The other day I had to park my car on Buffalo Street, which runs down one of Ithaca's most treacherous hills. It got me wondering: Could a street be so steep that it'd be impossible to park on it? On a severe enough incline, a car could theoretically start sliding downhill, even with the parking brake set and the wheels locked, because the traction from the tires wouldn't be enough to hold it.
With the help of a little high school physics and trigonometry it's not hard to figure out the incline of such a monster hill. If we idealize the street as a straight ramp that makes an angle a with the horizontal (so a = 0 would mean a perfectly level ramp and a = 90 degrees would mean a vertical ramp climbing straight up like a wall), the relevant equation turns out to be
tan(a) = f
where a is the critical angle we're looking for; f measures the friction of the road surface (technically, it's the road's "coefficient of static friction," for my fellow geeks out there); and tan is the ever-popular tangent function from trigonometry.
For hard rubber tires on dry pavement, f is typically measured to be somewhere around 0.7 to 1.0. Let's assume the larger value of 1.0, corresponding to very sticky tires. Then, when tan(a) = 1.0, we find the critical angle a is 45 degrees.
That may not sound especially steep, but after running this number by a few friends of mine, I've realized that most of us underestimate how terrifying a 45 degree incline would be. The steepest residential streets in the world -- Baldwin Street in Dunedin, New Zealand; Canton Avenue in Pittsburgh; Prentiss, Filbert and 22nd Streets in San Francisco; Eldred Street in Los Angeles -- have angles around 19 degrees, less than half the theoretical maximum. Or to put it another way, their slopes, which are given by tan(a), are about 0.35, or what road builders call a 35 percent grade. That's far less than the 100% grade at which parked cars inevitably start sliding. (I won't even tell you how mild Buffalo Street is by comparison. It'd be embarrassing.)
So yes, you should be able to park safely on the world's steepest streets -- at least when they're dry and conditions are ideal. But if they're wet, icy, or snowy, you'd better redo the calculation.