Constraining Complexity

A couple days ago, I sat down to write a physics problem that would quantitatively illustrate the concept of power to my students.  Those of you with some physics education know that power is work done per time or the rate of consumption/expenditure of energy.  Here’s the setup:  the proud owner of a new Porsche 911 Turbo S* decides to test Porsche’s claim that the car will achieve 60 mph (~27 m/s) in a mere 3.1 seconds.  The approximate mass of the car is 1350 kg.  Determine the average power that will achieve this goal.  The problem can be done in a couple ways, but the simplest is to apply the work-energy theorem, which equates the net work done on the car to its change in kinetic energy.  Kinetic energy is 0.5*mass*velocity^2.  Go through this calculation, and the result is about 160kW or about 210 horsepower.

On the face of it, this is pretty standard introduction to physics stuff.  Nice and simple.  Illustrates how to use the new equation for power they’ve just been shown and relates it to something in the real world.  For me (and hey, maybe my students too once I talked about it**), the interesting bit is when the result is compared to the horsepower rating that Porsche gives to their engine, which is 530hp.  Now, Porsche isn’t lying.  These things can be checked, and often are.  The big difference between the two figures comes from a couple of things:  (1) Our calculation incorporates all the other forces acting on the car during its 0-60mph sprint.  Drag and contact rolling friction are forces which oppose the propulsive force delivered from the engine to the wheels, and what we’re reading out (210 hp) is the propulsion minus those energy sapping effects.  (2) 530 hp is, at least as far as I can tell, brake horsepower, which is the power that the engine delivers directly to the output shaft.  From there, bits and pieces of that power are used up by all sorts of things before it ever gets translated to the wheels.  Power steering, air conditioning, fuel pump, water pump, alternator, frictional losses in the transmission, the differential, etc, etc…all these get a piece.  All these effects combined take us from 530 hp at the engine to 210 hp “on the road” so-to-speak.

But wait, you say, that isn’t so bad!  We’re still about 40% efficient in terms of translating raw engine power to the road even with all those parasitic effects!  Indeed, that is a testament to the engineering prowess of Porsche (or any other major car company).  Of course, the real inefficiencies come from the fact that we’re using a heat engine to produce that 530hp in the first place.  I’ll write a follow-up on that subject whenever I get a little sad about heat engines not being in the curriculum*** for Physics 100 at Cal Maritime.

* If you’ve got a spare $160,000, you too could be the proud (and possibly broke) owner of this car.

** Hope springs eternal.

*** Physicist rage!!!