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Every picture of an Antminer S1 I've ever seen has the unit oriented horizontally, where the fan blows air from the front through the blades and out the back.

I'm thinking that if it was oriented vertically, the hot air off the blades would rise naturally. The fan blowing cool air from below would be even more effective as it pushes the hot air out the top.
I haven't done this yet myself because I don't have a wire/mesh platform to put the unit on so that the fan's intake wouldn't be blocked. I'm also thinking about building some kind of a mount rack (probably wood) so I can attach the Antminer vertically to the rack. I might take apart a small bookshelf to make a wooden rack.

Any thoughts or comments on this?

You'd have to check the temps before and after to know if it's effective. It might be, especially if you have close to the cool ground (like concrete basement floor). The reason why they put it horizontally is that it's more stable and the fans aren't blocked.

Interesting idea.  Horizontal allows better stacking on shelves/racks.  If oriented vertically you need to use a single layer with unobstructed airflow below and above - appears less practical.

Cheers

There was a post either here or on reddit where the blades were taken out of the frame and set up vertically with fans blowing directly on them (I'll try to post a link if I find it).
The setup looked pretty nice but I can't remember the temps.

I have mine chip side down because that's how they fit in the space I had available. With additional fans drawing air out the other side they run at about 46 (with factory settings)

Since the heat sink runs the entire length of each blade, it seems that heat would be trapped between the fins if the unit was positioned horizontally. The fan is needed to help blow air through the entire length of the blade. But if the unit was positioned vertically, maybe a fan wouldn't be needed since the hot air would rise naturally through the vertical fins.

I doubt it. Passive cooling requires more surface to spread the heat than active (that's why passive PC coolers are much bigger and usually have thinner fins), so if you remove the fan without adding a bigger radiator or adding AC to the room you'll get higher temps.

Here's the link...

"Silent AntMiner"

http://imgur.com/a/RUAX5 (http://imgur.com/a/RUAX5)

https://i.imgur.com/cF9lvCb.jpg

Ahh, so he split the Antminer into two pieces and attached those huge fans. I like it! :) 
I might try that too! It would be easier to mount each blade separately on, say, a wood board that way.

I have mine mounted vertically in my garage....so far this summer the miners have never gotten hotter than 47C

http://hhttp://regularthinking.com/sites/regularthinking.com/files/IMG_0957_0.jpg

Wouldn't the heat from the power supplies have a tendency to go toward the miner's fan?

No, the PSUs pull in their fans and exhaust out the ports at the top and the fans on the S1s are blowing up to take advantage of natural convection

I eventually ended up remounting the PSUs at the bottom of the case anyway...everything still stays plenty cool.

just noticed that the image wasn't loading properly....am reposting with a smaller version to see if that works

http://regularthinking.com/sites/regularthinking.com/files/IMG_0957_0.jpg

Re: the picture above. That is exactly what I'm thinking. Vertical mount so the air flows from bottom to top.