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Above is a link to an illustration of a load case of our frame with an overly soft layup for illustration. Here it is loaded 100 kg applied at the drive side pedal.
We are using Altair Hyper Works FEA, with is the leading industry analysis tool as used by MacLaren and others.
You are viewing the frame from the rear nds. The flex is magnified, again for illustration, but the impact is clear. The frame will flex in a manner that will not be contained or harvested by the drivetrain, resulting in forward propulsion. The work done flexing the carbon spring/frame is essentially lost and dissipated through heat in the engine/pilot/cyclist. If we could harvest this flex in the manner of a trampoline or bow as suggested by some we would have an instant ban by the UCI on our hands...
The other effect that is clear from the illustration is how the rear wheel will 'crab' under load. This is akin to the crabbing of an airplane and is of course resulting in a loss of efficiency.
To infuse the discussion with a measure of rocket surgery: Rockets are fired straight up for this very reason.
Andy2 comparing a rocket with a bike is ludicrous as the whole dynamics are different.
The best answer why this model is not enough to answer this question is the simple admission of solid wheels versus wheels with tires.
Solid wheels have less flex and don't deform, so they are much faster... except they aren't, solid wheels are absolutely crap. Quite simply, flex does not equal speed loss.
A few things about which I have absolutely confidence are true:
1. Cornering a "horizontally infinitely stiff bike" will suck compared to a normal bike.
2. Even speed on a strait stretch on a horizontally infinitely stiff bike is less than that of a normal bike.
3. Aero (Moser, Obree, Boardman) gave bigger speed gains than stiffness. In fact, Moser's bike most likely was a complete noodle with it's thin Columbus tubing.
4. Frame flex is countered and made worse by body flex. The joints of the cyclist are not static. When a rider flexeshis frame, he also will flex his body. It remains to be seen if taking away the flex in the frame simply means all that flex will all of a sudden become forward speed instead of being transmitted towards the riders body. Considering the solid wheel versus wheel with tire evidence the latter is certainly an issue.
Sure, a bike certainly can be to flexible, but nowadays that is extremely rare (some exotic titanium). Considering the speeds reached on much, much more flexible frames than we have now it's extremely hard to maintain that stiffness is a big issue.
Sorry Andy, the notion that the gains of having an infinitely stiff drivetrain offsets the bad handling and comfort issues simply don't seem to be true. The real world evidence overwhelmingly suggests a bike needs to be flexible.