Thought experiment: how many arcane spellcasters in a fantasy combined arms army

[Seward]

OK I can speak to the floating disk problem. My TK-based Sorceress started her career with that as her first L1 pick and played it to 16 levels, including military scenarios.

What it can do: It can move at light warhorse overland speeds (which is the same as 30' movement speed hustle) as if on perfect roads, assuming the caster can somehow go that quickly. It can do it over water, swamps, inclines, rough terrain, whatever, basically anything a vehicle with really good shocks and a 3' ground clearance could do, which is most anything except a cliff, if the caster can manage it. If your base land speed is faster or slower than 30' that will affect your mobility as it can only keep up with your base land speed. So a gnome casting the spell only has riding-dog overland speed levels.

What it can do without support for military: The most effective way I found to use the weight limit was to have fully equipped soldiers sit on the disk, in a ring, with any heavy gear in the well between them. Usually they could work something out with rope or backpacks or something, but basically each disc could move several soldiers (about level 8, she moved a platoon across a swamp, just by burning enough spell slots (3 soldiers per disk, 14 discs, 40 soldiers and 2 officers) and then casting Phantom Steed and going slowly enough to not pop the disc).

What it can do if you have a good carpenter and maybe a cart. Or Fabricate. My sorcereress owned a light warhorse and a cart (you have to put those size large greataxes to toss with telekenesis somewhere and until she had a chest of holding, no extra-D space she could get could manage size or sharpness, although she had to switch to greatswords for the chest to work).

What you do is cast a disk under the axle of each wheel (4 discs, usually, 3 if you have a two-wheeled cart, the third you put under the front near the kingpin you'd usually attach to a horse or ox or something), and raise it to the full 3' height. Now have a floating cart, perfect for piling its entire weight limit of stuff or people or whatever. Ride your horse in front of it maybe with purely cosmetic "harness" and closer to the ground if you don't want to scare the natives. Or just go with phantom steed and raise two middle fingers to the ignorant peasants as your cart floats serenely 3' over every surface.

I could move arbitrarily large amounts of stuff with this technique, although since I owned only one cart I'd have to purchase (or ask a wizard with fabricate to manufacture or similar) extras as needed. You can do a cruder version with just a raft of some kind that works nearly as well, it just isn't as well suited to carrying equipment without any tipping off, or being more subtle about what you are doing. On some adventures I actually would buy a small boat and do the same thing, although you really do need a carpenter to fit the discs on the load-bearing keel without having it tip. Carts are easier, they're designed for weight to land on the axle near the wheels. It is worth the extra effort on a boat though if your disks go away while over water--or might. Levitate is a really handy spell for if something like this happens, because if a raft or boat is on the surface you can't get a disc under it the way you can with a cart on land.

Part of why this works is you can control the disks, including height over the ground. The key though is to never outrun your disks with a faster mount, or by teleporting too far from it or whatever or your carts etc go crashing to the ground (another reason to go for minimal clearance where terrain permits, it is less hard on the cart and contents if the disks are suddenly dispelled or go "poof" if some stupid Vrock TK-violent-thrusts you AND your size large greataxes away from your discs....yes I may have lost a little sleep over the hazards of other telekenetics at times....)

Finally if you have a good craftsperson in the party you can actually build some kind of container that the disk fits into mechanically and can hold a lot of volume vertically (think a giant cone, with bottom anchored mechanically on the disk, which is slid in sideways, then something screwed down on the shallow depression to hold it all in place). This can let you transport all kinds of things that aren't soldiers using only 1 disc, and if you use a relatively light but strong material you get most of the benefit of the lifting capacity of that disc. Honestly though, I usually used servant hordes for that purpose instead of a single disc when I lacked a cart, and accepted the slower overland speed.

Two heavy horses have a medium load of 800 pounds, and at 50ft base speed they'll still move faster than the Disk... in addition to being able to bring more than one barrel of foodstuff.

Two heavy horses need food and water for every day they're active. Not a problem if you have goodberry or Hero Feast or something, but for a normal military it's a real constraint that gives diminishing returns when crossing anywhere without ample water available in the terrain and a lot of high quality grazing (grass won't do it alone with heavy exertion over time)

Also 50' base speed is not faster than a 30' tenser's disk over time. The disc doesn't get tired, so it can hustle forever, where going more than 25' per move action will fatigue and eventually kill your heavy warhorses.

Using Mount+Tenser's disks (assuming a not-very-heavy spellcaster) you can achieve 60' overland speed with no weight devoted to food or water and you can do it over any terrain a horse can navigate (you can hustle the horse to keep speed up when it is 3/4 or half speed due to terrain and so what if force march damages it? Summon another with your pearl of power 1 or extra sorcerer slot when it dies. Or if you have a druid traveler mount+easy trail will make that light horse fast enough to keep that 60' overland speed regardless of terrain most of the time).

A tenser's disk baggage train moves at "pony express" speeds or at least "light infantry on forced march "speeds. It is significantly better, but does burn spell slot resources. When I did this sort of thing in actual play, my sorcereress still had all her L3-4 spells to fight the actual battle with, burning L1-2 slots to bring her army along with her (I count her phantom steed as a combat spell she'd have in a battle anyway, it is a valuable tactical tool). Quote from GM in actual battle after 2 black tentacles messed up most of his archers.... "How many of those damn Black Tentacles do you have" "Two more..."

I brought the dwarf heavy infantry. The lighter troops made it to the battle the hard way.