Can´t you use gears? The efficiency is higher.

Check the racing bike scene. They look for high efficiency (for example chains with oil vapor infiltrated)

I thought about using gears but I am somehow concerned about the tolerances and the fact that the only engine burns will be sudden and quite abrupt - the engine will accelerate to 5000RPM in 10 seconds once or maybe twice per lap. However, it is a two staged reduction so I presume that I could use a gear in the first reduction and a roller chain in the second? Does that seem like it would offer any advantages in terms of efficiency?

I advise you to use gears. It is the best solution. its mechanical efficiency is of the order of 0.96 to 0.99.

Ahmed would you be able to provide me with some information/guidance as to how to proceed with the gear design/calculations etc..? 

What if you use a flywheel? The motor activates the flywheel that activates the chain. You´ll probably need a kind of clutch for the chain/flywheel set.

At the moment we are planning on using a centrifugal clutch that engages at a certain engine speed. How would you add a flywheel to the design?

I have no idea... Would need to see the entire project... Ideally it should be on the bottom, to lower the gravity center... You need to take the dimensions of your vehicle into account. I was thinking that the motor could be connected to the outer diameter of the flywheel and a clutch would connect the flywheel to the chain.

you may wish to check "Shell Fuel-a-thon" , it was an ultra-fuel economy competition that Uof W engaged in during the '80 s and '90 s. A good lube is any thing with MoS2; Pay close attention to your freewheel/overrunning clutch, which is a major source of friction (as well as your tires and wheel bearings, of course). If you go with the freewheel on the rear wheel the efficiency of the chain is likely not important, but a shaft drive may save some weight. If you choose to use moly lubricants, use them sparingly: in some sliding applications their non-Newtonian characteristic may create significant drag.

Agree with Bert, from my EcoMarathon participation a couple of years a go I know that the free-wheel is the limiting factor - you need to find the optimum here in order to minimize the free turning friction while still being able to take the engine torque during your two engine runs.

I used to be part of a Supermileage and Eco-marathon team in my B.Eng years and we had a lot of thought about the same issue. The one main consideration you need to have in mind is that weight is the hearth of the matter. Every gram you need to move is expended energy. Then come engine efficiency wich is also 1:1 in terms of efficiency/fuel economy gains, and then comes the transmission efficiency.

First, a quite high reduction ratio is required so it is impractical to make it a single stage roller chain setup as the driven gear needs to be so much bigger than the driving one, the wrap angles become very narrow and the chain will, at best lose efficiency and at worst, will want to skip teeth. Therefore a two stage transmission is required and the first stage can be gear driven to improve efficiency. However, as gears change the rotation direction, it might be required to have an additional gear just to bring the rotation right and then the overall efficiency advantage of gears may be lost to the additional weight of the gear+shaft+bearing+casing+lube and the additional stage efficiency penalty.

Timing belts are also more efficient than roller chains, although the weight of the large pulleys needed need to be accounted for. It might be good to use a compact timing belt setup as a first stage, followed by a roller or silent chain (which I think has higher efficiency, but I'm unsure of the weight advantage/disadvantage).

@ Gustavo Kannenberg, The weight of these machines is very low and a flywheel adds too much weight to the car. We had a thorough evaluation of the flywheel cost/benefit and it was definitely better to make the flywheel just big enough to have the single-cylinder engine start and run smoothly and to prevent stall at clutch engagement. Otherwise, super-high flywheel speeds (read tens to hundreds of thousands RPM) are required and these may become a safety hazard quite fast.

Good luck,

Laurent

Edit: I also need to second Bert Habicher on the importance of having an efficient clutch and freewheel. A good freewheel will make a huge difference as it is a direct braking torque at the wheel when coasting. That is in part why you would want to have your engine just barely strong enough to make the care accelerate and run at  the desired pace within its efficiency range and run all lap long. It prevents the freewhell from going in coasting/braking mode. Also, remember that many losses are proportional to speed or speed raised to the power of two. Therefore, the more time you spend above the minimum average speed is excess energy expended.

Ok, now that is answering questions that weren't asked so I'll leave it there.

If possible use timing belt. it is lighter , quieter.