First of all, as an engineer and an HVAC professional, allow me to apologize for the way my fellow engineer has approached this subject. Many engineers have a problem with people they suspect are not on the same "level" with them, and since engineers as a whole do not communicate effectively with non-engineers, they tend to come across a little demanding and unfriendly.
That doesn't make it OK, but I am sorry for you guys to have to deal with it.
Now, on to the matter at hand:
Dear Unregistered:
If you are indeed an engineer, then you are familiar with unknowns. The question you have asked has many unknowns. Some of these unknowns can be calculated or measured. For instance; paramount among the information necessary for your equation is the heat loss and gain of your house at different outdoor temperatures, and the thermal lag associated with your home's construction. Also measurable or able to be looked up is the average temperature change per 12 hours in the area where you live.
But, unable to be looked up or calculated is your specific system's heat out put at a given indoor/outdoor temperature set. Even though the manufacturer publishes data at 17º and 47º outdoor temp, those data points are independent of the indoor unit, ductwork efficiency losses, the coil and filter cleanliness or lack thereof, and many other variables associated with a mechanical system's operation.
So, let me run down a verbal description of this equation you are asking for:
Heat leaks out of your house at a set amount per hour based on variables such as the indoor/outdoor delta T, construction style, indoor air velocity, outdoor air velocity and air exchange rate.
This heat leakage is offset by many factors, including the heat output of the heating system, heat output from appliances, lights, electronics, people and animals and solar gain, to name a few. Thermal mass of the construction style also plays a role in your balance point, as heat is stored in the mass of the house and then given back to the space as a function of temp change and specific heat indices for all the masses.
Now that we have an equation for your "NEED" for heat, we can begin to look at those variables associated with the "economic balance point" of your system.
Your heatpump balance point seems to be, based on your reported observations, about 25º outdoor temp. Assuming for a moment that your indoor temp is not variable, let's examine the thermal lag of your home. How long does it have to be 25º outdoors before your system begins to fall behind and call for furnace heat? This would give you an idea of the thermal lag factor. Let's assume for this discussion it is 4 hours. (a reasonable number). So we need to examine how often the temp falls below 25 for more than four hours where you live. Your heatpump balance point may not be 25. It may be 35. I hope you are following me here, because I am getting tired of this analysis.
Let's move on. The ONLY way to determine accurately your heatpump's KW/KW output is to put your entire house inside a psychrometric facility and measure it. Even if you know the COP, EER and other rating points (you can look them up at
www.ari.org) of the outdoor unit, or even if you have that data for the indoor/outdoor unit combination, you still do not know the data for your installed system. (refer back to ductwork)
You also need to know the exact efficiency of your furnace as it is installed and maintained. The rating you gave us is the manufacturer's rating, and is for reference only. The conditions at which those reference data are collected do not exist in most occupied dwellings.
Now, based on your prior expressed knowledge, and the information I have given you here, you are the ONLY person who is in a position to apprehend the information you are seeking. Unless you would like to pay me to come to your house and figure it out.
The original response you got from Steve was given to him by me. This response was based on 20 years experience designing, selling and maintaining HVAC systems, a Master's Degree in mechanical engineering, and 4 years of experience as a design and specification engineer for HVAC manufacturers. I stand by it as the only reasonable response to a question such as yours in a venue such as this. A P.E. stamp gives me the ability to approval of disapprove calculations such as you are asking us to give you, and I summarily disapproved this one, based on lack of knowledge and information I know will remain missing.
Now, to your behavior. You came to a website to ask assistance from professionals. They gave you their best response based on the information you gave them. You then berated, ridiculed and corrected them. If you (assuming you are what you claim to be; an electrical engineer) were asked to help design my home's electrical distribution network, would you be happy to hear me say you were wrong and had no clue what I was asking for? It is my humble opinion you owe these gentlemen an apology, but since this is the Internet and you think you are anonymous, I doubt one will be forthcoming. In fact, I'll wager you are all poised right now to give us all a piece of your anonymous mind, right?
Save your typing for someone who cares.