Steepest Grade? Sharpest Curve?

Any idea what the steepest main line grade is/was?

How about the steepest branch line grade?

Patton No. 1 Branch from Patton, Pa. to Carrolltown, Pa., where it connected with the New York Central, was 4.0%.

How about sharp curves on running tracks (not industrial or yard)?

The northward leg of the wye at Cherry Tree Junction, Pa. was 14 degrees (the southward leg was just over 12 degrees).

IIRC, the steepest branchlibe gradient was the Madison, Ind incline which was just under 6%. There were a couple of specially equipped diesels (SD-9's?) assigned there in later years.

Okay, following the Madison Incline's 5.89% grade, what was next?

Norfolk Southern used to have the Saluda Grade on it's "W" Line which
was 5.1% and a very busy line. Now embargoed. The original SP Siskiyou
main has a maximum grade of 3 to 3.46% with 12-14 degree curves. thrown in.
The 4-mile Silverton Northern extension from Eureka to
Animas Forks had the distinction of being probably the
steepest grade ever operated by rod-type steam engines in the
USA – the average grade was 5.8% and the ruling grade was
close to 7%! I am sure that many logging railroads had grades
over 4% as well.

Shlustig-- Close, but not quite: they were SD-7, with low-speed gearing (the same as that used on the EH-15 F-3 units) giving them a higher continuous tractive effort (at, of course, a lower speed) than PRR's later SD-9 units.
--
Not quite PRR, but "affiliate" Lehigh Valley had some dynamic brake equipped SW-8 switchers, didn't it? Were they used on some very steep branch?

Not Southern, not Southern Pacific, not Silverton Northern - Pennsylvania. Let's keep focused. Apart from the Madison Incline, what was the steepest main line and branch line grades?

2nd steepest branchline gradient may have been the Crown Secondary in Macedonia & Twinsburg, Ohio. Can't find a track chart to verify the grade, but IIRC about 4%+ at points.

Branch was constructed to serve the Chrysler Stamping Plant at Twinsburg and will remain in service even though the Chrysler Plant is closing.