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I was looking for WW2 aircraft indicators and I found one navigation equipment called API (air position indicator). But I couldn't find how it works exactly????

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    $\begingroup$ Can you be more specific which kind of information are you looking for? This description: timeandnavigation.si.edu/multimedia-asset/… (first search result, "It took inputs from airspeed sensors and gyro magnetic compasses and continuously computed latitude and longitude. ") seems to cover the basic principle quite well. What else do you want to know in particular? $\endgroup$ – Martin Mar 24 '18 at 14:41
  • $\begingroup$ How does it get the latitude and longitude from airspeed and heading??? by which formula? $\endgroup$ – MajidMozafari Mar 26 '18 at 5:25
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    $\begingroup$ It has the departure point's Longitude and latitude entered before takeoff. The uses airspeed and heading to calculate location as it flies along. A crude but effective approximation of actual position. The pilot uses map references for terminal guidance. In effect, a a much more inaccurate version of a modern INS. $\endgroup$ – Mike Brass Mar 30 '18 at 10:52
  • $\begingroup$ This question would be even more interesting if it mentioned some examples of aircraft that actually used this type of instrumentation. So basically this system automates the ded. reckoning process; very interesting. $\endgroup$ – quiet flyer May 27 at 17:39
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    $\begingroup$ Insert joke here about the "Air Position Indicator" being another name for the blue half of the Attitude Indicator. And the "Ground Position Indicator" being another name for.... $\endgroup$ – quiet flyer Jul 12 at 21:23
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The API uses not only heading and airspeed but they are fed to mechanisms within the instrument that solve the navigation problem using sine, cosine and secant functions. The output was latitude and longitude from the departure or a known fix (geographical position) to give the no wind position of the airplane. This was then used by the navigator to give a dedreconing position by plotting the last known wind vector from the no wind position.

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These links (to download documents) give interesting information about a "Ground Position Indicator" from 1953, which sounds like an "Air Position Indicator" with added capability to correct for assumed wind speed and direction. The device took into account the spherical shape of the earth, but apparently did not incorporate acceleration sensors as per a true Inertial Navigation System.

(Click on all 3 links under "Ford Instrument Company")

http://analogmuseum.org/english/library.html

And here is a link for information about the "Air Position Indicator":

https://timeandnavigation.si.edu/multimedia-asset/air-position-indicator

Apparently the only inputs to the "Air Position Indicator" were true airspeed, gyro-magnetic compass heading, and initial lat/lon. It automated the ded. reckoning process, taking into account the spherical shape of the earth, and magnetic variation, but assuming no wind. Apparently the pilot or navigator then corrected the result for assumed wind speed and direction.

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