When a manufacturer rates their cars horsepower does the horsepower include the turbo boost or is is actual engine horsepower? Depending on the answer, what is the difference between a turbo charged car with 227 horespower and a non-turbo car with 227 horsepower? What are the advantages of a turbo? Thanks  

Forced induction systems (turbochargers and superchargers) are power adders. On an engine with forced induction the amount of boost the FI system makes is measured seperately, but its effects on horsepower and torque are measured on the dynamometer along with how much the engine makes. Example: The 2007 Subaru Impreza I makes 173hp@6000rpm and 166lb-ft of torque at 4400rpm from its 2.5l H-4 normally aspirated (no turbo or supercharger) engine. The 2007 Subaru Impreza WRX uses a turbocharged version of the same engine, which makes 230hp@5600rpm and 235lb-ft of torque at 3600rpm (source: Edmunds.com).  

When a manufacturer rates their cars it is a measure of horsepower at the flywheel with all the goodies applied. If you take your car to be dyno’d though power is measured at the wheels and consequently there will be a around a 15% drop due to losses in the drivetrain(friction). Now there is no difference in 227 horsepower in a turbo car or 227 horsepower in a naturally aspirated car. But there are differences in the amount of torque and the available power under the power band. Example two cars

Dodge neon srt-4
Hp-230
Torque-250
¼ mile-14.0
Weight-2900

Honda S2000
Hp-240
Torque-153
¼ mile-14.4
Weight-2973

Obviously you can see from the stock numbers that the dodge would stomp the car in a quarter mile run even though it is lacking in horsepower, but as you can tell the dodge also stomps the Honda in torque by a lot. That is primarily due to the torquey turbo 2.4
Against a high tune na 2.0, don’t expect the srt-4 to win in any other area though against the 2000. The benefits of a turbo are seen easier horsepower, and lots of torque, some of the torque is due to the extra .4 liters of displacement. A turbo car’s disadvantage though is lag. You have to wait for the turbo to spool this depends on the sizing of the turbo in respect to the engine. Some like the high power and torque of a turbo, and some like the high reving power and throttle response of a na. Drive all types of cars and figure out what you like the best.  

And this is where superchargers come in.  They, too, are forced induction systems, but function completely differently than turbos and therefore have different properties.  They also have different applications.

First, there is how they work.  Turbos use the force exerted by the exhaust gasses to spin an impeller, forcing more air into the intake manifold.  The upside to this is usually alot of high-end power and there is no parasitic power loss.  The downside is that an improperly-sized turbo is laggy.  Superchargers are powered by the crankshaft via a pulley and belt system.  The upside to this is that the throttle response is greater and torque down-low is better, but the system usually dies off at higher RPMS.

Second, there are 2 types: A centrifugal supercharger and a Roots-Type.  Centrifugal superchargers look like turbos, only bigger.  The main difference is that it runs off a pulley.  Roots-Type is more like a big air compressor that has 2 screws which force air into the intake manifold.  In both cases, the low-down HP and torque are great, but the flow dies off at the end.

Another difference is appliations.  Certain engines are difficult to supercharge but easy to turbo, and vice versa.  Generally speaking, V-configuartions engines are easier to supercharge than I configurations, and generally yield greater results.  Of course, this isnt law, merely a generality.

Furthermore, a supercharger (regardless of type) is limited to about 12 psi before the rest of the systems on the belt begin to suffer.  Even at that, the supercharger causes parasitic losses higher up (and the trick is to make sure you make more power than the supercharger uses).  A turbo can easily get to 20-30-40 psi, if not more.  Obviously, the higher the boost, the more air that gets into the engine, the more gas you need, and the worse the lag.

Of course, both systems cause a bit of throttle response lag compared to a naturally-aspirated engine.  

Personally, I prefer lots of torque to high horsepower.  Which is why the plan thus far is to supercharge my miata.  Its really up to you.  

Whoa there chief, you made a few mistakes. Centrifugal superchargers are way different then roots type. They do not make significant boost until high rpm's. And they definitely do not die off at the end. They are dead at the beggining and wake up at higher rpm. And there is no it is easier to supercharge v vs turbo i, it just depends on application and where you have room. I don't know about the 12 psi boost limit for sc but law dictates that the smaller gear you use for the sc the more boost you can get. In theory there is no limit to the amount you can boost. A size 0 pully on the hp would make infinite boost but you will never be able to make a pulley with a diameter of 0. Usually sc kits don't always have intercoolers(especially roots type) so you dont want to push too much boost or bad things will happen. And second of all if you are going to push that much boost it makes a lot more sense to turbo. They are just more efficient especially at higher boost.  

Like I said, the 12psi limit is more of a logistical problem.  When you change the pulley on the SC, it affects everything else on the belt.  The smaller wheel will mean slower or faster speeds for the other things, causing a loss/overpowering of the systems.

I never said Roots and Centrifugal chargers were the same.  They're inhenrently different being only similar in the fact that they're run by the pulley and push more air into the engine.  

Also your idea of a size 0 pulley is totally wrong.  Sure, a smaller pulley will mean more boost, but an infinite level of boost woudl only be attained by a size 0 pulley on the SC and a pulley with an infinite radius on the crankshaft side.  

I also never pretensed that Im an expert.  

You said that both create low-end torque and that both die off at the end. I never said you were an expert and neither am I. And yes a theoretical size 0 pulley would yield infinite boost and would not depend on the crankshaft. Supercharger speed is proportional to the crankshaft pulley size over the sc pulley size. Any number divided by zero yields infinity. Also all other accesories would not be affected by the size of the sc pulley. The only thing that dictates the speed is the crank. The size of the sc pulley will affect the tension of the belt, but that can easily be taken care of by sizing of belts and tensioners. The only thing that would happen is more parisitic loss. Pushing too much on a roots is very inefficient, way too much heat. Trying to get good boost at low to mid rpm on a centrifugal and you better hope to god you have a way to bleed excess pressure at high rpm. A turbo is inherently better for high boost.  

Centrifugal boost exponetially. Say at redline(8000) you want 9psi at 4000 psi you would have 2.25psi. on a roots at 9psi at 8000rpm you would have 4.5psi at 4000 rpm. Roots are linear and centrifugals are exponential by a factor of 2.  

now the only problem is that the roots is over simplified in that problem. Because it is a blower and not compressor it is just pushing air into the manifold where it is pressurized by more and more air coming in. So because of this the engines volumetric efficiency will start to catch up to the sc and this leads to the effect of the roots type sc to lose steam at the end.