# Why are highways banked when they curve?

Asked by Flavio (1109) July 3rd, 2007
Observing members: 0 Composing members: 0

I'm thinking it's to stop cars from rolling if they are going at high speed.

Tennis5tar (1255)

Yes, I think we actually had this in physics class in high school-- as you go around the turn, the force that pushes you to one side is also pushing the car's center of gravity to one side. If the side force exceeds the weight of the car (not hard at 60mph), the wheels will pick up.

Well before that point, the car will start to skid. You'll notice that highways are less banked in places that get snow and ice frequently-- if they banked the highway to 55mph, when people went around the corner at 25mph in ice, they would slide down the hill.

bpeoples (2546)

bpeoples is right ... but here's the answer with actual physics equations ...
Weight of Car (mg, also known as W) points straight down
road inclined at (theta - 0 is as close as I can get) angle
you split W into vectors perpendicular and parallel to slanted road surface: W sin 0 perpendicular to road surface, W cos 0 parallel to road surface
Normal Force from road (to prevent car sinking into ground) = Fn = W sin 0
so, centripetal acceleration (ac) = v^2/r, where v = linear velocity of car (the stuff it says on spedometer or whatever) and r = radius of curve (assuming curve is along a circle, not an ellipse
between wheels and road, there is also force of friction (Ff) = u (latin letter mu - coefficient of friction, which depends on road condition ... snow, rain, etc) * Fn

so as long as the W cos 0 (force making car slide down slope) - Ff = mac (mass of car times centripetal acceleration) car will stay stable in turn. If left of equation too big, car slides down slope, if left side too small, then car skids up the slope

as you can see, diagrams are our friend, but I'm sorry I don't have one. This is a common problem in physics classes (probably AP or college level, although Honors might also have it) and is usually found in the section on "friction" and maybe "splitting vectors into their component vectors" or "Newton's Second Law: F = ma"

hope this helps! ^_^

mabelrxu (61)

FYI, you can use Greek letters theta and mu by typing &theta; or &mu; like this: θ μ

Also, there are a few diagrams linked to a the bottom of this page: http://en.wikipedia.org/wiki/Banked_turn

sferik (6086)

wow i didn't know that ... lemme practice

μαθ

cool!

mabelrxu (61)

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