On Tue, 2 Aug 2005, Earl Purple wrote:

And actually, a road, if used properly, will usually take a greater
volume than a railway. On a D2 dual carriageway, for example, if cars
are travelling at a 2-second gap,

Then they're travelling too close together. Unless the traffic's flowing
at 40 mph, at which speed 2 seconds is almost enough.

I'm basing this on highway code rule 105, which says:



105: Drive at a speed that will allow you to stop well within the distance
you can see to be clear. You should

* leave enough space between you and the vehicle in front so that you
can pull up safely if it suddenly slows down or stops. The safe rule is
never to get closer than the overall stopping distance (see Typical
Stopping Distances diagram below)



The diagram it references gives the following stopping distances for
various speeds:

Speed (mph) Distance (m)

20 12
30 23
40 36
50 53
60 73
70 96

If you divide the distances by the speeds, you get the following times:

Speed (mph) Time (s)

20 1.35
30 1.73
40 2.03
50 2.39
60 2.74
70 3.09

If you're talking about a dual carriageway, then presumably you're hoping
for a speed of 70 mph, which would require a gap slightly longer than 3
seconds. Of course, if you're talking about a road in London, then 40 mph
is probably quite realistic!

you get 30 cars in each lane passing per minute. If each car has 2
occupants,

Then that's very good going. The average occupancy is about 1.5.

that's 120 passengers a minute in each direction.

Or, if you use realistic numbers, 60.

You'd need to run a very frequent train service to carry that many.

Let's go with your number of 120 pax/min, which is 7200 pax/hour.

Let's compare that to a reasonably modern and efficient tube line, the
Central - the nominal capacity of one of its trains is 620 passengers, and
it runs 30 trains per hour, for a capacity of 18600 pax/hour, over two and
a half times that of your motorway, for a fraction of the land take. And
if you have the ability to use 12-car mainline-gauge trains, like
Crossrail, then it's even higher.

tom

--
We must perform a quirkafleeg

In article , Tom
Anderson wrote:
Then they're travelling too close together. Unless the traffic's
flowing at 40 mph, at which speed 2 seconds is almost enough.

Your arithmetic is wrong in that during the period you are stopping
your average speed is only going to be about half the initial speed,
so you would need to double your calculated times. What you ignore,
and what lies behind the 2 second rule on faster roads with good
visibility is that the car in front is not going to stop dead -
unless something really catastrophic happens.

Being a old guy who passed his test in imperial days the formula for
stopping distance was m(1+m/20) feet: the first term is basically the
distance travelled whilst your brain is getting your foot to press
the brake, the second the actual time needed to stop.

So if the car in front is doing 60 (88ft/sec) the total stopping
distance is 240ft - 60ft thinking, 180ft to actually stop. You're 2
seconds (176ft) behind the car in front when you see his brake
lights. He comes to a halt 180ft further down the road - 356ft from
where you are at the point when you see his brake lights. Assuming
your reactions and brakes are equal to the Highway Code you stop in
240ft from this point, 100 ft or so to spare.

--
Tony Bryer

Tony Bryer writes:
Being a old guy who passed his test in imperial days the formula for
stopping distance was m(1+m/20) feet: the first term is basically the
distance travelled whilst your brain is getting your foot to press
the brake, the second [that travelled in] the actual time needed to stop.

However, that is an oversimplification. The distance needed to stop
under maximum braking force (or any particular force) varies as the
*square* of the speed.
--
Mark Brader | "Forgive me if I misunderstood myself, but
Toronto | I don't think I was arguing in favour of that..."
| -- Geoff Butler

On Tue, 02 Aug 2005 16:43:40 -0000, (Mark Brader) wrote:

Tony Bryer writes:
Being a old guy who passed his test in imperial days the formula for
stopping distance was m(1+m/20) feet: the first term is basically the
distance travelled whilst your brain is getting your foot to press
the brake, the second [that travelled in] the actual time needed to stop.

However, that is an oversimplification. The distance needed to stop
under maximum braking force (or any particular force) varies as the
*square* of the speed.

Which is presumably why the quoted formula has an 'm squared' in it
(once you expand the brackets).

I (Mark Brader) wrote:
However, that is an oversimplification. The distance needed to stop
under maximum braking force (or any particular force) varies as the
*square* of the speed.

This response is posted:
Which is presumably why the quoted formula has an 'm squared' in it
(once you expand the brackets).

Awk! So it does. I'm not used to seeing it written that way, but
that's no excuse -- sorry, folks.
--
Mark Brader, Toronto | "Mark is probably right about something,
| but I forget what" -- Rayan Zachariassen

In article ,
Tony Bryer wrote:
In article , Tom
Anderson wrote:
Then they're travelling too close together. Unless the traffic's
flowing at 40 mph, at which speed 2 seconds is almost enough.

Your arithmetic is wrong

Irrelevant (and arguable).

When using _your_ figure of 120 pax per minute per lane - which is
somewhat optimistic and assumes ideal conditions - you still get a
answer which says that a 3 lane motorway has the same capacity as
the central line.

It may be interesting to compare the projected cost of crossrail
with the projected cost of a 4 or 5 lane motorway over the same
route.

They would probably have equilvilent capacity according to your
figures; I'm assuming that crossrail capacity will be half as much
again as the central because it has longer trains, but that's a
somewhat back-of-the-envelope calculation.

--
Mike Bristow - really a very good driver

On Tue, 2 Aug 2005 18:31:12 +0000 (UTC), Mike Bristow
wrote:

When using _your_ figure of 120 pax per minute per lane - which is
somewhat optimistic and assumes ideal conditions - you still get a
answer which says that a 3 lane motorway has the same capacity as
the central line.

The fallacy in your argument is the comparison of cars with a full
train. You ought to be comparing 80-seat coaches with a train to get
the true figure. With a 2-second interval, that is a coach every 176
feet at 60 mph or about 4 coach lengths. If you can get that density
of seating (not seated and standing) on your train, you will be doing
very well.
--
Terry Harper
Website Coordinator, The Omnibus Society
http://www.omnibussoc.org

On Tue, 2 Aug 2005, Terry Harper wrote:

On Tue, 2 Aug 2005 18:31:12 +0000 (UTC), Mike Bristow
wrote:

When using _your_ figure of 120 pax per minute per lane - which is
somewhat optimistic and assumes ideal conditions - you still get a
answer which says that a 3 lane motorway has the same capacity as the
central line.

The fallacy in your argument is the comparison of cars with a full
train. You ought to be comparing 80-seat coaches with a train to get the
true figure.

Wrong. We're not talking about idealised fantasy busways here, we're
talking about transport corridors as they are found in the wild -
motorways really are full of cars carrying an average of ~1.5 people each,
and tube lines really are full of trains carrying 500 people each (the
620 pax/train number i used is the planned capacity; actual passenger
loads are actually even higher than that).

With a 2-second interval, that is a coach every 176 feet at 60 mph or
about 4 coach lengths. If you can get that density of seating (not
seated and standing) on your train, you will be doing very well.

Well, if you're going to start running 1800 bph with every seat full, i
hope you don't mind if i increase the frequency of my trains to something
equally ludicrous to maintain my lead .

tom

--
No hay banda

On Tue, 2 Aug 2005, Tony Bryer wrote:

In article , Tom
Anderson wrote:

Then they're travelling too close together. Unless the traffic's
flowing at 40 mph, at which speed 2 seconds is almost enough.

Your arithmetic is wrong in that during the period you are stopping your
average speed is only going to be about half the initial speed, so you
would need to double your calculated times.

No, that's irrelevant - HC rule 105 sayeth that "the safe rule is never to
get closer than the overall stopping distance"; that applies to cars that
are cruising at constant speed, in which case my calculations are correct.
The stuff about average speed during braking is captured in the
calculation of that overall stopping distance.

What you ignore, and what lies behind the 2 second rule on faster roads
with good visibility is that the car in front is not going to stop dead
- unless something really catastrophic happens.

True, but whoever wrote the HC didn't seem to think that mattered - rule
105 commands you to "drive at a speed that will allow you to stop well
within the distance you can see to be clear". Perhaps they had those
really catastrophic somethings in mind?

tom

--
No hay banda

In article ,
Tom Anderson wrote:
No, that's irrelevant - HC rule 105 sayeth that "the safe rule is never to
get closer than the overall stopping distance"; that applies to cars that
are cruising at constant speed, in which case my calculations are correct.
The stuff about average speed during braking is captured in the
calculation of that overall stopping distance.

If we're to play with real-world numbers, throwing the HC out the
window would be the best bet. I think that a gap of 2 seconds
between vehicleS is reasonable (ie, 30 cars per minute per lane).

--
Mike Bristow - really a very good driver