Seven men and a crank

In 1776 a one-man wooden machine called the Turtle was towed out into New York harbour and then cranked toward the British flagship HMS Eagle. Its inventor, David Bushnell, had fitted it with hand-turned screw propellers, one to drive it forward and one to move it up and down, at a time when almost nothing else in the world moved by propeller. Its operator, Sergeant Ezra Lee, reached the Eagle but couldn't fix his explosive charge to her hull. He cranked away exhausted, and the attack failed.

Eighty-eight years later the idea finally worked, and it cost everyone involved. On the night of 17 February 1864, the Confederate submarine H. L. Hunley crept out of Charleston toward the blockading sloop USS Housatonic. Seven men sat in a row along a crankshaft that turned the propeller, and an eighth steered. Hunley rammed a charge on a long spar into the Housatonic, which sank within minutes. Hunley never came home. Her wreck was found in 1995 and raised in 2000, with her crew still at their stations along the crank.

The Hunley's top speed was a few knots, about a fast walking pace. That wasn't a failure of courage. It's what a handful of people turning a crank can push through water. To understand why, you need the most important equation in underwater propulsion.

Thrust, drag, and the cube law

Thrust. A propeller or thruster makes force by throwing water backwards. Push a mass of water astern every second and the vehicle is pushed forward by the same amount. Bigger, slower propellers move more water gently and do it more efficiently. Small, fast ones churn.

Drag. Water resists motion with a force that grows with the square of speed: drag = ½ × water density × drag coefficient × frontal area × speed². The drag coefficient is the shape's score. A blunt box might be near 1, and a well-faired torpedo shape can be a tenth of that.

Power. Power is force times speed, so the power needed to push through water grows with the cube of speed. Double the speed and you need eight times the power. That's why the Hunley's crew could barely improve on walking pace, why torpedoes are long and thin, and why the AUVs of Week 1 cruise slowly. It is the same cube law you ran into in Friday's mission planner, seen from the other side.

The real bill. Not all the shaft power becomes thrust. Propellers lose some to swirl and spray, and motors lose some to heat. A good thruster turns perhaps half its electrical power into useful push. Everything you build pays for drag twice: once in the battery, and again in how far you can go before it runs out.

Put crew on the crank (about 80 watts each, sustained) or swap in an electric thruster, choose a hull shape, and see the top speed and how long it takes to reach a target four nautical miles off the harbour. Then try to double the speed.