Why doesn't the transmission allow me to put the car in any gear I want (e.g. first) at any speed I want?
Is the transmission (including the synchronous gears) disconnected from the flywheel when the clutch is pressed in?
- I assume they are disconnected because I can feel the synchronous engaging when I lift my foot off.
If they are in-fact connected, why do downshifting methods (e.g double clutching) exist then?
There are physical limits to sychronizers.
When you upshift the synchronizer slows the clutch down which is relatively easy. When you down shift the synchronizer has to speed the clutch up which is much harder. Going down just a single gear is not that bad. When you're on the highway, shifting into first is not possible because you're asking the clutch to speed up to well over 10k rpm. That kind of speed is difficult to achieve if not impossible from just a little puny synchronizer. Further the clutch may come apart from that kind of speed.
You miss understand how a synchronizer works.
The power train is broken up into 3 pieces; (engine up to and including the flywheel), (the clutch - input shaft - counter shaft - constant mesh gears) and (synchronizer hub-shift sleeve). When you push the clutch pedal the flywheel and clutch disc are disconnected. The sifter is connected to the shift sleeve. When you shift the shift sleeve is slid over by the shifter. The sift sleeve pushes on the struts which in turn push on the blocker ring. The blocker ring pushes agains the synchronizer cone and through friction causes them to match speed. When the speed is the same the shift ring slides into place and engages the dog teeth locking the transmission into gear.
The friction between the blocker ring and synchronizer cone is how a synchronizer works. That friction is enough to change the speed somewhat but not a lot.
Well you can definitely shift to first gear even when cruising at over 100 mph. But the consequences can be disastrous. Firstly your wheel rpm and the engine rpm are same(1:1 ratio) ,considering it as top gear. Now when you are trying to put the gear into first, the gearbox input shaft rpm will rise to a very high level and when u engage the clutch back there would be excessive friction wear and the engine tries to provide resistance to the drive-line. Because of this your car may skid out of control. Also by doing so, u may end up reducing the life of the clutch facing to a great extent and sometimes it may cause complete failure of the clutch friction plate.