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Can you clear something up?12 am is ambiguous.Do you mean noon, or midnight?
Is it cloudy, or can I see the stars?
I was disappointed by a recent TV program in which a group of engineers and survival experts spent several days sweating in the desert and arguing about how to convert a wrecked plane into a car, to drive 10 km to a main road. Knowing were the road was, they could have walked out on the first night.
In either case the sun will rise at some point on your journey. If you know the local time and season, you can estimate an east correction from its first appearance, then use a stick and watch as a sun compass as you march.
You need a bit more subtlety south of the equator
use a stick and watch as a sun compass as you march.
The sundial shadow goes in the opposite direction in the Southern hemisphere, so you have to do a mental mirror-image of the hour-hand position (ideally taking into account any daylight savings, of course).
Quote use a stick and watch as a sun compass as you march. That used to work when people had watches with moving hands. You have to use more imagination when everyone has digital watches. Maybe your smartphone has a retro "analog" display mode?
it is possible to survive on a cupful of water in a hot desert per day.