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The ancient Romans used underfloor hot air heating (hypocaust) that are easily seen in viewing the ruins, and well documented in architectural history books. Likewise, "Korean" floors are common and well known in Korea and Japan, at least. FLLW undoubtedly would have seen them in both Italy and Japan, and as has been noted used them beginning in the Imperial. And indeed, anyone who has lived with them know how cozy they are. When he was designing Hanna in Palo Alto, the Hannas opted for hot air instead, because they felt the slow reaction time of heating a concrete slab would not work in that climate, where there can be great temperature swings in a short period of time, and a ten minute blast of hot air is all you need to take off the morning chill. Nonetheless, hot water radiant floors were successfully used in thousands of Bay Area Eichler houses in the mid-20th c, and are quite common in new high end houses in the Bay Area today.
So what we know is that there was floor heating at the Imperial Hotel, but only an electric type in the bathrooms. Wright had intended to use it at Nakoma and the Johnson Administration building, but the first application of his "gravity heating" was at Jacobs 1.
So I guess Neutra had floor heating (1934 Beard house) under a concrete slab (waterless...) in a house before Wright, but clearly Wright was working toward this goal for many years prior to 1936.
The radiant floor heating in Eichlers was especially important due to the fact that though there were a number of efficient floorplans which were employed, not all were necessarily taking full advantage of solar gain. One house might receive southern sun in the winter, and an identical floorplan in another location would not. The radiant heating evened this out and was quite effective.
For two years I lived in an A. Quincy Jones design in San Rafael, Ca. when I was in high school. It was my introduction to architecture as well as the comfort of radiant floor heating. Thanks to Joe Eichler for renting the Hanna house by Frank Lloyd Wright, a life changing event for him, which in turn was the catalyst for the production of the best tract housing developments of the mid twentieth century.
There are two essential books about Imperial: Cary James' "FLW's Imperial Hotel" (1968) and "Frank Lloyd Wright In Imperial Hotel" (1972) in Japanese plus English captions (used copy available on Amazon for $1,415.88; reprinted in paperback 1994). The second book, 268 pp, is an extraordinary document done just before the hotel was demolished with copious photographs and excellent plans, elevations, sections, details and even furniture drawings. Yet nowhere is there a section that includes a bathroom to show a dropped ceiling. There is, however, a single photograph of a bath (plate 231) showing a barrel-vaulted ceiling which seems, at its peak, to fall short of the bedroom ceiling height with enough space to contain the heating system he describes.
I would like to interject here - is there anyone out there who knows of a hot water radiant heating system that will continue to perform as installed for more than 100 years? Even though the system is extremely comfortable, it appears that all piping, be it copper, wrought iron or the new plastics oxidize over time, requiring costly and extensive slab/tile removal for repair.
It would seem that a hot air system would perform much better over time.
The new material for this purpose is PEX (cross-linked polyethylene) tubing. I don't know if it is being encapsulated in concrete slabs -- but it is
apparently bullet-proof when placed beneath various floor surfaces. I've seen several installations documented in "This Old House" projects -- often
clipped into aluminum fixtures fastened to the underside of a subfloor. Whether there is insulation of some sort beneath that, I don't recall.
In man's endeavors, the idea comes first, and then the material means are found to embody that idea. Sometimes the idea occurs long before the
correct and effective means are found. . . ?