form of circular slide rule used in aviation. They are mostly used in flight training, but many professional and even airline pilots will still carry and use their E6Bs. E6Bs are used during flight planning (on the ground before takeoff) to aid in calculating fuel burn, wind correction, time en route, and other items. In the air, the E6B can be used to calculate ground speed as well. The back is designed for wind correction calculations, i.e., determining how much the wind is affecting your speed and course.

1 Construction
2 Calculations
3 History
4 References in popular culture
5 External links

[edit] Construction

They are usually made out of aluminum and plastic, with lettering and markings engraved into the metal. Some are made out of cardboard and plastic, usually for students. Otherwise identical, these are less expensive but also far less durable.

Electronic versions are also produced, resembling calculators rather than manual slide rules. Aviation remains one of the few places that the slide rule still is in widespread use. Manual E6Bs remain far more popular than the electronic ones because they are lighter, smaller, less prone to break, easy to use one-handed, and do not require power.

Many ASI (airspeed indicator) instruments have a movable ring built into the face of the instrument which is essentially a subset of the E6B. Just like on the E6B, the ring is aligned with the air temperature and the pressure altitude, allowing the TAS (true airspeed) to be read at the needle.

In addition, computer programs to emulate E6B functions are also available, both for desktop computers and PDAs (Personal Digital Assistants).

[edit] Calculations

Instructions to ratio calculations and wind problems are printed on either side of the computer for easy reference and are also found in a booklet sold with the computer. Also, many computers add Fahrenheit to Celsius conversion charts, various reference tables and other at-a-glance information sources.

The front side of the E6B is a logarithmic slide rule that performs multiplication. Throughout the wheel, unit names are marked (such as gallons, miles, kilometers, pounds, minutes, seconds, etc.) at locations that correspond to the constants that are used when going from one unit to another in various calculations. Once the wheel is positioned to represent a certain fixed ratio (for example, pounds of fuel per hour), the rest of the wheel can be consulted to utilize that same ratio in a problem (for example, how many pounds of fuel for a 2.5-hour cruise?)

The wheel on the back of the calculator is used for calculating the effects of wind on cruise flight. A typical calculation done by this wheel answers the question: "If I want to fly on course A at a speed of B, but I encounter wind coming from direction C at a speed of D, then how many degrees must I adjust my heading, and how fast along that course will I really be traveling?" This part of the calculator consists of a rotatable semi-transparent wheel with a hole in the middle, and a slide on which a grid is printed, that moves up and down underneath the wheel. The grid is visible through the transparent part of the wheel.

To solve this problem with an E6B, first the wheel is turned so the wind direction (C) is at the top of the wheel. Then a pencil mark is made just above the hole, at a distance representing the wind speed (D) away from the hole. After the mark is made, the wheel is turned so that the course (A) is now selected at the top of the wheel. Then the ruler is slid so that the pencil mark is aligned with the true airspeed (B) seen through the transparent part of the wheel. The wind correction angle is determined by matching how far right or left the pencil mark is from the hole, to the wind correction angle portion of the slide's grid. The true ground speed is determined by matching the center hole to the speed portion of the grid.

The mathematical formulas that equate to the results of the E6B wind calculator are as follows: (desired course is A, true airspeed is B, wind direction is C, wind velocity is D. A and C are angles. B and D are consistent units of speed). $π$ is 3.14159...

Wind Correction Angle: $WCA=\sin^{-1}\left(\sin(C-A)*D/B\right)$ .

True ground speed: $GS=\sqrt{ B^2 + D^2 -2*B*D*\cos(C-A-WCA) }$ .

Wind Correction Angle, in degrees, as it might be programmed into a computer (which includes conversion of degrees to radians and back): $WCA=\sin^{-1}\left( D / B * \sin((C-A)/180*\pi) \right) /\pi*180$ .

True ground speed is calculated as: $GS=\sqrt{ B^2 + D^2 -2*B*D*\cos( (C-A-WCA)/180*\pi ) }$ .

[edit] History

Closeup photo of a metal E6B.

The device's original name is E-6B, but is often abbreviated as E6B, or hyphenated in other variations for commercial purposes.

The E-6B was developed in the United States by Naval Lt. Philip Dalton in the late 1930s. The name comes from its original part number for the U.S Army Air Corps in World War II.

Philip Dalton (1903-1941) was a Cornell University graduate who joined the United States Army as an artillery officer, but soon resigned and became a Naval Reserve pilot from 1931 until he died in a plane crash with a student practicing spins. He, with P. V. H. Weems, invented, patented and marketed a series of flight computers.

Dalton's first popular computer was his 1933 Model B, the circular slide rule with True Airspeed (TAS) and Altitude corrections pilots know so well. In 1936 he put a double-drift diagram on its reverse to create what the US Army Air Corps (USAAC) designated as the E-1, E-1A and E-1B.

A couple of years later he invented the Mark VII, again using his Model B slide rule as a focal point. It was hugely popular with both the military and the airlines. Even Amelia Earhart's navigator Fred Noonan used one on their last flight. Dalton himself felt that it was a quickie design, and wanted to create something more accurate, easier to use, and able to handle higher flight speeds.

So he came up with his now famous wind arc slide, but printed on an endless cloth belt moved inside a square box by a knob. He applied for a patent in 1936 (granted in 1937 as 2,097,116). This was for the Model C, D and G computers widely used in World War II by the British Commonwealth, the US Navy, and even copied by the Japanese and Germans. These are commonly available on collectible auction web sites.

The US Army Air Corps decided the endless belt computer cost too much to manufacture, so later in 1937 Dalton morphed it to a simple rigid, flat wind slide, with his old Model B circular slide rule included on the reverse. He called this prototype his Model H; the Army called it the E-6A.

In 1938 the Army wrote formal specifications, and had him make a few changes, which Weems called the Model J. The changes included moving the "10" mark to the top instead of the original "60". This "E-6B" was introduced to the Army in 1940, but it took Pearl Harbor for the Air Corps (by then the Army Air Forces) to put in a really large order. Over 400,000 E-6Bs were manufactured during World War II, mostly of a plastic that glows under black light. (Cockpits were illuminated this way at night.)

The base name "E-6" was fairly arbitrary, as there were no standards for stock numbering at the time. For example, other USAAC computers of that time were the C-2, D-2, D-4, E-1 and G-1, and flight pants became E-1s as well. Most likely they chose "E" because Dalton's previously combined time and wind computer had been the E-1. The "B" simply meant it was the production model.

The designation "E-6B" was only officially used on the device itself for a couple of years. By 1943 the Army and Navy changed the marking to their joint standard, the AN-C-74 (Army/Navy Computer 74). A year or so later it was changed to AN-5835, and then to AN-5834 (1948). The USAF called later updates the MB-4 (1953) and the CPU-26 (1958). But navigators and most instruction manuals stuck with the original "E-6B" name. Many just called it the "Dalton Dead Reckoning Computer", one of its original markings.

After Dalton's death, Weems [1] updated the E-6B and tried calling it the E-6C, E-10, and so forth, but finally fell back on the original name which was so well known by 50,000 World War II Army Air Force navigator veterans. After the patent ran out, many manufacturers made copies, sometimes using a marketing name of "E6-B" (note the moved hyphen). An aluminium version was made by the London Name Plate Mfg. Co. Ltd. of London and Brighton and was marked "Computer Dead Reckoning Mk. 4A Ref. No. 6B/2645" followed by the arrowhead of UK military stores.

[edit] References in popular culture

"My eyes are dim I cannot see, I have not got my E-6B with me, over the Valley of the Ruhr". (World War II USAAC ditty)
"His computer is the instrument on which he stakes his life ... Don’t ask for his computer, for he’d sooner lend his wife". (Navigator's Song, 1943)
In Star Trek episode The Naked Time, Mr. Spock uses an E-6B to calculate the time of impact of the Enterprise with a planet. In the episode Who Mourns for Adonais?, he is again seen holding an E-6B.