In pilot training, we all learned to use an E6-B or something similar, along with winds aloft forecast to do our flight planning. The values were pretty good, about as good as we could get considering it was all we knew. If the trip was short (about 500 miles or less) being careful, it can be nailed pretty well.
Now imagine flying a jet, over 2500 miles non stop, flying airways, in or near the jetstream, with an E6-B and the winds aloft forecast. It can be very accurate, but will be very time consuming to calculate. The interpolation alone will be a tremendous effort, and then calculating along the route, and keeping it all added correctly can be quite a challenge.
The computer has a small advantage in calculating the flight plan. Computers are great at keeping track of all the numbers, and interpolating. The National Weather Service (US NWS) and UK Meterological Office (UKMO) all model the weather in little rectangular 3D shapes, that the computer can look at and determine winds and temperature for the airspace.
There are multiple wind models used in various systems for flight planning. The Global Forecast System (GFS) model is pretty good, and available almost world wide. The GFS model is run 4 times a day, and forecasts can go as long as 16 days, with the first day having a specific forecast every hour, starting the second day every third hour up to 8 days, and every twelfth hour up to 16 days. The 3D rectangles are about 27km square and about 500 feet thick. The US also produces a finer grained model, called RAP or Rapid Refresh model which is updated more often has smaller 3D rectangles (13km squares, by about 600feet) and only covers the CONUS for 12 hours. (A high resolution rapid refresh model (HRRR) is being developed with 3km squares).
If a flight plan is created that will take an aircraft from Los Angeles to New York, flying at FL370 using the route:
OSHNN4 DAG J100 LAS J146 DVC PUB SLN SPI J80 CREEP APE CTW KODIE PSB LVZ LENDY6
The computer will look at all the 3D rectangles that the aircraft will pass through, and using the winds and temperature for that airspace, calculate the ground speed, distance and time for the aircraft in that area. The accumulation of all the times will be accumulated, and the end result will be the total flight time. That result is most of the time, then the book values for the aircraft can be used for climb to, and descend from altitude.
Normally the flight planning computer will expand out the OSHNN4 departure to all the waypoints, and calculate them individually to top of climb (TOC) then start calculating in the in the 3D rectangles at altitude. The flight planning computer will expand out the LENDY6 arrival and determine the top of descent (TOD) calculating everything up to that point using the flight level 3D rectangles, and the proper rectangles on the way down.
For airlines, a dispatcher will normally generate these flight plans. The dispatcher will look at the flights coming up for their area, and maybe run a preliminary plan (just an FYI, the Jeppesen Jetplan Flight Planning Engine takes about 6 seconds to run a plan similar to the Los Angeles to New York above). The dispatcher can look at the flight plan result, and plot it on a map to see where there may be weather or other congestion, and adjust it accordingly.
Once the dispatcher is happy with the plan, they will file it with the FAA ATC. The FAA ATC can look at that plan, and suggest changes or let the pilot fly it as it is. The FAA will keep the plan on file and use it in various calculations, including URET and other collaborative decision making (CDM) systems.
Overall, the computer makes flight planning much easier. There is much more to flight planning, this only covers winds and temperatures aloft, and how it applies to flight planning.
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