Some Victorians were wary of the railways. First there was the speed. Anything over 30mph and you wouldn’t be able to breathe. Then there was the noise. It could be enough to disturb your vision, damage your eyes and turn you completely doolally. And then there were the tunnels! Speed, noise, smoke – best not speculate what all this would do to you in these stygian caverns.

Oddly, nobody was that concerned with pressure changes. Well, perhaps it wasn’t that odd as pressure changes only became a significant concern once trains started to run a little faster – or a lot faster – than in those early days.


A couple of recent tunnel incidents caught the eye(s) of Rail Engineer magazine. Location cabinet doors had been ripped off ‘by a passing train’ as – in separate incidences – were the covers of some equipment boxes on a train itself. Then there was the episode when permanent way trollies were sucked out of a tunnel recess to land up under a train. Looking back in the archives, these were by no means just one-offs.

Of course, it wasn’t the ‘passing train’ wot dun it. Rather it was the blasts of wind caused by the pressure waves associated with the trains. Tunnel pressure waves were also behind the firebox blowback that happened in 2012 when the steam locomotive 70013 ‘Oliver Cromwell’ entered Wood Green tunnel with the firebox doors open.

Extra confidence

Tunnel pressure changes can cause significant problems and so, with this in mind, Rail Engineer set off to meet an expert in the field (or rather tunnel) – Richard Sturt, an Arup Fellow. Apart from train aerodynamics, his expertise is in numerical modelling of the Laws of Physics that relate to engineering design.

He’s involved in the modelling of structures in earthquakes, for example, dealing with the response of buildings to extreme loading. “Often, we want detailed numerical models to back up the engineers’ intuition that their design is suitable and right from a common sense point of view. But to get that extra confidence, it’s often very useful to do numerical modelling based on fundamental theory. Of course, it all depends on having decent validation against experiments, but that builds up over the years.”

Great Western Railway train emerging from a tunnel, 1840-1845.

Great Western Railway train emerging from a tunnel, 1840-1845.

Increased speeds

We’ve mentioned damage to peripheral infrastructure but, long before that starts to happen, it’s the frailty of the human body that alerts us to pressure waves. Pressure affects all parts of the body, but it’s those delicate mechanisms accessed through orifices that can be the most sensitive to rapid changes, such as those in the head that link with the eardrums.

Those early Victorian travellers were far more occupied by the noise and smoke and the general terror to be even aware of pressure. Indeed, the pressure issues were unlikely to arise as the trains just didn’t go fast enough.

Move forward a few decades and a number of factors started to change the aerodynamics.

Demand for shorter journey times resulted in more powerful traction, smoother track and more comfortable rolling stock. Speeds increased and the bulk and length of the trains increased. Pressure effects increase by the square of the speed and so passengers – and indeed everyone on board – began to report discomfort in their ears whilst going through tunnels. They also noticed the bang when two trains passed each other at speed. The carriages would sway, windows would blow open and everything would judder.

Laws of Physics

The aerodynamics of trains passing through a tunnel can be seen as both simple and complex. It’s simple because everything behaves as per the Laws of Physics. As we’ve mentioned, the pressure increases by the square of the speed. It’s worth repeating that it’s not linear – it’s by the square.

Pressure is also a function of the cross-sectional area of the train profile and the cross-sectional area of the tunnel bore. The less room available for air to pass back around the train, the higher the pressure in front. The longer the train, the more friction between the train and the air and thus the higher the pressure in front, in accordance with the well-known ‘bicycle pump principle’.

The smoother the transition between one carriage and the next, the lower the friction between train and air. This means that older stock, with deeper profile recesses between carriages, leads to more friction, which reduces the ability to dissipate pressure at the front of the train.

Complex analysis

These are the simple issues. How they all interact with each other and with the vagaries of the tunnel profile is the stuff of complex analysis.

Further complications – which can all be modelled – are what happens when a train passes vertical or horizontal ventilation shafts. Additionally, the pressure waves that propagate in front of the train are reflected back from the ends of the tunnels (or down the shafts) and meet the train and even more pressure waves head-on.

An analogy is to look at the pressure changes as behaving a bit like a ‘Slinky’ spring stretched out on a frictionless table. Flick the slinky at one end and waves will move along the spring to end and then will bounce back. With a continuing flicking of one end, the resultant pressure collisions can be appreciated.

While it all appears quite daunting, this sort of analysis has been carried out for many years now, allowing the program that studies tunnel pressures to run on a laptop for just a few seconds.

Richard’s view is that “any computer model is, by definition, open to doubt, because it isn’t reality.

“I’ve been working in various kinds of analysis and simulation for over 30 years now and one thing I’ve learnt is that you can’t treat these computer programs like an infallible black box. You’ve got to be very careful and always try to validate and verify against real-life measurements whenever you can.”

Of course, you can’t just randomly go out and take measurements in a railway tunnel, because there’s the little issue of having to arrange possessions! However, there’s plenty of material in the literature where other people have gone out and measured things and, in many cases, they will have recorded enough information about the type of trains and the size of the tunnel. So, you can replicate the experiment that they did at full scale in the computer models and check that it matches their measurements as well.

Massive catapult

Over the years, there has been a programme of experimentation using physical models to further validate the computer results. Some of this was done at a facility called the TRAIN rig (TRansient Aerodynamic INvestigation) in Derby. It used to be part of British Rail Research, but it’s now operated by the Birmingham Centre for Railway Research and Education, which comes under the University of Birmingham’s civil engineering department.

The geometry is all to a scale of 1:25 (although other scales can be adopted if required). The trains are 25th scale and the tunnel is 25th scale, but the speed of the train needs to be the real-life speed. It’s not a scale speed because this involves pressure wave transmission and that happens at the speed of sound. No matter what the geometric scale, if it’s air then it is always going to be 340 metres per second and, for that reason, the speed of the train must be the right proportion of the speed of the pressure wave.

The rig needs a massive catapult system to fire the model trains at the actual speed of the real trains. Seeing these models fly by at 125mph or more is truly startling – a case of “blink and you miss it”. And the arrestor system at the end of the test track certainly has an important job to do…

The results from the scale model are useful in their own right, and also act as test cases for validation of the computer simulations. Once that’s done, the simulations can then be trusted to predict results for different configurations, different speeds, and different railways.

Japanese high-speed trains have close-coupled carriages and flexible fillers to minimise sonic boom.

Japanese high-speed trains have close-coupled carriages and flexible fillers to minimise sonic boom.

Tunnel boom

The issue of really high speeds is particularly relevant to a phenomenon sometimes called ‘tunnel boom’, a problem first encountered in Japan in the 1970s. When the Sanyo Shinkhansen line was extended to Hakata, there were many complaints from the nearby population of loud bangs coming from a tunnel long before the train emerged.

These bangs were the result of the pressure wave, caused by the train entering the tunnel, concentrating into a shock wave (a step-change of pressure) as it propagated along the bore at the speed of sound, to emerge as the tunnel boom when the wave reached the far end.

The Japanese quickly realised what was going on and came up with a mitigation design. This involves extending the bore of the tunnel entrance into the open air and then perforating the extension with holes. This slows down the rate at which the wall of air builds up in front of a train at the tunnel entrance and prevents the formation of a shock wave further down the tunnel, thus eliminating audible boom.

With train speeds in those days being no more than 200-280km/h, the effect was found to be noticeable only in long tunnels with slab track – ballasted track counteracted the process. However, as train speeds increase in future, and with the all-important gradient of the pressure wave increasing with train speed cubed, the issue has to be considered with every tunnel on new high-speed routes and there is increasing focus on finding the most effective designs for the tunnel extensions.

Wind effect

Computer models can now put design numbers to the distress felt by lineside equipment. The cabinet doors and doors to cross-passages and escape routes can be designed to withstand the pressure pulse at the nose of the train, and the mirror image suction at the tail of the train, while the whole assembly can take into consideration the fatigue loadings.

There’s also a wind in the tunnel caused by the train. Any surfaces that are perpendicular to the flow along the tunnel are going to feel the wind on them, particularly as the train goes by. That wind effect could be damaging as well as capable of dislodging even heavy equipment such as permanent way trollies.

Don’t panic

Train manufacturers have adapted to aerodynamic effects for as long as they have been known. They build into their trains the structural strength needed to withstand the rapid increases in pressure as well as designing body shells that are sealed to isolate passengers from the effects.

The Victorians had cause to fear train travel through tunnels. Gradually, the smoke has been eliminated, the noise has been managed. Those early travellers had no knowledge of ‘Slinky’ pressure waves bouncing along the tunnels or up and down the shafts.

It’s just as well that there are now experts who can inform the design of high-speed travel, otherwise we too would find rail tunnels at high speed to be very uncomfortable.

This article was written by Grahame Taylor.

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