After dreaming about making one for a long time, I finally went ahead and did it. It was a lot of fun to make, and it worked pretty much as advertised. The biggest problem I encountered is that I was over driving the fan motor and I probably could have chosen a more powerful one that could have handled more tubing (more weight). I will solve this problem for revision two.
Anyhow, without further ado, here is how to make your own.
Step 1: Go Get Stuff
You will need:
A box fan
A 1' foot metal tube with a diameter slightly bigger than your motor shaft
A rod clamp slightly bigger than your metal tube
Step 2: Take Apart the Fan
Remove the front cover from the fan.
Forcibly pull the fan blade mount from the motor shaft.
Step 3: Measure
Measure the diameter of the shaft and get an extruded 1 foot metal tube with an inner diameter of that value.
Also get a rod clamp with a set screw that can fit around the tube.
Step 4: Clamp
Tightly clamp the metal tube to the motor shaft with your rod clamp.
Step 5: Strip the Umbrella
Remove the cloth from the umbrella.
This may require breaking, bending and/or sawing off a clamp at the top of the umbrella that is holding the cloth in place.
Step 6: Saw Off the Handle
Saw off the handle of the umbrella in such a way that you will be able to remove the base off the shaft when done.
Step 7: Remove the Spring
Carefully free the spring from the umbrella. Be careful as the spring is springy and this may cause the spring and/or the pointy bits of the umbrella frame to launch towards or away from you.
Step 8: Simplify
Break off the sharp pointy bits sticking off the edge of the frame (the part that extend past the folding joint).
Step 9: Free It
Entirely remove the folding part of the frame from the main umbrella shaft
Step 10: Remove the Extra Hangy Bits
Carefully break away any extra pieces that may dangle, make noise or otherwise be a hindrance when the frame is mounted on a rapidly spinning motor shaft.
Step 11: Fasten the Umbrella
It is time to fasten the umbrella frame onto the extended drive shaft.
Simple lower the bottom part onto the shaft and don't worry about securing it for now (it will be held in place later by zip ties).
Bring the top part of the frame near the top part of the shaft and drill completely through both the top bracket and the shaft. Insert a metal pin through this hole and bend it to lock the top in place. If the top is loose, you can insert a rubber O-ring to solve this problem.
For my pin, I sawed in half one of those "dangly bits" from the last step, inserted it through the hole and bent it upwards. This worked great.
Step 12: Cut Tubes
Cut your tube into 8" to 18" sections.
Step 13: Zip Tie
Zip tie them onto the motor shaft and frame so that they make a nice 90 degree arc.
While zip tying them, you should also determine that approximate height you want the bottom part of the umbrella frame to sit at and zip tie this in place as well.
Step 14: Plug and Play
Plug it in and let it drone.
I found that you shouldn't run it for more than a few minutes as you are typically over-working the motor and it starts to get worryingly hot.
I have not had the chance to properly record this yet, but I would imagine the ideal place to have a mic would be in close, below the spinning mechanism, pointing upwards at 45 degrees.