0-60 change based on differential ratio change
 

Anyone know a way to calculate a 0-60 time if a different differential ratio is installed? I understand there are many variables. I am looking for a equation where nothing changes except the gear ratio.

As an example. if the 0-60 time is 10 with a 3.00 differential ratio and nothing changes except changing the differential ratio to 4.00 what will be the new 0-60 time? And, is any change a constant such as if the 0-60 time was 10 and the ratio was changed from 3.00 to 3.50 would the same formula still be applicable?

I doubt you could calculate that because of too many variables. It should be possible to take the torque and power curve to make an estimate using the F=ma solved for a: a=F/m.

If you take a plot of the torque curve v RPM that is the same as Force (force*length=torque. Length stays the same so force can interchange with torque)

If you use the ratio of the two different rear ends you will get a value such as 1.2. You would plot a new torque v RPM to determine the increased @ wheel torque (it will be the equivalent of the engine having more torque)

The speed of the car drops by the same ratio. You would have to factor that in.

You could either make plots and do the math to figure out the actual acceleration at say every 1/10 of second. Reverse engineer the actual force applied to get your car to 60 based on actual tests performed.

Once you have the actual force from each 1/10 s figured out, you multiply that by the differential ratio ratio to make a new curve. Then calculate a new set of force values every 1/10 s. You could probably get pretty close.

The easier way is to Google search the results of somebody else that already did the same thing. Try to find a similar engine doesn't need to be X5 but maybe heavier sedan like 740.

You will get say 10-15% more acceleration but the gears have to run 10-15% longer which you would think will cancel out. The whole point off a higher ratio rear end is to shift some of the highest effort acceleration into a more torquey part of the power band. The trade off is less power at higher rpm so it's "all about the bass no treble". (all low-end).

It's quite possible you would end up no faster 0-60 but hella faster 0-30.

You can use an app like dash command for aromatic 0-60 measurements it uses the accelerometer in the phone to determine launch and taps into the car computer to know the speed.

I would be very interested to know the results. Oh you will surely get lower mpg keep that in mind.

I am familiar with what ratios do to speed, rpms, etc and the variables having made many swaps over the years. I've made swaps on many combination of HP/TQ engines. I know the time over any measured distance will be reduced with a lower ratio. I need a formula for dummies. I don't expect it to be spot on but would like a ballpark estimate before I start the project. I don't want to use real life results of someone due to the variables. I have several ways I can accurately measure times that I can use after the lower ratio install. I know it will reduce mileage, don't care. There are many plug the numbers online to calculate time over distance. I need one that includes diff ratio in the calculation. Can't find one.

You can't find because I don't believe it exists. Find an example where someone else has already done a similar ratio change

I'm not surprised if it doesn't exist. I have done lots of searching.

Read this article: http://www.badasscars.com/index.cfm/...rod/prd446.htm

Do a zero to 60 (well 70 or so). Detemine the speed at the shift just near that speed.

If the ratio ratio will move that shift point before 60 you will have a slower 0-60 if you put in a shorter rear end. Hmm. How do you change the rear without the front?

Anyhow since a shift at least one possibly two will be involved there can not be a simple formula involved as your first post, however with some very good info harvested from the linked URL I think you can get somewhere.

Mostly that you can determine a rough idea of the shift points at what mph and rpm possibly and if you can pick a rear end ratio that will keep your shift far enough from 60 to avoid top over rpm before 60 not shift just before 60 either

That info is simple ratios and will give you a go-nogo before you start.

There is a program called cartest (window) that has cars programmed Into it that you can put in different rear ends to get estimates of 0-60 and 1/4 mile.

I did some searching for exact examples of somebody before and after values when changing the rear axle and saw some who said when the shifts happen before the trap you will get a slower time.

I'm sure you can find a chart already done with 0-60 of your car so you can determine the exact shift points.

Simple ratio will move those shift points to the modified speed @ shift. If you don't move a shift point slower than 60 from above you will speed up the process.

That app mentioned should give an idea of how much.

Unfortunately there is just no way it can be a simple formula because the torque curve changes a lot over the RPM range.

Well.. this isn't 0-60 calculator and is for e46, but might want to look at this.

BMW E46 Gear Ratio / Cruising RPM calculator

Thanks. I am familiar with that article. I understand the ins and outs of changing dif ratios from the good ol' trial and error days. I have only one option for a lower gear ratio. I have 3.91s and am going to 4.10s out of a 3.0. I purchased them more than a year ago. With the 3.91s Number of shifts will be the same. It is necessary to change both diffs. Usually the extra shifts referenced in the article are for a manual trans. Not nearly as much of a concern with an automatic. Most of what I do is from stoplights. I want the extra torque for the launch where I have the advantage over 2 wheel drive even if they have launch control. I will check out cartest.

Out of interest are you looking for pure 0 to 60 improvements or other ranges 50 to 90 etc?

I have a full Quaife set up on my E53 and that allowed me just over a second improvement in the 0 to 60 range simply by letting me floor the accelerator without losing any traction. This made up for not having any fancy modern computer controlled launch control.

Of course having a few extra horses under the hood also helps so maybe some engine upgrades?

SB

I've gone as far as I can go with engine mods and power adders. Don't need limited slip as traction is not an issue. Only interested in 0-60.