Dave, Jim, etc.
Your question - “Why they would suddenly feel the need for spiral curves is a bit of a mystery.” - could be any number of reasons.
Having worked professionally in designing roads and subdivisions and railroads (mostly in industrial parks), look at a local highway and a local subdivision street. The subdivision street has tangent to curve with no easement and the interstate/freeway has easements.
When you drive down the tangent in a subdivision, you hold the steering wheel basically on one position. When you get to the curve, the steering wheel does not jump to the correct radius. As you turn the steering wheel, the car is still moving ahead and so you are tracing an easement (spiral) even though the road does not have one.
Easements are used in several ways. First to keep the magnitude of the acceleration vector constant. As you change direction, your forward acceleration and your horizontal (left-right) acceleration both change. This is for comfort of the passengers in the car. Where the flanged wheel in a train uses the railhead to resist the need to remain in a forward motion, friction of the tires and the pavement provides the same for an automobile.
With a narrow wheelbase to prevent overturning, a high center of gravity in the vehicle will provide a more likely event of an overturned vehicle. That is why automobiles are much less prone to turnovers than tractor trailers or vans or SUVS.
The government over time has learned that certain types of construction is safer for the public.
The Public Service Commission (PSC) or the Railroad Commission of each state came into being between about 1890 and 1920. These bodies (as well as possible DOTs) determined that easements are a must regardless of the physics of the particular situation. For instance, Georgia formed its predecessor to the PSC in about 1898.
What could have happened was that the state government or local government put out a law or a mandatory code about easements and the last part of the SV had to have easements.
AAR (Association of American Railroads) guidelines are that if the offset from tangent to curve is less than 0.3 feet (3.6 inches), no easement is required. This offset is directly related to track speed.
For 36” gauge (taken from the tables in my book) and a speed of 21 MPH, the radius requiring an offset of 3.6” is about 420 feet (based on AAR recommendations).
I hope this helps out your understanding.
Doug
