How many revolutions per minute would a stationary bicycle have to achieve to power a T.V. if harnessed:?

Question

: to a generator?

Answer 1

It's impossible to perform that calculation without a lot of facts you don't specify. Nevertheless, I've actually seen a television powered by a exhausted human being on a stationary bicycle, so I'll give it a go.

One horsepower (USA) is equivalent to 746 watts and the athlete who pedaled the Gossamer Albatross across the English Channel was able to generate about 1/3 horsepower continuously (meaning until exhausted).
746(1/3) = 248.667 watts
My 19" TV draws 350 watts, so it's too large to be human-powered. Let's assume we have a very small TV that dissipates just 150 Watts.
150w/746w = 0.2010723 HP
Another way to express one horsepower (USA) is 33,000 ft-lbs/min. This means we can express the required power in mechanical terms.
0.2010723(33000 ft-lb/min) = 6635.39 ft-lb/min
Next we assume the pedals are being turned at 2 revolutions per second and the wheel is geared-up 1:3. Thus the wheel is revolving at:
3(2 rps)60 = 360 rpm
If we assume a 24" wheel (1 ft raduis), the rim has a:
2(1 ft)3.14159 = 6.2831853 ft. circumference.
The speed of the wheel's rim is:
360(6.2831853) = 2261.9467 feet per minute.
The drag on the rim of the wheel, exerted by our hypothetical generator is:
(6635.39 ft-lb/min) / (2261.9467 ft/min) = 2.9334864 lbs
This seems reasonable and possible. Let's do a bit more. Because the wheel has an assumed radius of exactly one foot, we can say the torque required to turn the wheel is:
(1 ft)(2.9334864 lbs) = 2.9334864 ft-lb
Because of the 1:3 sprockets the torque at the pedals is:
3(2.9334864 ft-lb) = 8.8004592 ft-lbs.
If the crank arms are 6", or 1/2 foot long the force applied to a pedal must be:
(8.8004592) / (1/2) = 17.600918 lbs.
Of course, a cyclist cannot apply continuous torque through a complete revolution of the pedals. A quickie approximation might be that each pedal gets pushed for 1/4 revolution. Since there are two pedals, torque can be applied to the pedals only 1/2 of each revolution. This means that the force that must be applied to each pedal for 1/4 of a turn is:
2(17.600918 lbs) = 35.201836 lbs.
The bottom line is that the stationary cyclist must turn the cranks at 2 revolutions per second and apply a "foot-force" of 35.2 lbs to each pedal for 1/4 second @ twice per second. This is a lot of hard work to generate a puny 150 watts. Still, it actually is possible.............

Answer 2

It's not necessarily a matter of RPMs. It is a matter of power in Watts. You can always use gears to provide the proper RPMs for a particular generator to achieve the optimal power output for a range of RPMs, but you still need to have that level of mechanical power from the person riding the bicycle.

When I ride an excercise bicycle (with a power meter attached) I can maintain about 200 Watts for 20 minutes before I am tired. A "tour de France" class bicyclist can output that level (about 1/4 horsepower) for several hours.

200 Watts is plenty of power to run a TV -- if you get the proper 120VAC generator, and the proper gear ratio (or pully/belt ratio) to get the proper RPMs for THAT generator.

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