Drag in water compared with drag in air
What changes when the fluid is eight hundred times denser.
Drag in water works by exactly the same mechanism as drag in air, an object shouldering fluid out of its path and leaving disturbed fluid swirling behind it, but water is roughly eight hundred times denser than air, so the very same shape moving at the very same speed meets a resistance hundreds of times larger, and that single multiplier reshapes almost every decision made about how an underwater vehicle's outer surfaces are drawn.
The previous article dealt with the extra load an object feels the instant it speeds up or slows down underwater, a load that vanishes once it settles into steady travel. Drag is the load that remains after that settling, the resistance a hull feels simply for continuing to move at a constant speed, and it is governed by a different multiplier altogether.
Density, area and the square of speed
An object moving through any fluid has to push the fluid ahead of it out of the way and let fluid close back in behind it, and doing that work continuously is what the object feels as drag. How much work that takes depends on three things multiplied together: how dense the fluid is, how large an area the object presents to the oncoming flow, and the square of how fast it is travelling, all times a shape-dependent constant describing how cleanly the object lets the fluid pass (in symbols, drag is proportional to ρAv²C). Because density sits as a plain multiplier, swapping air for water multiplies the drag of an identical shape at an identical speed by hundreds.
The shape constant is where a designer has real influence, since neither the fluid's density nor the frontal area can be argued with once the job has decided how much the vehicle must carry. A rounded, gradually tapering body that lets the fluid close back in gently leaves a narrow wake; a blunt one leaves a wide, churning wake behind it, and the outer lines of a hull are the one part of the relationship still open to change.
Jogging through waist-deep water
Anyone who has tried to jog through waist-deep water in a swimming pool has felt the difference directly. The same legs, driven with the same effort that would carry a jogger briskly along the poolside, manage only a slow, exhausting wade once submerged, tiring within a couple of lengths in a way the same distance on dry concrete never would. The muscles and the effort are unchanged; the fluid doing the resisting is what changed, and pushing water aside on every stride costs vastly more work than pushing aside the same volume of air.
Speed as the cheapest lever
The eight-hundredfold density gap sounds as though it should demand eight hundred times the power, but the speed-squared term works strongly the other way. Halving speed cuts drag to a quarter, and since the square root of eight hundred is about twenty-eight, a hull moving through water at one twenty-eighth of some speed in air meets the same drag it would have met in air at that speed. An underwater vehicle rarely tries to match an aircraft's pace for exactly this reason, because speed is by far the cheapest lever available for reducing drag, cheaper than any amount of shaping.
Power makes the lesson sharper still. Power is drag times speed, so it rises with the cube of speed, and a vehicle that doubles its cruising speed needs eight times the power to hold it. Once battery capacity, rather than motor size, limits how long a mission can run, the steady cost of simply continuing to move dominates the energy budget, and designers will chase a fraction of a knot of extra cruising speed per unit of stored energy because it translates directly into how far a fixed battery can carry the vehicle before it has to surface and be recovered.
The same arithmetic explains why a submerged vehicle's surfaces receive more care than a similarly sized aerial vehicle's usually do. A protruding bracket, an exposed cable, or a poorly faired joint costs far more drag underwater than the identical feature in air, and a power budget that pays for that drag at every moment of a mission has little room for features that were never streamlined.
Viscosity and the Reynolds number
Treating water as air multiplied by a single density factor is a useful first approximation, but it understates how much the character of the flow can change between the two fluids. Drag also depends on the Reynolds number, a figure that folds a flow's speed, the object's size, and the fluid's own resistance to flowing into one value that predicts whether the flow stays smooth or tips into turbulence. Water is thicker than air, but by a much smaller factor than it is denser, and once the two properties are combined, water's Reynolds number comes out roughly fifteen times higher than air's for the same size and speed. A submerged hull therefore sits at a different point on the smooth-to-turbulent scale than the same shape in air at a comparable speed, which is why a hull drawn purely from aerodynamic intuition, however cleanly it slips through wind, is not automatically the shape that slips most cleanly through water.