Gradients

Including Britain, although many older signs with a ratio still exist (from my limited experience on visits in recent years).

The old signs in the 1950s they used to say "STEEP HILL - 1 IN 4".

The 25% hill from Exmoor down into Lynmouth used to have a sign at the top saying "STOP HERE - ENGAGE FIRST GEAR BEFORE PROCEEDING". On a recent visit I noticed that the emergency escape lanes have signs in multiple languages warning drivers not to park in them.

That being the land of my youth I remember well the old A39 which had about 12 hills at 1:4. Four of these were between Porlock and the top of Lynton! On my last visit to the region almost all of those hills were modified to lesser slopes! The steepest road I ever did see was at Pylle Hill which was a downhill to a steel fence above the retaining wall of the GWR cutting. It was about 1:3.5 and the back wheel spun on my bicycle when trying the escent. No trademen ever ventured down there in their vans! Peter

its those foreigners, they want everything the same so its expressed in terms of a hundred even if that renders it meaningless. Most people cant do maths so they are supposed to remember a sample number. If its bigger then its steeper. Of course they cant remember which way round it is anyway :-)

Dont worry about the votes, there are seperate booths for men and women. The ladies ballot box has no base so the vote just goes into a dustbin.

Cheers, Simon

This explains why so many model layouts have what look like unrealistically steep road gradients. "There's a prototype for everything!" ;-)

Wolf K.

It's just what you're used to. When revisiting the UK, I used to translate those 1 in5 and 1 in 12 and so on into percent grades....

Wolf K.

And as I am sure you will know the scene for one of the hardest Lifeboat launches ever undertaken.

If it is unit rise per distance travelled it isn't tan theta but sin theta.

And in the U.S.

Not widely done, though. Most states/provinces still use a Steep Hill warning sign without numbers, though often with "Trucks stop and check brakes..."

Wolf K.

Along with the incomprehensible "degrees of curvature", as opposed to using radius.

John

Yes, of course! My statement concerned slope as defined in mathematics =3D Tan (opp/Adj)

Peter

I can't speak for the eastern US, but it seems pretty common to me in the Rockies and west of them.

But I've *never* seen a 25% grade here. There may be one somewhere on a minor road. I've gone down an 8% with 10,000 pounds of 5th wheel trailer behind my pickup and that was quite enough for me :-).

Degree of curvature makes sense in the field, because it is a direct measure of the angular offset of each successive station when laying out the line on the ground: you swing the transit through the degree of curvature, measure to the next station, and so on. Specifying a curve radius as, say, 1,000 ft is singularly unhelpful for laying out the line. You have to convert the radius to degree of curvature first.

On the typical layout, radius makes sense, because the curves are small enough that a reasonably sized template can be drawn on a piece of cardboard taped to the floor (or dining room table, if you think you can get away with that. ;-))

Either way, curvature curvature imposes constraints on the operation of the railroad.

HTH Wolf K.

When I worked on a survey crew in Alberta back in the 60s, a 6% grade was considered maximum acceptable on secondary roads. Our crew surveyed the realignment of an access road that crossed a creek at the bottom of a ravine. The engineer in charge and the transit man worked for several hours trying to adjust the line to minimise the cut at the top of the grade in order to avoid slicing off a garden that the property owner kept in memory of his wife. The original alignment had not followed the road allowance, which had been used for the garden. They couldn't shift the centre-line too much, because the road-allowance was fixed, but a shift of about 20ft east enabled them to keep the grade into the ravine to 6%.

Wolf K.

Hyde Street down to the Bay in San Franciso is close to 25%. Cable Car gripmen delight in scaring passengers by releasing the brake at the top and saying "OK, we're going staight down into the Bay!". The actually brake by clamping onto the cable, which keeps them from going over 9 mph.

The claims for this New Zealand Street to be the steepest have also suffered from the confusion of those used to one method or the other. Either way the Tale that architects far away designed it without knowing the terrain and it still got built is reasonably amusing

Yes, I know that it makes sense in the field. I just find it very difficult to visualise.

Interesting that here in Australia the various railway authorities have always quoted curves as a radius, typically (in pre-metric days) expressed in chains. I wonder how the line was surveyed and laid out?

John

I had this problem recently when laying out a 4'6" radius curve in the garden, where the theoretical centre of the circles was (and still is!) in the middle of the pond.

A few minutes' doodling***** reveals that one can very quickly lay off way-points from the two intersecting tangents that come off the straight section.

We might muse today at how the standard of mathematics teaching has fallen in this country (Hardly surprising when you see who is doing the teaching?), but even in the 1960s, what we had to learn in geometry was trivial compared to what the Victorians had to do ... not only to reproduce Euclids' proofs, but having to use exactly the same letters to annotate the proofs!

visualise.

quoted curves as a radius, typically (in pre-metric days) expressed in chains. I wonder how the line was surveyed and laid out?

By calculating the degree of curvature, of course. "Degree of curvature" is surveyor's concept, devised to make laying out the line easier. It depends on the length of the "stations" (the standard distance between surveying points), so will vary with the local surveying practices. Its use in N. America is a historical accident. For operational purposes you do have to know the sharpness of the curve, but as long as everybody uses the same designations, it doesn't matter whether you use radii, or degrees of curve, or even (as Hornby does) some sequence of arbitrary numbers.

FWIW, in Austria, the radii are quoted in meters (to one decimal place, or roughly the width of the rail head, which is absurd, considering how much the track shifts with temperature changes.)

HTH Wolf K.