Nobody knows what the range circle represents. There is not just one range for an aircraft as there are many variables:
- Cruise technique, LRC, MSC, MRC, cost index etc.
- Take-off and climb thrust (de-rate = higher overall fuel consumption)
- For piston engines, best economy vs best power mixture.
- Weight, including extra fuel uplifted (it costs fuel to carry fuel).
- Atmospheric conditions, temperature + pressure + humidity (= density).
- Optimum altitude, also taking into account the wind speed and direction.
I suspect the range circle is what the manufacturer uses for marketing purposes so in best case scenario. In real life for a small GA aircraft weight does not have a big influence on fuel consumption so all calculations are normally performed at max. weight (as are the charts in the aircraft AFM), the altitude to fly is normally chosen based on airspace structure when flying VFR or airway structure when flying IFR. Then calculate the GS by correcting the TAS for forecasted wind at that altitude times the fuel consumption from the AFM tables.
Minimum altitude is based on obstacles and terrain, when required corrected for low temperature, non-standard pressure and windspeed vs terrain height in mountainous areas. Maximum altitude might be limited due to supplemental oxygen requirements.
For airliners its much more complex as there are different take-off and climb-out techniques, de-rates to reduce engine wear but increase overall fuel consumption, carrying extra fuel to reduce fuel costs at destination if the fuel is considerably more expensive (this is also a complex situation by itself as it costs fuel to carry fuel, there is a break-even point somewhere depending on fuel carried and difference in fuel price), different cruise techniques, optimum altitudes while also taking into account wind effects just to name a few.
On a large aircraft the aircraft weight has a huge effect on fuel consumption and thus range. I have done manual calculations in real life and it works best in this case to work backwards. So from alternate arriving with final reserve fuel + extra fuel, then calculate back to the destination and calculate back to the departure aerodrome. Normally the manufacturer has simplified charts included into the AFM which gives you the “sector” fuel taking into account the weight at the start, flight level, a correction for wind and separate tables for ISA -10C, ISA, ISA+10C, … etc. Otherwise you need to calculate the take-off, climb, cruise, descent and approach fuel separately, that’s a real mess
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Luckily the airline normally prepares those papers, normally it includes a table with the effect of altitude on time and fuel, so filed level +1000 ft, +2000 ft, …, and same for below. Often there is some text showing loss / gain in euros / dollars per ton of extra fuel uplifted and a correction table to correct for higher / lower take-off weight than planned as deciding to take some extra fuel for example will otherwise render the whole calculation useless.
So it is pretty much impossible to show the range accurately on a map taking into account all the variables. On my EFB in real life I can draw circles based on groundspeed and time, in practice I only use those to determine if I can use something as an alternate (max. 1 hr in still air, one-engine out, ISA for non-ETOPS) otherwise there isn’t much use in them.