Many of us around the folding bike forum are engineers and, as engineers, we cringe at the seemingly endless supply of fallacies perpetuated about small wheels (by both proponents and opponents alike).
Below is a short summary of what I've found to be the most common myths and the facts which dispell them. Theoretical and experimental proofs of the facts have been posted over the years in this forum and elsewhere and are left as an exercise to the reader.
Myth: Small wheels are slower because you have to pedal more.
Fact: No. The invention of the mechanical geartrain eliminated wheel size from the consideration of how fast one needs to pedal at a given speed. If this were not the case then even 700c or 26" wheels would not be able to go faster than a walking pace.
Myth: Since small wheels have less inertia they accelerate faster.
Fact: No. Since a properly designed geartrain will make small wheels spin faster (so you don't have to pedal more) they will not have less inertia and they will not accelerate any faster unless they are lighter. Physically speaking this is really the same myth as the "pedal more" myth, but, paradoxically, proponents of small wheels usually cite the former while opponents usually cite the latter.
Myth: Since bigger wheels have more inertia they are faster.
Fact: As above, bigger wheels do not have more inertia unless they are heavier. Anyone that's ever ridden a bicycle knows that a heavier bike is not faster. Although some "flying start" world speed record bikes have purposely added weight to their (small) wheels, "flying starts" are an exception because the extra weight allows one to essentially cheat by generating and storing energy before the clock starts ticking.
Myth: Small wheels are slower because they generate more friction by spinning faster.
Fact: While this may be true in theory, the effect is likely far too small to make any measureable difference. Most world speed records are set on small wheels and to the best of my knowledge the aforementioned friction is not even a consideration for these bikes which are literally designed to be the fastest bikes on earth.
Myth: Small wheels are generally slower because they are more difficult to manufacture and/or profit from the manufacture of quality wheels.
Fact: This may actually be true.
Myth: Small wheels are weaker/underbuilt.
Fact: No. Just as stretching pizza dough into a bigger pie makes it thinner and more likely to tear, so also bigger wheels are weaker. Most small wheels are seriously overbuilt to the same specifications as their larger weaker counterparts.
Myth: Small wheels are unstable and/or have poor handling at high speeds.
Fact: No. At high speeds the most important parameter influencing handling/stability is trail which can be arbitrarily set with a properly designed frame for every wheel size. The source of this myth probably stems from the fact that a small wheel fit to a frame designed for a large wheel will result in less trail and, thus, less stability just as we might expect any number of strange problems to occur from using incompatible parts. Small wheels are also clearly more nimble at low speeds; So small wheels can have the best of both worlds.
Myth: Small diameter wheels have difficulty on rough surfaces and bumps.
Fact: While this may be true if tire width is not increased to compensate, since the tires used by smaller wheels require less material to go around the circumference of the wheel, the weight penalty for increasing tire width is much much lower. One could argue that larger diameter wheels actually have more difficulty on rough surfaces and bumps because they can't accommodate wide tires without a significant weight penalty.
Myth: But wide tires are slow.
Fact: No. Wide tires are actually faster because they have lower rolling resistance and, once again, small wheels are superior in this regard because they can accommodate the wider faster tires without a significant weight penalty. While increasing wheel diameter can also lower rolling resistance for skinny tires, comfort is inherently compromised unlike with wide tires on small wheels which can regain comfort by simply having their pressure lowered.
Myth: Small diameter wheels are less comfortable.
Fact: Not if wider, lower pressure tires are used, at which point they are more comfortable than large diameter wheels with skinny tires without incurring a significant weight penalty.
Myth: But low pressure tires are slow.
Fact: Yes, low pressure tires have greater rolling resistance on smooth roads, but lower pressure tires may actually be faster on rough roads. However comfort is not as much of an issue on smooth roads anyway. So small wheels again offer the best of both worlds with the least weight penalty: wide high pressure tires with low rolling resistance on smooth roads and wide low pressure tires for comfort and low rolling resistance on rough roads.
Myth: Small wheels are less able to climb curbs, logs, offroad obstacles, etc.
Myth: Small wheels are dangerous because they are more likely to fall into potholes and stop short, sending the rider flying.
Fact: No. Wheels do not fall into potholes at speed, they mostly sail over them (falling mere centimeters for every meter traveled forward at even moderate cycling speeds). Moreover, naturally occurring potholes do not have tall steep edges like curbs, so there is no reason to expect a wheel that has fallen in to stop as opposed to roll out as if going over a miniature ramp. The actual danger of a pothole is that the impact may cause one to lose control of the bike as the sideways forces on the wheel surprise or overpower the rider who may then be unable to correct the steering before crashing. If this were not the case it would be near impossible for a pothole to cause a crash with a 26" wheel (or even a 20" wheel) and, yet, we know that hitting a pothole is not an uncommon crash cause. So small wheels are actually safer because they give the rider more leverage to hold the handlebars steady and allow the rider to correct the steering more quickly. Wheel trail can not help in these situations because the self correcting property of trail depends on the interaction between the rolling wheel and an even road, which is literally undermined in the case of a pothole.
Feel free to post more myths and facts if you have found a convincing scientific proof.