Choosing engine based on peak fuel efficiency RPM
 

I have heard there is a certain RPM (just below peak torque) where the petrol engine produces power most fuel efficiently.

If I require 2.5kw to maintain cruise speed (100kph for example) should I choose an engine that produces 2.5kw at it's most efficient RPM?

I am thinking a 10kw 125cc petrol engine that produces 5kw just above idle speed will have too much power to cruise efficiently at 2.5kw. Would it be more fuel efficient to use a 5kw engine?

That's too vague a question. You really need to have a Brake Specific Fuel Consumption map (BSFC map) to show what kind of fuel consumption the engine delivers at what load and speed.

Then if you know what kind of load your particular chassis and weight generate at your target speed, you can dial in whether it is a better match than some other engine.

Generally speaking, and I'm certain you know this already but it's worth repeating:

1) Wider throttle openings are more efficient in general. This is part of why diesels are so much more efficient as they are wide open all the time and do all of their speed control via fuel metering.

2) Slower (to a point) engine speeds are more efficient. I don't remember where I saw it but I recall reading somewhere that a peak piston speed of 1200fpm is about what you want to see at the engine's cruising revs.

3) Lighter is better. No point in taking a bunch of unnecessary steel for a tour of the countryside, it isn't paying for the trip.

4) Hotter is better (to a point, obviously). Having the engine already at operating temperature before you load it eliminates wasteful open-loop mode operation. Someone else recommended letting the engine run until it was warm, which is burning fuel without achieving any portion of the actual goal of getting somewhere, which is much, much worse and I just wanted to slap that guy.

5) Ancillary loads are unnecessary loads. Power steering, air conditioning, and daytime running lights are unnecessary and should be converted to the least power requirement option. This can sometimes be impossible; it's damned hard to find a car with manual steering in the States anymore, for instance. And if DRL are required by law, convert to lower-amperage LEDs for as little alternator drag as possible.

- a - If you live in a ridiculously hot climate, air conditioning may not be optional, but then again humans evolved up until the last 100 years without it, so your viewpoint may vary.

After that it comes down to chassis peculiarities and driving style. You can take the most efficient vehicle ever made and make it into an absolute fuel hog by driving like an idiot, or squeeze modestly thrifty performance out of a Veyron if you know what you're doing.

If you could match best bfsc with flat ground cruising speed, you would not be able to climb any significant grade.

regards
mech

Pretty sure OP is talking about a motorcycle.