...where the fack did you get that idea?

Here is the long and boring nerd way to add some validity to the power debate. Let's figure out how much power it takes to compress the air to make some serious power. We will do this in two ways: we will figure the differences in intake air temp for a turbo, a Roots supercharger and a centrifugal supercharger. Then we will show how much power it takes to turn the supercharger.

First, let's calculate Delta T for the various compressors. Delta T is the change in the intake air temp after it is compressed.

Delta T = Intake Absolute Temperature x (Pressure Ratio to the .238 power -1)/ Compressor Efficiency

Let's assume our engine is going to run 20 psi of boost or a pressure ratio of 2.36.

Pressure ratio = boost pressure + 14.7/14.7

The temperature scale engineers use for absolute temperature is the Rankin Scale. On the Rankin Scale, zero degrees is absolute zero. So assuming our intake air temp is 85 degrees, lets call that 545 degrees Rankin.

Let's say our match car is a hot Acura GSR with a B18C motor. By using the compressor matching equations...we figure that the B18C can flow about 45.3 lbs/min going full tilt at 20 psi.

So here we go. Let's figure out Delta T for our good turbo first. Let's assume an efficiency of 78%, as there are many turbos that can do that at the given flow and pressure ratio.

Delta T = 545 x (2.36 to the .238 power -1)/0.78
Delta T = 158 degrees

A 4-cylinder sized centrifugal supercharger is probably much less than 70% efficient at this point but let's be kind to it and assume that plugging and chugging gets us a temp of 177 degrees.

Now there are not any current Roots blowers on the market that can support this sort of boost pressure on a small 4-cylinder car but let's suppose there is and let's be very kind, assuming it will get 60% compressor efficiency at 20 psi and 45.3 lbs/min of flow...Plug and chug and we get a Delta T of 206 degrees.

Now Delta T is the difference in temperature after being compressed. What would our intake temp be for the Roots assuming an intake temp of 85 degrees?

85+206 = an egg frying 291 degrees with no intercooler!

Now let's figure out the power required to make the boost from these three compressors. The equation for the power needed is:

Power in BTU per minute = Mass Flow x Cp (a coefficient) x Delta T/Compressor Efficiency

To convert BTU per minute to horsepower divide by 42.4.

Power = 45.3 x .242 x 158/78 = 2220 BTU min/42.4 = 52 hp recovered from the exhaust.

So here is the horsepower that won't be taken from the crankshaft but recovered from the exhaust stream by the turbocharger on our GSR.

If you check out the gas power cycle in a thermodynamics book, you need to correct the power equation a little for a supercharger. Since a supercharger adds pressure to one side of the motor and the turbo adds it to both, we need to do an estimation of the power recovered by the supercharger on the intake stroke. The equation is:

(Boost Pressure x Engine Displacement in cubic inches x RPM)/2)/12 x 60 x 550

So for our B18C:

(20psi x 110 x 8500 rpm/2)/396000 = 24 hp

To figure out how much power the centrifugal supercharger takes from the crankshaft, let's plug and chug again, getting a 65 horsepower, subtract 24 hp and you get a crankshaft power loss of 41 hp.

Repeating for the Roots blower gets us a loss of 65 horsepower stolen from the crank.

So simply reducing our meager data, if you calculate the potential hp of our turbocharged B18C, we will get about 453 hp. This might be around 412 hp from our centrifugally supercharged version of the same motor and 388 hp from our Roots equipped motor.

Now this example has been vastly oversimplified and does not take into account differences in volumetric efficiency, air density differences for intercooler effectiveness or lack thereof, dynamic matching to compressor maps and engine tuning variables that have to be different between the types of compressors. Of these variables, all of them except for VE differences would be in favor of the turbo. This shows that all other things being equal, the turbocharger does have an advantage when it comes to sheer power output. The compressor efficiencies we used for the superchargers were very conservative. In real life the superchargers would probably be much worse at 20 psi. If we upped the boost higher, to higher pressure ratios where turbochargers really shine, the calculated differences would be even greater.