Here's my damper relay and how it's wired. I only have one powered damper, and it's in the supply duct connecting the wood furnace to the main house supply duct. I DON'T have my wood furnace cold air connected to the main house cold air. I believe you do because your furnace is in the garage....IIRC?? In this case my diagram will only work for your supply damper, if it works at all. It uses the 120V EAC (electric air cleaner) circuit on the LP furnace and the 120V circuit from the wood furnace's snap switch. I have a spring open, power closed damper with a 120V motor, which ends up being powered by the EAC circuit of my furnace. The ONLY time my damper closes is when the LP blower in the only one running. ALL other times it remains open. This means in summer the damper is powering close when the AC kicks in and springs open when it shuts off.
I believe for your return damper placed on your LP furnace's return duct you would want it OPEN at all times except when the wood furnace is the only one running, correct? You would then use another relay and swap the positions of the EAC and snap switch leads and then the ONLY time the damper closes would be when the wood blower is the only one running. ALL other times it would remain open.
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This is the wiring for my three relay wood furnace blower motor control. It's VERY messy, sorry. The wood furnace blower is under control of the speed control (which is powering the high speed winding on the blower) at all times -except- when the LP furnace is also running at the same time. When the LP kicks in AND the wood blower is still active, then the wood furnace's blower's low speed winding is given 120V instead of the speed control. This was done because whenever the LP kicks in the wood furnace's blower is running very slow at the end of a burn. The LP's blower then backfeeds the wood furnaces blower. Not good! Adding that relay rectifies that situation, as then both blowers are running on low speed. I also have wired up a fail-safe in case the speed control stops working. In this case I have a second 200° snap switch installed in my plenum. If plenum temps ever get that high and that snap switch ever closes, it will take power away from the speed control and send it to the low speed winding of the wood furnace blower.
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