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E30 Air Resistance Numbers for the community

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    E30 Air Resistance Numbers for the community

    After much searching and a little guessing, I believe I have captured accurate numbers for figuring out air resistance at a given speed against the E30 body. I've never found all this info in one place, and certainly not with any sort of source or tests for validity.

    Drag Coefficient: 0.35
    Front area: 1.9417 m^2 (20.9 sq. feet)
    Air Density: 1.174 kg/m^3 (happens to be today, where I live)

    I then went ahead and graphed the numbers given high speeds, and also plotted M20 torque from peak to redline, assuming a slight drop in torque. The goal was to figure out if my equation and numbers were anywhere close to reality. I decided that if they were, that the force at the wheels should drop below the force of air resistance pretty close to the rated top speed of the vehicle.

    Assumptions
    1. 15% drivetrain loss.
    2. 15% loss in torque from peak RPM of 4300 to redline 6700. This was based on eyeballing stock dyno charts.
    3. Getrag 260 mated to a 3.73 diff with stock tire size 195/65/14



    So what do you guys thing? BMW rates the 325i at 142mph. Did I come pretty close? I feel this is accurate enough to give me close to reliable air resistance numbers at lower speeds.



    Higher Resolution

    Notes:
    This graph does not take into account rolling resistance, though error in drive train loss and torque fall off probably eclipse any amount of rolling resistance.

    I am aware that the maximum speed of a vehicle is not when acceleration reaches 0. That would take near on forever. I am however unsure at what point of acceleration they call it quits and mark the velocity. Is there an industry standard for this?

    I wrote everything in metric units, and for the graph I converted it to torque numbers so that you guys could make some quick sense of it. This is why the values are sort of odd, and why peak torque shows up at 100mph (4237rpm) instead of the more accurate 102mph. If you care to see this graphed in Nm and m/s let me know ;)

    Calculator for air density.

    Drag Force Calculator.
    -------------------------------------------------
    1989 - E30 - M20B25 - Manual. Approx 300,000+ miles - Track Rat & Weekend Fun
    2000 - E46 - M52TUB28 - Manual. Approx 130,000 miles - [not so] Daily Driver

    sigpic

    I'm looking for a Lachssilber Passenger Fender and Hood. PM if you have one or both to sell!

    #2
    The thing with engineering models is that they will all just be an approximation to the real thing. That's why there is still physical testing of vehicles. It just ensures that the assumptions and simplifications that the engineers decided to incorporate into their models are accurate, and that the model represents reality to within a certain tolerance. Here you are showing a 1-2% difference between your model and the OEM published values for the vehicle. In the professional world, we'd say that you are pretty close, and could definitely use that for a baseline drag model. The published top speed of the vehicle likely comes from a BMW engineering model (like the one you have built) that was verified to match the actual performance of the test vehicle. BMW did not just put the car together, jump in, and record the highest speed they could get the speedometer to show!

    If you want to make a more accurate model of your particular car, you could instrument your car, and record a bunch of data. Then you could reduce that data, develop a better model, and then throw the some standard conditions at it to see how the performance of your car has changed over the 20+ years of life on the streets!

    Alpine II 318is

    Comment


      #3
      Originally posted by flying_violin View Post
      The thing with engineering models is that they will all just be an approximation to the real thing. That's why there is still physical testing of vehicles. It just ensures that the assumptions and simplifications that the engineers decided to incorporate into their models are accurate, and that the model represents reality to within a certain tolerance. Here you are showing a 1-2% difference between your model and the OEM published values for the vehicle. In the professional world, we'd say that you are pretty close, and could definitely use that for a baseline drag model. The published top speed of the vehicle likely comes from a BMW engineering model (like the one you have built) that was verified to match the actual performance of the test vehicle. BMW did not just put the car together, jump in, and record the highest speed they could get the speedometer to show!
      In my professional world 1% is not good enough, but I work in software. We're supposed to be able to know all the variables are some crap like that ;-)

      This entire "project" was for my own education and edification. College took all the joy out of physics and higher math for me, and I'm just starting to get back into it, to see if I retained any amount of knowledge. I'm not trying to solve a real world problem or anything...at least not yet.

      I'm sure BMW uses models to come up with a number, and then verifies it. But I wonder (out of curiosity) what they consider in their models to be the "end of acceleration". It can't be when acceleration hits zero, right? That would take way too long for a real world vehicle to get to. Hitting something a couple mph under the limit would be more realistic.

      If you want to make a more accurate model of your particular car, you could instrument your car, and record a bunch of data. Then you could reduce that data, develop a better model, and then throw the some standard conditions at it to see how the performance of your car has changed over the 20+ years of life on the streets!
      I started down this road because I was trying to solve my own vehicles rolling+drivetrain resistance. Using a camera I timed how long it took to shed mph on an empty flat road. I quickly realized that rolling resistance would be linear, while wind resistance would be exponential (v^2, what a brat). While I could come up with two equations, and fiddle with them until they came pretty close, I needed a starting point. My intuitive math solving abilities aren't that great :)

      Given my limited equipment (and desire to solve this using my brain, not a $10,000 device), my own speedo and camera were chosen. While I could eliminate wind resistance almost entirely from the equation if I took measurement from 30mph-0mph, I can't accurately measure that. I can however (more) accurately measure 80mph-40mph. Besides, solving wind resistance for the vehicle sounded like fun.

      Thanks for responding!
      -------------------------------------------------
      1989 - E30 - M20B25 - Manual. Approx 300,000+ miles - Track Rat & Weekend Fun
      2000 - E46 - M52TUB28 - Manual. Approx 130,000 miles - [not so] Daily Driver

      sigpic

      I'm looking for a Lachssilber Passenger Fender and Hood. PM if you have one or both to sell!

      Comment


        #4
        Now here is the interesting thing, the rear end on an E30 M3 was designed to lower the c.o.d from that of the normal E30. Here is what I found on the M registry

        "How is the M3’s exterior different from that of a normal E30 3 Series?
        Because the E30 M3's shape had to be homologated for racing, all exterior body panels except the hood are unique to this model. The fenders are flared. The front and rear fascias contain unique 2.5-mph bumpers. The rear window is re-angled and the glass, both front and rear, is bonded. The trunk lid sits over 1.5-inches higher than the normal E30 3 Series, has a wing-type rear spoiler and is met by an extended cap over the C-pillar, all of which lower the Cd to 0.33 from 0.38. There is a roof-mounted radio antenna at the front. All window trim is of the blacked-out "Shadowline" variety. “M3” badges appear on the grille and decklid."

        It was a drop from .38 to .33. I'm assuming that was figured out in real testing in a wind tunnel.

        Still, interesting stuff. I'm fascinated by the effects of aerodynamics on things. Its pretty cool how just minor adjustments can have major effects.

        Will
        '59 Alfa Romeo 101.02 Giulietta Sprint
        '69 Alfa Romeo 105.51 1750 GTV (R.I.P)
        '69 Datsun 2000 roadster Vintage race car
        '88 BMW M3

        Comment


          #5
          Originally posted by BlackbirdM3 View Post
          Now here is the interesting thing, the rear end on an E30 M3 was designed to lower the c.o.d from that of the normal E30. Here is what I found on the M registry

          "How is the M3’s exterior different from that of a normal E30 3 Series?
          Because the E30 M3's shape had to be homologated for racing, all exterior body panels except the hood are unique to this model. The fenders are flared. The front and rear fascias contain unique 2.5-mph bumpers. The rear window is re-angled and the glass, both front and rear, is bonded. The trunk lid sits over 1.5-inches higher than the normal E30 3 Series, has a wing-type rear spoiler and is met by an extended cap over the C-pillar, all of which lower the Cd to 0.33 from 0.38. There is a roof-mounted radio antenna at the front. All window trim is of the blacked-out "Shadowline" variety. “M3” badges appear on the grille and decklid."

          It was a drop from .38 to .33. I'm assuming that was figured out in real testing in a wind tunnel.

          Still, interesting stuff. I'm fascinated by the effects of aerodynamics on things. Its pretty cool how just minor adjustments can have major effects.

          Will
          I may have to add .38 as a possible variable. When I was looking for these numbers most of what I got was internet forums using language like "I think I read once that...".

          I believe that .38 and .33 probably are wind tunnel test numbers. I know that the E36 was the first BMW to use computer modeling software. Given that, I don't know how they could come close to accurately modeling wind resistances of the E30 without real world tests. That said, they probably didn't care what the exact number was until the M3 came along and they wanted to improve on it. They probably took an educated guess and found that it worked with their models to within 1%-2% :)
          -------------------------------------------------
          1989 - E30 - M20B25 - Manual. Approx 300,000+ miles - Track Rat & Weekend Fun
          2000 - E46 - M52TUB28 - Manual. Approx 130,000 miles - [not so] Daily Driver

          sigpic

          I'm looking for a Lachssilber Passenger Fender and Hood. PM if you have one or both to sell!

          Comment


            #6
            E30 drag co-efficient is somewhere between "flying brick" and "tugboat."
            RIP: Delphin '89 E30 with S50 swap and lots of goodies :'(

            Then: '04 Evo 8 RS, 500 whp/420 wtq 2900 lb E85 AWD turbo shits 'n giggles

            Now: 2003 BMW M5 in Sterling Gray

            Comment


              #7
              Originally posted by Earendil View Post
              I am however unsure at what point of acceleration they call it quits and mark the velocity. Is there an industry standard for this?
              None that we have found. It seems every manufacturer has a different way of coming to these numbers. Perhaps some balance of technical input and marketing lingo.

              There are few things sweeter than a fresh M20 cruising at 120+ for long stretches. In a word: Sonorous.

              Comment


                #8
                .38 was the number for cars with diving boards, higher arches and center of gravity in general right? i thought with the facelift it was down to .35

                Comment


                  #9
                  Originally posted by bmwstephen View Post
                  .38 was the number for cars with diving boards, higher arches and center of gravity in general right? i thought with the facelift it was down to .35
                  That very well could be. Te M3 was introduced (ad certainly designed) before the 325/318 facelift. Thus the number .38 is probably for the earlier configuration. Whether the newer look also has a reduction in drag, is the question. I'm inclined to think no, since the guys who race these things today (pro3/spece30) tend to use both models equally. Many even favor the older style. If at the end of a mile long drag the early models were behind by 4 feet, no one would race them me thinks :)
                  -------------------------------------------------
                  1989 - E30 - M20B25 - Manual. Approx 300,000+ miles - Track Rat & Weekend Fun
                  2000 - E46 - M52TUB28 - Manual. Approx 130,000 miles - [not so] Daily Driver

                  sigpic

                  I'm looking for a Lachssilber Passenger Fender and Hood. PM if you have one or both to sell!

                  Comment

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