Since the torque on the crank shaft is the product of that force and its distance from the shaft, the force correlates exactly with the torque.
Having to kniow the rotational position of the crank shaft to get your distance from the crank shaft centerline just adds complexity to the project. The OP said "and too expensive to put a rotative sensor."
I can understand both your arguments: torque needs force distance AND angle, then if the pedal is not spinning too fast, an accelerometer on the shaft will tell the angle. But the accelerometer will need to be wireless to prevent wire wrapping.
Measuring torque at the crank or the wheel is how all commercial power meters on a bike already work. The most accurate way to develop a load cell to do this uses strain gauges which is fully detailed on my site already mentioned in this post. (keithhack.blogspot.ca). There is a video tutorial on how to install them. Torque is just perpendicular force x distance from the axis, power is just Torque * omega. (omega is rotational velocity in Rad/s).
Several other places online have mentioned trying to measure chain tension with a spring loaded derailleur. The short answer is that it isn't accurate, you've got too many things interfering causing it to move around - plus, if this isn't on a fixed gear bike then you have to deal with the chain moving. If you do some digging you'll find that Polar originally developed a device that senses chain natural vibrational frequency which is related to tension. It was the most accurate of the chain methods - and a market failure due to lack of accuracy. +/- 5-10%.
There was talk about measuring against something "resistive". I can only assume you mean the opposing forces on a bike, namely acceleration and aerodynamic drag, which accounts for 90% of a cyclists power output at a constant speed. Remember sum of forces = mass * acceleration, and that there are many forces. If you have enough information on acceleration, air speed, air density, a guess at your Cd coefficient, and drive train loss you can back out the power input... however it's been also regarded as inaccurate. +/-5% at best, more like +/-15% in worse case scenario if your Cd is way off. See ibike. It's best used in conjunction with a real power meter which means it gives you your drag coefficient in real time.
kwakeham:
Torque is just perpendicular force x distance from the axis
There was talk about measuring against something "resistive". I can only assume you mean the opposing forces on a bike, namely acceleration and aerodynamic drag, which accounts for 90% of a cyclists power output at a constant speed.
Yes, hence my comment that the best way to start is with the bike stopped. But I thought the whole exercise was impossible without even getting round to addressing the biggest obstacle. Apparently I was wrong about that.