Friday, 29 July 2022

Fantasy Finance: Make your child a millionaire

Make Your Child a Millionaire

In an article which came to my attention a week or so ago for some reason, Rob Gardner, who was described as a ‘financial expert,’ wrote in an article unequivocally titled ‘How parents can make their child a MILLIONAIRE’ in the Daily Mail dated 25/02/2018, that if you open a bank account for your child on the day he (she) is born,


  • …the daily saving [of £5·50 a day] can grow into a £1m pension pot for child [sic]
  • Contributing £5·50 a day equates to £6·88 a day due to tax breaks
  • By the time they reach 10 years old, the pot will reach a total of £25,000 [misrelated pronoun sic]
  • If money has been invested wisely, it could have grown to £35,000 — £40,000 [incorrect sequence of tenses sic]
  • Compound interest means the pot will roughly double every decade

Since I did something similar for my children back in the days when I had a job and interest rates were higher than they are now, I was most curious to find out what I had done all wrong. My children had ended up only with what I had paid into their accounts and a light spattering of interest.

I tried Mr Gardner’s schedule of payments on an Excel™ work sheet. I assumed a bank interest rate paid on savings accounts of 2% pa and an annual inflation rate of 3½%. In order that you may judge how realistic a projection that is, here is the Bank of England’s own diagram of recent interest rates. If anything, 2% appears a bit higher than you might realistically expect.

Bo-E-Database-export I did not consider tax on the interest payment, quite likely 20%, or management fees. Since the child has an income tax allowance, currently £12,570 in his own right, interest payments would have to be very large before you had to think about hiding your wealth off shore, like Members of Parliament do.

Firstly, the annual contribution that the parent has to make into the child’s account, £5·50 per day, evens out at £167·41 per month, taking leap years into account. In addition to the contribution to the account that the parents pay in, the bank also contributes interest on the capital that’s in the account already, as well as on payments that were made during the year. If you pay money into the account in January, it will have earned some interest by the time December comes round.

So, if the parents don't increase their daily contribution to account for inflation, this is how the account for the first ten years will look:

Paid in
Amount at
year end
0 £0·00 £0·00
1 £2,008·88 £2,028·96
2 £2,008·88 £4,098·51
9 £2,008·88 £19,791·79
10 £2,008·88 £22,216·59

At that point, the child’s tenth birthday, Mr Gardner tells us to stop making payments into the account.

  • When [the child turns] 10 years old, stop contributing. By this point the pot will have grown by almost £50 a week, or £2,500 a year, to a total of £25,000.

Actually it hasn’t, but at £22,216·59 it isn’t too far off target. Then Mr Gardner asserts that,

  • Because of the miracle of compound interest, if left alone this pot will grow (roughly doubling every decade) to over £1million by the time your child turns 65.

Ha! So that’s the secret of feeding a crowd of five thousand from a current account with nothing in it but five loaves and two fishes. That’s how to make bricks without straw. That’s how to catch a Woozle. The rabbit was in the hat already. It’s all done by smoke, mirrors and compound interest.

Well, no, it isn’t.

With a bit of mathematical reverse engineering, we find that in order to double every ten years, the loaves and fishes have to be invested at a minimum of 7·17734% pa interest. (Solve the equation (1 + r)10 = 2 if you don’t believe me.) In 2018, when the article was originally published, bank rate was ½% pa and even now (July 2022) bank rate is only 1¼% pa, which is well short of what you would need for the child to find a million pound legacy in his current account on his sixty-fifth birthday.

Here is the result of stopping payments. I allowed for the likelihood of the government increasing pensionable age to 70 years, but it does not make the child's position much easier, even though by now he walks with a stick, has grey hair and a tweed jacket, listens to Radio Three and can't work any technological device more complicated than the thermostat on the central heating.

Paid in
Amount at
year end
10 £2,008·88 £22,216·59
11 None £22,660·92
65 None £66,021·71
70 None £72,893·31

At this point, I ask myself, is there anything we could have done to rescue this poor soul from spending the rest of his life in grinding poverty? Is Mr Gardner’s vision actually practicable? Can you really endow a millionaire for only £5·50 per day?

I suppose the first thing would be for the parents to index their contribution for inflation. Let’s assume an inflation rate of 3½% pa. Now those first ten years look a little better, and we’ve achieved Mr Gardner's way-mark of £25,000 in the account by the child’s tenth birthday, but the total at age 65 or 70 is still nowhere near a million pounds.

The daily contribution will rise from £5·50 in year 1 to £7·50 in year 10. After that, the parents don't contribute any more.

Paid in
Amount at
year end
0 None None None
1 £2,008·88 £2,028·96 £5·50
2 £2,079·19 £4,169·52 £5·69
10 £2,737·89 £25,917·22 £7·50
65 None £69,758·47 None
70 None £85,035·19 None

The result is a bit closer to a million pounds than before, but it is still a long way off target.

The parents are going to have to spend more months making contributions. For how long might they continue?

My first child arrived when I was 25 years old, and I drew my old age pension at the age of 65. Let’s assume for the sake of argument that everyone else, including the parents of this hypothetical name on a passbook, does the same. Then the parent will retire after forty years of making payments.

Things look more favourable if the parents continue to make regular payments, indexed for inflation, for forty years after the birth of their child. Then they stop making payments and leave their child’s retirement income to the mercy of time and chance.

Paid in
Amount at
year end
0 None None None
1 £2,008·88 £2,028·96 £5·50
2 £2,079·19 £4,169·52 £5·69
10 £2,737·89 £25,917·22 £7·50
40 £7,684·69 £236,877·47 £21·04
41 None £236,877·47 None
65 None £388,622·59 None
70 None £429,070·75 None

We are beginning to see some encouraging results. By age 40 the child will have £¼m and by age 70, getting on for £½m.


We need to get more money from somewhere, so let's make the assumption that by age 43, the child's own eighteen year old children are gainfully employed, so that between the age of 43 and pensionable age, the child can contribute something out of his own pocket every day. Assume he pays the same as his parents did, indexes it for inflation and makes his first contribution on his 44th birthday.

We now look close to success. If the child makes his own contributions at the same rate that the parents did, then by age 65 the pension fund looks quite reasonable:

Paid in
Amount at
year end
65 £18,160·81 £736,293·73 £48·04
70 £21,569·35 £918,741·16 £57·06

Which is close enough to a million pounds, but no cigar.


Going back to Mr Gardner’s original scheme, what size contribution would you need to make it work at 2% pa interest? Again, we can try some reverse engineering and see.

Poundcoin At 2% pa interest, accumulating one million pounds by age 65 by making deposits every day for ten years and then leaving compound interest to do the hard graft requires contributions starting at £83·31 per day and indexed for inflation.

Poundcoin It would also be possible to accumulate one million pounds by age 65 by making deposits of £5·50 every day for ten years and contributing nothing after that if the interest rate were higher than 6·70% pa.

Poundcoin If you made contributions for forty years, at 2% interest your child would have a million pounds in his bank account by his 65th birthday if you contributed £14·15 a day instead of £5·50.

Conclusion: In the financial environment at the time when Mr Gardner’s suggested savings plan appeared in the Daily Mail, it was possible to start from nothing and pay daily contributions into a bank savings account, but it is considerably more expensive than Mr Gardner says it is. His payment plan only works if the interest paid on the account is guaranteed to be 7% pa or more throughout the period in which the savings are being amassed.

By that time, of course, with our guesstimated 3½% inflation, one million pounds in Year 65 would be worth a mere £109,012·79 in Year Zero money,

Wednesday, 27 January 2021

A route out of lockdown

Road-map Out Of Lockdown According to today's paper, our Prime Minister is working hard to create a road-map out of lockdown.


In order to save Mr Johnson (no relation) a lot of hard work, the Johnson (me) Road-map Corporation has done the hard graft for him:

Wednesday, 30 September 2020

Fantasy Engineering: The plan that failed — the Union Canal Waterbus

The plan that failed Could a passenger water-bus service operate on The Union Canal in the western suburbs of Edinburgh?

The Union Canal runs for 32 miles from Camelon, near Falkirk, to Tollcross in west Edinburgh. At Falkirk, the spectacular Falkirk Wheel joins the Union Canal to the Forth and Clyde Canal, which runs west to Port Dundas, Glasgow and to Bowling Harbour on the River Clyde near Dumbarton. and east to Grangemouth.

The Union Canal and the Forth and Clyde Canal were built to carry freight in what was then a heavily industrial area. There was a shale oil industry which covered mining, extraction and refining and produced motor spirit. There were mining and quarrying industries. The first detergent washing powder was also manufactured in the canal’s catchment area.

Here’s a map:

Map showing the Forth and Clyde Canal and the Union Canal
The Forth and Clyde Canal runs from Bowling (near Dumbarton) and from Glasgow in the west to Falkirk and Grangemouth on the east coast. The Union Canal links Falkirk to Edinburgh.

The Union Canal took four years to build, opened in 1822, became disused by 1920, closed in 1965 and re-opened to traffic after the completion of renovation work in 2001. Other transport infrastructure was being built in the same corridor at the same time. The railway from Edinburgh to Glasgow via Shotts opened in 1848, and the M8 motorway was built in stages and was completed in 2017.

An unusual feature of the design of the Union Canal, and one which makes it very suitable for passenger traffic, is that it has no locks. The canal follows the level of the 240 ft contour along its entire length. This means that the canal is appreciably longer than the 24¾ mile straight line distance from Camelon to Tollcross, but it is appreciably faster than a canal with locks would have been. Canal locks were a constant source of delay and irritation.

The canal towpath runs along the northern bank of the canal, except for the stretch that runs through Polmont in tunnel. In the tunnel, the bargee had to lie on his back on the barge and kick the roof of the tunnel to push the barge through it. The proposed passenger boat service does not run through Polmont.

Picture of the Falkirk Tunnel on the Union Canal
The Falkirk Tunnel on the Union Canal carries the canal beneath Prospect Hill in Falkirk and carried mainly cargoes of coal at the time.

I was moved to put computer, keyboard and mouse together and speculate about restoring a regular passenger service to the Union Canal when I read that ‘Swift Boats’ operated on the Forth and Clyde Canal in its early days and achieved a speed of ten miles per hour (8½ knots), providing a passenger service over the 24¾ miles between Lock Sixteen in Falkirk and Port Dundas in Glasgow at a speed distinctly faster than a stage bus. The Swift Boat service was heavily used, even though the single fare was four shillings (4s) in first class and 2s in second class. (That translates into £14·32 first class and £7·16 second class in today’s money, the first class fare coming remarkably close to the £16 cost of a ticket for a tour bus in Edinburgh today. See here.) The speed of ten miles per hour was achieved by using two horses to haul the boat and changing the horses often. Today the maximum speed of a barge is 4 mph (3½ kn), and Scottish Canals would be unlikely to agree to a higher speed for just one customer. Though, you understand, I’d have to ask.

I was curious to know whether it would be possible to operate a water-bus service on the Union Canal today, starting in Tollcross and conveying passengers ten miles or so to the western suburbs of Edinburgh.

Drawing of a Swift Boat
A Swift Boat, like this one, pulled by two horses, achieved a speed of 10 mph in passenger service on the Forth and Clyde Canal

Water bus services in cities, of course, are not particularly unusual. Venice has a whole network of vaporetti where other cities have bus services or trams. London has the Thames Clipper services on the Thames between Chelsea and the O₂ building at Greenwich, as well as a water bus service on the Regents Canal between Little Venice and Camden Lock, operated by the London Waterbus Company.

A water bus of the London Waterbus Company
A waterbus on the Thames

In Scotland, The North British Railway operated ferries on some lochs to convey passengers from lochside villages to their railway stations. They ceased to operate years ago, but Sweeny’s Cruises still operate a tourist boat service in summer from a boarding point on Loch Lomond.

Waterbus operating on Loch Lomond
A double deck luxury waterbus operates on Loch Lomond, near Glasgow

A waterbus stop on the Union Canalcould be as simple as a sign and a pontoon with mooring posts to enable the bus to stop and board passengers safely. A more elaborate waterbus stop would have lighting and a shelter adequate for Scottish weather conditions. The design has to take into account that a heavily used cycle path runs along the bank of the canal.

Design for a full featured waterbus stop on the Union Canal
Design for a full featured waterbus stop on the Union Canal

In Edinburgh, at the moment, there is no regular passenger boat service on the Union Canal, although numerous passenger boats are available to hire.

Armchair transport engineers, and I include myself, usually delude themselves that it would be possible to operate useful services over any disused railway, footpath or canal that could conceivably be re-opened, refurbished, re-built or re-used, and such services would be so popular among travellers that they would elbow, or if necessary fight, their way on board. If the service were steam hauled, that might even be true. Sadly, though, I had to conclude that in this case, commercial success of a passenger service on the Union Canal between, say, Port Buchan in Broxburn to Edinburgh would be impossible.

First things first, or, Drawing Maps is Fun.

I shall start by showing where the boarding points of the proposed service would be. Here is a map of the Union Canal showing the proposed stopping points. The service starts from the canal basin at Tollcross, on the west side of Edinburgh, and runs westwards to Port Buchan in Broxburn, a distance of thirteen miles. Then it turns round and comes back again. I chose Port Buchan because it is a rather quaint, usable canal wharf in a built up area where some residents might want to commute to Edinburgh, or just ride to Edinburgh for fun on the boat.

Map showing the Union Canal and boarding points
A map of the Union Canal showing the extent of the waterbus service and its boarding points
Running a public transport service on the Union Canal

Drawing of a Union Canal waterbus
A design for a waterbus carrying 40 passengers on the Union Canal

The maximum speed limit on the canal is 4 mph and a stop is expected to take three minutes. This includes time for the waterbus to come to a stop, moor at a pontoon waterbus stop, wait for passengers to embark and disembark, and for the waterbus to cast off from the pontoon bus stop and accelerate to the operating speed of 4 mph (3½ Kn.) This includes deceleration and acceleration, but since a passenger carrying vehicle cannot accelerate or decelerate at more than 0·1 g, acceleration from rest to full speed each take about 2 sec., which is regarded as negligible. We can compute journey time as 15 minutes per mile plus 3 minutes per stop.

Map of timings and distances
Timings and distances in miles between boarding points on the Union Canal

Waterbus Boarding Points

Bus Stop Tollcross is the original eastern terminus of the Union Canal, on the site of Fountainbridge Brewery. The terminal is ¼ mile from Lothian Road and ¾ mile from Princes Street. It is also close to recently built office blocks and to the Edinburgh Stock Exchange.
Bus Stop Fountainpark is an area given over to entertainments like cinemas and restaurants, functioning as a community hub. There is a large pedestrian square here with pubs, restaurants, a cinema and other amenities, as well as a walkway to Dalry Road. Haymarket Station and tram stop are just under one mile from Fountainpark. There are a number of student residences at Fountainpark.
Bus Stop Harrison Park is a recreation ground. There are public facilities for servicing narrowboats at the western end of the park, adjacent to the canal. Harrison Park is just over half a mile from Heart of Midlothian football club.
Bus Stop Colinton Road is intended to serve Craiglockhart, Morningside and Slateford in suburban south Edinburgh. This boarding point also offers an interchange with buses 18, 27 and 45.
Bus Stop Longstone boarding point is at the western end of the Slateford Aqueduct, which is one of the more impressive features of the Union Canal. The boarding point also offers a stairway down to the Water of Leith Centre and the Water of Leith path.
Bus Stop Kingsknowe is next to Kingsknowe railway station. The railway crosses the canal just east of Kingsknowe boarding point. The boarding point also serves Kingsknowe golf club and is half a mile from the cyclepath from Redhall to Balerno.
Bus Stop West Side Plaza boarding point is 350 yards from West Side Plaza, which is a dreadful 1960s shopping precint with a bus station, a cinema and a public library. West Side Plaza is in the middle of Wester Hailes, an area of system built blocks of flats erected in the early 1970s. There is unlikely to be much commuter traffic to Edinburgh from West Side Plaza because the bus services are excellent and the journey by water-bus takes about an hour. There is also a railway station close to West Side Plaza. It is on the Shotts line. Kingsknowe station is on the same line and is closer to the canal.
Bus Stop Sighthill is an industrial area which includes several large workplaces and Hermiston Gait [sic] shopping centre. There is a tram stop at Hermiston Gait. This boarding point is 1¼ miles from Heriot Watt University. If there turned out to be a demand from students for daily travel between the student residences at Fountainpark and Heriot Watt University, a boarding point could be added at Hermiston House Road, ¾ mile from the university.
Bus Stop Ratho is a village on the outskirts of Edinburgh. This boarding point also serves Newbridge industrial estate, which might generate some commuter traffic.
Bus Stop Climbing Arena is close to the Edinburgh International Climbing Arena, which would generate some leisure traffic. The Climbing Arena is also very busy on those days when it is used to host competitions.
Bus Stop Clifton Road serves Clifton Hall School which might generate some school traffic and some leisure traffic. This boarding point is just over half a mile from the western edge of Newbridge Industrial Estate and might generate some commuter traffic.
Bus Stop
M8 Park and Sail was an attempt to provide an interchange between the waterbus route and the M8 motorway, which crosses the canal just south of Broxburn. Building this boarding point requires the construction of about half a mile of slip roads, as the nearest exit from the motorway is at Newbridge. This boarding point would allow convenient access from the motorway to the canal, which would benefit tourist traffic travelling by car from outside Edinburgh.
Bus Stop Port Buchan is the western terminus of the passenger service. It is a quaint canal basin in Broxburn, a former industrial suburb to the west of Edinburgh. Broxburn is a residential district, but East Mains Industrial Estate is one mile to the east and Houston Industrial Estate is 2¾ miles to the west.

At the start, I decided to create an operating timetable which assumed
a. that there were two mooring areas for waterbuses, one at each end of the route,
a. that the first journey from Port Buchan to Edinburgh should arrive in time for commuters to travel to work,
c. that there should be an interval schedule throughout the day.

My first thought was to timetable one waterbus per hour in each direction throughout the day. The first waterbus eastbound was to leave Port Buchan at 05:00 and the first waterbus westbound was to leave Tollcross at 05:30. The last eastbound service was to leave Port Buchan at 21:00, arriving in Tollcross at a quarter past midnight, and the last westbound service was to leave Tollcross at 21:30, arriving in Broxburn just before one o’clock.

There are two possible standards of viability which could be used. One is that the whole of the cost of the service should be met from fares. The other is that one half of the cost should be met from fares and the other half should come from a government or local council subvention. The whole of the cost includes salaries, running costs and repayments of loans used as start-up capital.

The resulting timetable has no chance of being commercially viable, because the journey times are so long that the waterbuses could not be used by commuter traffic:

First Last      First Last
Port Buchan 05:00 21:00 Tollcross05:3021:30
M8 Park and Sail 05:1821:18 Fountainpark05:3521:35
Clifton Road 05:4321:43 Harrison Park05:4421:44
Climbing Arena 06:0022:00 Colinton Road05:5121:51
Ratho 06:1422:14 Longstone06:0422:04
Sighthill 07:04and23:04 Kingsknowe06:14and22:14
West Side Plaza 07:15hourly23:15 West Side Plaza06:27hourly22:27
Kingsknowe 07:29until23:29 Sighthill06:39until22:39
Longstone 07:3923:39 Ratho07:2923:29
Colinton Road 07:5223:52 Climbing Arena07:4323:43
Harrison Park 07:5923:59 Clifton Road08:0000:00
Fountainpark 08:0800:08 M8 Park and Sail08:2400:24
Tollcross 08:1300:13 Port Buchan08:4300:43

For a start, in order to arrive in Tollcross before 08:30 it is necessary to leave Port Buchan at around 05:00. Since a bus journey from Broxburn to Princes Street takes 45 minutes, it seemed unlikely that a waterbus would turn out to be a convenient way of getting to work.

But, worse, it takes all but eight hours to make a round trip from Tollcross back to Tollcross, or from Port Buchan back to Port Buchan. Since each bus takes 3¼ hours to make a on waay trip, an hourly service needs twelve buses, each with a crew of two or, more likely, three. and working time regulations would limit each crew member to about 40 hours’ work per week.

Driving public transport is a strenuous job. A Commons debate on 6 June 2019 (see Hansard, Volume 661, Column 184WH) heard that about 40% of bus drivers work more than 90 hours per fortnight. If we accept 40 hours as the crews’ maximum working week, then a crew can only work one eight-hour return trip per day. The cost of a 28 seater waterbus is estimated at £95,000, which is the price of a low end single decker road bus. The cost is equivalent to an annual payment of £11,000 at 3% interest. Crew are estimated to cost £26,000 salary p a. So the cost of running a waterbus service of this frequency is about £1·6 M per year.

So, having ruled out providing an hourly service calling at all boarding points, I have to consider instead the possibility of serving the tourism industry. That means providing at most three services in each direction in the middle of the day in summer when the Edinburgh Festival is operating, and one service in each direction per day during the shoulder season.

If the traffic available is tourist traffic, then the facilities on the boats have to be of a high enough standard to attract tourists and holiday-makers. That probably means hot food and sales of licensed drinks.

The problem is that because of its design, following the 240 ft contour, the Union Canal doesn't really go anywhere except from Falkirk to Edinburgh. Although the canal runs through the middle of Polmont and Linlithgow, the towns and suburban centres of western Edinburgh do not lie along the canal.

That, of course, can be seen as poor urban planning. Where transport routes exist, it would have made sense to site trip generators along them. It would be easier to provide public transport instead of catering for the endless use of cars if airports, cinemas, parks, hospitals, housing estates, industry, office blocks, schools, supermarkets and so forth were located along roads, railways and canals instead of being plonked onto green-field sites miles from the nearest railway station.

In Edinburgh even such large trip generators as Edinburgh Airport, the Western General Hospital, Hermiston Gait shopping centre and Heriot Watt University were not sited near railway lines, and bus and tram stations have had to be provided for them.

Sunday, 28 June 2020

Fantasy engineering: The other way to build a high speed railway

Fantasy Engineering: High Speed Railways Instead of HS2, build 1700 miles of broad gauge main line and enjoy the higher speed and greater stability of trains on the broad gauge.

Proposed network of broad gauge high speed lines

One hundred and seventy five years ago, in 1845, the Royal Commission on Railway Gauges made a serious error of judgment. They decided that in future any new railway in Britain (but not Ireland, the whole of which was then part of the UK) would be built to the ‘standard gauge,’ that is, a distance between the rails of 4′ 8½″.

The Commission continued to sit and issue reports from time to time (no point wasting a good sinecure) and in 1893 they compounded their error by ordering that the Great Western Railway re-gauge its 177 mile long main line from London to Bristol and Penzance to ‘standard gauge’. The genius Isambard Kingdom Brunel, the chief engineer of the Great Western Railway, completed the re-gauging work in the space of a three day Bank Holiday week-end, beginning on 21 May 1892 and finishing on 23rd, a feat of engineering and project management which, I suspect, could not be done today.

The present debate about the need to build a special high-speed railway line, HS2, would not have come about if the Commission's decision had gone the other way and all the railways in Britain, except the Great Western and some narrow-gauge mining lines, had been re-gauged to Brunel's broad gauge of 7′ 0¼″, half as wide again as the standard gauge. We would probably be taking 200 mph train services for granted.

There are several ways of increasing the speed of a train service. You can reduce the load, for instance by building carriages out of lightweight materials. You can speed up the train, for instance putting a second locomotive at the back of the train. You can speed up the schedule, for instance by leaving out some station stops. Or you can speed up the track.

HS2 requires the building of completely new track. (Here is a map of it.) But there is a cheap alternative, which is to bring back the broad gauge on the routes that you want to accelerate.

Brunel's broad gauge Great Western services to London were noted in their day for going faster and giving a smoother ride than other main line competitors. This is not coincidence. Research carried out a century after Brunel's broad gauge was abandoned showed the relationship between track gauge and maximum speed. Many factors affect the maximum speed of a train on a track — gradient, curvature, weight and power — but other things being held constant, the greater the track gauge, the higher is the speed at which the train becomes unstable on the rails, and the wheels begin to ‘hunt’ from side to side. The speed at which the wheels begin to hunt is the train's maximum speed. There is an explanation of what keeps a train on the track in this Scientific American article, Train Wheel Science, and a full discussion of ‘hunting’ in this Wikipedia entry, Hunting Oscillation.

Lion Steam Locomotive
A replica of Lion, one of Brunel's broad gauge passenger steam engines

A replica of a broad gauge second class passenger carriage

Speed and journey times. The target to beat is a journey time from London to Birmingham, 101 miles, of 52 minutes, since that is the expected journey time on HS2. That would require an average speed of 117 mph. Trains can only accelerate gently, at a maximum of 0·1 g (3·2 ft.sec⁻²,) otherwise any standing passengers will fall over and hurt themselves. Therefore the maximum speed has to be appreciably higher than the average speed. You need a maximum speed of 175 mph to travel 101 miles from a standing start to a standing finish in 52 minutes.

Since the German ICE 3 train achieves a maximum speed of 206 mph in service on standard gauge track, and the Italian Frecciarossa achieves 187 mph, a maximum speed of 175 mph on broad gauge track does not appear over-ambitious. The difference is that ICE 3, Frecciarossa and the French TGV all run on specially built track. The broad gauge trains which I am proposing here run on existing track with modifications and, in general, require little by way of land acquisition.

The same maximum speed and acceleration suggest that the journey from London to Edinburgh, 440 miles, would take 3 hr 43 min, (118 mph) compared with the current fastest time of 4 hr 20 min (101 mph.)

Construction of HS2 is due to finish in the year 2035, so the development time for a broad gauge network has to be similar.

Broad gauge trains run on two rails seven feet apart, but that doesn't mean that Network Rail will need to rip up thousands of miles of standard gauge track and re-build it. It is sufficient to add a new rail to standard gauge track, like this:

Dual gauge track. The leftmost rail is common to both track gauges, the middle rail is used by standard gauge trains and the rightmost rail is used by broad gauge trains.

Dual gauge track is not unusual in many countries, though as far as I know there is none anywhere in Britain except for some replica track at Didcot Railway Museum. Greece and Switzerland, for example, have dual metre/standard gauge lines.

Broad gauge in its heyday: The Flying Dutchman passes Acton station, London, on dual gauge track at sixty miles an hour in the 19th century.

With careful attention to the profiles of broad gauge rolling stock, it should be possible to fit the broad gauge track under existing gantries, bridges and tunnels. Where platforms are adjacent to the common rail, they may be used unchanged, although platforms on the other side of the track will need re-locating, or a special track formation to allow standard gauge track to stop at them.

It is worth mentioning that Talgo technology allows a train to change from one track gauge to another as it moves. Adopting Talgo technology on broad gauge trains would mean that a train could leave the broad gauge and travel on a standard gauge line for reasons such as diversions. Talgo uses wheels mounted on square axles and track arrangements that change the gauge of the train as it travels.

British Profile
Profile of a British standard gauge passenger carriage

British Profile In Tunnel
British standard gauge passenger carriage fits into a 12′ 6″ diameter tunnel with 6″ clearance all round

Proposed broad gauge passenger carriage fits into a 12′ 6″ diameter tunnel with the same clearance, but the trackbed has to be raised slightly and the floor to ceiling height of the carriage is less than in a standard gauge carriage

Estimated costs. These are back-of-a-fag-packet figures, but we live in a world where any estimate of costs is considered better than none. (Ask Diane Abbott if you don't believe me.) In general there is very little land purchase cost, because the broad gauge track is achieved by dual gauging existing standard gauge track and keeping down the cost of re-building gantries, tunnels and bridges by designing broad gauge trains to fit within the present standard gauge clearances.

The cost of the proposed bridge across the Irish Sea is excluded, because the bridge is a separate infrastructure project and not in general financed by the railway.

It is possible to give an idea of the cost using figures from the report Guide to Railway Infrastructure Costs on the cost of recent reconstructions of railway lines. Those where the cost is expressed per mile range from £4½M per mile for the re-opening of Wisbech to £11M per mile for the Borders Railway including all infrastructure. The schematic diagram at the top of this page shows 1700 miles of dual gauge track, meaning the cost at 2020 prices might well lie between £8Bn and £14Bn.

It is estimated that a half hourly high speed service on each route could be provided by 68 trains. 68 broad gauge diesel locomotives cost about £136Mn (Railway Technical) and 12 passenger carriages per train cost in total about £122Mn (Transport Watch.)

A discussion of the cost of adapting the track and building broad gauge rolling stock begs the question of whether the adaptation should be carried out as a single project over, say, fifteen years like HS2, or whether it could be carried out in stages as different lengths of track take their turn to be renewed or repaired so that the dual gauging is done in an opportunistic way over, say, 100 years, or as long as it takes. Railways have been with us for all but 200 years and some projects have been carried out opportunistically, such as the electrification of the network, which could be said to have begun with the Volks Electric Railway as long ago as 1883, and which is still not complete. (There is an interesting precedent for this approach. In 1920 the Dutch government took a decision that where a road was renewed or replaced, the replacement would include a cycle track. After 100 years the Dutch road network is unique in its generous provision of cycle tracks.)

Opportunistic dual gauging reduces the cost greatly by taking advantage of workers and machinery which would have been in place anyway. It also raises the possibility of increasing the loading gauge.

Loading gauge. An opportunistic dual gauging policy could also include the raising of the loading gauge. This proposal suggests that the locomotives and passenger carriages of broad gauge stock should fit inside existing clearances, so as to avoid the need to enlarge bridges and tunnels. This includes the clearances for tilting trains, which are more comfortable at high speed, but have to be built so as to fit inside the same clearance as trains that don’t tilt.

The British railway network was the first in the world and, therefore, made all the mistakes. One of these was setting the maximum vertical height of a train at 12′ 6″. Other countries set their loading gauges higher, meaning that they were able to increase the capacity of a train by running double deck carriages.

The British Great Central Railway was built to Continental clearances and would today have offered faster and bigger trains between Manchester and London, but absurdly it was closed by Marples and Beeching in stages ending in 1969.

As was observed at the time, ‘surely the prize for idiotic policy must go to the destruction of the until recently most profitable railway per ton of freight and per passenger carried in the whole British Railways system, as shown by their own operating statistics. This railway is of course the Great Central’ (Daily Telegraph, 28/09/1965)

Map of Great Central Railway
Map of the Great Central Railway from Manchester to London Marylebone

The closest that British railways have come to a double deck train is the 4DD class electric multiple unit, which had interleaved upper and lower decks and ran on the Southern Region in the 1950s.

SR Class 4DD
Southern Region's 4DD class double deck commuter train

Interleaved decks
Interleaved upper and lower decks

American Superliners take advantage of the high loading gauge of 16′ 6″ in the western states. European railways have a slightly lower loading gauge, but still big enough to allow the operation of double deck trains.

American Double deck carriage profile
Profile of American double deck Surfliner carriage

By permitting the re-gauging of the tracks and the increasing of vertical clearance to take a very long time, opportunistic enlargement of bridges, tunnels and gantries will allow double deck trains to operate on the British main line… but not until about the year 2120.

An express passenger train on the new broad gauge network might then look like this:

Double deck train in British Railways maroon livery
Double deck train in British Railways maroon