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How can I find the flight paths near an airport (e.g., Heathrow or Pearson) including cruising altitude, descending speed (variations)?

Specifically, I need a figure showing the height vs. speed of a plane as it's landing starting from the cruising altitude.

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You might consider using a website such as Flightradar24, which will show you real-world realtime flight paths (including vectors or holds that may be assigned by air traffic control, as opposed to ideal approaches). You can click on a particular aircraft to see its track, then click "speed & altitude graph" on the detail pane to see speed and altitude at one-minute intervals.

There's also a speed/altitude graph for each flight tracked on FlightAware.

If you check out a variety of flights into the same airport, you can see what approach paths are used by aircraft arriving from different directions for the current wind conditions.

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You can find a great deal of approach path information here but that will only give you the path, and perhaps some intercept altitudes for a given approach it will not give you any speed information. Cruising altitudes will also vary heavily by aircraft type.

Specifically, I need a figure showing the height vs. speed of a plane as it's landing starting from the cruising altitude.

This is broadly specific to each airframe as well as the loading of any given aircraft at a given time. But you can find the information if you know the airframe in question, there are also some limits depending on where you are in the world. The FAA (and presumably most legal entities) cant have different rules for everyone so they broadly break down approach speeds into categories. That should give you a fair idea of the approach speeds. Keep in mind these are airspeeds and local wind will alter ground speeds on an individual day basis.

If you start from the cruising altitude there will be a few phases of the decent that will see various speeds. This depends on what ATC clears you for and what the local conditions call for more on that here.

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    $\begingroup$ The SID, STAR and approach charts for Heathrow are here: nats-uk.ead-it.com/public/… and that site will give you similar information for other UK airports $\endgroup$ – Dave Gremlin May 1 '18 at 21:56
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Look at the Approach Charts for the airport of interest. In the US, speeds are also limited to 250 knots below a certain altitude and I think distance from an airport (I never had to worry about that, my Vne (redline airspeed) doesn't go that high!).

I don't think you'll find speeds from cruising altitude as speeds are adjusted to match traffic flow. And cruising speed varies by airplane type as well.

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