Engineering Loop-The-Loop Highways
Out of all my virtual impressions of fatal transportation- racing around a vertical loop remains the most lasting.
As a child of an era where PlayStation’s didn’t have numbers after them, my introduction to driving was a fast, furious and blocky affair. To this day I still have fond memories of scaling near-vertical cliffs, bouncing off incredibly rigid trees and glitching my way through the barriers. All of which contributed to a very disappointing learning curve when I finally got behind the wheel.
Out of all my virtual impressions of fatal transportation- racing around a vertical loop remains the most lasting. As and when the time comes that someone stupidly puts me in charge of the world, let me assure you, Civil Engineers will need to be ready to append 360° roller-coaster loop-the-loops to our forever ageing highway infrastructure. Perhaps some of you will scoff at this idea, but we all know that if you’re willing to pay enough someone will build it for you.
The loop-the-loops of my childhood video gaming career were almost always just an extension of the road; which tended to a mean a continuation of the full road depth rising from the ground as a monolithic concrete structure (although in the case of Sonic the Hedgehog it appeared to be a naturally occurring chequered geological formation). In real life, however, my roller coaster experiences have only ever been timber and steel.
Forgetting how it stands up for a moment (I believe this is called architecture), let’s consider the deflected shape of the vertical loop as our bewildered test-granny drives around it. The response is cyclic, and most importantly tensile; the car is doing its best to pull the structure apart. Unfortunately concrete is only really good in compression, which is why everyone’s favourite man-made rock is going to have to sit-out for this one.
As with concrete, doubly so with masonry; despite the superficial similarity to a railway arch the nature of the loading is completely reversed. It also turns out that very few timber loop-the-loop roller-coasters have been built, and even less survive today. By observation (what a great engineering term), our new vertical-loop infrastructure initiative is going to have to be built out of steel.
In the UK the DMRB sets out the basis for highways design in 10 easy steps (and 100 hard ones). A quick browse tells us that the maximum gradient a road should aspire to is 6%; less for busy roads (of which our junctions undoubtedly will be). Playing devils advocate, however, it doesn’t specify an absolute maximum; and thus it is expected that the new loops will get permission with a “departure from standard” for employing vertical gradients between -∞ and +∞.
At a glance I’d say I’m most worried about fatigue- there will be a phenomenal amount of fully reversed cycles on our loop.
Annoyingly, however, the DMRB does consider vertical transitions to be essential, and requires them to maintain certain sighting distances and standards of comfort. Arguably the sighting distances are not as bad as all that, as the loop is fully visible from a distance and cars will not be able to halt mid-way through. Similarly typical obstacles such as pedestrians and badgers are unlikely to be found in the blind-spot that the apex will become.
The requirement for comfort comes in at a maximum vertical acceleration of 0.3m/s², and this is a bit of a bugger. Avoiding delving too much into the exciting world of centripetal dynamics, you can say without picking up a pencil that at one point (at least) the vertical acceleration must be 9.81m/s² or else the car will succumb to gravity and fall off, which will arguably be even more uncomfortable.
When approaching this problem I was instinctively concerned with the speed that the car would be doing. A little more though, however, reveals that speed has little to do with this problem; in fact it turns out all we need be is a bit clever about our geometry and we’ll get to prescribe the vertical acceleration at every point. Although allowing for articulated lorries, however, is likely to result in a loop with some significant dimensions! In this case it makes sense to aim for a scenario where the upside-down drivers are subject to the same amount of gravity as upside-up ones.
The humble bicycle wheel is an ideal form; the track will form the rim with spokes running along the central reservation.
Throwing some static equilibrium at the problem: people feel like people when they have weight, people have weight when they are subject to gravity, people at the top of the loop are subject to gravity in the wrong direction, they need twice as much gravity to feel like they have weight in the right direction, thus the design force must be twice the weight (not mass) of the traffic. Given the relatively short ‘span’ and the continuous supports this is unlikely to be difficult to design for; although somewhat more ardours than the normal bridge loading!
At a glance I’d say I’m most worried about fatigue- there will be a phenomenal amount of fully reversed cycles on our loop, which is pretty much the absolute worse thing you can do. Providing a steel deck means full penetration welds everywhere. Arguably this will make us very unpopular with the contractors, but it’s unlikely to stand up for any length of time if you do anything else.
Probably the best structural form can be found by looking down (if you’re me, during my commute to work). The humble bicycle wheel is an ideal form; the track will form the rim with spokes running along the central reservation. Spokes are, in this case, essentially tensioned bars; and as the cars attempt to push out the rim, the spokes will hold it all together; resulting in a very stiff structure. In fact, given the concerns surrounding fatigue, it would even be possible to replace the spokes and re-tension the wheel.
Unfortunately, as the cars loop the structure the acceleration will have to come through traction, which will tend to feed the loop through itself. This means that our structure will just happily roll like a hamster wheel; something that might upset the drivers. Extending the bicycle analogy, a break system is likely to be the most effective way of preventing this effect, rather than attempting to hold it steady through the axle (which would involve significant torque). In this case we’ll be talking v-breaks, as a disc approach would spoil the view!
So that’s it, easily built, although perhaps foiled by stationary traffic…
As it turns out, however, a somewhat less permanent version of a highway vertical loop does exist- and thanks to TopGear and Dunlop you can see proof that a car really can loop-the-loop; although I expect that this form is too high in g-force and too low in durability for my 120 year highway designs.
Finally I have to finish off by pointing you in the direction of this guy, who does a much better job than I do at explaining the physics behind the loop.