# Calculating the optimal weather compensation curve

Continuing the discussion from Infer radiator spec and system volume using the MyHeatpump app

I’ve been combining the formulas for radiator output with my calculations of heat loss coeffiecient to produce the optimal weather compensation curve for my property:

• Radiator output at Δ50: `18,000W`
• Target room temperature: `19 C`
• Heat loss coefficient: `260 W/K` + `880 W`
• Minimum heat pump output: `4,000 W` (though this varies with COP)
• Flow - return delta: `5 K`

My calculations:

• Heat loss = `(outsideT - insideT) * coefficient - constant`
• Flow = `(heat loss / radiator output) ^ (1/1.3) x 50 + insideT + dT / 2`
Min flow is the same but with heat loss bounded by minimum heat pump output

The lowest temperature the heat pump can run at is 37 C, which matches the stable heating periods I’ve observed. If I’m willing to accept a duty cycle of 66% when it’s not freezing weather, then this drops to 33 C.

Here’s my spreadsheet if you’d like to do the same - make a copy and input your own numbers.
Adding more radiator output moves the line downwards. Reducing heat loss flattens the curve.

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Bloody hell, Tim, I do have a real job to try and keep on top of too!!!

Stop tempting me away with more spreadsheets and graphs!!!

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Hi Tim,
I did something similar in a slightly different way, armed with little more than Q=U.A.dT in a recent test on my most significant room (the lounge).
Happily, the external temp was constant for a whole day (12degC), so the ASHP exit sat at the WC temp (42degC) all day too, and the room reached a constant temp (i.e. steady state with heat lost = heat gained).
Based on the MCS-based U values (as used by my installer in his heat loss calcs) for extl/intl walls, ceiling, floor and windows, and their respective areas and dTs, I calculated my steady-state heat loss Q.
Then I used this Q in the same equation for my radiators (known A) to calculate the U for them. This was 48W/m2/degC, which compares with Vendor’s 61W/m2/degC (I can believe my figure as I have furniture items near the rads which limit convection).
Armed with these U values for rads and losses, it’s easy (spreadsheet) to look at different outside temps and different rad temps (which I assume to be very close to ASHP exit temp), so I will be able to tune the WC accordingly as we go into my first winter.

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I was working on the same lines myself one rthe weekend, and I’ve just seen this excellent piece of thinking, and spreadsheet. However, how did you arrive at the Base Heat figure?

The simple method is to take the average daily electrical consumption that isn’t for the heat pump, and divide by 24, and add a 100 W for each human (70W for children). This comes out at 950W for me, which turns out to be a bit too high, perhaps due to some humans going outside sometimes. I’ve also not considered ~50W of heat “lost” from the cylinder than contributes to warming the house.

The more accurate method is to follow the “heat lost coefficient calculation” linked from the first post. Whatever offset is required to make the trend line fit through 0,0 is therefore the base heat from appliances and occupants. The additional (measured) heat from the heat pump then makes up the rest to match the heat lost from the property.

For me there’s quite an impact from solar gains as well. I only have limited data for now but in early January I need around 3 kWh/degree day in heat whereas now it’s starting to dip below 2.5.