How does the frame geometry change if you replace your front wheel with a smaller one?
Why would anyone do that? Let`s leave that question aside for now. Here is a simple drawing of your 80`s road/touring bike with its 27″ wheelset.
You also have a modern bike with a modern front wheel. One day you take its front wheel and mount it onto your old bike. Let`s assume the modern wheel is much smaller than 27″, so it looks kind of funny.
How did the frame geometry change? Head tube and seat tube angles got steeper while the top tube and stem are no longer parallel to the ground. Obviously, the frame itself has not changed. The fork rake is the same as before. So is the distance between centers of the wheels, but that distance no longer seems to define the wheelbase. The green line shows the new wheelbase, where red line was the original wheelbase. The blue line is the difference between the radii of the two wheels. The entire frame seems to have rotated counter clock wise around the rear wheel hub. Using the green–blue–red right triangle and some trigonometry, we can calculate the little black angle. This angle gives the amount of rotation, which at the same time is the amount of change in head/seat tube angles.
If you switched from 27″ to 700c, you probably will not notice any difference (as long as the tires are similar), except that your front brake pads are now rubbing the tire (at least when you brake). But all you need is to place the brake pads 4mm lower to make it work again, and if you are lucky, your front brake will have that much room for adjustment.
If you switched your front wheel from 27″ or 700c down to a 650b, you are likely to notice several changes. Up to 1.5 degree change in head tube angle is likely to noticeably change your bike`s handling. Your bike may have transformed from a mid trail bike to a low trail bike (preferred for front loads such as handlebar bags), or it may have become a super low trail bike that is no longer very stable. According to my quick calculations, your seat & stem have moved, up to 2 & 3 cm respectively, following an arc, but mostly downward. But their relative position has not changed that much, so perhaps you can easily restore your comfortable position if you can move your stem up 1 or 2 cm.
The most unfortunate consequence of going down to 650b is that your brake pads now need to be lowered by 23 mm. If you had short reach brakes, and replaced them with long reach brakes, and placed pads as low as you can, then you might be able to keep this wheel and have a front brake too.
I hope you now have some idea of what to expect if you ever decide to share a front wheel between two bikes.
Now, what do you think will happen if you switch to a smaller rear wheel ? Hmm…