I was surprised when I first heard that in kart racing it is important to go fast enough to lift the inside rear wheel so you can take a tighter line.
But I have also seen a glorified kart at a hill climb where the internals of a car diff were used with a sprocket attached where the crown wheel normally goes - the actual differential assembly can be surprisingly compact.
I have made parallel depth gears for the differentials on both my 3" Foden and 2" traction engine. They are an interesting exercise but worth the effort. The main area of potential difficulty is getting the spur gears dead on their centres and running true otherwise the crown wheel will tend to bind in places. Also the dividing head being used needs to be of good quality to give accurate stepping.
I've just been doing some research and have noticed that hand drills now seem to come with aluminium gears. The "Kennedy" hand drill from Cromwell claims die cast and might be zinc but doesn't say. Unfortunately, that looks like it has brass pinions.
Scrap that Idea for long term use. Unless you can find a couple of friends with the older Stanley drills with cast iron gears and steel pinions, that they don't want any more. Sorry, I still use mine :-(
Indeed, do have a look in your books, and look for Austin Seven. These all had such differentials.
I had a little to do with one of the very early 'production' machines when Karting first became popular in UK around 1959. This was a Cal-kart, and had such a differential, whilst it was also chain driven. With the limited suspension provided by pneumatic tyres we found that too much wheel spin resulted with the differential and they were abandoned.
I have done a quick rough drawing which (I hope) illustrates the general idea ..................
Mike that is brilliant! I can follow how it works. But looking at it with the amount of machining and gears available I can see why bevel gears became the norm. I guess that using effectivly 8 gears whilst being ok when no differential action was required would have caused more drag when turning and also be quite noisy. I also guess that, although much of the case work can be done on the lathe and drill with a rotary table I would still be simpler with bevel gears once made.
Anyway your comments above also give me a potential problem area to consider, and that is not wheel spin during drive, but the single disk brake I have fitted to the present axle would not work very well if a diff is fitted as the diff would still allow one whell to free run either with or against the engine rotation through the clutch. Effectivly only braking one wheel rather then the two back wheels.
So perhaps I leave as is for the time and just try to enjoy the kart rather then engineer it into a full road going vehicle!
I agree that does make it a little more complicated but not impossible - I think you could solve that one by mounting the brake disc on the diff carrier as well.
The hillclimb "kart" I saw used a Morris Minor diff (I think), I've also taken a Triumph Spitfire/Herald one to bits and the differential bits are very compact As I recall the bevel gears are about 35 mm dia. A difficulty for your application might be lubrication - the hillclimb kart greased the diff and then wrapped the diff carrier in duct tape - that might be OK for the relatively clean short duration use of a hillclimb but on a beach sand would stick to grease and make grinding paste.
But if you're planning to use it on grass then a diff would slow down the conversion of grass to mud.