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        riddles >> easy >> Broken computer fan
        
(Message started by: Simon_Pelletier on Jun 26^th, 2003, 5:03pm)

Title: Broken computer fan
Post by Simon_Pelletier on Jun 26^th, 2003, 5:03pm

Your computer fan is broken; one of it's 12 blades is broken, making the fan unbalanced and quite noisy. You have only some basic tools and no shop or replacement for the fan. How can you reduce the noise significantly while not losing too much of the cooling power? The fan is screwed quite tight and still making a lot of noise.

Title: Re: Broken computer fan
Post by Icarus on Jun 26^th, 2003, 7:29pm

Break off the opposite blade.

Title: Re: Broken computer fan
Post by Simon_Pelletier on Jun 26^th, 2003, 7:33pm

Easier than I thought, I guess...

Title: Re: Broken computer fan
Post by James Fingas on Jun 27^th, 2003, 8:34am

What if your fan has 15 blades?
What about 13 blades?

Title: Re: Broken computer fan
Post by Sir Col on Jun 27^th, 2003, 10:38am

Nice variation, James.

::[hide]
Suppose the fan has n blades and the n^th blade is missing.
Let k be the greatest proper divisor of n. With the n^th blade already missing, remove every k^th blade. For example, if n=15, greatest proper divisor is 5. So with blade 15 already missing, remove 5 and 10.
If n is prime, there is no solution, as you would need to remove all the blades.
[/hide]::

I suppose the next challenge is to prove that the above result is optimal.

Title: Re: Broken computer fan
Post by James Fingas on Jun 27^th, 2003, 1:07pm

Sir Col,

You're saying there's no solution at all for 13 blades? Surely you can come up with something...

Title: Re: Broken computer fan
Post by Icarus on Jun 27^th, 2003, 4:04pm

Yes, you you break off half - by weight - of the two blades farthest opposite the broken blade. This requires a little more care than just a complete removal, but it is also a better solution than Sir Col's for other odd numbers as well, since it leaves more blades on the fan.

(And yes, I know that "half" is only an approximation, since you really want to match moments, not weight. And I am also ignoring the forces from the air its moving. But if you've got the time and money to afford to measure it that sufficiently, why not just replace the fan?)

Title: Re: Broken computer fan
Post by Sir Col on Jun 27^th, 2003, 4:20pm

I'm not sure if the fan would balance, as I imagine that it's more to do with the aerodynamic forces generated by the symmetry of the rotating system? Imagine a 3-blade fan and removing one of the blades: simply snapping the two remaining blades in half will not balance the system, as we're not attempting to achieve reflective symmetry, we're looking for rotational symmetry.

Title: Re: Broken computer fan
Post by James Fingas on Jul 2^nd, 2003, 12:39pm

Sir Col,

All we have to do to "balance" the fan is ensure that the center of mass lies very close the the center of rotation. Rotational symmetry will ensure this, but objects with no rotational symmetry can also rotate without vibrating.

The problems with air resistance may be significant, but we could also approximately balance the air resistance with some more trickiness.

As both you and Icarus have pointed out, breaking off half-blades may not balance the fan even theoretically. But if each fan blade is roughly as large as the spacing between the blades (very likely), and they have roughly-constant thickness and width (quite common), then it should be a good-enough approximation, even for small n.

Title: Re: Broken computer fan
Post by zero on Jul 15^th, 2003, 1:28pm

on 06/27/03 at 16:20:07, Sir Col wrote:

how about this for a 3 bladed fan

snap the other 2 in half and then use one of those half and glue it to the the place blade 3 was

this could work

Title: Re: Broken computer fan
Post by towr on Jul 16^th, 2003, 1:18am

If you can glue things back, why not glue back the original broken off fan-blade?

Title: Re: Broken computer fan
Post by aero_guy on Jul 17^th, 2003, 1:07pm

Col, yup I had read this before, but did not think there was much to add.

In fact I have done research on rotorcraft where you have opposite blades identical but adjacent blades different. This will actually reduce noise levels without significantly increasing vibration (no increase in the kind of vibration you are experiencing here). Unfortunately, the kind of noise that is reduced is not the same kind of noise that is being produced here.

My end word would be that you break off a section of each of the two "opposite" blades, though how much depends upon the geometry of the fane and is way to intricate to be worth a three dollar fan. The aerodynamics are already sufficiently messy that the change in blades would matter little for the noise you hear.

IN my experience it seems that the fan manufacturers have noted that their products break easily and have been kind enough to build them with an even number of blades (I have done this before).