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Underground > Laboratory >

A ramp that runs the length of Britain (simple physics query)

12:52 / 25.03.02

Right, I'm going to build a ramp that will allow cyclists, wheelchair users, skateboarders, people in shopping trolleys and other man-powered, wheeled vehicles to coast idly all the way from the north coast of Scotland to the Isle of Wight (roughly 750 km / 500 miles).

My first thought was that it should be a simple slope with a constant gradient. But I'd also like to have it so that yer coastee travels at a constant speed once they've got going. Is that possible without the use of brakes? Or would they naturally accelerate? I feel dumb asking this, because I know that a free-falling body accelerates till it reaches a certain speed - but I'm not sure how that works with very VERY gentle slopes and friction and that. Could a consistent average speed be achieved with undulations in the slope?

Answers much appreciated.

Ooh, ooh, also: what do you think would be the ideal gradient, and how high would the top of the slope have to be?

[ 25-03-2002: Message edited by: Saveloy ]

12:57 / 25.03.02

I think you want to look at roller coaster design for this one. On a roller coaster, the only time that energy is added to the system is when the car is pulled up the very first hill... the rest is all momentum and energy transfer, so your ramp could work similarly.

12:57 / 25.03.02

ah, but what about those who want to go the other way - from the isle of wight to scotland?

13:05 / 25.03.02

Well, the speed obviously can't stay constant on any constant grade--acceleration is inevitable. Your best bet is the gentle undulation/constant average speed model, will a slightly more precipitous drop at the end of the ramp to give 'em a boost.

Added bonus: this model would allow the ramp to be used in either direction. The downward slope needed for initial acceleration doubles as the upward slope needed for coming to a stop, for travelers going in the other direction.

Of course, you need to take terrain into account: the ramp's undulations cross over and under an imaginary line, and this line must be at an absolute height, i.e. relative to sea level, not to the neight ground level. Great Britain is not exactly mountainous, but neither is it completely flat from shore to shore, or else it would have all been flooded long ago: so your ramp would be underground for great stretches of its length, perhaps for the majority, unless its terminus was located high up (which presents a whole set of other problems as far as access), and would have to be supported as it passed over valleys and such, sort of like a suspension bridge.

[ 25-03-2002: Message edited by: Jack Fear ]

13:13 / 25.03.02

Persephone:
Ah, good suggestion, I'll have to do a bit of research in that direction. I suppose what I'm thinking of is the slowest, least thrilling but longest roller coaster in Britain. Would be a great way to see the country, coasting along with a cup of tea in your hand (which you'd picked up from a ramp-side vender on route, without stopping). You could have specially designed carriages for groups of 2+, and the route would be lined with b&bs.

shortfatdyke:

You're right, there should be two ramps. Should they be right next to each other, to allow for continuous rides back and forth, or would it be better to have one on each coast?

Jack Fear:

Good point about the hills. I was thinking the North to South route should have you start on top of a mountain and end up on a beach. Whilst the terrain generally becomes gentler as you travel further south, that would, I'm sure, take you through a few cuttings - which would be great every now and then, but ideally you want to be above ground for the majority of the journey. Maybe an elevated wiggly route is the solution?

[ 25-03-2002: Message edited by: Saveloy ]

pointless and uncalled for

13:14 / 25.03.02

Actually Jack the coastee would achieve a constant speed. It's called terminal velocity. However terminal velocity is likely to exceed a speed that would be considered coasting.

An undulating model would be unlikely assure a complete journey as frictions and resistances being variables would often likely cancel out increases in momentum bought about by the only force bringing increase (gravity).

For an undualting model to work the system would have to be controlled beyind reasonable means.

13:22 / 25.03.02

quote:However terminal velocity is likely to exceed a speed that would be considered coasting.
everyone could wear parachutes, or a big suit that made them look like a fruitbat

[ 25-03-2002: Message edited by: fridgemagnet ]

pointless and uncalled for

13:27 / 25.03.02

Or, they could wear the fruitbat suit and be catapulted through an undulating tube with controlled weight linked thermals.

Haus about we all give each other a big lovely huggle?

13:28 / 25.03.02

Hillis has worked out a system for the clock of the long hour - www.longhour.org - wear the curves and length are set in such a way that any unexpected acceleration automatically cancels itself out through the added momentum it brigns to the curve. You could try doing that....

pointless and uncalled for

13:34 / 25.03.02

Still need to respond to unexpected decelleration.

Haus about we all give each other a big lovely huggle?

13:40 / 25.03.02

But likewise - you pick up speed if you take a bend beneath the optimum speed, slow down if above. All very clever.

13:42 / 25.03.02

quote:Originally posted by heterodox:
Still need to respond to unexpected decelleration.I think Saveloy's intital idea addresses this--the start of the ramp would be substantially higher than the end, so that the overall direction would be a gradual downward slope, with the undulations providing managed decelerations to keep the speed reasonable, and the overall downwards slope compensating for friction / unintended deceleration.

This does, however, make for a one-way journey only. Hm.

[ 25-03-2002: Message edited by: Jack Fear ]

pointless and uncalled for

13:45 / 25.03.02

The link isn't working for me so I can't see all of the info before I begin to apply scenario conditions.

I'll try and find it when I have some time.

However, unless the system is closed, I can probably create a disruptive scenario.

13:53 / 25.03.02

Haus:
Sounds interesting, but I can't get that link to work. Is that the right url?

Jack:
Two ramps with the same start/end points but sloping in different directions would solve that. There could be a junction at the mid point where both ramps are at the same height, allowing travellers to break off and return to their starting point.

pointless and uncalled for

13:56 / 25.03.02

Actually if Haus' description is comprehensive enough it would work in both directions.

The Return Of Rothkoid

14:17 / 25.03.02

Given that I'm a physics dullard, I found this page to be useful in explaining some stuff...

20:33 / 25.03.02

Which side of the isalnd do you want to stop at? It make negligable difference to the distance (about 5km's, but I could have made that up), but the side hearest Southampton is flat, while the far side (with Blackgang) is fast restreating cliffs.

Would this affect anything at all?

I still don't like it here, you know, even if my knowledge of the place has come in handy, um... now and never before.

yawn - thing's buddy

08:57 / 26.03.02

(PUTS OFFICIAL HAT ON) current britsh building regs says that any ramp designed for wheelchair use needs to be at a gradient of 1:20.

(takes off official hat and puts on balaklava)

so thats 20 metres travelled in the horizontal to rise or fall 1 metre.

its about 1120 km from north tip of scotchland to isle of white.

so the top of the ramp at north tip is 56km (1120 divided by 20) high falling to 0km high at isle of white over a distance of 1120 km.

sounds great.

can I design and build it please.

08:57 / 26.03.02

Rothkoid:
Good link, ta. The page on 'simple rollercoaster physics' is especially useful.

Glint:
It has to slice through Fort Cumberland and terminate next to the hovercraft terminal at Ryde so that you could zoom back up it by hovercraft, which should only cost you about a billion quid a shot.

yawn:
Good work, thanks. I knew the start point would be high but 56km is in space, isn't it? I'm sure we could reduce the gradient - do the regulations allow for LESS than 1:20? And 1120km - is that as the crow flies? I made it 750, and that was using the highly accurate method of measuring an on-screen map with my fingers, so I couldn't possibly be that wrong.

[ 26-03-2002: Message edited by: Saveloy ]

08:57 / 26.03.02

Hang on... I think we're all missing something very important! This would consitute a Fixed LinK! Which, as far as I can see, is an Evil Thing. Really. Eveyrone here hates the idea of a fixed link to the mainland.

I mewan, I'm against it, bit I'm against other people being against it. Why? Becuase they're agaisnt it cos we'd loose our "island status", and I'm aginst it cos it wouldn't be between Cowes and So'ton, which is currently a very cheap and simple way to get off of here. And the Ryde Portsmouth hovercraft is easy for getting the train. So basically: Hmm...

08:57 / 26.03.02

Okay, either we make it terminate on Southsea beach (next to the mainland hover terminal) - the decision to have it end at the Island was arbitrary anyway - OR we keep it on IOW soil but, to retain island status, we make it impossible to leave the ramp en route and have the other end start on an artificial island just north of the Scottish coast. That island will be built using IOW soil and become, officially, one of the Needles and therefore part of the IOW. Obviously it'll crumble to nothing within a week of construction, but we'll deal with that later.

[ 26-03-2002: Message edited by: Saveloy ]

yawn - thing's buddy

13:03 / 26.03.02

saveloy: any less than 1:20? course you can! but it wouldn't be much of a slope.

as for the 1120km thing - just a guess

17:48 / 26.03.02

i dont think you can have a ramp that works the same for bikes as for cars. different efficiency of axles, tire-to-road friction, etc.

06:20 / 27.03.02

Its a bloody daft idea. Who in there right mind wants to go to the Isle of Wight?

[ducks]

09:48 / 27.03.02

Who wants to go to the IOW? Anyone who's just spent 5 days doddering down a concrete slope at 4 mph, that's who. It's the perfect acclimatisation process!

10:00 / 27.03.02

grant:

Hmmm, I wouldn't allow actual cars on there (unless they'd had the engine removed) but you're right anyway. I'd like to have the ramp divided into lanes of varying bumpiness, so that the overall angle of descent is the same but you can choose (and switch between) a flat ramp and an undulating one. Vehicles suffering from great friction would take the flat route and either use breaks to stay below a max speed (maybe some sort of auto breaking system could be fitted, with an onboard comp monitoring and reacting to the speed) or skillfully make use of the ascending (and therefore descelerating) sections on the undulating tracks.

19:52 / 27.03.02

The Great 'Lith Dynasty (exp, JackTB and Dawntreader) used to come here as small children. But that doesn't mean they wanted to...

14:19 / 28.03.02

Shouldn't this be in the Laboratory instead of the Conversation?

01:19 / 29.03.02

Probably, at this point.

Nevertheless, my two points--I mean cents.

To have an absolutely steady speed (once you got started), you would have to have an almost perfectly flat incline, rather than an undulating ramp. The ramp would have to be exactly steep enough to counter the force of friction on the riders.

01:52 / 29.03.02

Ok, so, unless anybody objects, I'll be moving this thread into the Laboratory. I give you 24 hours for objections or whatever.