Bfeboi,
The difference between the diff ratios is basically this - the higher the number, the more revs the car needs to do for a given speed. The engine spins at big numbers, but the road wheels don't spin anywhere near as fast. A Mini's wheels generally spin at somewhere between 1040 and 1100 rpm at 100km/h. This is a high number - any car with bigger wheels will have a lower wheel speed. For instance, a WRX is about 850rpm at the road wheels. Others have mentioned, a 3.444 diff is around 3600rpm in 4th gear at 100km/h. A 3.765 diff will spin more like 3950rpm in 4th gear at 100km/h (using the same wheels/tyres).
Skip this if you want, but if you're a stickler for detail, here's the math for my road wheel speeds - correct me if I'm wrong with any of it! Using a 165/70/R10, you have Tyre OD = 485, circumference = 1524, at 100km/h = 27.77m/s, 27.77/1.524 = 18.23rps, times 60 = 1094, there'll be variation for tyre pressure, etc, correct me if I'm wrong. Interesting point, this gives a 3.444 diff at 3767rpm in 4th (1:1 gearing) at 100km/h. 3600rpm at 100km/h with a 3.444 diff requires a rolling diameter of 507mm - is the LS 12" tyre a 145/70/R12? If so, the numbers are spot on! A 165/60/R12 is a about 502mm rolling diameter... A variation of 35 rpm at 100km/h. These numbers are straight theory, tyre pressure/loaded profile does have an influence, I don't know which way it would skew the numbers - though I'd guess the tyres rolling diameter would increase with speed, due to centrifugal force... Sorry, I'm rambling...
If you've only got 848cc motivating you, a 3.765 diff is the better option, as revving the engine higher generally means you use its power sooner. Any given engine will accelerate faster with a 3.765 diff than with a 3.444 diff, but you'll be revving higher for any given speed - not good for noise or economy, or ultimate top speed. If you've got an 850, ultimate top speed isn't as important as getting up to speed as quickly as possible, so the 3.765 makes more sense than the 3.444. If you've got a quick large bore engine, the 3.444 makes sense because you've got the performance to make up for the slower acceleration.
Pretty well every car in existence has the speedo drive taken off before the diff but after the gearbox - whether it's taken off at the gearbox end or the diff end (or, in a Mini's case, both!). Thus, your speedo has to be calibrated to suit your diff. If you have your speedo calibrated for the right diff, you'll be in the right ball park (although very rarely 100% accurate). If, however, you line up DBR33N's 4.11 diff (not an unusual ratio for a modern car - think WRX) with a speedo set up for a 3.444 diff, you will have errors. In that case, the speedo will be very optimistic - it'll tell you you're doing 100km/h when you're doing 83km/h!
Annoying for the guy following you, but you don't have to worry about tickets. If you got a speedo set up for a 4.11 diff and you ran a 3.444... The officer would be handing you a ticket for 119 in a 100 zone.
So it's important you match your speedo with your diff.
Your tacho... Well, it depends on how it works. I don't know about mechanical ones, I've never seen where they take their drive from. Electrical ones usually work off the ignition system, and therefore don't have anything to do with the diff.
Hope the novel helps, and doesn't scare you off! Sorry if it's more basic than what you were after - or too technical! I hope it doesn't put you to sleep!
Now all I need is a tacho to figure out what my diff is...
Couldn't be bothered doing it the other ways... Not that critical really - it goes fast enough, and the speedo's close enough!
