Just west of a creek and just behind a Walmart in Philadelphia lies one of the curviest stretches of railroad on the Northeast Corridor, Amtrak’s heavily traveled route from Washington to Boston.

mobile map 1

That stretch of track, called Frankford Junction, is where a northbound Amtrak train derailed last month while going over 100 miles per hour, leading to eight deaths. Here — by splitting the corridor into mile-long segments of track and ranking each stretch for straightness — we identify the eight sharpest curves on the Northeast Corridor (excluding entrances to stations). Frankford Junction emerges as the most curved stretch between Washington and New York.

map #1

Thousands of trains pass safely over these curves each month, but curves can be dangerous if trains go too fast, as seen in the Amtrak 188 crash and the December 2013 crash of a Metro-North Railroad train on a curve in the Bronx. When tracks bend, the Acela, Amtrak’s high-speed rail train, can’t maintain its fastest potential speeds of 150 m.p.h — let alone travel as fast as high-speed trains in Japan, China or France that routinely go as fast as 200 m.p.h. (The Japanese have developed a train that can go well over 300 m.p.h.) Slower American regional trains top out at 125 mp.h. on straightaways.

Amtrak officials say their operating procedures — like speed limits — ensure that trains can travel safely. Nevertheless, the Federal Railroad Administration is asking for Amtrak and commuter railroads to add new rules to make travel on curves safer.

Slowing a train, though, costs passengers significant time. While a sports car’s acceleration is quoted as zero-to-sixty in a few seconds, the acceleration time for Amtrak’s most advanced locomotive for slower regional trains is measured in minutes. It takes more than eight minutes to accelerate to 125 m.p.h. when pulling 18 cars (though trains are often shorter).

In these maps, the most curved sections of track are red. Straight portions are dark green. Bends aren’t a significant problem when a train enters stations because it has to slow down anyway, or when it exits stations, since the train won’t have had a chance to fully accelerate. So in our ranking of Northeast Corridor curves we excluded track segments entering or exiting a station.

Other track features besides sharp curves can be problematic. A curve in the tracks in Elizabeth, N.J., is infamous for its low speed limit, even though it’s not sharp — it’s shaped like an elongated letter S.

One of the two sharpest curves on the Northeast Corridor is in New York City: a nearly 90 degree turn on Randalls Island near the Hell Gate Bridge. A curve in Queens, north of the Sunnyside yard, is a bit less curvy, the sixth-most curved.

map #2

New England hosts some of the most tortuous sections of track. Three of the top eight curves are along the coast in New London County, Conn., where the snaking railroad crosses several rivers over aging bridges and sometimes runs right along the shoreline. The curve in Stonington, Conn., is the sharpest on the corridor. Two other sharp curves (not shown) are in New Haven and Pawtucket, R.I.

map #3

A new high-tech safety feature protects trains entering five sharp curves in New England from unsafe speeds. This system, called Positive Train Control, isn’t ready on most of the rest of the Northeast Corridor south of New Haven, including the curves in New York City and the crash site in Philadelphia. Amtrak says it will activate the protection system for the whole route by this December, after it finishes testing.

An older and more rudimentary system called Automatic Train Control is installed on the entire corridor. This system, which can be adapted to enforce speed limits, was installed at the Philadelphia derailment site immediately after the crash to prevent similar accidents.

Speed limits on curves, enforced or not, aren’t the only things keeping Amtrak’s trains from reaching speeds like those attained by high-speed rail in France or Japan. Many bridges, particularly in Connecticut, and tunnels, like a 140-year-old one in Baltimore, need to be replaced. Another way Acela trains travel quickly is by mechanically tilting their cars in the same direction as a turn, allowing them to maintain a higher speed. But tracks on the New Haven Line are so close together that the railroads feared trains could sideswipe each other. Tilting trains on this stretch were banned out of that fear, though it was found baseless by an engineering study. (A rule against it was recently lifted, Amtrak says, and a pilot project to allow trains to tilt there is in progress, though speed limits won’t immediately be raised.)

Amtrak has dreams that Acela trips to Boston and Washington from New York could take about an hour and a half — cutting the Boston-New York trip in more than half. (The Washington-New York leg now takes 2 hours 45 minutes.) If its master plan for the Northeast Corridor goes through, officials think it could happen by 2040. A more realistic plan: Amtrak hopes to shave 15 minutes off a trip by 2020.

Nearly two hours could be cut off the New York-to-Boston trip if a new inland route were built, bypassing the serpentine curves and ancient bridges along the Connecticut coast. The Federal Railroad Administration is rethinking the Northeast Corridor’s route in a project it calls N.E.C. Future. It might decide instead to bypass or realign some of the curves along the Connecticut coast with shorter stretches of new track, depending on public input, environmental review, inevitable eminent domain fights and, of course, that bane of massive public transit projects in the United States, the battle for government financing.

Cheaper and quicker than new routes is a plan to straighten the curves, which is also on Amtrak’s 2010 master plan wish list of proposed capital projects. “We view curve improvements as a trip time strategy,” said Stephen Gardner, Amtrak’s vice president for Northeast Corridor infrastructure and investment development. One of the sites to be realigned is the Frankford Junction curve.