So you’re traveling on a two-lane state road, and every now and then you see the yellow pennant that says “No passing zone”. The dotted yellow line in the middle of the road becomes solid. Or vice-versa; suddenly you get some dotted lines, and you can pass.
How is it determined when it should be legal to pass? I mean, by the people who make those decisions.
I’d assume there is some standard of how far down the road there is an unobstructed view. If the road ahead disappears at a predetermined distance due to hills, corners, curves, etc. then a no passing zone or solid line is applied.
There are definite standards based on sight distance and speed. They’re in the MUTCD,
85th-Percentile or Posted or Statutory Speed Limit Minimum Passing Sight Distance 25 mph 400 feet 30 mph 500 feet 35 mph 550 feet 40 mph 600 feet
That’s Manual on Uniform Traffic Control Devices.
An informative article here describes how roads are currently surveyed using a team of vehicles, and also proposes a more economical method using LIDAR to survey roads using a single vehicle:
As well as the standards that determine the suitability of specific spots there is also necessary consideration of other factors that figure in road safety, such as presence of driveways and how well they can see before exiting, on a long climb having some ability to bypass trucks and heavy loads, whether flow of traffic is into the sun, adequacy of road verge if someone needs to pull over in a hurry.
The overall aim is safe traffic flow in expected conditions and contingency for the things that could predictably go wrong. Facilitating drivers being able to get from A to B at max speed is one but not the only or even main objective in road design.
In the UK, a normal country road has a single white line in the middle. As you approach an area of restricted visibility or some other hazard, there will be a double white line which basically means no overtaking.
I read somewhere that the people who mark out the roads after resurfacing, use a length of twine with one person at each end. This is how they determine the start and end of a double line.
At least, this was how it used to be done. It may now be determined using accurate mapping and global positioning.
Which, as a US citizen, confused me to no end when I drove there the first time. In the US, solid white lines generally can’t be crossed, except in emergencies. For example, when one merges onto a major roadway, the change from a solid line to an interrupted line (or no line) is the indication that you may now move from the merging lane.
I have heard more than one patrol officer state that if they saw a vehicle they felt deserved to be checked out, but did not otherwise have sufficient reason, they would pull it over “just for crossing a solid white.”
I can’t believe some of the old 2 lane roads I drove and passed on, and in a car that lacked in acceleration and top speed. These were former country roads that had become crowded in the rush hour from being used to skip around the busier arteries. Sometimes you get past a couple of bottlenecks at lights on the main road, but just as easily a line could form behind a car waiting to turn left. As I think back at a couple of the times I barely managed to get ahead of some cars and back into my lane I am even more shocked at how reckless and lucky I was in my youth.
Aren’t we all? 
Unless you’re in California, then they’re in the CA MUTCD.
I was driving on a road on Fri, 45 mph speed limit, paralleling the river in a rural area, maybe a single parking lot (to the trails) on one side but that was it; no cross streets, houses, or businesses. > 4/10ths of a mile flat & straight with double yellow lines but you could still see the old, single dashed line, indicating you used to be able to pass there. I don’t know why they changed it, but it’s not the only road that I used to be able to pass on that I no longer can.
but if you were to compare it ti the Fed’s version you’d find them remarkably similar, like word-for-word similar on probably 90+% of the two manuals. Sure, the sections might be numbered differently or in a different order but the underlying specs for a sign or wording in some traffic law is identical.
I suspected that. If you look at the poster of traffic signs, you can see that roughly that amount have a (CA) after their sign number.
Most recommendations in the MUTCD can be modified based on a study or “engineering judgment” Maybe there was an accident there, or a series of them.
A series of accidents is the surest way to shift someone’s engineering judgement and/or to meet warrants.*