The Gaming Den

RandomCasualty2 wrote:I wouldn't bother with the rubber band theory and all that. That's probably more complex than you care about.

Why not just say that the islands are immovable. Like a giant immovable rod. Then you have magic spells which can move them.

If you want them to move on their own in some kind of drift pattern, you can say that the drift is linked to movements of planetary bodies in the heavens, and no other force can move them beyond that.

The big issue is that flying rocks, islands, and islands are a huge ''ooh shiny!" beacon to players who will attempt to do all sorts of strange things to them. Having some sort of idea of how they work will help GMs figure out what happens when PCs pull some shinaigans. It also helps forewarn potential issues where you realize you set up a perpetual motion machine or something. Others have pointed out the issues with the rocks being ''immovable.''

On a related note, even with their huge size, these floating rocks will move around even if only relative to their focal point. Either they have to be physically tied down (good old anchor principle), skymages have a "park" spell, or floating rocks require arbitrarily larger force than their size would indicate to move (heck even the largest ships float around).

Also can I move my skyship without a skymage by hooking up some dragons to it like a chariot? It doesn't have to be a good idea, but sometimes you don't have a skymage.

Manxome wrote:If you do that, then any skymage that happens to get his hands on an island can use it as a battering ram to crush cities, and can maneuver it horizontally with just as much speed and responsiveness as a sky ship. And that's kind of dumb.

That is indeed dumb. Let me add something extra to avoid that. The maximum force that can be applied increases with the size of the floatstone. The speed at which the focus point can be moved decreases with the size of the floatstone. As before, there's a minimum size. This gives you your nimble surfboards and your ponderous islands, and is, as you say, intuitive.

Your solution works great too. I guess I was feeling like I wanted there to be a purpose for both big floatstones and small floatstones. Either way, I think there will be some risk from rogue skymages, and that is all to the good for plot-hook potential.

MartinHarper wrote:That is indeed dumb. Let me add something extra to avoid that. The maximum force that can be applied increases with the size of the floatstone. The speed at which the focus point can be moved decreases with the size of the floatstone. As before, there's a minimum size. This gives you your nimble surfboards and your ponderous islands, and is, as you say, intuitive.

I...don't think that does what you want it to do. That means that if the sky mage keeps pushing the focal point in one direction as fast as he can, the floatstone is going to end up oscillating like a pendulum relative to the focal point (as it moves at its constant maximum velocity), which is a rather weird result--skyships in a real hurry will end up with their speed bouncing up and down based on invisible forces.

And putting a limit on something's velocity is just kind of icky when the position of that object ends up determining the acceleration of something else. Except in a few special cases, you probably can't even calculate how the floatstone should move without differential equations.


On an unrelated note, there's a potentially important mechanic that you don't seem to have considered: is it possible to "turn off" a floatstone and make it fall like a rock? (Other than by pushing so hard that you snap the "rubber band?") If it is, then your system apparently needs special rules for turning floatstones off and on that makes it more cumbersome for large stones. My system allows you to describe a single operation, "set new focal point," where the new point may or may not be "null," and this takes the same amount of time and power no matter what point you want to set (for any point that's legal at all), and it simply overrides the previous point, no matter what it was. So the fundamental mechanics of manipulating floatstones can be described more simply under my suggested rules.

Maybe no snapping is possible.

Maybe it's more of a "hook" in the sky, and the float stone is hanging from it via aetheric 'cables'.

Bang, none of this "how do I snap the rubber bands" questions.

Instead the question is "How much mass can a Skymage move, if a Skymage could move mass?"

Breaking a sky-hook takes as much time as was needed to establish the skyhook in the first place, and a partly taken apart sky-hook can be repaired by any skymage of any level of ability.

I'm sorry, could you clarify for me exactly how that helps, and why we no longer care about the issues that prompted the introduction of the "snapping" rule in the first place?

Well, it depends on how you look at the connections between a focal point and a float stone. Are their distances from each other always slowly moving? or are they more rigid?

The first means that sky islands are always slowly bobbing; about as much as an aircraft carrior's interior bobs on a calm day at sea. Not a lot, but enough for people to talk about their "sky/island legs" and "land legs."

The second means that the islands stay in place, but means that they can't be moved relative to each other, they both move at the same time.

In the presence of friction, a platform suspended from a rubber band will come to rest, and will remain absolutely motionless unless acted on by an outside force. Things like wind or people walking around qualify as "outside forces," of course, but I'm somewhat skeptical about them being strong enough to cause noticable bobbing. It would depend on the mass of the island and the strength of the "rubber band."

A absolutely rigid connection between the island and the anchor implies that we've got irresistible forces and immovable objects, which is...probably not a good idea. You can, of course, approximate rigidity to an arbitrary degree by making the spring force arbitrarily strong.

...which is exactly the opposite of what we were trying to do for the last few posts, which is to place reasonable limits on the strength of the forces that any given skymage could command. On the theory that it's a bad thing if an apprentice skymage with a floatstone pebble can knock down any structure ever built (or naturally-occurring). (And yes, I know there was a suggested minimum size, that addresses a different issue.)

But even ignoring that problem, I'm still not sure what you're driving at here. Why bring this up? What's the goal? What is accomplished by increasing the spring force coefficient to infinity?

Snapping the bands offers a method for people to fight against sky ships. If you apply enough force to a stone, it will push far enough out of position that it will fall. A skymage on hand can bring it to rest by continually resetting the focal point to something in range, slowing it as it goes down until it stops, but if the sky mage isn't on hand (unconscious or thrown from the stone), then it plummets into the earth.

That's good because it means that other people aren't confronted with irresistible forces that they cannot fight against.

-Username17

I assume there is to be a limit on how much floatstone a single sky mage can manipulate, in both number of anchors & total floatstone mass?

Is an island largely a single MASSIVE floatstone with buildings stacked atop it, or is an island a conglomerate of both massive floatstone foundations and floatstone stone structures?

I'm trying to figure out the logistics in both raising an island and potentially moving said island after its constructed.

So the falling stone minus a sky mage isn't an irresistible force?

-Crissa

Crissa wrote:So the falling stone minus a sky mage isn't an irresistible force?

-Crissa

No more than any other falling rock is.

-Username17

Manxome wrote:That means that if the sky mage keeps pushing the focal point in one direction as fast as he can, the floatstone is going to end up oscillating like a pendulum relative to the focal point (as it moves at its constant maximum velocity), which is a rather weird result--skyships in a real hurry will end up with their speed bouncing up and down based on invisible forces.

I've been tacitly assuming that the magicmaglev force is damped, so you don't get that type of oscillation - whether in moving stones or in stationary stones.

Manxome wrote:Except in a few special cases, you probably can't even calculate how the floatstone should move without differential equations.

With air resistance and whatnot, that's probably true regardless. That's all going to be abstracted away with the game rules, though, just like gravity gets abstracted away by falling damage.

Manxome wrote:On an unrelated note, there's a potentially important mechanic that you don't seem to have considered: is it possible to "turn off" a floatstone and make it fall like a rock? (Other than by pushing so hard that you snap the "rubber band?")

I'm happy with "no" as an answer. That means that a sufficiently large floatstone is essentially permanent, since you can't move the focus point fast enough to snap the rubber band.

MartinHarper wrote:

Manxome wrote:That means that if the sky mage keeps pushing the focal point in one direction as fast as he can, the floatstone is going to end up oscillating like a pendulum relative to the focal point (as it moves at its constant maximum velocity), which is a rather weird result--skyships in a real hurry will end up with their speed bouncing up and down based on invisible forces.

I've been tacitly assuming that the magicmaglev force is damped, so you don't get that type of oscillation - whether in moving stones or in stationary stones.

There will presumably be some drag from air resistance and such, and I guess you could add on some arbitrary magical additional damping if you really wanted, and if you have sufficient damping then the system will eventually reach equilibrium (if the focal point has constant velocity), but you're kind of missing the point. That was just one easy example to point out that the forces you're using are incredibly bizarre. You'll probably need lots of damping to prevent the speed from oscillating for a while before it stabilizes, and there are probably lots of other weird, counter-intuitive results in other situations that we just haven't discovered yet because your system is extremely difficult to reason about.

MartinHarper wrote:

Manxome wrote:Except in a few special cases, you probably can't even calculate how the floatstone should move without differential equations.

With air resistance and whatnot, that's probably true regardless.

No. When the limit is the maximum distance you can keep the focal point at rather than the maximum speed at which you can move it, calculating the acceleration pattern and maximum speed is vastly easier, with or without air resistance.

In fact, if you can move the focal point as fast as you want, but only within a limited area, then this is exactly like having a simple reaction engine that you can throttle up and down and point in different directions: you just control the magnitude and direction of the force within defined limits. It follows a simple, well-understood model that players will already be familiar with.

MartinHarper wrote:That's all going to be abstracted away with the game rules, though, just like gravity gets abstracted away by falling damage.

If you don't care about whether the game rules are consistent with the theoretical model, or whether it's possible for players to fall back on the theoretical model in situations the game rules don't cover (or don't cover well), then the theoretical model is just flavor text and we should be discussing the game rules first. You are proposing that these rules are OK because they will never actually be followed.

If you want to talk about mechanics more in terms of actual gameplay than theoretical models, fine, but give me a proposal for rules that you actually want to enforce, not that you want to put in as pure fluff.

Manxome's scheme

I worry I will mis-describe this. The key point is that focus points can be moved arbitrarily quickly, but the "rubber band snaps" if the force is greater than X. To float a person you use one floatstone. To float a ship you use many floatstones. To float an island you use thousands of floatstones.

The maximum sustained speed with air resistance is given by something like the following calculation:

g = the force of gravity (or "gravity")
M = the mass of the floating island.
F = the accelerating magilev force at maximum distance. Because the island doesn't sink, we know that F > gM. However, to move a floating island horizontally some of the magilev force will be cancelling out gravity, and some will be providing horizontal motion. Simplifying assumption: horizontally, F=gM
D = the drag force due to air resistance. Drag is complicated, but the internet tells me that we can approximate it with the following equation:

D = uAv²

where v is the velocity, u is some constant based on the density of air and suchlike, and A is related to the cross-sectional area of the island and its aerodynamic properties. Maximum speed is attained when F=D, so we discover that:

v² = (g/u)*M/A.

M/A is proportional to the length of the object being moved, so we end up by saying that v² is proportional to the length of the object. Therefore, floating islands have a maximum cruising speed that is larger than that for skyships, and skyships have a maximum cruising speed that is larger than that for skysurfers. It would be good to plug some numbers into that equation to ensure that it gives us sensible values, but I'll leave that for now.

My scheme

To float a person you use a minimum-sized floatstone. To float a skyship you use two medium-sized floatstones. To float an island you get two or three of the biggest floatstones you can find. A big floatstone can generate big force, because its focus point can be further away. However, its focus point can only be moved very slowly. Small floatstones can generate enough force to keep a person aloft, but their focus point can be moved much faster. In any case, "the rubber band snaps" if a floatstone exceeds its maximum force/distance.

Maximum cruising speed is typically given by the maximum speed you can move the focal point, which is given by some equation such as v = c/m, where m is the mass of the floatstone, and c is some constant. We can adjust the equation and any constants as we like to get the desired behaviour in terms of the relative speed of different floatstone-powered objects.

Manxome wrote:If you want to talk about mechanics more in terms of actual gameplay than theoretical models, fine, but give me a proposal for rules that you actually want to enforce, not that you want to put in as pure fluff.

The game rules I'd want would be something like stats for a variety of islands, ships, and surfboards, such as:

Catamaran
Maximum cruising speed: ? mph.
Manoeuvrability: Medium
Attains 90% of cruising speed in ? minutes.
Falling damage caused:

Isle of Man
Maximum cruising speed: ? mph.
Manoeuvrability:
Attains 90% of cruising speed in ? days.
Falling damage caused:

If someone creates a custom craft, the DM would come up with stats for it based on an understanding of the underlying model, and/or comparisons to crafts that have stats. However, I think it will be much easier to come up with a model that makes sense, and use that to generate stats, rather than to come up with stats, and try to fit a model to that.

MartinHarper wrote:To float a person you use one floatstone. To float a ship you use many floatstones. To float an island you use thousands of floatstones.

I actually want floatstones to be decomposable, so that if you've got a hundred cubic meters of floatstone, you don't care whether that's "one floatstone" or "many little floatstones," because the stuff you can accomplish with it is the same either way. If the rules do care, then you get into arguments over exactly how much damage or repair you have to do to a floatstone before it changes the number of floatstones present.

MartinHarper wrote:M/A is proportional to the length of the object being moved, so we end up by saying that v² is proportional to the length of the object. Therefore, floating islands have a maximum cruising speed that is larger than that for skyships, and skyships have a maximum cruising speed that is larger than that for skysurfers.

It's only proportional to the length if you hold the shape and density of the object constant.


But all of this only holds when you assume that F = gM, which is only going to be true for vehicles composed almost entirely of solid floatstone driven by a group of skymages with unlimited power. If the limiting factor is the number of skymages you have to pull the thing, then force is better approximated as a constant based on the number (and perhaps personal power) of the skymage(s) involved.

So without gravity:

v² = F/(uA)

Which means that your maximum speed is basically just a function of your orthogonal area (broader ships are slower, slim ships are faster). And the time it takes you to reach that speed basically just depends on your mass, so lighter ships are more maneuverable and heavy ships take a long time to speed up or slow down.

With gravity, you have to devote a larger percentage of your total force to staying aloft the heavier the ship is, so the maximum horizontal speed is also lower for heavier ships, everything else being constant. You could presumably get some of that force back by attaching wings to generate lift when you're moving at high speed, but that's another layer of complication.

MartinHarper wrote:My scheme

...

Maximum cruising speed is typically given by the maximum speed you can move the focal point

What's the basis for this?

Obviously, the maximum speed at which you can move the focal point gives an upper bound to your average speed over a long flight, but it's not at all obvious to me that it will be possible to reach that upper bound all the time (or even "typically"), and this says nothing at all about the speeds you can achieve over short stretches.

In fact, if you keep the rule about the rubber band snapping, then your ships are also subject to the maximum speed you calculated for mine (v² = (g/u)*M/A), if that happens to be lower--because any average speed faster than that would cause the ship to crash. So at best, your "cruising speed" isn't v = c/m, it's v = min(c/m, sqrt(Mg/Au)).

You also haven't discussed maneuverability or how long it takes to achieve "cruising speed."

I've thought of another couple of game stats I'd want for flying vehicles/islands/surfboards: minimum number of skymages required to keep aloft, and minimum number of skymages required to move.

Manxome wrote:It's only proportional to the length if you hold the shape and density of the object constant.

True. I'm not expecting those to vary significantly, in comparison to the vastly increased length of an island relative to a surfboard, but that's a fair point. Different skyships, for example, will have different cruising speeds based on their aerodynamic properties.

Manxome wrote:All of this only holds when you assume that F = gM, which is only going to be true for vehicles composed almost entirely of solid floatstone driven by a group of skymages with unlimited power.

Horizontally, F=gM is true if you have a ~41% excess of skymages, compared to the number you need to keep the thing from sinking due to gravity. Alternatively, F=gM/2 is true if you have a ~11% excess. I don't think you'd want to go with a smaller excess than that.

Manxome wrote:If you keep the rule about the rubber band snapping, then your ships are also subject to the maximum speed you calculated for mine.

Yes. My instinct is that, with good choices of the relevant constants and equations, skyships and islands will be limited by how fast the focal point can be moved, whereas surfboards will be changing focal points as a minor action, and will be limited by air resistance in the same way as your scheme.

Manxome wrote:You also haven't discussed maneuverability or how long it takes to achieve "cruising speed."

Yes. This needs to be done for whatever underlying model is used. I ran out of time last night.

Also, I'm not sure about damping any more. You raise good points, and I like the idea of needing to get your "island legs".

The speed of any float stone is ultimately capped by friction. However, the important point is not the friction of the air, but the friction of the spring. We know that the spring has to have friction, and a fair amount of it because you can move these things without crashing them.

A frictionless spring would, upon being pulled taught once (from its original point A), generate precisely enough force to bring the stone to the middle, then carry itself over to be pulled taught in the opposite direction (call this point B). At this point it would become a harmonic oscillator passing between points A and B with a regular period based on the tightness of the spring. If, however, the focal point was reset to be again taught in the same direction (as would always be done whilst moving the stone towards a goal), the stone would have enough force behind it to catapult it past the new midpoint and indeed past the edge of Point B - snapping the band.

Since this is not desirable, the band is very definitely going to have to provide enough friction such that by the time the stone gets to the mid point it has substantially less kinetic energy than it got potential energy from the initial repositionment of the focal point. Which means, that the friction of the band is so severe as to be quite noticeable even over a single pass of the stone from outlying point to focal point.

This is good, because it means that the limiting factor on stone movement speed is magically derived and essentially arbitrary. Which means that game balance and world building criteria can take precedence over "realism" in this instance. The maximum speed of a float stone is simply whatever the world being written can handle, and the frictional coefficient of the spring can be derived.

-Username17

FrankTrollman wrote:The speed of any float stone is ultimately capped by friction. However, the important point is not the friction of the air, but the friction of the spring. We know that the spring has to have friction, and a fair amount of it because you can move these things without crashing them.

When a skyship is at cruising speed, both the ship and the spring will be continuously moving at the same speed, so their relative speed is zero. I would think that means that there will be no spring friction force in this configuraton?

MartinHarper wrote:
When a skyship is at cruising speed, both the ship and the spring will be continuously moving at the same speed, so their relative speed is zero. I would think that means that there will be no spring friction force in this configuraton?

That's... an excellent question.

I think I'm at the end of my physics rope, so to speak. I can see how in an ideal situation that could be true. But on the other hand, I can't help thinking that the "no free lunches" paradigm of thermodynamics would bone you.

Certainly in a "piston" situation where the focal point is kicked out in discrete shoves, the distance between the focal point and the stone's CoM would constantly be changing and generating spring friction. But I can't help feeling that spring friction would be generated simply by the interaction of the stone moving after the focal point.

Hmmmm.

-Username17

If the distance between the stone and the focal point remains constant, then the damping force (spring friction) will be equal to the spring force and create no net force, which is why their relative distance is unchanging.

I'm not sure how the sky mage is moving the focal point though, whether it's by exerting a magnified force or pure displacement at a finite speed.

MartinHarper wrote:

FrankTrollman wrote:The speed of any float stone is ultimately capped by friction. However, the important point is not the friction of the air, but the friction of the spring. We know that the spring has to have friction, and a fair amount of it because you can move these things without crashing them.

When a skyship is at cruising speed, both the ship and the spring will be continuously moving at the same speed, so their relative speed is zero. I would think that means that there will be no spring friction force in this configuraton?

In this scenario, the internal friction of the spring would be nonzero and upper-bounded by the coefficient of friction for the spring's material multiplied by the normal force (in this case, gravity acting on the ship). To get the breaking point you'd need to invent some other silly constants and solve a differential equation or three.

There's also the Gordian "This rubber band has hardness 5 and 10 hit points" solution.

You just had to bring in elastic functions, didn't you?

FrankTrollman wrote: Deserts aren't immobile. If you press on them, you don't lose all your momentum. There is nothing in the universe that is an immovable object.

Yeah, from an abstract infinite force point of view, maybe. But from a possibility point of view, the earth is an immovable object. No one person or vehicle or what not is going to push it at all. Further trying to move contents or even islands is effectively impossible unless you want to do it bite sized chunks. You're just not going to get a bulldozer or ship big enough to push Crete.

There's nothing gained by putting giant infinity and zero signs next to things, and there is something lost. Immobile objects is just half of a perpetual motion machine. There's no advantage to having them in the setting. Especially not when perfectly adequate physics can be written up to get the thing you actually want (floating islands you can stand on).

The thing I like about immovable objects is that it stops you from having to worry about a bunch of crap that comes from trying to use real physics. PCs just say "Ok there are floating islands." where as with physics you get PCs to want to try all kinds of crap with putting floatstones in thier armor, trying to secure floatstones in existing structures to try to cause damage, and all that other stuff.

I mean one of the problem with having physics is that you're going to have people try to abuse whatever laws you set in motion. Immovable objects aren't very abuseable actually, and that's pretty nice.

I've always believed that when you put in a feature like floating islands just because "it's cool", you should try to worry about physics only minimally, because the more physics you put in, the greater chance it will be abused, especially when you have spells that effectively bend the laws of phyiscs one way or another.

RC wrote:The thing I like about immovable objects is that it stops you from having to worry about a bunch of crap that comes from trying to use real physics.

Holy shit, you're right. We could also simplify things by making all quest-important NPCs invulnerable and make the cursors urn red when they move over enemies.

-Username17