If I have a mountain that is, say, 3,000m high, how could I work out how wide it should be? Does anyone have any guidelines that would let me work out the bounds for the width of a mountain given its height?
You'll need to also look at how old the mountain is, and how strong gravity is on your planet, and what the environments is like... Young mountains can be very steep, but as they age, glaciation and other forms of wisdom make them slump.
So a young mountain may be 20000m high and very steep (perhaps an average of 50 degrees on a planet with earth gravity) but as it gets older you should expect it to shrink and get wider, so an old mountain could be more like 15000m high and much less steep, maybe 20 degrees.
And you can work out how wide your mountain needs to be from that sort of information.
As Rory Alsop says:
- the older mountain is, the lesser are its sides steep
- the older mountain is, the lower it is
But I would take also material and origin of mountain into consideration for setting of its high.
Following four materials are the most common ones that probably should be taken into consideration (and that I was able to remember very quickly)
- very soft (and fragile) material
- mountains are so low that only word hill is used for them
- mountains did not passed any rapid changes
- Elbe and Moldau plains (even Barrandien)
- very hard (but fragile) material
- mountains are mostly higher than chalk massives but still not much high
- mountains did not passed any rapid changes but weather had not so much time to shape them
- Česko-Saské Švýcarsko (Saxon Switzerland)
- very hard (and not so fragile as sandstone)
- older volcanic hills
- mostly low mountains, but with steeps sides
- České středohoří (Czech central mountains)
- very solid material
- mountains created by folding
very high mountains with quite steep sides
Krkonoše, Jizerské hory, Beskydy (oldest mountains, and therefore not so high and with not much steep sides)
- Tatry (a bit younger maintains, quite higher and with steeper sides)
- Himalayas (the youngest, very very high - and also the most largest - and with extremely steep sides)
This is a bit more exact (but I am not geologist, so I could do mistake). But your world may have a different geology - if you yould pay attention to it, at all.
But as far as I read (and watched) fantasy and science fictions not much fantasies and also science fictions pay much attention to geology.
You may have your own geology and materials and so your mountains may have a different height and width.
There is no rule. It will depend on a great many factors. For example, this is Mount Asgard, at 2,015 meters high:
Mount Asgard rises essentially vertically on three sides (the back side, not visible, is more sloped but still steep). Mount Rogers is a glorified mound.
Based on an average angle of repose (40) and assuming a uniform conical shape. The mountain would be 7150 m wide (diameter) at the base.