Power

One goal of this project was to have the computer display power. Since my old Cyclops trainer is not adjustable, power should be a function of speed. Fortunately power curves for some Cyclops trainers are published : http://www.cycleops.cz/files/trainers.pdf. I decided to use the Fluid2 curve - my trainer's older than that but hopefully close enough. A curve-fit using Excel gave :
Power[W] = 0.0128V3 - 0.0163V2 + 8.2864V where V is speed in [mph]

The Computer End

Here's the Arduino interface. Black and yellow wires at left come from the reed switch on the bike. Pin 2 senses the reed switch (yellow wire). The 100ohm resistor is to protect the Arduino in case pin 2 gets configures as an output by mistake. A 10k pullup resistor connects to the 5v pin (red wire). Then LED is activated by pin 12 (green wire)  - it is programed to change stage as the magnet passes the reed switch and is helpful for quickly checking the system works.

Connecting Bike to Computer

Magnetic reed switches were found at the local hobby store. Professionally installed with some heat shrink, wire ties and some old telephone cable. Wheel magnet was from a defunct bike computer. It would make more sense to attach the switch it to the trainer so the bike is removable - future modification.