there is NO WAY in hell a supercharger can be more efficient than a turbo for 1 simple reason: a supercharger runs off a pulley, meaning it uses a little engine power to make more power, which is good but the power used off the pulley is a direct loss of efficiency. A turbo on the other hand uses exhaust energy which is normally wasted to make more power meaning a turbo uses virtually nothing (waste) to make more power with minimal loss of efficiency. Be careful of the words you use - here I'm talking about actual thermodynamic and mechanical efficiency and a turbo has a clear advantage.
Yes supers have minimal lag because they run at engine speed, but that is also a limiting factor. The blades of a turbine are set at a certain fixed shape and angle - 'pitch'. The blades of any given turbine will flow the most air at the best efficiency at a specific speed. below that speed and the turbine cuts through the air, not pushing as much as it should, above that speed, the blades cavitate which creates wasteful swirling eddys behind each blade. Now thats not to say the turbine is useless except at a certain speed, but thats when it works best. Now since supers spool up so fast, their blades are pitched to provide top air flow in the low to mid range, to do otherwise would be a waste of the superchargers characteristics. A turbo's blades are pitched to provide mid to high end torque to take advantge of the fact that the more exhaust that flows (high rpm) the faster and therefore more air a turbo can flow which in turn produces yet more exhaust energy to drive the turbo. So you can see, the turbo is only restricted by exhaust flow while a super is limited by actual engine speed which are 2 completely different things.
But enough theory. Lets look at the differences between real world superchargers and turbochargers. Its rare to find a super that will pump out much more than 8psi of boost. The Paxton NOVI-2000 puts out 27psi and thats a hardcore racing state-of-the-art super. (remember to also take into account the VOLUME of air at any given boost pressure - its easy to pressurize air, its hard to pressurize and flow large amounts of it.) Now look at turbos, the dinky lil IHI RHB5's flow 15psi. While a race built IHI RX6 (state-of-the-art) will flow 6bar of boost (70+psi). apples to apples, pound for pound a turbo will always be better. A mid-size (ie. T3/T04E) turbo can double or triple an engines output, while most popular supers give a 15 - 40% increase.
Torque increase for common supers:
Whipple super for Ford 6.8L V6 - 55% increase
TRD for Toyota 3.4L - 23% increase
PowerDyne for LT1 engine - 35% increase
dont get me wrong, a super is a great tool to get more out of an engine, particularly power that would be helpful in daily driving situations and taking an average car and making it a 'quick' car, but if want raw crazy power it always has and always will be a turbo you want.
Here is a graph for a Whipple supercharger for the Ford 6.8L engine. Notice how torque actually drops with engine speed and how the curve with the super closely follows the curve of the stock engine, while supplying more torque of course.
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