As an amateur go-kart driver, shooting the races was always in my mind. It's fun and you can review your mistakes later with the same perspective that you have on-board.
This is a cheap and pratical way to attach a camera to a helmet, with great results. My cam is a Fuji Finepix Z1, which doesn't have a mount screw. I planned to use card board to mount it on the curved surface of my helmet, but it's not as easy as it seems, and you can't rely on it when it rains. Then, I figure out that clear packaging tape, in conjunction with a double sided foam tape would do the job. I called it "tape frame". It looks fragile, but it can resist to speeds over 100km/h.

Step 1: What Do You Need

Any double sided foam tape can do the trick, but certainly the 3M VHB tape it's a lot stronger than the average. It's imperative to use a foam tape as both surfaces doesn't have the same shape and it will act as a dumper against the wind and vibration. This tape will be used to hold the inner surface of the camera against the helmet.
I choose clear packaging tape over the brow tape because I think it's thicker, but I might be wrong. Be sure to have enough before start, because this will be responsible to hold the other side of your camera. Don't save tape or you may lose your camera during the race!
Remember to clean you helmet, or the tapes will not work properly.

Step 2: Cutting

Cut the foam tape at the lenght of one side of the camera. The Z1 have flat sides, which eases the job. One good trick it's to cut the corners, making them round. By doing this, the double sided tape will last longer in place, as it will be more difficult to got dirt at the endings.

Step 3: Aiming the Camera

This is the most important step of all, and where most of the mistakes are done. Initially, you might think that the helmet will stay at the same position that you have it on a table, aiming the camera on a parallel line to the ground.
The problem is, when you wear a helmet, it rolls slightly frontwards, as you look right below the horizon. To correctly align the camera, hold the back of your helmet up, as if you are looking to someone wearing it, and notice that the line of sight follows the top of the visor. On that position, find the place to attach you camera, somewhere

Step 4: Fixing the Tape Frame

There will be three parts to building that frame. Start with the back, fixing one ending to one side of the camera and the other ending on the back of the helmet. Remember that the front frame will pull it to the front, stretching the back frame. Test it, pulling gently with your hand.

Step 5: Fixing the Tape Frame - Part 2

The second step it's to fix the front frame. This one will go on a diagonal line, fixing the other ending in front of your mouth. At this time, pull the camera to the front until the back frame pull it back firmly, then attach the front frame to the helmet.

Step 6: Fixing the Tape Frame - Part 3

The upper frame is the last one. It's aligned with the front frame, and goes up to the top of the helmet. It helps to hold the camera in position, as it avoids to the other frames to pull it down. The ending on the camera must match a few inches with the front frame, ok?

Step 7: Final Step

The borders of all frames it will become a little loose, no matter how tight you fix them. This will create a noise as you build up speed. To avoid this noise, fold the borders to their insides. It also brings up a solid construction to the tape frame.
Remember to check before start. Before the race, it's possible to do some corrections on the camera position, and see if there's enough battery power, memory and if the lens are clean. It's a good idea to have someone experienced to power on the camera and start recording.