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Flying gliders can have glide ratios (ratio of horizontal distance vs vertical distance) around 50 or 60. How would that change when the fluid density changes, in particular under water. Could a craft designed for under water gliding achieve a similar glide ratio, or does the increased drag reduce it? Would the reduction be linear to density?

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    $\begingroup$ Wouldn't the situation be radically different. A glider is in the category of heavier than air flight and must proceed at greater than stall speed. A submarine can have neutral buoyancy and therefore has no stall speed. For that reason it could glide at the most gentle downward trajectory very very slowly for a long long time. $\endgroup$
    – Transistor
    May 10 at 20:10
  • $\begingroup$ @Transistor I would assume OP is referring to no ballast or "equivalent" ballast to an airplane and just hydrofoiling. $\endgroup$
    – DKNguyen
    May 10 at 20:11
  • $\begingroup$ Do submarines need wings to provide lift? how do the sizes of the "wings" compare? How do the functions of a wing on a glider and on a sub compare? $\endgroup$
    – Solar Mike
    May 11 at 5:52
  • $\begingroup$ And gliders can do more than 50 or 60 for a glide ratio using thermals - copied from birds: nature figured that out... $\endgroup$
    – Solar Mike
    May 11 at 5:54
  • $\begingroup$ Consider the "glide ratio" of a hot-air balloon when it is just below neutral buoyancy. That's really all you are asking about. $\endgroup$ May 11 at 12:15

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If all things were somehow magically equal, density does not affect things because although density increases drag it also increases lift by the same proportion. So the glide ratio doesn't change.

But not all things are equal and what density does influence is the Reynolds number and this changes the glide ratio. The Reynolds number is the ratio of inertial forces in the fluid to viscous forces. Higher Reynolds number indicates the fluid behaves with more inertia and less viscosity (like water) and lower Reynolds numbers indicate the fluid behaves with more viscosity and less inertia (like honey).

The Reynolds number also depends on speed. Increasing fluid density has the same effect as moving faster where both increase the Reynolds number. Increasing speed or density helps inertia overpower viscosity.

Another effect that influences Reynolds number is "size" or more specifically the path length along which the fluid is guided and flows across the surface of the object. This is the chord for airfoils.

In fact, water is so dense compared air such that a submarine experienced a higher Reynolds number than an airplane even though it is traveling much more slowly through it's fluid medium.

Similarly, as aircraft and flying animals get smaller, this also reduces the Reynolds number since the chord length of their airfoils decreases and their smaller size tends to translate to slower flight speeds.

For an airplane to experience the same Reynolds number as a submarine it would have to fly impractically slow (almost a standstill) or be impractically small (microbe size). For a submarine to experience the same Reynolds number as an airplane it would need to move impractically fast (torn apart by the drag and friction from travelling at hypersonic speeds or faster through the water while also vapourizing it) or be ENORMOUS (I suspect it would not fit into the ocean).

That's why there are hummingbirds are all small, or birds that glide like albatrosses or soar on thermals like vultures are all huge.

Insects, in particular, experience a Reynolds number in air so low that they are swimming through the air more than they are flying through it. It means they can't glide but the benefit is that hovering is easier.

So for your actual question:

If we're talking about glide ratios, the glide ratio of a submarine I would expect it to be higher than that of an airplane...if submarines were actually built with wings to produce lift capable of supporting its own weight.

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  • $\begingroup$ Edited because I had opposite mixing things up. $\endgroup$
    – DKNguyen
    May 10 at 22:17
  • $\begingroup$ There's also the ratio of aircraft density to air vs. ratio of submarine density to water. As I mentioned in the comment to the question, a submarine is more like a blimp or balloon in this respect. $\endgroup$ May 11 at 12:18
  • $\begingroup$ Not how it's done. Take any air glider. Now take a second one ballasted so that it weighs the same in water as the air glider does in air. Now all the driving forces are balanced and the geometry is the same. Both are released and develop a constant sink rate. What is the Reynolds number difference? What makes the glide ratio different given that the induced drag can be parameterized in terms of lift? The only thing that changes is the vehicle's friction drag. This is usually analyzed as the coefficient of drag at the zero lift condition. So which has a higher coefficient of friction? $\endgroup$
    – Phil Sweet
    May 11 at 22:42
  • $\begingroup$ See here - en.wikipedia.org/wiki/Lift-to-drag_ratio $\endgroup$
    – Phil Sweet
    May 11 at 22:42
  • $\begingroup$ @PhilSweet I was answering with the (admittingly unsaid) notion that the speeds of the two test cases match the speeds of their normal counterparts. TBH, I did not intend to say that it only depends on the Reynolds number. It depends even on speed and density of the medium and the craft. $\endgroup$
    – DKNguyen
    May 11 at 22:56

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