They tilt train tracks around curves based on the expected speed. Why don’t they bank curved high-speed roads, like at interstate entrance/exit ramps? (or do they?)
They do. In fact when a curve is banked wrong for the speed it can be quite noticeable.
Curves are banked out west, too.
They do, slightly. When you work through the math for centripetal acceleration and traction, you find that a minor bank angle makes a major improvement in the amount of lateral acceleration that can be had for a given static friction coefficient.
As to “why not MOAR bank angle?” My guess is that the DOT doesn’t want to scare Grandma (the average driver would wet their pants lapping Daytona), and they also don’t want to create a circumstance where stopped vehicles tend to slide off the road during slippery conditions.
Also, why not more of a bank angle? I think the DOTs don’t want to encourage higher speeds.
Or possibly, they are banked correctly (or close to it) for the posted advisory speed, and people are simply driving too fast.
I think the OP’s question is relevant whenever the posted advisory speed is less than the posted speed limit on straight sections of that road, e.g. an interstate highway with a posted limit of 70 MPH rounding a curve with an advised speed of, say, 50 or 60 MPH. Why not bank such turns so that the driver can continue at the posted speed limit?
One answer for very tight turns like cloverleaf interchanges is that if we set them up so you can run them at 70 MPH, in addition to making Grandma wet her pants, you may overload the chassis. Consider a cloverleaf loop with a radius of 200 feet. at 70 MPH, the lateral acceleration would be 1.6G; if you bank the turn so that no lateral traction is required (about 60 degrees in this case, i.e. your door is closer to horizontal than the underbelly is), then the suspension is loaded to 1.9G. Suddenly your 4,000-pound sedan’s suspension is bearing nearly 8,000 pounds. NASCAR and Formula 1 vehicles are designed for this kind of thing; your Accord is not, and you’ll be popping tires and deforming coil springs.
Because centrifugal force is not the only factor. Visibility is generally a more important reason for limiting the speed through curves - e.g. if there is debris on the road at the curve, can you stop in time?
I thought banked curves were rated for the speed posted. Not the speed limit (for on- and off-ramps at least), which is the legal limit on straightaways, but on off ramps and such they have yellow warning sings that say “warning, 20MPH” or whatever. And those are the numbers used to design the bank. If the interstate curves I believe they are banked according to the speed limit (but not 20mph over the limit that we all like to drive).
By “designing the bank to a speed” I mean that there is a speed (at that particular angle of the bank) at which the bank does all the steering. No steering wheel needed.
Highways definitely have banked curves to a degree determined by the nominal speed limit. The bank is sometimes called camber but more technically, superelevation. I don’t particularly recall noticing it on onramps and offramps which tend to have fairly low advisory speed limits as you go around the bend but no doubt they’re there to the extent necessary.
I found this informative description somewhere:
Superelevation in road design is defined as the rotation in the pavement during an approach to and then through a horizontal curve. It is written as a decimal that represents the ratio of a pavement’s slope to its width and has a range of 0 to 0.12 feet. Superelevation counteracts the lateral acceleration that is produced. As of 2015, the United States Department of Transportation allows maximum superelevation rates between 0.04 and 0.12. Each state establishes its own maximum allowable superelevation, which is based on variables such as terrain, location of the road, climate, and frequency of slow-moving vehicles. For example, states that experience a high frequency of ice and snow conditions may choose a lower maximum.
The recommended amount of superelevation for the highway speed, or conversely the advisory speed for a given curve design, can be established with a device called a ball-bank indicator in a test vehicle or computed with a formula. Here’s one such formula:
V[sup]2[/sup] = 11.7R * (e+f)
where:
V = advisory speed (km/h)
R = curve radius (m)
e = superelevation rate (m/m)
f = unitless coefficient of side friction
Designing the bank to speed, to me (and thinking of a force diagram), means the centripetal acceleration at that speed matches exactly the gravitational component tangential to the road surface.
As for those yellow caution speed signs, you can usually easily double that speed around most curves and negotiate the curve safely, as long as you have a decent-handling car or motorcycle, and of course if you have safe sight lines through the curve.
Remember that cars aren’t the only vehicles on interstates. IANA highway engineer, but I’d imagine a safe bank angle for a car taking an off-ramp at, say, 50 mph is quite a bit different than what’s appropriate for an 80-foot long twin trailer setup with a GVR of 80,000 lbs.
As an example, here is a link to the Texas Roadway Design Manual. See page 2-15 (which is page 43/311 in the PDF) for a table that shows the superelevation rate as a function of speed and radius.
http://onlinemanuals.txdot.gov/txdotmanuals/rdw/rdw.pdf
(BTW - the superelevation rate is on one “axis” these days whereas previously it was the data in the table and curve radius was on an axis. I don’t know why they changed it because I thought it made more sense the other way around but I only bring it up since I referred to the table as having “superelevation rate as a function of speed and radius” and I guess that’s not really the case with the way they present it now.)
This table is for the 6% maximum superelevation rate and the next page has the table for the 8% maximum rate. I don’t recall if I’ve ever used the 8% table. If you poke around the document you can see other tables such as for low speed urban roads, high speed roads without superelevation, maximum relative gradient (how quick you transition from normal crown to superelevated), how much of the transition is outside/inside the curve, etc.
The superelevation rate is based on the design speed, which may or may not be the posted speed. Usually the design speed is 5 to 10 mph faster than the posted speed whenever that’s possible. But I’ve seen plenty of cases where the design speed is the same as the posted speed and one case recently where the design speed was atually lower than the posted speed - which seems like a lawsuit waiting to happen - but that wasn’t my design.
The speed in question is based on the travel path. So the mainline speed wouldn’t be used for designing a ramp. You would base the superelevation on the expected speed of the vehicle on the ramp.
One of the challenges of setting those advisory speed limits is that if they’re too low, drivers will basically ignore them or greatly exceed them, which can be unsafe in many circumstances. And then if they’re too high, large or unstable vehicles may get in trouble, too.
I would certainly not say you can “easily double” the advisory limit, but you can certainly exceed it a lot most of the time, depending on the car and road conditions. There is one particular interchange that I’ve learned to be careful on. It’s a broad sweeping curve with limited forward visibility due to concrete abutments, bridge pillars, sound barriers, and other crap. It looks like it’s just going to take you on a gradual high-speed turn onto the other freeway, but as you proceed the turn gets tighter and tighter, and you really don’t want to be traveling too fast at the point that you may first be discovering that it’s a much tighter turn than you thought it was!
For some reason, the concrete barrier bordering the outer edge of the curve at that point is covered in scratches and scrapes and paint marks of all colors!
They do that so the barrier is easier to see so people won’t hit it. Can you imagine if it was plain old concrete colored - it would practically be invisible. People would be hitting it all the time!
There was a curve on I-75 in Metro Detroit (between 8 and 9 mile) that used to be rated at 50 MPH. It was resurfaced a few years ago, and they banked the turns slightly, enough to help but not enough to really notice. The turn is now rated at 60 MPH.
I take it you didn’t consider semis and oversize loads?
Highway 17 over the Santa Cruz mountains here – same thing, scrapes on the concrete barriers. I used to do that commute every day by motorcycle, in rain or sun or on black ice. A fun road by bike, normally.
And they have it on dangerousRoads.org: Driving the Hazardous California State Route 17.
IIRC, one relevant equation for calculating the ideal bank is tan(theta) = v^2/rg, where theta is the angle from the horizontal by which the road is banked, v*2 is the square of the velocity for which the bank is designed, r is the radius of the curve and g is the gravitational accelation at the Earth’s surface (9.8M/s^2).
Applying algebra gives a solution for a banking angle at a given velocity or an ideal velocity for a given angle of bank, depending on which is the fixed variable. By ideal banking angle is meant an angle at which the force acting on the vehicle in question is perpendicular to the surface of the road, so that no questions of sideways drift arise.
Note that this equation does not include the mass of the vehicle. It doesn’t need to because the downforce is straight down relative to the surface of the road, nor does it include a friction variable for the same reason.
Now, calculating a maximum velocity for a given angle of bank does indeed depend on variables of mass (including center of mass of a particular vehicle) and friction co-efficients, because once one exceeds the “ideal” velocity derived above, centrifugal effects will tend to make the car appear to want to climb outwards/sideways up the incline of the bank as velocity increases, and friction and mass will determine the limits of the capacity to maintain an upright path that is still within the boundary limits of the road, and does not involve the vehicle toppling.
I’ve noticed more aggressive superelevation on older highways and ramps, especially ones from the 1950s when cars really got fast and engineers were doing a lot of experimenting (i.e. they had no clue what they were doing). Previous posters mentioned fully loaded tractor trailers, which I think is a good explanation for why the amount of banking has been significantly toned down. Same for wet or slippery conditions. Too much superelevation/speed and hitting some ice or even just wetness with bald tires can easily cause a vehicle to go flying up and over the edge. The curve has to be designed so vehicles are stable when stopped as well, so aggressive banking combined with snow and stop/go traffic can easily see vehicles sliding down to the inside, especially if it’s a fully loaded truck.
The most highly banked ramps I’ve experienced are the ones on the US-52/Business-40 cloverleaf in Winston-Salem, NC. The southbound 52 to eastbound 40 ramp is signed for just 15mph because it’s so tight. Being a traditional cloverleaf also means you have next to no time to accelerate back to highway speed because the ramps are so close together. Unfortunately Google Street View’s wide angle camera doesn’t do the slope justice.