A very theoretical question. on final drive

imagine a rear wheel drive car, say, 360 modena.
suppose you have only 1 gear in the car.
suppose your RPM-limited top speed is 80mph
suppose you are not willing to exceed 80mph, overwhich you are not comfortable.
supppose the friction between tire and tarmarc is unlimited ( i.e. there will be no wheelspin in whatever situation)
suppose there is no wind resistance.

Now you changed your differential, and the final drive changed from 4:1 to 4.5:1.

the question: does this change of differential gear ratio reduce your 0-60mph time by 0.5/4 = 12%?

 

other way around
if you went from 4:1 to 1:1 then you would be doing, well, very fast

 

but your 0-60 would be very slow

 

Drag race cars typically use numerial higher rear axle ratios to get the car moving as quickly as possible from rest in first gear. However, the fastest acceleration occurs when the engine is operating at the RPM that produces the maximum torque. In your example, if the higher rear axle ratio prevents the engine from reaching the RPM for maximum torque, then the acceleration time would be reduced. In normal circumstances, the fastest acceleration occurs when one shifts to a higher gear at the RPM for maximum torque. The torque curve drops off as the engine reaches its red line.

 

yes totally misread the question

 

With your simplified assumptions, I think the equation would be:

Time for 0-60 with 4.5:1 gears = (4.0/4.5) * Time for 0-60 with 4.0:1 gears = 0.889 * Time for 0-60 with 4.0:1 gears = 11.1% faster

Are you trying to change a 360 into a dragster? These modern 6~8 speed transmissions with one, or two, very large overdrive top gears are great at giving both awesome low-end acceleration and good freeway driving behavior, but just changing the rear diff ratio on an existing car to improve low end acceleration can make freeway driving very annoying/almost unacceptable.

 

I have a custom differential laying around that will put the top speed of the 360 to only 255km/hour (as tested on track on another 360)
So I was thinking that, maybe I can improve acceleration by installing this.
I rarely go to freeway. its pretty much 100% city drive. Also, the track I usually go to , the long straight is only about 600 meters, so I can't reach 300km/h anyways.
So ............... I think the only thing concerns me now is that I have to be careful when downshifting because the TCU will over-rev the car, or won't it?

 

Sure, if your applications are limited as you say, why not. Here in TX, we have a fair number of 75 mph and 80 mph toll roads that come into everyday use so could be a little "buzzy" (and fuel thirsty) for that use. In the 360 OM that I checked, it shows the stock diff ratio as already being 4.444:1 -- is your custom differential near a 5:1 ratio?

 

Percentage in gearing reduction wouldn't be an equal percentage gain in acceleration.

Some losses will be had in accelerating the mass of the engine/driveline. (shorter gearing will be more RPM/sec so more inertial loss unless you reduce reciprocating mass).

And of course this is also assuming this doesn't result in traction issues, which it may, especially from a dead stop.