For a Bombardier CRJ:
I don’t understand how air that is being sucked in the front and bypassing the combustion chamber can produce so much of the thrust. Presumably this air doesn’t go through the compressor stages and is sucked in the fan and just “bypasses” all the compressor stages, combustion, and the turbine. Can anyone explain how this works?
Think of it as a ducted fan with a turbojet in the middle to spin the fan.
The combustion chamber produces all the power, but not all the thrust. Keeping things simple, the bypassing is a glorified propeller in a can that uses the power from the engine core to push air along.
In case you were wondering why they have such a high bypass ratio, it is more efficient for propulsion to accelerate a large mass of air a little bit than to accelerate a small mass of air a lot.
Got it in one.
And this is why helicopters work relatively well and baring Mr Fusion power packs things like hovering cars and personal jet packs will remain “tricks” at best.
Actually there are some reasonable projects for “hovering cars”, but they use ducted propfans rather than jet engines and aren’t supposed to be more efficient that helicopters - just more suitable for operation in tight urban environments.
Helicopters have been around for DECADES.
where is ONE working hovering car?
And get off my lawn.
Also, I understood that the DOD is interested in developing an “urban canyon” military aircraft to operate in places too close for open-rotor helicopters. Can anyone corroborate?
And I said “working”.
Go ahead. Invest your life savings. Moellers distant jewish cousins will be quite happy.
This is also (indirectly) why sailplanes have long slender wings.
This one is working (in the video anyway).
Yes, the Moller200! Designing new ways pedestrians can get julienned. 
For a questionable definition of working.
I’ll assume you posted that a joke
Okay, along with this thread and some of my own reading I think it makes sense. While I have your attention, if you don’t mind another question: is N1 speed the speed of the compressor (inlet fan or compressor rotors?) and N2 the speed of the turbine (aft the combustion chamber)?
I understand why N1/N2 are given as a percentage, but what does it mean to go to 110% N1 or N2? How can you be higher than the maximum? Or is it like overclocking a CPU and higher than the recommended maximum?
Not a hover car, but rocket packs seem to be real: Rocket man flies into record books at 180mph | Technology | The Guardian
(You can find some videos of the flights on YouTube)
One could also argue that a harrier jet is a type of hover car–just not one that is economical nor safe for the average user.
I don’t think so. My experience is with turbo props but the basic function of the turbine is the same. The PW123 (turbo prop fitted to the Dash 8 200) has a two stage compressor and two stage turbine. Each compressor stage is directly linked to a turbine stage, so the compressor speed is the same as its respective turbine speed, however the different stages have different speeds. On this engine they’re named NL and NH, NL being the low speed compressor/turbine and NH being the high speed compressor/turbine. I’m thinking that N1 and N2 refer to compressor/turbine pairs in a similar way in your case.
It’s just a nominal figure. It may be chosen as the maximum normal operating speed or something. It’s not uncommon to be able to exceed “100%” in some circumstances. For example the PW123D fitted to our Dash 8 200s have a normal take-off power of 97.5% (torque) but they can be operated up to 107.5% for up to 5 minutes in case of emergency (failure of the other engine normally.) They can also be operated up to 114.2% torque in normal operations with the propeller RPM below 1024. On the other hand the PW123E fitted to the 300 series Dash 8 uses 90% as normal take-off power, 100% as maximum emergency power, and 96% below 1125 prop RPM. As you can see the use of percentage figures is largely arbitrary.
A small correction to myself. NL and NH are the low and high pressure stages .
How long can a helicopter hover?
How long can a jetpack hover?
Forget helicopters with their couple of hours aloft. Now, Zeppelins can hover for weeks! That’s the future! 
Seriously though, your analogies are invalid. There are some tasks that helicopter can do better, there are some tasks that airliner do better. And it seems that some tasks can’t be done by either - hence people still are developing new constructions and test new ideas. Nothing wrong with that.
Making “hovering car” sure is engineering challenge, and sure it’s not gonna be efficient enough to replace helicopters in what they do. But there are conceivable uses for them and, who knows, maybe even significant market niche.