"Dragging it in" is definetely NOT a technical term and means different things to different people at different points in their flying career. To me, at 38 years and 5000 hours, it means approaching in nearly level flight at the minimum speed for my weight where nearly full power will (maybe) keep the aircraft from stalling. NOT A GOOD ROUTINE APPROACH!
Let's review the power curve one more time: Any airplane in LEVEL flight has a wide range of speeds determined by design and engine power. From maximum speed in level flight it requires less and less power to go slower up to a point at a minimum amount of power. This is close to the max angle of climb speed and similar to the minimum sink speed in gliders. Below this speed, more and more power is required to maintain level flight up to the point where maximum power will not keep the aircraft from sinking and/or stalling.
For most aircraft, the minimum level flight airspeed (minimum power required) is slightly slower than the normal book approach speed, indicating that the approach speed is just above the point where the power required curve goes back up again, and thus is on the "front" side of the curve. Pull back on the stick without changing the power and you will go up or at least down more slowly. Plenty of speed and elevator authority to flare and deal with mild sink on final. Life is good and small errors in airspeed or power are not a problem.
As you get below that speed, MORE power will be required to fly level at a slower airspeed, and due to the nature of the curve the required power increases nearly exponentially to the airspeed loss. If you have ever seen this graphed, it looks like a J tilted over onto it's right side.
So, operations on the backside of the curve start reasonably safely at a speed just below that of the published short field approach speed and progresses rapidly into a highly dangerous flight regime where a very experienced pilot must know his aircraft and environment perfectly to achieve minimum landing distances that are well below the book figures.
This is NOT something to try on a gusty hot afternoon! Operations like this have resulted in many bent aircraft over the years.
I think it is reasonable for a pilot to approach slightly behind the power curve as he gains experience in a specific aircraft, particularly at lighter weights. The short field approach speed, if noted, is always at gross weight, and you can safely approach at speeds several knots below it when light. The key to recognizing when you are getting real close to the edge is if you need more power to flare properly in calm conditions.
For me, I like that speed where I do not need more power to flare, but closing the throttle during or at the end of the flare results in a three point touchdown after only 50 or so feet of float. I have experimented at length with slower speeds and found that at best I could shave another 100 feet or so off the rollout, and for me the added risk was simply not worth it in all but the most critical situations. I used to take pride in planting my aircraft on the numbers all the time, but after stubbing my tires on the edge of the pavement a few times and taking out a runway light or two I decided that maybe landing in 600 feet instead of 500 was good enough.
For any lowtime pilots that want to experiment, you should be able to hold your approach speed within one (1!) knot, and you can decrease your speed one or two knots at a time, with five nearly identical landings to a full stop at each speed before progressing to a slower one. (So you want to be a test pilot, eh?) My guess is that you will quit before shaving much more than 6 knots off the book figure, and now you know how little operations far on the backside of the curve will really improve on good normal short field approaches.
Still, any pilot that want to operate out of short fields needs to understand and be comfortable with the concept and it's application in his particular aircraft at various weights.
Good Luck and try not to hit too hard!
Rocky