Is there a relatively reliable way of calculating the time until sunset, without any specialist equipment, when I'm in the wilderness?
One method I've found to be particularly reliable is the finger method - hold your arm straight out in front of you, facing towards the setting sun like so:
Place your hand so your little finger is level with the horizon, and your fingers are stacked on top of each other. Each finger represents around 15 minutes of sunlight before the sun sets behind the horizon.
This method can be used relatively accurately up to two hours before sunrise, by using both hands.
See also this page.
Another method I've grown accustomed to over countless sleepless nights is the "amount of light" metric.
If you spend a long enough time at the same latitude and environment, you will get an idea of how bright the sky is at any given time of day and year. Angle of attack of sunlight? Intensity? White, yellow, red, blue or white? Experience.
It's easiest to spot when half-dead awaiting the morn but still works for normal situations. Colour of the sun and clouds, height, angle, nearby obstructing peaks - pull all those in the organic neural network and hope for the best. If you survive - readjust.
PS: I use @berry120's algorithm daily when hiking!
There are a number of influencing factors, and the further you are from the equator, the more important they get:
season/time of the year. The further you are from the equator, the more prominent is this effect.
longitude and local time zone: very much as a rule of thumb, your position within the current time zone makes a difference of ±30 min.
Some places of course use time zones other than the "naturally closest one" and/or daylight saving time.
latitude has a huge influence on how long the sun takes to travel a given vertical angle (declination):
- at the equator, 12 h day/night is a decent approximation all year round. At the polar circles, that's true only at equinox - at solstice you have 24 h of day or night.
- useful twilight at the equator is maybe 20 min, but more than an hour at 50° and all night long in summer in Scandinavia.
weather obviously plays a role, too. Dark rain clouds can cost you several hours here (50 °N), snow or bright moonshine can make the whole night useful twilight. Again, I'd expect the effect to be the stronger, the further you are from the equator.
topography: e.g. horizon in the Soča valley can be +20° - +25° up.
Local rules of thumb
I live at about 50°N (quite central in Germany). Here,
- the sun takes about 4 min from first hitting the horizon till being completely down.
- In addition, we get a more than an hour of decently useful twilight* (until the sun is ≈10° below the horizon) all year round (± weather, vegetation, light pollution, obviously).
(At 40° N (north side of the mediterranean) twilight is only about half as long. This caught me many times, even when I was living in Northern Italy! Lighting conditions were reminding me rather too late to look for a place to stay for the night.)
- The daily shift in sunrise/sunset is about 3 min around equinox (and approximately 0 at solstice)
If you have been at roughly this location for a while, knowing yesterday's sunset, maybe an approximate adjustment (like the 50° numbers I gave above) and the approximate duration of twilight shoud give you a decent idea.
If you go somewhere far from your usual home, consider looking up sunrise/sunset and twilight (and maybe know the current moon phase and what that means in terms of moonrise and moonset) as part of planning your tour.
Since daily changes are not that huge (not even far from the equator) and you anyways cannot plan day tours to the minute, noting maybe one day per week should be sufficient - that's a piece of paper that shoud fit into any outfit.
Being in a deep valley
End/beginning of civil twilight is defined as the sun being 6° below the horizon. You can use this together with twilight duration (from tables) to approximately adjust sunset for being in a deep valley (this approximatin becomes worse at high latitudes in summer - but then you have anyways very long days).
Actual twilight will be somewhere between the sun 6° below your apparent horizon (mountain range) and 6° below azimuth (astronomic horizon).
More precise numbers can be read from a sun path diagram: where you can see when (time & date) the sun is at what elevation (angle).
Some calculators calculate sunrise and sunset based on a so-called shadow file that gives the apparent horizon. There are tons of such diagram generators available nowadays (they are used e.g. to evaluate locations for solar power)
Once printed out, this may be sufficiently low tech to fulfil your needs.
* Decently useful for outdoor purposes for me is somewhere in between civil and nautical twilight, I's say until -10° elevation. Adjust according to your night vision.