I believe that the posts regarding hot/high ops shortening range refer to airliners and not small planes. It is probably a good idea to specify which you mean because there are differences in the way they are operated that are as great as the obvious difference in sizes.
Reply #1 is correct enough when speaking of light planes and normal full-size airports. But very misleading if we are talking about airliners.
A Cessna 152 has very little range of weights. One person or two people. Maybe a ten gallon difference between a light fuel load and a heavy load. Whereas, even the little Airbus I fly may have a twenty thousand pound range
of possible fuel loads and a thirty thousand pound range
of possible payloads. The Cessna can accelerate to terminal velocity on a runway too short for an airliner to use. So the considerations are very different.
Sorry but I have to speak from the reference point of US regulations and operational practices because that is my training and my experience.
The maximum allowable
takeoff gross weight of an airliner, when it is less than the maximum certificated
takeoff gross weight is a figure that will vary with density altitude (combined low pressure and high temperature being the worst) runway length available, obstacles in the departure corridor, runway slope, wind during takeoff, runway contamination, inoperative equipment or missing exterior pieces that affect airflow and that sort of thing as well as other factors.
All of these things can mean that we have to download the plane in order to have the required performance for this takeoff, be that accelerate-stop distance, climb gradient with an engine inoperative, gear/flaps down, gear up/flaps takeoff and finally gear/flaps up. There are other things too but you get the idea.
So if we can only lift X pounds on this takeoff and if the payload is fixed
then we must reduce our weight in some way, and fuel is one variable. This would normally not be done on scheduled passenger flights. Normally the airline would opt to keep schedule and leave passengers/freight and for sure, the non-revs behind.
But where the load is a fixed quantity fuel must be reduced. I have done sports team charters that departed a hot/high airport, flew a hundred miles or so to a sea level airport, refueled and then continued to destination.
The most extreme example I have heard of this was a USAF
cargo charter flight by a civilian DC-9-30F. It departed Hill AFB near Salt Lake City (4000+msl and hot) for Warner-Robbins AFB in Georgia. If takeoff performance had not been a factor they could have gone non-stop. But MGTOW was very limited by takeoff conditions and so this is what they did.
They put on a reduced fuel load and flew from Hill to Mountain Home AFB near Boise Idaho. (about 2500'msl but just as hot) Then from Mountain Home to Mather AFB near Sacramento California (sea level, hot but very long runway) From there they flew nonstop to Warner-Robbins, the original destination. If you have a map of the US handy you can see that this was a long way out of their way, but dictated by geography/topography. There was no fuel stop available to them going east from either HIF or MUO.
And that is how hot and high airports can affect aircraft range. It is limited by the required takeoff performance.
Happiness is not seeing another trite Ste. Maarten photo all week long.