What is the tractive force of Tenser's Floating Disk?

Question

Playing D&D 5th edition, I am currently using the Tenser's Floating Disk to make a self-propelled vehicle. My DM already accepts that the structure works and moves in his world, so this isn't a duplicate of Speed of a Tenser's floating discmobile. However, we are both puzzled as for what exact tractive effort to give the disk, in order to calculate acceleration as well as max speed.

The vehicle is set up in the following way: I cast it in a perfectly sized hole at the back of a light structure. At the front of the structure there's a movable seat, whose default position is almost (but not quite) 20 feet ahead of the disk. I then sit on the seat, then move it a bit forward. This causes the disk to try getting back within 20 feet of me, essentially giving traction to the floating structure, which causes said structure to go faster and faster.

Now, I know that \$F=ma\$. The mass \$m\$ is easily known (by the weight of the structure + my own), and I guess the disk's tractive effort is constant, so the acceleration \$a\$ is as well (e.g., if acceleration is 5 feet per second and base speed is 30, then speed at turn 2 is 35, then 40 at turn 3, and so on).

But the question is: What is the tractive force \$F\$ of Tenser's Floating Disk? It is required to find the acceleration from a known mass with \$a=\frac{F}{m}\$. It is probably not extremely high, as the disk can get stuck behind a wall as per the spell's description. However, it's still at least high enough to transport 500 pounds without problem. So how would you rule it as a DM?

PS: if you want to take account of air resistance, then the resulting force will get lower as speed goes up, until a maximum speed is reached. Then the exact air resistance is required to know the exact max speed.

Answer 1

As asked, this question is unanswerable. However, I'll expand on a few points of clarification that would make this answerable, and answer based off of that.

The problems here, are these.

1. We do not know the maximum speed (in 5E) of Tenser's Floating Disk
2. We do not know how it interacts with obstacles

The problem is that Tenser's Floating Disk does not operate according to Physics. It can carry precisely 500 pounds, can overcome a maximum of a 10' elevation change, and moves to stay within 20' of you. Under most circumstances, this is more than enough information to properly interact with TFD. However, there are scenarios that the 5E version of Tenser's Floating Disk do not cover...

If you find a way to increase your speed, does it go faster as well? If you teleport 99' away from it, how quickly does it move back within 20' of you? If you hopped aboard the very back of a Spelljammer and accelerated to ludicrous speeds at ground level, could it keep up?

If I don't know where its speed caps out, in game terms, I can't compute its acceleration.

And, as a second point of unknown, can it actually push things across the ground, and how does it actually react in the case of an obstruction. And what counts as an obstruction? Could a person grab it and stop it from moving? Will it try to move anything that is touching the ground? If it was in a pit that was precisely 10' deep in loose-packed sand, would it plow away the top layer of sand so it could get out of the hole, or would it bump into an obstruction it couldn't overcome and simply stop? And, if it tries to push past an obstruction, what's the limit on how heavy something can be that it is trying to move?

Based off this, it is simply impossible to determine the force that a TFD would apply, as it could be anything from Zero to Ludicrously High.

So, unless your DM can answer those two questions for you, this question is unanswerable.

The closest thing I can offer to an answer would refer back to D&D 3.5E, and make a whole bunch of assumptions about the way the spell behaves.

In 3.5E, Tenser's Floating Disk was speed-capped at the normal Speed of the caster, and can perfectly keep up with its caster. Meaning, TFD can accelerate at the same rate a human can, when not Dashing. We're going to have to take some serious liberties here with our numbers, because humans reach a brisk walk very quickly.

So, we'll provide the very upper case for what this could look like.

Usain Bolt's initial acceleration in his world-record-setting 100m dash capped out at 9.5m/s². For sanity's sake, we'll just halve that and call it good. Thus, we can say our spellcaster (and thus his Tenser's Floating Disk) accelerates at about 4.75m/s².

Throwing that into \$F=ma\$, considering that the disk can manage this acceleration while carrying 500lbs (226.8kg)...

$$ F=226.8\times4.75=1,077.3\,\text{N} $$

However... TFD is, in this case, still capped at 30' per six seconds...so, ultimately, it won't move any faster than the caster could walk.

As mentioned before... unless I explicitly define the Acceleration and Top Speed of Tenser's Floating Disk... this equation is unsolvable. But, assuming you import 3.5E restrictions... your vehicle will reach a walking pace about as quickly as you could reach a walking pace, and then will hold that pace until the spell wears off.

(Bear in mind, while designing this vehicle, you'll need to put a cap on top of the 'hole' where you keep the Disk. Otherwise it might just hop out of the hole in order to come to you... unless you're building your vehicle to be 10' tall.)