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This is related to the question Will dark gutters stay ice free better than light colored gutters? The current consensus seems to be that the mass of the gutters and limited light may make simply painting them black insufficient.

In my particular application the two major gutter runs are facing East and West so get decent amount of sun light. Physical location is Pittsburgh PA.

From an engineering perspective, these are some of the questions that would need to be addressed:

  • How much would I need to raise the temperature of the gutters to prevent ice build-up?
  • How can I calculate the energy required to raise the temperature of the gutters?
  • How much energy can I theoretically obtain from sunlight throughout the day for a given area during the winter at my latitude?
  • How would the analysis change if I also wanted to melt ice that had built up during the night?
  • What other factors should one consider when designing such a system?
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    $\begingroup$ I like the idea of the question, but it is a bit ambiguous as is. The amount of energy needed will depend on the temperature of the ice (i.e. the outdoor temperature). $\endgroup$ – Chris Mueller Jan 29 '15 at 21:27
  • $\begingroup$ Actually @ChrisMueller, that has very little to do with it. Ice forms on eaves and gutters when snow melts higher up on the roof (from both solar heat and heat leaking from within the building) and the water runs down to the eaves, which are cooler. The key to preventing ice buildup in the gutters would be to keep them slightly above freezing whenever water is flowing down from the roof. $\endgroup$ – Dave Tweed Jan 29 '15 at 22:11
  • $\begingroup$ @DaveTweed While that may be true, the amount of energy required to keep the gutters above freezing will still depend on the ambient temperature. $\endgroup$ – Chris Mueller Jan 29 '15 at 22:19
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    $\begingroup$ @ChrisMueller: Not really. When the water is flowing, it is pretty much exactly at freezing temperature. So the amount of power required is primarily related to the amount (mass) of water flowing at any given time. Sure, some of the heat will be lost to the air, and that loss is related to air temperature (and wind speed, etc.), but the heat lost to the water will be the more significant amount. $\endgroup$ – Dave Tweed Jan 29 '15 at 22:23
  • $\begingroup$ "Other factors": How to keep snow from thoroughly covering the solar collectors. $\endgroup$ – SF. Feb 3 '15 at 11:29
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And so, as promised, I'll do it.

First assumption: Let's work with 1m long strips of gutter. It'll be easier to calculate everything starting from here.

Let's say the gutter is already full of ice. (We'll work on the ice filling problem later on)

The standard gutter size (according to this site) is 5-inch K-Style, or 6-inch half round. If we use the half round version, we can learn it holds around 9L of ice. The latent heat of fusion of 9L of ice is 3000kJ, or 833Wh. This means that if you wanted to melt this ice in an hour, you'll need 833 Watts of power. For each meter of gutter.

But what's the available solar energy?

Second assumption: Let's say the sun shines all day, with the perfect orientation regarding the gutter, and the gutter absorb all the energy it receives from the sun. Let's assume it's the shortest day of the year, at the US mean latitude (around 38°N).

According to the third chart, the length of day on the shortest day of the year is around 9h30m. Let's round this up to 10h (I like round and easy numbers for my ballpark calculations).

The cross section of our gutter is around 0.15m². The sun irradiance reaching the ground stands at around 1000W/m². This means around 150W reaches our gutter. On a 10h day course, that would be 1500Wh. Hey, that would be enough! Well, yes, if you take your gutter and put in the perfect orientation regarding the sun. Which it's not true.

In this case, the energy received will be lower. Moreover, one also has to take into account the efficiency of the energy conversion. High quality solar thermal collector (which collect solar radiation and convert it to heat) typically have efficiency at around 60%. This means, in our case (where the efficiency will be lower, we'll receive at best 900Wh.

If we take into account the fact that our gutter has a fixed orientation, the energy received will be even lower than that. Thus, we won't have enough energy to melt the ice.

Given this data, I'd say it's not possible.

As for the ice filling the gutter. The problem is still the same. Making sure that the water flowing from the roof stays hot enough will still means providing enough energy to keep it above freezing. Also, usually, water melts on the roof, but doesn't flow alone, i.e. it brings down some snow and ice in the gutter, which you'll have to melt of you want to prevent ice buildup in the gutter.

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  • $\begingroup$ And on a cloudy day? Or if it is -20 degree celsius outside? $\endgroup$ – Trilarion Feb 3 '15 at 16:13
  • $\begingroup$ All my calculations were made on a sunny day. If its cloudy, it'll receive less energy than that. If it's waaaaaaaay below freezing (i.e. -20 degree celsius), it will need more energy than that. $\endgroup$ – gromain Feb 3 '15 at 16:31

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