This is a must read site (bikethink.com). The author tells us that in general frame flex is returned to the drivetrain to do useful work when the springiness of the frame flexes back. Whatever force is lost would be minimal and returned as heat I imagine. That said than I still feel, as does the author, that a stiff frame brings benefits in terms of confidence in a sprint, or responsiveness or the feeling of a direct transmission of energy. Other benefits of a stiff frame can be observed in handling. In the Miata (car), designers maximized this direct feel when they added a Power Plant Spine, which is a solid piece of metal to which the engine is bolted, as is the transmission and the rear end differential. The result is experienced as a direct transmission of energy from the engine to the rear end. None of the engineers suggested that the Power Plant frame is more efficient, only that it improves the feeling of response and eliminates some squishiness that upsets handling. Of course the horsepower of the human is so small that any losses are undesirable but at least this one analysis puts the loss at the level of negligible.
A second more important loss of human energy can be postulated when we actually ride one of these super stiff bikes that now populate the scene. I have ridden them (aluminum frames with Oversized tubing), and I feel that the transmission of energy is more direct, but that the ride is so jarring that I loose momentum because my concentration is blown as I fight in vain to maintain souplesse or smoothness. Here again the human machine is so horsepower limited that even a small psychological effect can loose us precious feet per minute (maybe 83 rpm in a given gear instead of 85 for example). Once that small gap is created by a lead rider, the trailing rider can loose draft and heart, and the cascading effects can put you well behind the pack where all is soon lost. My conclusion is that whatever microscopic energy that is lost with frame flex and a few extra pounds of weight that comes with a classic steel frame, are more than made up with smoothness and comfort and not to mention the pleasure I gain, not having a saddle jackhammered into my perineum. Sheldon Brown's pod cast lecture mentioned that the current cost of producing an aluminum bike frame approaches $8. I can't imagine a steel lugged frame comes anywhere near that price, even if they were produced by underage, underclass children on the planet Mars. It is economics that has kept the super stiff aluminum frame at the forefront, and not anything to do with steel's physical disadvantages (IMHO).
Garth Libre in Miami Fl.