How your car gets from 0 to 60mph

Car guys talk about how fast a car can accelerate to 60mph.  Not that you ever get a chance to actually do that.  But if you've taken Physics 101, you should be able to predict a car's 0-to-60 time just by knowing its horsepower and weight.  It turns out it's a little trickier than that.  One day I got curious and figured out why.

In its simplest form, the calculation says that the car's power times the length of time it accelerates equals the car's kinetic energy at 60mph.  Kinetic energy is 1/2 the mass times that velocity squared.  We know the power, weight, and speed.  The thing is, this says my car should reach 60mph just 4.6 seconds after I floor the gas - and I can tell you it doesn't.  Most family sedans take eight or nine seconds, a sport/luxury car takes six or seven, a serious sports car will be down in the four to five range, and to get to 60mph in less than four seconds you'll have to pay six digits.

So why is acceleration so inefficient?

http://www.automobilemag.com/reviews/lexus/0710_2008_lexus_is-f_dyno_chart/index.html

First, "horsepower".  When they say a car like mine has 156 horsepower, it's not all available on demand.  You only actually get that when the engine RPM is high - see the red power curve in the graph above.  So even if you floor it, you have to wait until the car speeds up to about 30mph before you're at full power.  And then of course it shifts into the next gear.  So in the process of going from 0 to 60, on average 30% of my car's horsepower is unavailable.

Second, friction.  There's a difference between the amount of horsepower the engine puts out and how much power the wheels actually put down to the road.  Manufacturers put the engine number in their brochures - partly because it's a larger number, and partly because it's a lot easier to measure.  In the example above, the Lexus IS-F is rated at 416hp but delivered only 333hp to the wheels, a loss of 20%.  Friction takes 10-25% of the power produced by an engine - more for AWD systems with automatic transmissions, less for two-wheel-drive stick-shift cars.  My car is a front-wheel drive automatic, so I'm assuming it's fairly efficient.

Finally, shifting.  The car can't accelerate while the transmission is between gears, and no car can get to 60 in first gear.  Those six-digit cars can shift in one or two tenths of a second, but I figure most cars take closer to half a second.

Add all that up, and the calculation says my car goes from 0 to 60 in a much more realistic seven and a half seconds.  In fact, Car & Driver magazine actually measured it, and got 7.4 seconds.  Not bad for a back-of-the envelope scribble!