I am currently working on this game called the Trail Hogs where you ride a recumbent bike with bumpers and joust your fellow rivals, the Skidmarks named appropriately because they leave long skidmarks on the trails so you know they were there. Anyways, the bicycles of the Skidmarks are recumbent and similar to those of the Trail Hogs but there is one difference - the Skidmark bicycle has a jet engine on the back and one that is human powered! So how would this work? The pedals transfer power to a belt transmission where you tighten and loosen belts to either transfer power to the back wheel when starting or to transfer power to the compressor portion of the jet engine. So you would initially pedal to run the wheels and then when you're coasting you transfer power to the compressor. However, there is one huge problem - this won't produce any thrust. So what is a Skidmark rider to do? Well, this is where solar power comes in. The jet engine has a number of stacked Fresnel lenses on top on the elbow shaped jet engine that increasingly narrow and transfer solar energy to a point about an inch wide. (The whole structure looks like an upside down pyramid.) The structure is connected to a pipe which penetrates the jet engine's hot chamber and heats a copper pipe which is contained within perforated cylinder similar to the flame can of a turbojet. The only difference is that this container is in the middle of the hot chamber and there is no drive shaft going through it. (As mentioned before the compressor is completely human powered.) The idea is that the air is compressed rapidly by the compressor and then heated to a higher temperature where it expands and produces thrust! The faster the rider pedals the more air enter the hot chamber and the more thrust. In the game the purpose of this is to reach high speeds, like 30 - 50 mph with less effort. The Skidmarks compete with the Trail Hogs so they must upgrade their bikes quite a bit.

What do you guys think? Would something like this be possible.

I'm already starting to build a crazy bike like in the game.

There is a visual to show you what the bike looks like: 

And of course my bike:

Hmm... no one can comprehend this... I will build it, though.

I don't have much input, sorry... But the human powered helicopter was also sci-fi/fantasy until it was recently built. This sounds like a fun concept.

I will build it one day... Actually, unlike the human powered helicopter this jet engine is partially powered by the sun! If I could successfully create it I could also possibly build the helicopter too since jet engines have great power to weight ratio.