As part of my Archmage setting, the eponymous archmages distinguish themselves from common wizardfolk by their ability to expand their spellcasting range over vast ranges... limited by line of sight.
For this reason, archmages like to build enormously tall towers and set up all of their ritual materials and spellcasting support apparatuses in a room at the very top.
This also makes assaulting an Archmage's Tower an interesting endeavour: First you must approach the tower in stealth or under cover to avoid the watchful eye of sentries atop the tower, then enter the lower levels and overcome all the challenges and defenses therein before confronting the wizard on the highest level.
Don't forget leg day! Those are an awful lot of stairs.
Now, to the central question of this post: What should the dimensions of a wizard's tower be? Assuming our medieval lack of material science is made up for by magically hardening stone, wood and iron, how tall and narrow can we make it and how much would such a thing cost to build? What other considerations need to be made?
This should give some reference - timeline of the three tallest structures in the world. From 2500 BC (the Great Pyramid of Giza) to 1888 (the Washington Monument) the tallest structures in the world had remained in the range of 150-170 meters tall.
Exactly how effective and expensive magical hardening is, is the question here. No, the number of hp/hardness don't answer it.
First of course you'd build at the top of a natural hill or mountain because that height is all but free. Failing that you'd build a motte (as in a motte-and-bailey castle). The latter gets up to ~100' tall.
With sufficient money you could get a 200' tall tower using medieval tech, easy. Why do you want it to be narrow, particularly?
Two reasons:
1. Wizard Towers as narrow spires are cool.
2. To save on cost for magical hardening.
If you assume that magical hardening doubles compressive strength, then if you can also control weather enough that there's no additional wind loading you can double the tower height. If you only reinforce selected structural bits you'd get less extra height but might drop the cost a lot.
RL big medieval-era towers seem to be about 1.5x as tall as their base length (they're much narrower at the top). Part of that would be wanting to fit a large number of people in the cathedral the tower is attached to though; eyeballing the pictures I think you could easily get 4x. Any additional magical hardening could extend height without adding to width.
Oh. Don't forget that ther should not be any staircases, especially in the upper floors. Minions shouldn't be up ther anyways, and you DO have access to magical flight after all.
Oh. Don't forget that ther should not be any staircases, especially in the upper floors. Minions shouldn't be up ther anyways, and you DO have access to magical flight after all.
Telvanni-style!
I am now considering adding a property that can be applied to structures that fixes them not onto a foundation, but pins them to space itself (relative to the planet). Basically, each stone is its own immovable rod. Ancient towers may be shattered and broken, but largely still standing and often with disconnected levels of the tower just floating above ruins.
Hooray for ridiculous consequences of magical materials!