# How are maximum speed limits determined for banked curves?

I was once told that the speed limits on banked highway curves (specifically off-ramps) were determined by assuming zero friction between the car and the road, such that as long as you stayed on the correct path of travel, the banking of the curve would prevent a vehicle from sliding outwards. That is, the angle of the banking would mean that the portion of your gravity vector normal to the road surface provides enough centripetal force without counting on your wheels to provide any 'sideways' friction.

I am not a civil engineer and have no familiarity with the relevant codes, but I was wondering if this is true, or a myth. If it's not true, is there a simple formula used to set these speed limits, or is it a much more complicated procedure/judgment?

• My instinct says that there's just about no practical level of banking that would turn a car with zero friction between the tires and road. I just saw a chart yesterday that listed dry asphalt as having a minimum coefficient of friction of 0.8, and slippery ice as something down to 0.1. Imagine how fast you can go around a curve when it's snowy or icy out, it's far below the posted curve speed. With no friction, you'd probably go straight over any real world embankment. Mar 14, 2015 at 17:10
• My instinct is similar to yours, but I also notice that tight curves often have very low posted speed limits, and I can go much faster than that in dry conditions. So I was hoping someone who actually knows the codes or engineers these kind of things could give a definitive answer. Mar 14, 2015 at 17:13
• I think that's a safety factor thing. No friction means that turning the wheel will do literally nothing, it's the same as your brakes locking up without ABS. Mar 14, 2015 at 17:14
• Understood. But on a banked curve with no friction, there would also be a tendency to slide downward, keeping you on the curve (if not in the right orientation.) I don't know if the two forces are anywhere close to canceling each other out, but they do both exist. The question is, what method is used for specifying the maximum speed, and is the amount of bank in the curve a factor. Mar 14, 2015 at 17:53
• One reason that very tight curves on two-lane highways in particular have very low posted speed limits is because of the decreased visibility. At higher speeds, drivers are much more likely to wander into the oncoming lane to "make" the curve.
– Air
Mar 16, 2015 at 18:44

This information comes from a design document by the Iowa DOT (US). It might not apply everywhere in the world, but the considerations are probably universal.

For clarity, the amount of banking of a turn is typically called super elevation. At least in the US, this is given as a percentage for roadways.

• The maximum super elevation is 8%.
• The typical high-speed super elevation is 6%.
• The typical urban super elevation is 4%.

The 6% typical super elevation was chosen for:

This reduces the risk of slow moving vehicles sliding down a superelevated roadway during winter conditions.

Speed

Design speed of a highway is not always the same as the posted speed. Drivers have this habit of not following the speed limit. Designers know this and make the roadway safe at these increased speeds as well.

There are only two ways that speed will affect the curve radius. Either:

1. The design speed has been set and the geometry limits are based off of that speed.
2. The geometry has been set and the design speed is reduced to still provide adequate levels of safety.

Both the super elevation and design speed are taken into consideration to determine the minimum radius of the curve. These also consider the maximum side friction from both the vehicle's tires and the comfort of the driver. These values are listed in tables for easy look up or in a spreadsheet.

The friction of the vehicle's tires on the road is incredibly variable. It depends on the weather, condition of the road, condition of the tires, etc. Because of this, the values used for design are very conservative.

The other factor controlling curve design is driver comfort. It is surprising how ofter roadway design is controlled by human factors. In this case, the typical driver will be concerned about the amount of horizontal acceleration they are feeling and slow down before the vehicle is in danger of sliding sideways.

Result

So in the end, there are limits on the super elevation of curves that are based on low friction. But this is the controlling factor at low speed and not high speed.

These super elevations are no where near the amount that would be required for no side friction. As you can imagine you never know when there will be a traffic jam on a road because of a wreck. You don't want trucks to tip over toward the center of the curve if they are forced to stop!

The minimum curve radius is then determined based on looking up the information in tables. Often there are other concerns that also might after the curve such as sight distance or vertical curves.

How it works in design

Setting the roadway cross section details (of which super elevation is one) is usually done last in the sequence of design. The sequence usually goes like this:

1. Set design details, e.g. design speed, road type, number of lanes, etc.
2. Set the horizontal alignment. This would be where the curve radius is set. This is also where geometric constraints are found that might require reducing the design speed.
3. Set vertical alignment. This stage can also reveal more geometric constraints.
4. Set details of cross section, e.g. super elevation, cross slopes, embankment slopes, ditches, etc.
• Thanks! So the superelevation is related to the design speed, but not usually the controlling factor, and the design assumes conservative, but nonzero friction? Mar 15, 2015 at 2:19