Tell your wife that there is too much to gain by sticking with a 650c bike. First of all you take her height which is 5'6" or 66". Take the average male rider whose height is 5'11" or 71". This represents a size difference of 7.6%. Now take the wheel diameter of 650c vs 700c. The difference between these two sizes is 7.7%. In other words, the differences are virtually identical when compared side by side.
If one can say that a 5'11" man riding a bike with 700c wheels is considered a perfect fit, then likewise a 5'6" woman should reasonably want to have a 650c wheel to achieve the same perfect fit.
There are other reasons why she should stay with the smaller wheelsize. As mentioned, they have a smaller frontal area which reduces the amount of aerodynamic drag that she will experience while riding. Then there is the fact that a 650c wheel will spin up more quickly which allows for faster accelleration. This is a very important factor, even when one is maintaining a steady speed over flat terrain. Then there is the obvious weight saving factor in that 650c wheels are lighter than equivilant 700c size ones, no matter how you slice it!
The reality of cycling is that when you are pedaling your speed is NOT constant. In fact, if you analyze it literally inch by inch as you travel along, you will find that each pedal stroke begins with a micro accelleration because during the transition period between the end of one leg's pedal stroke and the beginning of the other leg's stroke, the bike has decellerated just a fraction of a bit. This results in each pedal stroke having to put out just a little extra power just to make up for this loss in order to maintain a constant speed. This is true no matter how well you are able to "pedal in circles".
Taking this a step further, imagine that you are really great at pedaling in circles and your speed loss represents just .1% of extra power needed to be inputted as extra to compensate for this by using 700c wheels as opposed to 650c wheels. This means that after a 40km ride you will be 40 meters behind as a result than if you had been using 650c wheels. While this might not seem like much, it does represent a time difference of about 10 seconds assuming an average speed of about 18mph. This assumes all other factors being equal and you are riding on a totally flat road course.
In reality the difference can be much greater when you factor in all the advantages, lighter weight for the 650c wheel, less aero drag, and speedier accellerations. Your time difference will more likely result in a minute or more in savings depending on how hilly your riding course.
As for myself, I am a male 5'9" and normally ride a bike with a 700c wheelset on it. I am, however, planning on building a mountain ascending bike for use in uphill time trials. It is because the 650c wheel is faster in recovering from these micro-decellerations (which are much more pronounced when going up steep grades than on the flats) I am going to be using 650c wheels for this specific bike. Doing the math, I figure to save somthing like 15 seconds or more for each mile of 6% grade that I climb, this savings will increase as the grade increases. Since most of these types of time trials are anywhere from 5 - 9 miles in length, this adds up to a huge time saving over all.
In summary, tell your wife that she should look at logic and reasoning before considering making a switch and not to listen to the uneducated rabble speaking from stupidity.
