As the hardware and triathlon fan I am very interested in a bike power meters. There are lots types of bike power meters, but the principle of operation is similar.
The equation for torque is T = F * r. F is force and r is the distance from the center of rotation to the point where is the force applied.
So the equation for the bike power is P = F * r * w. On a bike the force and angular velocity can be measured. The hardest part is the force measurement.
The strain gauge is using for measurement the force. This is insulating flexible backing which supports a metallic foil pattern. It is attached to the object by a suitable adhesive. As the object is deformed, the foil is deformed, causing its electrical resistance to change. This resistance change, usually measured using a Wheatstone bridge.
The key of the bike power measurement is to put the strain gauges in some bike part. The strain gauges usually put in bottom bracket, rear freehub, crankset, or pedals.
When the place of force measuring is known, r distance from the center of rotation to the point where is the force applied is easy to determine. For example, when strain gauges are put in the pedals crank length must be known (170mm, 172.5mm, 175mm, 177.5mmm…).
If strain gauges are put in bottom bracket, crankset, or pedals w angular velocity is the same as the cadence (number of pedal revolution per minute). If strain gauges are put in rear freehub w angular velocity is the same as the bike wheel angular velocity. The cadence or the bike wheel angular velocity can be measured with magnet (measure the time of revolution) or with gyroscope.
I was thinking about the bike power meter project. I was planning to put strain gauges in a bike shoes cleat. This would be interesting for Kickstarter, but someone was faster.