I could probably figure them out if I put my mind to it; but hey, someone else might be interested.
The way I understand it, the first number in transmission ratios get smaller as one shifts to a higher gear. Pulling numbers completely out of thin air, first gear might have a 4:1 ratio. Second, 3:1. Third, 2:1. Fourth, 1:1. Fifth/overdrive, .85:1. So in first gear, using these numbers, the engine’s crankshaft turns four times for every revolution of the drive shaft in first gear, and one turn for every turn of the driveshaft in fourth gear. In overdrive the crankshaft is turning slower than the driveshaft.
Then the direction of rotation needs to be changed. Let’s say you have a 3.9 differential and a 4.5 differential. Does this mean that the driveshaft turns 3.9 or 4.5 revolutions for every revolution of the axle? Or does it mean that the axle turns 3.9 or 4.5 revolutions for every revolution of the driveshaft? It seems the former would give a greater speed for a given engine speed when using a 3.9 rear end, and the latter would give a greater speed for a given engine speed when using the 4.5 rear end.
First: Do I have the basics correct? Second: which way does the ratio go in the differential?
Here - if you look at this image, and see that the drive shaft is entering from the right, you can see it carries a small gear on the end of it. This meshes with the larger ring gear. Thus, in this layout (which is fairly typical of older-style RWD cars) the small gear will turn much faster than the large gear will.
Make that all cars, trucks, buses, motorcycles etc. Given the enormous mechanical disadvantage that comes from the relatively huge size of the final drive units (i.e. the tires) they can’t turn anywhere near the driveshaft’s speed.
Since this is the SDMB, where if you use absolutes and are ever wrong, someone will come in and whale on your ass then stalk you for years to remind you of how wrong you are, I’m not going to be the one to say “all”. 99.9999% of them, sure. But I’ll bet someone will come in soon to post how at one time, in the Belgian Congo, a car made entirely of hippopotamus bones and taro root had a final drive ratio less than 1, so obviously you have no idea of what you’re talking about.
Johnny you might want to think of it the other way around. For any given road speed a lower numerical geared differential will result in lower engine rpm.
For example at 70 MPH a 4.11 diff the engine RPM is 4,000. With a set of 3.73 gears the engine RPM drops to 3750.* Your acceleration will be slower with the lower numerical gears, but highway fuel mileage will probably improve.
Here comes the confusing part. A lower numerical gear is a “higher” gear. The lower the numerical value, the closer the input and output speed. Assuming that the engine has enough torque this would result in a higher speed for a given RPM. In the above example at redline the car with 3.73 gears would be going faster at redline than the car with 4.11 gears.
so if you talk about higher or lower gears, you need to say if you are discussing the numerical ratio or just in general.
[side story about gears] I had an old Volvo that had a 3 speed automatic transmission. The tranny was dieing so I bought a later 4 speed tranny to replace it with, and converted it over (pretty much a bolt in operation, I had to adapt a few things, but over all easy) The part I did not think about was that the 3 speed cars had a much different rear end ratio than the 4 speed cars. My car came with a much lower numerical ratio than a 4 speed car. Since I did not think about that, I did not change the differential.
Anyway after it was done, it was a complete slug off the line at a stop light. But once on the highway it was one hell of a nice ride. 2100 RPM at 70 MPH and 28 MPG (instead of maybe 20-21 before)[/SSAG]
*Above numbers are anally derived and are only an example, your numbers will be different.
Bored?
Want to screw around with rear end ratios and the first 6 forward gears on a computer-simulated car until you develop carpal tunnel along with a need for bifocals?
I bring you Cartest 4.5 for DOS! I’ve spent hours screwing around with gear ratios in it, at work, at my very boring old job.
Seriously, though, it’ll let you change rear end ratios on the modeled cars to your heart’s content and watch what happens to the 0-60 times, RPMs at given speeds, top speeds, and gas mileage.
You can multiply the gear ratio with the final drive ratio to get directly the reduction ratio at the wheel.
For example, suppose a car has a 1st gear ratio 2.615 and the final gear ratio is 3.889. Multiplying those numbers gives 10.170. This means that for every 10.170 turns of the crankshaft the wheel makes a complete turn (or, for every turn of the crankshaft the wheel turns 1/10.170 of a full turn).
Now suppose the wheel’s circumference is 1.850 meters. This means that for every complete turn of the wheel, the car has traveled 1.850 meters. At 5000rpm in first gear, the wheels make 5000/10.170 = 491.64 revolutions per minute. The car travels 491.64 * 1.850 = 909.53 meters per minute or 909.53*60/1000 = 54.57 km/h.
In motorcycles things are a little different. Instead of a final drive ratio there are two numbers: primary reduction ratio and secondary reduction ratio. The primary reduction occurs due to a set of gears inside the engine. The secondary reduction comes from the chain and sprockets. Again, you can multiply the two numbers and treat them as a final drive ratio for cars.
You might ask where those numbers come from. For gearboxes and chain-and-sprocket sets it is the number of teeth of the driven gear/sprocket divided by the number of teeth of the driving gear/sprocket. On a differential it is the number of teeth of the crown divided by the number of teeth of the pinion.
