Passenger Trains > Checking acceleration -- part 2

(Part 1 at https://www.trainorders.com/discussion/read.php?4,5643980

We assume a push-pull train accelerates just as well
pushing as it does pulling, but would be nice to be able
to check that. Can't do it at Berkeley or Emeryville or
Oakland, and don't want to go to Hayward. So, Richmond.
How to measure a mile on the curve?

Might as well do the eastward mile first. Lat-lons on
the SW rail of the NE track:

Alongside the "Cab Spot" signs 37.9370863N 122.353764W ( https://goo.gl/maps/2cV9LCh8NQBUEko1A )
Opposite the SW end of the SE girder of the SFe
overpass 37.9502473N 122.360051W ( https://goo.gl/maps/WeW6vw487GSuDMQ36 )

Those two points are 5124 feet apart, straight line.
Now we'll assume the curve is a circular arc. So we
just need to get a third point on the same rail, fairly
midway between the other two. I used 37.943284N
122.358045W. Radius of the circle passing thru
those three points comes out 9391.5 feet. So we
want the length of the arc subtended by a 5124-foot
chord, which turns out to be 5190 feet along the
SW rail of the NE track.

(The SP chart says the curve is a 36-minute, which
agrees pretty well with the calculated 9392-ft radius.)

Total curve in that mile is 31 degrees, so we'll say
"cab spot" to the end of the girder is 5189 feet on
the NE track or 5196 feet on the SW track. So if
you're sitting at the front end of the second car
of the train you're ready for an easy measurement.

Lat-lons on that same rail:

alongside the westward "cab stop" sign 37.936061N 122.3527705W  ( https://goo.gl/maps/PkTs2kaawMAg2qfDA )
a point toward the SE end of the curve 37.9337996N 122.350213W  ( https://goo.gl/maps/TLvE15R8x3rx8wvc9 )
the point opposite the SE end of an ex-Pullman? building 37.9264075N 122.340202W ( https://goo.gl/maps/CgPwN3Qxnq3PSH769 )

(Another view of the building https://goo.gl/maps/sNKL1BQQXACyCNQf6 )

I'm assuming the first two points are both
on the circular curve, so their straight-line
distance of 1105.6 feet translates to an
arc distance of 1106.2 feet, assuming the
same 9392-foot curve radius. The straight
line from the second to the third point is
3947.7 ft, and that straight line is always
within 10 ft of the slightly-curved rail we're
measuring, so far as I'm concerned the
straight-line distance equals the distance
along the rail. So, good a guess as any,
"cab spot" sign to the end of the building
is 5054 feet on the NE track or 5057 feet
on the SW track.

From the point opposite the end of the
building to the signal bridge comes out
520 feet.

Grade is slightly descending both ways
from Richmond, says Google Earth --
say 0.1% SEward, 0.15% NWward.



Edited 8 time(s). Last edit at 03/11/23 15:01 by timz.