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What is the maximum gradient allowed for the tracks at new platforms of stations in the UK or located elsewhere serving the UK? I've heard multiple numbers, including 1 in 500, 1 in 280, 1 in 264, 1 in 260, and 1 in 200. So, which is it? Also, at what points of the station are those measured/applicable for? Is it that the gradient limit should not be exceeded for the average of the station (chord connecting the tracks at the ends of the platforms), at the steepest point within the station, etc.?

On the topic of platform heights, it looks like it's a good thing that Brexit happened because they are finally able to them at around 1200 mm (I'm guessing 1250 mm because that is a huge international standard, which is used in Japan, Taiwan, China, and in the future, Indonesia and Texas, USA for HSR) for HS2 rather than 550 mm, 760 mm, or the special 915 mm allowance for the UK.

Also, how is Germany able to get away with the Ingolstadt Nord station (2.5%) and Stuttgart 21's (1.51%) underground Stuttgart Hbf with their platforms steeper than 0.25% if they're both on new track alignments that serve HSR that had their construction permits issued after the EU's Technical Specifications for Interoperability came into effect? As far as I know, the TSI (which applies to all new lines in the EU that serve HSR) doesn't allow for any exceptions to the 0.25% percent limit, unlike country-specific exceptions for platform heights.

Do most engineering manuals for the various networks of different types of railways all over the world all settle around a preferred maximum of somewhere between 0.3% to 0.35% at stations because it is the steepest gradient that is guaranteed to be safe from rollaways for passenger rolling stock in the absence of external forces? note: The UK is especially strict in preferring 1:500 = 0.2%, though it is no surprise because it built the Great Western Mainline, most of which is nicknamed Brunel's Billiard Table because its gradient does not exceed 1:660 east of Swindon, and 1:1320 east of Didcot Parkway. That is possible and probably the reason why the levelness of railways became a part of British railway design culture because the topography of England, which is the "country" (more like state or province) that controls all of the UK, is abnormally flat compared to the vast majority of other places. This still does not explain why the EU TSI allows a maximum of only 0.25% for high-speed rail platforms though.

The difference between 0.5% and 0.4% is huge though, because the former is 20% greater than the latter. I've long known that 0.5% is close to the minimum rollaway gradient from my experience playing Train Simulator since 2013. In that game, some vehicles start to roll away at 0.6% grade and once moving, all vehicles start to decelerate at 0.5%, though the physics might not correctly represent the real world. I'm actually wondering at what grade rounded to the nearest 0.05% or less does a train start to roll. Is exactly 0.3% guaranteed to be safe, as it seems like the engineering manuals of virtually all mainline railways (most mainline railways in the world actually have a preferred maximum of 0.3%, not 0.35%) and many metros (the remainder which has a preferred maximum of 0.3% instead of 0.35% still makes up a substantial minority) prefer not to go over that amount for the high-standard stations?

For any type of train or railcar on any type of railway, be it mainline freight or light rail, what are typically the respective minimum rollaway gradients when all brakes are fully released and no power is applied, in the absence of any external forces besides gravity and friction such as wind, seismic activity, or other objects pushing or pulling on it? If you have any personal experience, please also comment. It doesn't matter that you're dealing with UK trains because this is regarding all trains in the world, as indicated by the inclusion of gradients in UK format and Indian Railways. This is because the coefficients of rolling resistance are all very similar. I'm only listing US railroads here because those are the ones I'm geographically familiar with. Most mainline railroads (more accurately railways) and metros in the world limit the exceptional maximum gradient to 1% = 1:100 at station platforms, with 0.5% = 1:200 being the normal maximum, 0.35% = 1:285.7̅1̅4̅2̅8̅5̅ being the preferred maximum (which is also the standard minimum in underground and aerial structures for drainage purposes for the WMATA Metrorail), and 0.3% = 1:333.3̅ being the normal minimum in underground and aerial structures (including stations) for drainage purposes for some of the other metro systems. Most light rails and monorails limit the exceptional maximum gradient to 2% = 1:50 at station platforms, with 1% = 1:100 being the normal maximum, 0.5% = 1:200 being the preferred maximum (which is also the standard minimum for Sound Transit Link), and 0.3% = 1:333.3 being the normal minimum in underground and aerial structures (including stations) for drainage purposes. Most mainline railways limit the exceptional maximum gradient in parking and coupling/decoupling areas to 0.25% = 1:400, with the normal maximum being 0.2% = 1:500 and the preferred maximum being 0.1% = 1:1000, with India Railways even limiting the preferred maximum to 1/1200 = 0.083̅ %. Most metros limit the exceptional maximum gradient to 0.5% = 1:200 in parking and coupling/decoupling areas, with 0.3% = 1:333.3̅ being the normal maximum and the preferred maximum being 0.15% = 1:666.6̅ or 1:660 = 0.1̅5̅ %, which are almost identical to each other. Most light rails and monorails limit the exceptional maximum gradient to 0.5% = 1:200 in parking and coupling/decoupling areas, with 0.3% = 1:333.3̅ being the normal maximum and the preferred maximum being 0.25% = 1:400. Obviously, trains have been known to run away at exactly a 1% grade, with the Federal Express train collision in Washington Union Station on the Pennsylvania Railroad (now defunct) in 1953 happening with its brake failure on the approach with a grade as little as -0.73% (≈ -1:137 gradient), so that isn't a gradient that will prevent a train from rolling away. So, will a 0.5% grade prevent an unpowered, unbraked train from beginning to roll in the absence of external forces? Also, Pennsylvania Station in New York has a constant grade of +/- 0.4% = 1:250 on either side of the crest at the center of the station. So, for curiousity purposes, if any type of train or railcar (even those that do not operate in those tracks such as MTA subway or NJTransit River Line light rail vehicles) is parked entirely on either side of the change in grade, will that be gentle enough to prevent the same train from beginning to roll into the tunnels under the rivers? How about 0.35%, or even 0.3%?