[alancalverd]

As I see it, snow isn't the problem - it usually blows away or falls off and disperses from rigging. Things get particularly hairy on a ship or a plane when rain or, particularly, supercooled cloud, hits a cold surface and forms solid ice.

The other thing that bothers me is the idea of replacing cable anchorages with insulators. You need at least to de-stress each cable in turn, which means finding some way of supporting the cable's weight  or removing it and recabling from scratch. And then you need an insulator that doesn't creep, and matches the cable thermal expansion. Probably feasible, but is it economic? How many hours a year is the bridge closed for de-icing?

The trick on airplanes is to fit an inflatable rubber boot on the leading edge of the wing. When you have acquired a few millimeters of ice, you inflate the boot and the stuff cracks off. If you do it too soon the ice just accumulates on the inflated surface and the boot pumps up and down in a void beneath the ice - with potentially fatal consequences, so it's a bit of a critical art.  But you could encase each cable with a boot and do the same. No problem if you get a void - just close the bridge anyway!

[Bored chemist]

I’ve written this spreadsheet to calculate the specifications for the electrical power supplies

Glad to know you have found something to keep yourself occupied during lockdown.
I re-glazed my greenhouse.

[Peter Dow (OP)]

The other thing that bothers me is the idea of replacing cable anchorages with insulators. You need at least to de-stress each cable in turn, which means finding some way of supporting the cable's weight  or removing it and recabling from scratch.

Didn't you notice that these bridge cables are comprised of multiple parallel individually insulated strands?

Well those strands are individually attached and can be individually detached for replacement etc.

And then you need an insulator that doesn't creep,

Fibre glass.

and matches the cable thermal expansion.

Fibre glass stretches but it probably needs to be made into a glass fibre reinforced plastic insulating sheath to exclude water ingress defeating the insulation.

One could use a suitably lowish co-efficient of thermal expansion epoxy resin to arrive at an insulating sheath with suitable thermal expansion properties to match the steel parts it is insulating.

Probably feasible, but is it economic? How many hours a year is the bridge closed for de-icing?

It seems to be averaging at a few days closed per year.

The trick on airplanes is to fit an inflatable rubber boot on the leading edge of the wing. When you have acquired a few millimeters of ice, you inflate the boot and the stuff cracks off. If you do it too soon the ice just accumulates on the inflated surface and the boot pumps up and down in a void beneath the ice - with potentially fatal consequences, so it's a bit of a critical art.  But you could encase each cable with a boot and do the same. No problem if you get a void - just close the bridge anyway!

It works out at about 25 tonnes of ice per mm over the bridge's 70km of cables. I'm looking for a solution that doesn't require any bridge closures.

[Bored chemist]

bridge.png (376.19 kB . 627x354 - viewed 4558 times)What happens here?

As far as I can tell the set of strands  that make up the cable are all covered by the same cladding.

And if that's the case, then it doesn't matter which particular strand(s)  you choose to heat.
The overall effect will be  the temperature rise of the outside of the cladding will be related to the total power dissipation in the cable. (and the relation will be very close to "proportional to").

So, in that case, what does your spreadsheet tell us?
What model does it give for whatever that white coating is?

[Peter Dow (OP)]

I’ve written this spreadsheet to calculate the specifications for the electrical power supplies

Glad to know you have found something to keep yourself occupied during lockdown.
I re-glazed my greenhouse.

I didn't start programming the spreadsheet until 9 days ago when the Scottish Government agency in charge of the bridge - Transport Scotland - finally agreed to release to me the cable data - lengths, numbers of strands, stay pipe diameter - I had been asking for, for more than a year.

If this country is being held back it is not by the competence of our computer scientists.

[Bored chemist]

It's been a while, and you still haven't answered this properly.

I'm also intrigued by the notion that it matters much which wires you heat.
Metals conduct heat quite well.
If you heat the ones in the middle, the heat will diffuse to the outside.
If you heat the ones round the perimeter, the heat will diffuse into the core of the cable.
Fundamentally, the only place that (most of) the cable can lose heat is from the surface, so it hardly matters which bits you heat.

A bit of plastic won't matter much- it's not as if we are trying to get things "hot", just keep them above freezing.
And, if a bit of plastic does matter then the really important one is the overall wrapping of the cable.
So, why do you think it matters which of the hundred-and-odd strands we heat?

[Bored chemist]

I didn't start programming the spreadsheet until 9 days ago

That's OK, I waited until January before I refurbished my greenhouse.

If this country is being held back it is not by the competence of our computer scientists.

I wasn't aware that anyone had suggested it might have been.

[Petrochemicals]

And then you need an insulator that doesn't creep, and matches the cable thermal expansion.

You are probably on to something there Alan, as metal gains and releases heat faster, probably due to internal conduction, this problem could probably be solved to an acceptable level with insulation.

[Peter Dow (OP)]

bridge.png (376.19 kB . 627x354 - viewed 4558 times)What happens here?

As far as I can tell the set of strands  that make up the cable are all covered by the same cladding.

Correct. The set of strands are surrounded by a HDPE "Stay Pipe".

And if that's the case, then it doesn't matter which particular strand(s)  you choose to heat.

It does matter because you can't heat the inner strands because they will get too hot, the HDPE insulation will melt and then the cables will get damp air about them, rust or suffer hydrogen embrittlement and break and we couldn't have that, could we? 

The overall effect will be  the temperature rise of the outside of the cladding will be related to the total power dissipation in the cable. (and the relation will be very close to "proportional to").

The ideal overall effect will be when the heat flows evenly from the exterior strands that are being heated to heat the stay pipe evenly.

So, in that case, what does your spreadsheet tell us?

It tells you the specification for the electrical power supply required for each heating strand pair, as shown in this image previously helpfully linked to.

This is a screenshot – click to view a high-resolution image.

What model does it give for whatever that white coating is?

The heat flow characteristics across the thickness of the HDPE stay pipe can indeed be modelled but the heat transfer is relatively efficient compared to that between the strands across a mostly air gap to the stay pipe. So the temperature of the inside of the stay pipe is only 5 or so degrees hotter than the outside of the stay pipe. It is the much higher temperature of the strand sheaths that you have to watch.

These are complex calculations with multiple factors and mechanisms of heat transfer - conduction, radiation and convention, only some of which I have provisionally calculated so far.

Anyway, I'd want to confirm such calculations experimentally before committing to a certain heating power design - hence the power figures given are nominal and subject to a percentage factor yet to be determined.

[Peter Dow (OP)]

It's been a while, and you still haven't answered this properly.

I'm also intrigued by the notion that it matters much which wires you heat.
Metals conduct heat quite well.
If you heat the ones in the middle, the heat will diffuse to the outside.
If you heat the ones round the perimeter, the heat will diffuse into the core of the cable.
Fundamentally, the only place that (most of) the cable can lose heat is from the surface, so it hardly matters which bits you heat.

A bit of plastic won't matter much- it's not as if we are trying to get things "hot", just keep them above freezing.
And, if a bit of plastic does matter then the really important one is the overall wrapping of the cable.
So, why do you think it matters which of the hundred-and-odd strands we heat?

All that plastic which surrounds the metal strands is not in the least suitable for transferring heat so it matters very much to be careful to moderate the rise in temperature within the cable with the best design possible.

[Petrochemicals]

You may find this enlightening.

https://www.powerandcables.com/impact-mitigation-of-icing-on-power-network-equipment/

[Bored chemist]

The heat flow characteristics across the thickness of the HDPE stay pipe can indeed be modelled but the heat transfer is relatively efficient compared to that between the strands across a mostly air gap to the stay pipe.

The HDPE is surrounded by a much much bigger air gap.
That's my point.
The biggest thermal resistance is the loss from the cable "as a whole". The temperature gradient within the pipe is quite small.

In any event, we can make a simplifying assumption.
Imagine we just heat the outermost layer of wires.
The inner ones will be less hot than the (the inner side of) outer ones, so they will be OK.
If you can't heat the outer ones to a point where the cable sheds ice without damaging the outermost layer of wires,  then the task  is impossible anyway, and we can abandon it.

[Peter Dow (OP)]

The biggest thermal resistance is the loss from the cable "as a whole".

That really depends on whether it is raining ice cold water onto the cable or not. If it is then the thermal resistance of the cable will be very low. Lots of power and the cable surface temperature won't rise much above freezing.

On the other hand if it is a dry freezing night then the thermal resistance of the cable will be a lot higher - but that's actually a good thing, because it makes it a lot easier to heat the cable to above freezing, with just 10 watts per square metre - check out the "Ambient if dry" line plotted in my "Cable Heating Control" graph.

The temperature gradient within the pipe is quite small.

You don't seem to have studied and understood my aforementioned graph, which suggests that the temperature gradient between the strand sheaths and the inside of the stay pipe could be of the order of as much as 60 degrees centigrade!

Take another, longer look.

In any event, we can make a simplifying assumption.
Imagine we just heat the outermost layer of wires.
The inner ones will be less hot than the (the inner side of) outer ones, so they will be OK.

In simple terms, that's my plan. There are a lot of complicated details to do that in the most effective way, but in a nutshell, correct.

If you can't heat the outer ones to a point where the cable sheds ice without damaging the outermost layer of wires, 

Well my calculations suggest that we can.

[alancalverd]

A simpler idea that doesn't involve dismantling the cables, is to place a heating sheath over the entire cable. We used to wrap nichrome wire around exposed water pipes - it's called "trace heating". Or you can use a plastic boot and blow hot air up the tube. Wither technique has the advantage that you can also heat the surface of concrete and mass steel structures with it, so yoe can keep the entire bridge free from ice, not just the cables.   

Next project: find some way to prevent closures due to high winds! 

[Bored chemist]

There are a lot of complicated details to do that in the most effective   an unduly complicated way,

[Bored chemist]

Next project: find some way to prevent closures due to high winds! 

Put a building round the whole damned thing.

[Peter Dow (OP)]

A simpler idea that doesn't involve dismantling the cables, is to place a heating sheath over the entire cable.

Placing anything over the cable presents access difficulties.

We used to wrap nichrome wire around exposed water pipes - it's called "trace heating".

I mentioned "trace" "heating" in my OP.

Tower ice
To prevent the bridge piers or towers (with non-conducting concrete surfaces) from icing up, they could be surface fitted with new electrical heating trace cables which are then appropriately electrically-powered for deicing when necessary.

Then Bored Chemist mentioned it

There are a few ways I know of that they use for deicing planes.
Inflatable rubber bits, trace heating and antifreeze sprays.

In my own "Electrically de-icing the Queensferry Crossing cable-stayed bridge" blog post "trace" heating is mentioned in 3 places.

1
Already quoted in my OP.

2

Trace heating is a low-maintenance industry standard.

Using the bridge’s own cable strands to carry the trace current is innovative but equally low maintenance.

3
Then someone commenting on my blog mentioned it.

Trace heating is used as I’m sure you are aware, on oil pipelines in extremely cold environments, much colder than even the lowest temperatures we have in Scotland.

Or you can use a plastic boot and blow hot air up the tube.

The air will be too hot at one end of the cable and too cold by the time the air flow gets to the middle of the cable - 200 metres away in the case of the longest 400 metre cables.

Wither technique has the advantage that you can also heat the surface of concrete and mass steel structures with it, so yoe can keep the entire bridge free from ice, not just the cables.

I am proposing heated air for warming the bridge towers from the inside, but not for the cables.

Another option to consider is heating the hollow towers from within. However, considering the considerable mass and thickness of the towers, their surfaces would have to be kept above freezing temperature all winter long. Heating the towers from within, there simply wouldn’t be time to allow the towers to get freezing cold because there was no icing then suddenly heat them from the inside to deice a sudden incidence of icing.

So heating from within bridge towers would use more electricity, though the cost shouldn’t be prohibitive – surplus grid electricity is a common occurrence at times of high wind power generation, so the electricity grid managers should offer a very low price for such electricity (just the grid connection charge) – plus it should be a lot safer upgrade from the point of view of bridge users – far less chance of things falling onto the road during the fitting of the towers’ internal heating elements.

Heating the towers may be as simple as a big electric heater on the ground floor, the warm air rising up the insides of the towers, in between the open stairways and scaffolding.

 

Next project: find some way to prevent closures due to high winds! 

The Forth Road Bridge (opened 1964) has to close for high winds but the Queensferry Crossing (opened 2017) has wind shields that protect the traffic from high winds and so can cope with high winds much better.

So the Scottish Government's agency - Transport Scotland - have employed Balrick to come up with a cunning plan to divert / revert traffic in all weather conditions. 

[Peter Dow (OP)]

an unduly complicated way,

Complexity is duly required to optimise the design to allow for the greatest heating power to be safely used.

A simple design wouldn't be able to heat as powerfully or de-ice as quickly without the danger of melting the strand sheaths and causing damage to the cable.

[Bored chemist]

So, the simple design would work OK as long as someone checked the weather forecast.

[Peter Dow (OP)]

So, the simple design would work OK as long as someone checked the weather forecast.

No. Someone "checked the weather forecast" on the Titanic.