I was reading this PDF on the speed of sailing ships, and it occured to me that I need to determine the physics of the flying sailing ships in my world. Being flying sailing ships, there will be no water involved.

In my universe, there are two things that allow a sailing ship to fly:

  1. Ether: This is a fluid that occurs throughout the universe, that moves relative to large objects such as stars and planets, so that near such objects, the ether has zero relative movement. Most matter does not interact with the Ether, but some matter does.

  2. Etheric Keels: These are material objects that interact with Ether. They are able to move through the ether in one direction, 'along the grain' relatively easily, while if they are moved through the ether 'across the grain', the resistance is much higher, proportional to the volume of the etheric keel. Think of a chunk of Etheric Keel as being like a collection of parallel pipes, and the ether like a body of water. Regardless of density, etheric keels neither float nor sink in the Ether, there is no buoyancy effect between Ether and Keel.

There are other factors that would affect the speed of a flying sailing ship, such as gravity, air density, the pulling power of the sails and the drag imposed by the friction of air against the ship's hull and rigging, but while these are important, for purposes of this question, please consider them to be constants.

I envisioned a ship having multiple keels in controllable gimbals so that they can be angled to control the ship's lift, attitude and direction of movement, and if necessary, increase drag. Keel material could also be used as a 'screw' or 'propeller'.

I want to derive a formula that I can use to calculate the speed of a flying sailing ship given factors such as the drag of the hull and rigging, the properties of the sails, the density of the air, the vector of the wind and the desired direction of travel. These are all things that are well known.

However, I also need to know what the relevant properties of the keels and ether will be. I don't need values for these properties, I just need to know what they are and how each will affect the construction and performance of a flying sailing ship, and if these properties will affect the ideal shape of a keel, or if I just need 'chunks' of keel material.

The best answer will include as many relevant properties as necessary for both ether and keel, and as few irrelevant properties as possible, with ether and keel each being assigned the most logically relevant properties, with descriptions of how they will affect the performance of a ship.

I don't necessarily need the entire formula, nor do I need the values, just the relevant properties, with SI units.

EDIT: Just to make it perfectly clear and clarify an earlier paragraph, I anticipate flying sailing ships having multiple keels, probably at least two fore and two aft, to control pitch, yaw and roll, as well as to provide lift and to counter side-slip.

Ships will also most likely have masts in multiples of two, three or four, arranged symmetrically around the hull in order to provide balanced thrust.

EDIT 2: Again, to make it perfectly clear, these ships are heavier than air. They carry no lifting gas. They are intended to use the force of the wind in their sails to generate forward motion, and an appropriate angle of attack on their keels to generate lift and maintain a course not directly downwind by pushing against the ether.

  • $\begingroup$ Why not the same as water? I don't see a need to change shapes etc of the keel $\endgroup$
    – Kilisi
    Sep 4, 2023 at 9:14
  • $\begingroup$ @Kilisi Because the etheric keels work by volume, while hydrofoils or aerofoils work by surface area. Regardless, I still need to know what properties are going to be relevant to the keels and ether to calculate speed of ships. $\endgroup$
    – Monty Wild
    Sep 4, 2023 at 11:25
  • $\begingroup$ How turbulent the flow of ether is? Is it like a steady river, changing slowly or almost not at all, or more often, or is it even turbulent like eg. rapids (due to the planets and asteroids)? I suppose that will affect many aspects of the designs. $\endgroup$ Sep 4, 2023 at 23:44
  • $\begingroup$ @JaniMiettinen It's effectively still, until you get well away from a planet's atmosphere, and then it would seem to be moving somewhat with the nearest large body, but lagging a bit. $\endgroup$
    – Monty Wild
    Sep 5, 2023 at 0:12
  • $\begingroup$ Somehow I envisioned that those devices could allow space flight, too, as long as other important factors were covered (and why not). That frontier would probably be target for explorers if it was possible to get there. However, sailing in turbulent flow and linear flow might require different designs...but did my imagination go too far? $\endgroup$ Sep 5, 2023 at 0:29

2 Answers 2


The formula for speed would likely match the one used in normal sails

See, you have here two forces that make your flying sailship move: the force of wind hitting the sails (and body, as it would encompaass the whole ship), and the force of etheric keel resisting its motion against the ether. On the water, you have essentially the same forces. And regarding your keels' shape, your best shape would then be the orb, and its location as close to the ship's mass center as possible. The orb is best because it has most compact external dimensions for a given internal volume, and since your keels work by volume, you want to maximize this instead. Therefore your ships would probably resemble flying saucers, with masts and rigging above the main deck set, and the keel somewhere in between. Or maybe like wide but short ships of the sea, as you don't need excess length to contain the keel as it works by volume, while having your ship be wider would allow more cargo and stuff, as well as more rigging for movement power.

Regarding the quantity of keels, you would probably go well with a single keel located dead center, or somewhere between the mass center and the rigging center to have less angular momentum to be compensated by its gimbals. The sailing ship has riggings above the keel for the reason of catching more wind, as well as for stronger winds, as the speed of wind does somewhat increase when rising from sea surface. In your case the wind is all around the ship, but you would still need the bottom defined as your ships would have to land, and landing on rigging would crumple it beyond repair.

The gravity would require some other approach

You have the keel to also do gravity compensation, that is, preventing downward movement by applying increased resistance, so the ship in mid-air would hang over the keel, relying on it as the buoyancy center. You will still have to apply some upward force in order for these ships to lift off, maybe by inclining the keel "nose upwards" and unfolding the sails, so the ship would climb upwards on the ether like a kid being dragged uphill on a sled. But, this ability would require exact value of resistance difference for keel between "along the grain" and "across the grain" in times, say 1000 - sliding the keel along the grain requires 1000 times less force than across. If the value would end up too low, your ships would never take off the ground, as they would founder too easily.

With the ship's keel aligned orthogonal to gravity force vector, it would act as a stopping force for a falling object, making your ships to have a free fall terminal velocity calculatable by existing formula, but using the keel's volume multiplied by ether resistance as extra addition to drag component. Your ships should likely not exceed 1 m/s of terminal velocity in design regarding liftoff weight vs keel resistance. Should the keel be turned nose to zenith, the resistance would be effectively gone and the ship would fall off the sky as a normal wooden device. If the rigging is up, the sails would compensate this motion by using air resistance to turn the ship "masts up", yet they are expected to be more fragile than the hull, thus only a small libration is permissible for a ship mid-flight.

Ship's construction

Regarding ship control, you would have some problems with rigging vs hull balance, because if the wind resistance force center would also become below the center of the keel, the ship's equilibrium will become unstable and the slightest wind change would topple the ship. This never happens at sea regarding wind, yet there are known configurations regarding water and buoyancy that display such instability in water, which topple if allowed to rock sideways. Regarding gravity control, it's possible that having two keels spaced in "forward" direction and aligned like this \/ in vertical plane with a small angle between their axes would benefit towards static control of rocking the ship by stray winds and mass rebalance, so that the ship won't nosedive if a sudden gust of wind would cause a temporary balance shift forwards or backwards. (This configuration would also prevent the ship go all the way down if it would actually nosedive, as long as the keels' support is intact, with great forces applied between them to the ship's hull as it would start turning masts up.) But if the angle would be too big, the increased wind resistance (as it would be proportionate to sine function of that angle) would slow the ship to inability to lift up, so this angle should be constantly controlled, and a means to increase it rapidly towards stable formation should be implemented as a safety measure.


In order to steer the ship, you can use those two keels to also cause an angle between their axes in horizontal plane, causing ether resistance force to apply angular momentum to the hull turning it sideways, this will however also cause the ship to roll outside the turn due to keel configuration causing gravity resistance disbalance to the ship side wise, yet this is compensated by the same force as the mass center being below the keels would have been shifted inwards, applying reverse roll momentum. Also the roll would meet increased resistance from the keels, as when you rotate the keel around its "along" axis, the entire keel is moving "across", experiencing ether drag. Additionally, a steering "keel" might be implemented at the outermost point on the ship, like the tail on a dual-rotor toy helicopter, providing yaw/pitch momentum to the entire ship by its rotation.

Weight handling

There are several problems with those keels in mid-air regarding ship's structure, the primary is that the keels will be THE thing that would support the entire ship hanging in midair by its interaction with ether. This part is not too relevant to speed calculation, because it only covers limits on how the keels should be attached to the hull, but since the process of rotating the entire hull would cause resistance from the keel material, as a part of it would be moving "across the grain" while turning relative to ether, the best form to minimize that force would be a thin disk/plate with the "along" axis oriented along the smallest dimension, this arises some issues on durability, proper gimballing of keel pieces and overall weight handling.

As an example, a piece of keel that weighs 1 kg and is shaped into a cube with its axis along one of the edges, that is able to carry 1 ton of weight against gravity and founder at 1 m/s would have its ether drag parameter "across the grain" at 10000 N/(kg*m/s), and the attempt to turn its axis in a plane parallel to its side would cause ether drag force of 250 N/(rad/s). Making the keel thinner while retaining the mass and density would lower the required force proportionate to resultant thickness (say 2.5x20x20 cm brick would turn four times easier). This actually prevents using long keels on those airships, as the forces required to turn them mid-flight fast enough would exceed rigging durability. These same forces put a limit on the proposed "ether screw" as the keel pieces there would constantly experience drag, even if the whole engine is already moving at desired speed.


For efective operation of etheric keel-driven ships, you need to devise TWO factors for keels, one measureless, meaning how much harder it is to move the keel-material "across the grain" vs "along the grain", the other meaning how hard is it to move the keel-matter against ether, in N/(kg*m/s), either "along the grain" or "across the grain", and either as a constant or as a function of speed - this parameter also describes how does the keel-matter allow ships to stay afloat, and several factors regarding keel control mid-flight and when ascending. Descent is always done really easily, as you don't have any active means of ascent or air-floating. Rigging and hull might be the same as in water-based sailing ships, with additional control over wind resistance to avoid toppling, and over keel configuration to allow actual movement in mid-air, except for the fact that the entire ship would have to be hanging on the keels.

PS: if you'd ever desire an ether-based engine, you can have a track made of keel-material, working as the one on tanks, the lower part of the track should be aligned downwards, and the upper part should be aligned forwards. Then, as the track would start moving, the parts that face downwards would apply their ether resistance force to the construction driving it forward, while the upper part would provide almost zero interference, thus this device would propel the ship forward without interaction with the ground. So if you have a power plant on the ship, using this device would let you travel into space, provided you can climb with it faster than you would founder due to your main keels no longer preventing the gravity's entire power to pull you down. More, with this track its actual propelling power depends on its length, and losses due to required rotation of keels are constant per construction, thus it looks like a promising configuration to advance beyond the atmosphere.

  • $\begingroup$ The trouble with a single dimensionless number as the factor that describes with-grain vs cross-grain movement of a keel through ether is that it doesn't account for keel size, and doesn't say what the resistance is going to be in any direction. $\endgroup$
    – Monty Wild
    Sep 5, 2023 at 13:58
  • $\begingroup$ As for your postscript, a wheel with angled blocks of keel around the edge would work just as well, like a propeller. $\endgroup$
    – Monty Wild
    Sep 5, 2023 at 13:59
  • $\begingroup$ Re one factor, I've revised this and added the second factor, that's essentially ether drag coefficient for mass and speed (should read "N/(kg*m/s)" instead), meaning what force is applied against the movement direction to 1 kg of keel moving at 1 m/s relative to ether (either along or across the grain, or both, or use these as functions like for air drag, ignoring shape aspect as it's irrelevant for keel vs ether). Defining this, you will also find how large a force should be applied to rotate the keel, how large a mass can the keel hold without foundering too fast, etc. $\endgroup$
    – Vesper
    Sep 6, 2023 at 6:52
  • $\begingroup$ @MontyWild and re angled wheel, the problem is that it involves constant rotation of keel in the ether around itself, losing a lot of energy. The track rotates the keel twice per revolution, meaning it loses less energy for keel displacement. But yes, the wheel would act as a propeller for water, with the exception of ether essentially filling it instead of moving around it. $\endgroup$
    – Vesper
    Sep 6, 2023 at 6:54
  • $\begingroup$ I actually wonder the following: What woud happen with your keels if you arrange three equal pieces of keel into a Czech hedgehog, aligning its axes into a 3D orthogonal basis, so that moving the constuction anywhere would cause ether resistance to the entire device? It should founder very slowly as gravity is still being applied to the structure, but the "how slowly" would be determined by the ether drag parameter for low speeds and "across the grain". Actually such thing could be used to measure time, add weight to calibrate so that it would descend in exactly a day, and there, a clock. $\endgroup$
    – Vesper
    Sep 6, 2023 at 6:57

No righting moment, no sailing.

Water has buoyancy as well as a different density, a universal ether as you’ve defined it does not. Because “nothing floats in ether,” there is no righting moment provided by it; therefore, torque will do what torque does and just spin, flip, and twirl your ship around. Righting moment keeps a ship upright by countering the gravitational force with the buoyant force. Ballast controls the gravitational force, hull shape controls the buoyant force. Together they automatically correct the torques applied by other forces. More details below.

You don’t understand how sail power works. Wind force applied to a sail above the ship is not applying a force to the ship, it is trying to capsize the ship: it applies a torque. The force that converts the torque of the sails into a directional force is called the righting moment, that is derived from the hull design which changes the “center of buoyancy” of the ship as it rolls and pitches. Buoyancy counters the wind force torque to create a linear vector. If your ether is a homogenous universal fluid, it won't turn a ship like a keel would, it will simply apply a lateral torque when an external keel is acted on. The buoyancy of a sailing ship provides another vector to correct the direction of a vessel without rolling it over. A great deal of effort goes into properly loading a ship to maintain the center of buoyancy above the center of gravity because as soon as the center of gravity is above the center of buoyancy, the ship cannot right itself agains wind or drift moments. You have eliminated the buoyant force completely in this second fluid, and so your controls are left entirely in ballasting. It’s essentially just a beach ball in the ether. Nothing is “righting” the torques applied by the ether on the keels except ballast, and that has no direction in ether - no “pointy end of the boat.”

The keel must act in the center of aerial sail area.

The “center” changes every time the wind vector changes. There is no single “center” to any shape except a sphere.

The keel is providing the "centerboard force" of a sailboat, and your airships. Since you state there is no buoyancy force, the keel must apply its force vector to the point in the center of its sail area in the other fluid - air. You literally can not “mask” a sail from the air by wrapping it in a bigger sail (placing it inside the hull). The hull just becomes the proxy surface for your etheric surfaces.

Ballasting will have a limited effectiveness

You can offset the rotational torque from the keel somewhat by ballasting the vessel as a balloon does, which it will have in a limited degree already. However a balanced airship which also wants maneuverability is really hard to have a low center of buoyancy in the air, so the tendency to roll is much more pronounced as compared to a floating sail ship who's mass below the waterline is vastly lighter than the displaced fluid, or to a balloon which doesn’t need to maneuver.

The keel isn't providing hydrostatic resistance against yaw (there is no drag force)

Basically you can't tack in a vessel with only the keel in the second fluid. If you place the keel forward of the center of mass, a lateral vector on the keel will yaw the ship to follow the ether current. If the keel is aft of your center of mass, the lateral force will yaw the ship into the ether until the keel presents the smallest resistance to the ether flow. A sailing ship's hull running full length provides the hydrostatic resistance to follow a given tack.

A single small plane in the ether serving the centerboard force won't allow maneuvering

To avoid being driven by the wind force and apparent wind, You will need additional control surfaces exposed to the ether, and deal with centering your ether-driven forces directly against aerodynamic forces associated with the sail area of the ship. You will need something providing the rudder force in the ether as well, and this also has to be balanced against aerodynamic forces that are normally offset by buoyancy in sailboats. Note the rudder of a blimp is center mass. All of your ether control surfaces have this restriction.

A keel and rudder which resist both air and ether would be arbitrary

The variety of circumstances you could experience when a control surface is acting in two fluids with competing force vectors is infinite. There would be some situations giving you fair sailing, and others making you a slave to whatever the tides bring you.

  • $\begingroup$ "I envisioned a ship having multiple keels in controllable gimbals so that they can be angled to control the ship's lift, attitude and direction of movement" Probably two fore and two aft, to control pitch, yaw and roll, as well as to provide lift and counter side-slip. $\endgroup$
    – Monty Wild
    Sep 5, 2023 at 0:09
  • $\begingroup$ This doesn't answer the question. I asked for the properties of the ether and keels that I would need to know in order to calculate speed, and this reads as a critique of the design that I have already considered. $\endgroup$
    – Monty Wild
    Sep 5, 2023 at 0:17
  • 1
    $\begingroup$ You’ve already defined the properties constraining the answer: “a fluid that occurs throughout the universe, that moves relative to large objects such as stars and planets, so that near such objects, the ether has zero relative movement.” Thus you have no fluid boundary. Your keels are matter, therefore they interact with air. If they interact with the second fluid as well, there can be no control. Both fluids act on your keels (as many as you like) pushing them in the vector sum of the forces. Sailboats work by allowing control surfaces to exist in only one fluid at a time. You can’t do that. $\endgroup$
    – Vogon Poet
    Sep 5, 2023 at 2:24
  • $\begingroup$ Yes, keels would interact with both fluids, however, if the amount of interaction differs, that is sufficient. Consider the vertical rudder of a ship (say a hydrofoil): where it emerges from the water, it also interacts with the air, but much less than it interacts with water. You're not saying that such a ship couldn't steer, are you? $\endgroup$
    – Monty Wild
    Sep 5, 2023 at 2:30
  • $\begingroup$ Etheric material as screws and propellers works but you’ve left the world of sailing at that point. As a separate question, the qualities of ether should be denser than air when used for propulsion like this. $\endgroup$
    – Vogon Poet
    Sep 5, 2023 at 2:31

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