So, you want to make a propeller hat? Good for you. The propeller hat has been a symbol of geekdom for a long time. Geeks wore them even before the term meant more than a circus performer who bites heads off of live chickens. A propeller hat was worn by a member of the Little Rascals and by other awkward-looking children in black and white movies.
Step One: Get a hat or make a helmet shaped hat. The classic shape for the propeller hat is a helmet. A helmet shape can be obtained by taking the cap off of a baseball cap. You can use a Fedora, a Stetson, or a Bowler hat depending on your willingness to assault various fashions. You will want to use an inexpensive cap as the basis for your propeller hat. Remember that Fedoras, Stetsons and Bowler hats tend to be more expensive than baseball caps.
Step Two: Get or make the propeller. The propeller's shape is the most important thing for conveying the natural whimsical properties of a propeller hat. Pinwheels on hats are not as whimsical as propellers in a plane shape. Scientists are seeking an answer to this problem, but scientists are still years away from finding a solution. Card stock works slightly better than construction paper for making a propeller. Trace a pattern of an airplane propeller on the card stock. Poke a small hole in the top. You can also remove the propeller from a wind up toy plane. The axle of such a toy plane may also work as the axle for the propeller. Decide how to attach the axle to the propeller, but do not attach the axle to the base yet.
Step Three: Make a base that will secure the axle of your propeller hat. A small piece of plastic or balsa wood should work here. Make sure the base does not touch the head. The base touching your head will not make the hat unwearable, but it will make the hat uncomfortable. This should stabilize a propeller. The propeller hat's base should have a hole that can hold the axle. Create a hole in the top of the hat big enough for the propeller axle. Connect the propeller to the base. A small amount of glue can do this in many cases. Put the base on the bottom of the hat. Make the axle go through the hole made for this purpose.
Step Four: Attach the propeller to the hat. Put the propeller on the axle. Use a paper clip to keep the propeller from flying off its axle. Check to see the propeller spins properly. If it does not spin, you lose some of the nearly mystical whimsical qualities propeller hats possess. Make sure the propeller is fairly stable.
Step Five: When you have made your propeller hat, go out and wear it with pride.