Pen Rejuvenation - FAIL!

Like a lot of folks, I've got a desk drawer full of non functional pens. It seems wasteful to throw them out. If you shake one of them like an old fashioned mercury thermometer, it sometimes writes for a little longer. I got to thinking that maybe these pens could be rejuvenated by increasing the downward force of acceleration on the ink cartridge. After all, if you leave a pen upside down in your pocket, doesn't it sometimes leak? So shouldn't the opposite apply?

One way that to increase the downward force on the cartridge is to apply centripetal acceleration - like a bicycle wheel experiences. If I fasten pens to the spokes with the point facing the rim, as I ride, the acceleration from the rotation of the wheel should force the ink into the point and rejuvenate the pen. The question is, how many g's of acceleration can I get from a spinning bicycle wheel?

Notice that I'm going to make extensive use of conversion factors. Not only are they an easy way to get from one set of units to another, they can help you actually solve the problem when you don't know where to start.

This is the formula we need to solve:

r is the radius of the bike wheel and omega is the rotational velocity in radians/second.

Here's the math, assuming my usual biking speed of 10 mph:

First, what's the circumference of my 26 inch wheel bicycle wheel?

How many revolutions per second is my 26 inch wheel turning at 10 mph?

What's the acceleration in m/sec^2?

If my math is right (and please feel free to check it), the pen will experience a force of over six times gravity, with plus and minus 1 g impressed upon it twice per second from gravity.

According to www.jetpens.com there are rollerball pens with a water-based dye, gel pens with a water-based pigment, and ballpoint pens with an oil based ink. I've got some of each type.

I imagined that I could fabricate a plastic box that would clip onto my bicycle spokes, into which I could put pens, and by the time I got to work or school, the pens would be good as new. As a test, I flipped my bike upside down and used cloth cable-ties to attach various types of pens to the spokes. Then I spun the crank as fast as I could for about five minutes. 

Then I removed them and put pen to paper.

Wow, it's working, it's working, uh...., maybe not.

Maybe it wasn't the shaking that enables a pen to write for a little longer. Perhaps old pens just get dried up and the pathway to the paper gets constricted. Maybe extra gravity helps only until the ink beyond the obstruction is used. Looks like it's either back to the drawing board, or back to Jet Pens for more pens.