Sizing a small radiator

Recruiter

I am trying to calculate how many BTU's I need for a bathroom. I am running cast irom radiators on a fairly new FHW boiler. The previous owner replaced the radiator, during a renovation to install a tub, with a (copper) 4' Slantfin baseboard heater. Now, due to damage by a tenant, I have had to renovate the bathroom again.
I now know, from a previous thread, I shouldn't be mixing the cast iron and copper, so I am trying to calculate how many BTU's I need for that bathroom, in order to determine what size radiator I need.
A file is attached showing the dimensions and layout.
I've tried using the calculators, but none of them allow for a partial outside wall.
Thanks
Dave

Paul48

Does the bedroom closet have a door on it? If so, it's an unconditioned space and I'd just add that to the exterior wall. Just take the overall size of the bathroom, and add 10% to whatever you come up with. You want it warm and you can always put a trv on the radiator.

Alan (California Radiant) Forbes

For a proper heatloss calculation, we have to know the design temperature in your area. This is not the coldest temperature, but an average cold temperature. Can you tell us where you live? If it's a small town, then the closest large city.

Brewbeer

I want my bathroom to be warm, so I put a 4 foot radiator in it when a 2 footer would probably have been enough. Depending on how the system is piped, the performance of a cast iron baseboard radiator in the bathroom of an otherwise all fin tube system may be completely acceptable.

Recruiter

We live near Providence, RI.
The closet does have a door on it, so I guess it would be an unconditioned wall space behind the tub. That would also mean 41" of the right wall is unconditioned space too. The entire apartment is on a single zone thermostat, centrally located in the aprtment, so there is no separate control for the bathroom space.
The Slantfin baseboard radiator was put in almost 90 years after the house was built, but before the new boiler system was installed, during the first renovation. There used to be a cast iron radiator in the bathroom, but It is nowhere to be found.
A new radiator would most likely be placed on the 34" wall area.

Alan (California Radiant) Forbes

Providence has a design temperature of 7°F and I'm coming up with a bathroom heatloss of 2,343 BTU's. That's the amount of heat needed to keep the room at 70°F at design conditions and works out to 45 BTU/square foot which is kind of high, but that's what my math says.

Anyone care to confirm?

Paul48

Even with making the exterior wall 11' to account for the unheated closet, I come up with 1700 btus.

Recruiter

Let me see if I am understanding this. Currently, the kitchen and living areas have 5 tube, 23 in. radiators and the bedrooms have 3 column, 22 in. radiators. According to my calculations, based on 140 deg design temp, I will need 9 sections of either type radiator of the same dimension.
The bedrooms are 10 x 12.5 x 8.5H ft. each, and have 10 sections in each room. Does that sound right?
Thanks

Paul48

You are running 140* supply to your radiators?

Recruiter

Sorry, I mis-read some of my old notes about the system. My design temp is actually set for 167*. If I recalculate:
The sq.ft. of radiation per section is 3.
At 167*, the BTU's emitted per sq. ft. is about 148. Therefore, each section would emit 444 BTU's.
If I average the 2 calculations from Alan Forbes and Paul48, it comes out to about 2000 BTU's. This would mean I need 4.5 sections at that size. Obviously, I could change the sizes or configuration to get a closer result.
Does that sound more like it?

Paul48

Yes........I'd go larger and install a TRV.

Recruiter

Great. Thanks for the help, and all the feedback. The TRV sounds like a good option as well.