Suppose I had the tools and engineering know-how to rig a lightweight propeller to the back of my bike. Suppose further that I finagled the chains and gears in such a way that applying pressure to the pedals would not only apply torque to the rear wheel but also to the propeller.
Would this create a super-fast bike? Or would the energy required to move the propellers (meaning that less would go to the wheel) offset the potential gain from them?
If the gear ratios were right, I think it might work. In the early Wright Brothers era, didn’t some of the flying machines involve pedalling the props.
When I read the title, I thought you meant a propeller as in one from an airplane, with an engine attached and my first thought was that yeah, it would work for a second, then it would flip the bike on it’s side and smash up the propeller.
Watch the anime movie Kiki’s Delivery Service (Kirsten Dunst) Cute! Boy riggs a bike similarly, with amusing results. However, it is only animation.
The propeller would provide a force, but it would do so less efficiently than the tires. Better off sticking with just the wheels.
And what if you did it on a treadmill?
beat me to it. Damn!
No.
None that were actual flying machines. There were several such attempts, but they would be properly classified as non-flying machines or crashing-off-the-end-of-the-runway machines.
Given the weight of the materials they had at that time, it was not possible for a human pedaler to provide enough power to get a plane aloft.
It was the 1970s before Paul McCready (sp?) successfully flew a human powered aircraft. (Gossamer Condor) and just barely at that.
HOWEVER the original Wright Flyers DID use bicycle chain and sprockets to transmit power from their infernal combustion engines to the dual propellers, one side used a crossed chain to provide counter rotation, thereby canceling the torque effects.
Fan boats work fine, so I don’t see why a pedal powered ‘fan bicycle’ should not work, with the right design it could even be amphibious 
Why not add wings and cross the English Channel?
Because it’s 5000 miles away.
I think the FAA would want to have a word.
Try mounting it on a treadmill and tell us what happens.
The serious answer: NO. The only source of power is the person. Th goal is to convert the fixed amount of person power as efficiently as possible. That’s how you go as fast as possible.
When you couple pedalpower to a wheel via a chain you lose almost nothing to friction. When you couple pedal power to a prop you have essentially the same frictional losses.
BUT: which converts effort to motion more efficiently: a narrow tire rolling against the ground or a propellor pushing against the air? Answer, the prop has huge losses, the tire almost none.
So adding your prop just pulls power away from the drive tire & then spends it less efficiently than the tire could have. Net result: a loss of speed.
No for the question. A fan providing thrust in air, is less efficient at transferring power than the tire on asphalt.
Now here’s a variation that could provide bonus power for the rider. Replace the spokes on the rear tire with fan blades. The wind blowing from the correct side of the bike would reduce the need for energy provided by the rider. Wind from the wrong direction would require more energy supplied by the rider. Wind from the front or rear would not transfer power by the fan.
There is a fix to make the wind useful from both sides and most importantly prevent the opposite situation. . Make the blades moveable with stop pegs and springs. The blades will switch to the needed position when the wind hits them. You now have added thrust from the left or right side.
Just a tiny little clarification to prevent anyone from getting an incorrect impression: MacCready designed and built the Gossamer Condor and the Gossamer Albatross, but he didn’t fly them himself. He had professional athletes to power and fly the craft.
Also, before developing a wind tunnel, the Wright brothers tried measuring the lift generated by airfoils they were testing by mounting them (with a measuring device) on the handlebars of a bike.
I might have to steal your idea and build a prototype 
. Too bad I wouldn’t be able to race it. Has anyone actually built a wheel like this?
However, I don’t agree that mounting a rider driven propeller to the back of a bicycle will make it slower. You also have to account for aerodynamic drag which is what largely retards a decent rider from going faster on flat ground. By placing the propeller at the back of the bike and spinning it, you could keep the airflow over the rider/bicycle from becoming turbulent for a bit longer. This could have dramatic advantages. However, we will need a wind tunnel to find out what is the best combination and if there is actually any gain.
On a related topic, in one of my fluid engineering classes where we were studying fluid drag, my professor drew some pictures of cars and trucks and showed how air flowed over them. He pointed out how there is pressure drag on the front how it was turbulent behind the car. This got me thinking that if I attached a fan to the front of the car and run a tube to the back of the car to channel the air, I could lower the aerodynamic drag of the car substantially. I showed the professor my idea and asked him if it would work. He said yes, but the only draw back would be cost. I don’t think it would be very expensive to implement my idea given that it is basically a fan with a tube attached. I will have to try this out one day in a lab setting.
Possibly relavant.
For a (semi)recent human powered boat competition, one of the leading designs was an airboat. (actaully an air-hydrofoil) While the prop is less effective than a water prop, you also don’t have the drag of the driveshaft in the water.
Brian
A propeller doesn’t make it slower. It moves the bike forward less efficiently. You then must provide more leg energy into pedaling to go the same speed you did when all the forward motion was provided by the tire.
I figured it not going to make enough difference to get people off their ass in America and riding bikes. Have fun with the idea.
Which means that, for the same amount of energy expenditure, it’ll be slower. If someone’s propelling a bike at top speed, that means that that person is working as hard as e can to move the bike, so you can’t just say e could make up for the less efficient drive by working harder.