Tom, when I was your age I wanted to build a scale XKE Jag. Your task sounds much simpler. Still a lot of work, though. As Roy mentioned, I built a half scale book frame and suspension, powered it with an electric motor and added a single caliper hydraulic disk brake on the rear axle. My wife had a lot of fun with it, I could barely fit. I learned a lot and can share a few ideas.
1) You want to go at least 5/8 scale, and that's for a rear or mid-engine single seater. Trying to duplicate a full size Locost drivetrain layout with two seats, you'd have to go at least 3/4 scale. At 5/8 scale, chassis width is about 26". Take out a few inches for a drivetrain (in my case batteries) and you're not left with a lot. And that's just width. I made the pedals adjustable on mine, and still had to move them all the way forward, ahead of the front suspension, for my 5'6" wife to be comfortable.
2) I built a mock-up frame out of 1/2" square balsa sticks. Good thing, too, because the first one I made was way too small. Balsa isn't cheap so you can skip this step if you're sure your frame is going to be big enough (my first balsa frame was way too small).
3) I used 1/2" square mild steel tubing and it worked well, although it was 16 gauge, same as a full size Locost, and therefore pretty heavy. Not a huge issue. The floor was 18 gauge, 20 gauge would probably have worked just as well. I used 3/8" round tubing where 3/4" is specified in the book, and the good thing is I could make the needed bends by hand.
4) Use go-kart components wherever possible, and get them used if you can. The hydraulic brake kit cost me somewhere around $80, so things like that will eat up your budget quickly. Wheels and tires can really add up too. They don't sound like a lot, $15 for a wheel, $20 for a tire, but then add another $15 for an inner tube. I ran a spare, so that was about $250 altogether in wheels and tires.
5) My suspension turned out to be more for looks than anything else. I couldn't find soft enough springs anywhere, and travel was minimal, half an inch at most. Mobility scooters and the like are a good source for coilovers, and they're amazingly cheap new ($7-$12 each), although they don't actually have any internal damping so they're just a perch for the springs.
6) I used a solid rear axle for simplicity, but it created a tremendous amount of understeer and a huge turning radius, particularly at low speeds. Difficult to maneuver in close quarters. I would seriously consider next time using a split axle and only drive one rear tire, or add another motor (they're pretty small) and drive each half axle separately.
The project stalled because I was unhappy with the chassis size and the handling with the solid axle. My wife didn't seem to mind as much and enjoyed drifting it flat out in large circles, but you can only do that for so long before you get bored. If I ever finish it, I'll probably build a new, bigger frame, and redo the rear transaxle for independent drive axles.
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