[...] | I can't believe that something as simple as whether or not a dishwasher | drain hose must always form a loop (inverted trap) wouldn't be more well | known if it was common knowledge.
One problem is that code requirements have changed over the years and dishwasher (cost reduction) design has taken advantage of this. My house's original dishwasher (~1959) was hard plumbed directly to a trap in the basement. It had no high loop, no air gap, and no standpipe. It did have a positive drain valve solenoid that closed the drain when it was not trying to pump out water. It was also wider than current dishwashers. As far as I know, that installation was to code at the time.
The first replacement dishwasher (in the 80's I think) was a KitchenAid and while it did not have a drain valve it did use a separate pump for removing water. It was happy with a high loop but still hard plumbed to the trap in the basement. I _think_ the installation manual showed the hard-piped trap as a valid (though not necessarily legal) configuration.
The next replacement (I don't remember the brand) in the 90's (notice that life span is decreasing :) did not have a separate pump for removing water. Instead it manipulated the circulating pump in such a way as to cause a little plastic flap in a chamber to divert water out. This appeared to depend critically on the back-pressure at the drain and I was unable to make it work reliably with the hard-piped trap, regardless of high loops.
I was able to find a different brand that still worked with the hard-piped trap, but I decided that that configuration's days were numbered so I reworked the kitchen sink setup with a garbage disposal. The latest replacement dishwasher has a high loop and empties into the dishwasher port of that garbage disposal per the current preferred configuration.
IMHO, in general, a high loop saves you only if the drain hose opens to air before it gets back as low as the highest water level in the machine. This is the case with the garbage disposal port but not with a hard-plumbed trap below the floor and not even with a standpipe below the floor.
[...] | I'm not sure what that do-hickey is in the last diagram - identified as | an "air gap" that seems to protrude above the counter top. That can't | be a desirable thing to have poking through your counter-top.
As the name implies, it is a true air gap that both prevents siphon and diverts any reverse sewage flow onto your counter (which is arguably better than hiding it in the dishwasher). The aperture on the dishwasher side is smaller than that on the sewer side. This is currently the ultimate in safety and (I believe) required by code in some places. Something I'm not clear on is whether you can use an air gap and then hard-plumb the outlet to a trap under the floor. Somehow I think that even with the air gap you are supposed to enter a disposal or open sink trap.
Dan Lanciani ddl@danlan.*com