Half the paddle, twice the paddler.

"Half the paddle, twice the paddler" was the title of the thread on the canoeing message board that this origionally came from. I have expanded on it somewhat for clarity and to include more details.

A canoe designed with double paddles in mind, like some ultra-light pack canoes, has less rocker than one intended for use with a single paddle. Less rocker causes it to resist turning. That minimizes the side to side wiggle that occurs when using doubles. That also minimizes the amount of correction needed during a "J" stroke with a single paddle. Less effort expended in course correction means less effort overall. The result is that a less rockered or completely rockerless canoe or kayak is more efficient and easier to paddle fast, in a straight line, than a more rockered canoe or kayak. Actual top speed of a displacement type hull, like a canoe or kayak is primarily a function of hull length at the waterline. Assuming similar construction to eliminate things like surface friction from the comparison, a 17 foot canoe that is 34 inches wide at the waterline and a 17 foot kayak that is 24 inches at the waterline have virtually the same top speed. However, the wider canoe will need nearly double the effort to go the same speed.
The farther out from the centerline of the canoe you paddle, the greater the amount of turning force applied for the same amount of forward thrust. A gentle forward stroke of only 2 pounds of forward thrust, applied 2 foot out from the centerline of a canoe, results in 4 foot pounds of torque applied to the hull. 2X2=4. Using a double bladed paddle usually means you are paddling out a bit farther from the centerline. With a long enough double to be comfortable, you are paddling 8-12 inches out farther from the centerline (assume 10 for the calculation), the equation changes to about 2 X 2.9 = 5.8 lbs of torque applied to the hull. The canoe will turn nearly 50% more with each stroke of a double paddle than a single.
Energy, in the form of turbulence, is expended by each turn off course. Whether you correct that course change automatically with the next stroke of the double pushing it back or with the slight rudder at the end of a properly done "J" stroke is irrelevant. The energy was wasted and more was wasted in correcting for that waste.
When a double corrects for the waste, it is at the same distance from the center of rotation of the canoe as when it was wasted. Every bit of waste is corrected by the same amount of effort. When a single paddle corrects for waste, it is in the rearward extended portion of the stroke, farther from the center of your buttocks (for the purpose of argument, lets assume the center of your butt is the center of rotation of the canoe, like a solo canoe being paddled from near center) where it gets a mechanical advantage over the portion of the stroke that caused the waste. No it's not a form of perpetual motion, getting more for less. It's a matter of body mechanics. A few pounds of thrust applied close to the center of rotation can be countered by a few ounces of sideways thrust at the far rearward portion of the stroke.
The bottom line is that, in a straight line, a single paddle that is used properly is slightly more efficient than a double. The amount you notice is dependant on the amount of rocker and the hull length.
On turns, a low rocker design has to be leaned more to turn with the same effort of a more rockered design. A lean pushes the wider center of the canoe down into the waster and lifts the ends a bit. The primary resistance to turning is the ends of the canoe deep in the water. With the ends lifted a bit, a draw stroke forward of the center of rotation (ahead of your ass if solo and by the bow paddler if tandem) starts the canoe turning in two ways. By applying torque directly and by slowing the side on the inside of the turn. This is the simplest of the strokes use in Brownwater paddling and the style called "Paddling on the inside" taught by the canoe club I joined. This is the exact opposite of the paddle-on-the-right-to-go-left style of paddling, which causes you to speed up and run out of time to make a tight turn. The more rocker, the less effort needed to make it turn. More rocker makes it easier to turn with less leaning. What a canoe or kayak is best at is determined partly by how well it turns versus how efficient it is in a straight line. Thusly, the amount of rocker is a major factor in determining whether the canoe or kayak is best on open lakes, whitewater or the tight twisting turns of brownwater.
From a human engineering standpoint. The rest afforded by the recovery time when moving the paddle from the rear of a "J" stroke to the front to start over allows blood to flow more freely to nourish the muscles. Switching sides every ten minutes or so, uses different muscles and allows the tired ones to rest. The result is that good technique with a single paddle allows you to go farther and cover longer distances faster than with a double. Over short distances, the double has the advantage because you have less wasted time between strokes, with the disadvantage that you can use up the oxygen and sugars in you system faster than they can be replenished. You might be thinking about long crossings in a sea kayak as disproving this. However, you must compare apples to apples. A 21 foot 26 inch wide sea kayak is both fast and efficient, so much so, that the method of paddling is less import than sitting low and out of the wind.
The other major effect on what a particular canoe or kayak is good for is the hardness of the chines. That's a traditional canoeing term that doesn't make much sense to most people. It refers to the radius of the curve where the side of the canoe meets the floor as well as the number of degrees it encompasses. Math majors would recognize it as the radians of the radius. High numbers are "harder". Vertical sides and a flat floor with a tight turn in between is extremely hard chines. A gentle curve between flared sides and a shallow "V" or slightly curved floor is soft chines.
Hard chines give you primary stability. That means the canoe or kayak will sit flat on the water and resist leaning. You can still lean it to turn, but it will take more effort and when it reaches a certain point, it will flip with little or no warning. These canoes feel the most stable on flat water, but insist on leaning with the sides of waves when it gets choppy. Also, as you add more weight and the chines get deeper in the water, the tipping point gets closer to level. Overloaded hard chined canoes will flip. An example of a hard chined canoe is a standard Coleman canoe.
Soft chines give you more secondary stability. It feels tippy, yet resists leaning more and more as you lean it further and further. These canoes will ride diagonally across waves without heaving you side to side and turn easily with a minimal effort lean. A heavy load of gear will actually make this kind of canoe more stable. Overloading it will make it sink, straight down without tipping itself over. In return for the advantages of better handling, tighter turns and increased safety, you loose flat floor area for coolers and the initial tippyness makes beginners nervous. A good example is the Mad River Explorer 16. It's a favorite of summer camps for mentally disabled kids because it feels tippy, forcing them to pay attention, but in reality is much harder to tip over than a hard chined Coleman. It also gives the kids more feedback, by being responsive, so they can learn faster.
Most canoes are in between these two extremes. Softer chines gives you a hull that is useful over a wider range of loads and conditions because it’s easy to lean allowing easier turning in a less rockered hull. Because most kayaks have less rocker, to be efficient with double paddles, and harder chines, to feel more stable, kayaks tend to be more specialized than canoes.
Paddling a canoe leaned over, called "Omering" or "Canadian style" is a way a solo paddler can turn paddling an oversized freighter canoe into a shorter, more rockered, more maneuverable hull, by forcing the middle down and lifting the ends. It leaves you paddling a hull that's asymmetrical from side to side and not particularly efficient, but more manageable. This way a hunter, paddling solo, can get a nearly empty 18 foot freighter up a stream by himself and paddle it back loaded with a moose carcass. There is little practical use for this technique if you have the proper sized canoe to start with and aren’t hunting moose.
The real world bears out my assertions. The paddling time, loaded with camping gear, from Batsto Village, upstream to Lower Forge is 5.5 hours for the old, disabled, arthritic, president of my canoe club. I do it in less than 5 hours in the same kind of canoe. I have talked to other canoeists that have done it in 4.5-6 hours with differing loads and radically different canoes. All used a single paddle. Kayakers carrying camping gear don't even try it. I have met only one day tripper that has made it. Day tripping kayakers generally give up at Quaker Bridge, 1.5 hours short of Lower Forge. It takes them close to 6 hours to get there. I know it's an apples and oranges comparison. However, The kayaks that I'm basing my comparison on average 14 foot long and 26 inches wide, according to the various manufacturers catalogs and web sites. My canoe is 14 feet long and 27 inches wide and more rockered than the average kayak, giving them a slight speed advantage. If their water craft is so similar to mine, why do they take so long and or give up trying? The major difference is their double paddle versus my single blade.
In mixed groups of kayaks and canoes, paddling the narrow twisting rivers of the NJ Pine Barrens, the experienced single blade paddlers gravitate to the front. Experienced kayakers with doubles are in the middle and inexperienced canoeists with singles mixed in with them and behind them. The rear is taken up by canoes paddled with double paddles no matter what their experience level is. I think their rapid drop in speed on the turns gets them rammed in the ass till they decide to stay in the rear.
Remember, no indigenous culture whose survival depended on their choice of watercraft and paddles, chose a kayak and double over a canoe and single except where when low temperatures, high winds and waves made the deck and double necessary. The Hawaiians, facing just wind and waves, chose the open canoe and single blade for the body mechanics related advantages over the seaworthiness of a closed deck. Their round bottom is unstable, yet when combined with the weight saving deck-less design, gets them minimal wetted surface per pound of carrying capacity. The nearly rockerless hull is efficient and the stabilizing outrigger drags just enough to eliminate the need for the "J" stroke. When racing the paddlers often shift their weight just enough to lift the outrigger a few centimeters off the surface to further reduce drag and stabilize the canoe with their paddle strokes and steering with asymmetries in stroke thrust.
If you value long distance average speed, efficiency and hate sore muscles, pick a single blade over a double and learn how to use it to maximum advantage. If you want instant gratification and don't care to learn the nuances of paddling, buy a double. If you buy a double bladed paddle you should use a canoe with little rocker like a Discovery 164 or Penobscot or a kayak.