Diff Ratio and Gearing Analysis
 

Hi All-
I have been toying with someday changing the differential ratio on my 220D (because the engine SCREAMS at highway speeds), but I wanted to do an actual analysis to understand the benefits and costs. Hopefully some of this will be interesting/relevant to a few of you. If somebody wants it, I would be happy to recreate this analysis for a different vehicle.

My analysis used data from the OM 617, OM 617A SAE paper 780633, and I scaled it for my smaller OM615 (see first picture). I also needed to estimate the required engine hp at a given vehicle speed. I assumed a flat road and no wind, so power goes to overcoming rolling friction, air drag, and drivetrain losses. At a given vehicle speed and diff ratio, I can determine the engine rpm. Once you know the rpm, you can use the first graph to determine the max power capable of the engine at that vehicle speed.

Obviously if the max power exceeds the required power, the car could accelerate at that point. Once the two curves intersect, the car can no longer accelerate (this is the top speed). MB clearly chose their diff ratio for a particular vehicle to achieve the highest top speed. Maybe this is an obvious choice, but it surprised me. My vehicle has a 3.92 diff, and you can see that curve intersects the required power curve at 80 mph, which is the published top speed of my car.

So the key advantage of going from a 3.92 diff to a 3.69 or 3.46 diff is that at a given speed (say 70 mph), the engine doesn't have to turn as fast. These engines have peak efficiency (bsfc, specifically) at ~2400 rpm, so the lower the rpm the better for fuel efficiency at highway speeds.

And the key disadvantage of going from a 3.92 diff to a 3.69 or 3.46 diff is that the vehicle top speed is reduced (see second graph). So basically, MB really did pick the best diff ratio for my car. If you went higher or lower than the 3.92, the vehicle top speed would be reduced.

In conclusion, because my vehicle top speed is so close normal highway speeds, it would be a bad decision to reduce the diff ratio. For vehicles with a top speed well above normal highway speeds, it clearly could make sense to reduce the diff ratio. Basically, you are trading a lower top speed for better fuel economy at the speeds you actually drive.

So the good news is that I don't need to spend any money/time changing my differential. An evening of playing with Excel saved me a lot of work. The bad news is that I am stuck with a very noisy car at highway speeds.

in my experience you can reduce the numerical ratio and not impact top speed much. For instance, my 83 240d with the euro 300d motor and a 307 diff will go about 100 in fourth or fifth.....flat out.

I would not hesitate to go to a 369 diff in your 220 provided it has a stick. A 358 might work pretty well too.

Changing the Diff from a 3:92 to a 3:69 is about 5.8%.
3:92 to a 3:46 is about 11.5%, that is quite a jump.

I went to a 3:58 from a 3:69 in our 80 240D, and didn`t change a whole lot. but that is about 3%.

What is a 220, about 55hp?

Charlie

Would you be prepared to send me your calculations?

I'd be interested to see how you made these graphs.

Have you considered that your engine probably isn't as powerful as it was when it left the factory. In one of those Top Gear episodes they had to try to tune family cars to perform like race cars (or something like that) - they found that their older cars produced about 20% less power than they should...

...so OK this isn't very scientific - it was Top Gear! But it perhaps indicates real world situations.


Have you checked your graphs with a real world test with a GPS measuring your speed?

Top gear not scientific?:eek:

My world is spinning!

If this was facebook I'd do a "like"

This is an accurate conclusion for a vehicle with very limited available horsepower. The diff with the lower numerical ration will constrain the capability of attaining speed on the highway.

With vehicles that have additional power (617 turbo), the change makes some sense.

I will tell you, however, that a 617 turbo with a 2.88 runs right into power problems trying to climb a decent hill at 65 mph with the a/c running. It cannot hold that speed and quickly loses the turbo as rpm's fall below 2500.

what's a "decent" hill? that amazes me... my 85 seemed to have no issues with climbing anything I pointed it at... right up until the VP let go... GRRR... or are you talking about mountains? I've not gone to the apps yet with the car. I can see where a steep grade would cause issues with the car... especially if substantial weight is in it.
why would the RPM's drop? I would think it'd downshift to 3rd before the speed lost... I think 3rd will pull until 80 in the 85 no?

This hill is somewhere between 5% and 6%. The SD can hold it at 65 mph, just barely, without a/c.

Now, it could be very possible that my filters, and/or the IP need attention.............:eek:

If the '85 can hold a 6% grade at 70 mph, I definitely need to do some work............

Right now, my excel program is really badly annotated, so I will fix it up and make it a bit nicer for public use. I will post it asap, probably on Friday.

I have been spending some time trying to explain T Walgamuth's observation that he has the same top speed in 4th or 5th. His 4th gear is a 1:1 ratio, I believe. With 5th being 1:0.81. So far, I cannot explain it with my computer model, but if I make an progress there, I will let you know.

Yes, the loss of power after 45 years is definitely a big flaw in my model (amongst many others). I have yet to actually determine my actual top speed, so the fact that MB thought it was 80 mph may be irrelevant to my situation. But the loss in power over time simply reinforces that a lower numbered diff gear ratio does not make sense for my car.

Okay, so here is a dumb terminology question. When comparing a 3.46 diff ratio to a 3.92 diff, does the 3.46 diff have a "higher gear ratio" or a "lower gear ratio" than the 3.92? I have been struggling with my choice of words for some of this discussion.

My car had 57-59 hp when new, depending where you look (and which type of test was performed). Yesterday I got a german publication from the early 1970s with the real power data for my car when new, so I will post that when I get a chance. I don't know any German, so I got it via the library mostly for the graphs. The analysis I posted at the beginning estimated the power curve of my car from om617 data. So it will be interesting to see if my estimates were reasonable.

Don't waste too much time trying to justify that statement. It's factually incorrect with only one possible exception:

1) If the engine speed in fifth gear is slightly below the horsepower peak (say 60 hp and 3800 rpm) at a specific road speed (say 75 mph), and the engine speed in fourth gear is slightly above the horsepower peak (say 60 hp and 4700 rpm), the two road speeds would exactly match.

The flaw in this argument is the fact that 3800 is considerably below the horsepower peak and 4700 is just way too fast.

So, I don't see how the statement could possibly be factual for a 616 with the .81 overdrive gear as you stated.

What is the most likely scenario are the errors generated due to the very difficult task of actually determining the maximum possible speed of the vehicle. Any slight grade will dramatically affect the result when there is absolutely no additional horsepower to spare. It's nearly impossible to draw a factual conclusion.

Tom doesn't have a 616 in the car in question.
Also, this is a common phenomenon. Most motorcycles I've owned had nearly identical top speeds in either of the top two gears. Also my 240D (with the much discussed 3.07 rear end ratio) has the same top speed it did with the factory ratio (3.69 I believe).
My rationale is that horsepower is horsepower and the gear ratios only serve to change the torque multiplication (within limits of course). A vehicle is going to hit an aerodynamic "wall" at a given speed and at that point it can't go any faster without engine or aero mods.

Available engine horsepower determines the final speed of a vehicle, all other variables being equal. The gearing simply allows the engine to produce the maximum available horsepower by getting it right to its horsepower peak.

There is no "aerodynamic wall".

So you're saying that a given engine will produce the same top speed regardless of the vehicle it's in? I realize you said "all other variables being equal" but the key variable where top speed is concerned is aerodynamics. And there is an "aerodynamic wall" at which point the wind resistance rises to the point where the engine will not push the car any faster. We all know that wind resistance rises with the square of velocity don't we?
We're probably saying the same thing in different ways. But I can't come up with a better explanation for why many vehicles have the same (or nearly so) top speed in either of the top two gears.

To address the OP's issue, Shortsguy1 find my thread about changing the FD ratio on my 240D. I went from 3.69 to 3.07 and haven't been a bit sorry. I would have preferred a smaller leap but there was only the 3.58 in there to choose from and I deemed that too small a change to bother with.