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      06-30-2014, 07:55 AM   #1
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Horsepower and Speed - the graph

Here is the rough analysis of BMW’s 35i series of vehicles as discussed in my earlier thread. Different horsepower requirements at varying speed as a function of Cd, front surface area, weight (unloaded), and speed (in mph) become evident, especially prominent at top-end speeds.

For example, the aerodynamics of the 335i and 535i in this simple algorithm allow 130hp to obtain a speed of 130mph, whereas the X3 and X5 need almost 190hp to reach the same speed. Weight seems to have far less relevance on the shape of the curves. Surface area understandably has an effect, but it would seem much more difficult for designers of a given model type to dramatically change those parameters without changing the model’s intent.

Cd appears to have the greatest effect. As an example, if BMW can decrease our X3’s Cd from the current estimate of 0.36 to 0.33 with its next design cycle, in this basic algorithm it shifts the curve to mirror that of the X4. Please see the disclaimer at the bottom of the jpeg - there is no way my simplistic equations match the real world nor BMW's software calculations - it was just an interesting exercise to see how these variables might interact at differing speeds in a rough simulator fashion.
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      06-30-2014, 08:23 AM   #2
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A very interesting piece of work. Indeed Cd is a speed variant and so at sup 60mph the X range is very tight but at twice the speed the X1 needs 20hp less than an X3/X5.
Well done
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      06-30-2014, 08:32 AM   #3
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Very true. My brother has a 328 f30 and while the weight is somewhat within throwing distance, the fuel consumption is very different due to the upright shape of the X3.
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      06-30-2014, 08:45 AM   #4
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Is the graph for CdA, not Cd? It seems like it is (and it should be).
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      06-30-2014, 12:37 PM   #5
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Quote:
Originally Posted by plymjack View Post
A very interesting piece of work. Indeed Cd is a speed variant and so at sup 60mph the X range is very tight but at twice the speed the X1 needs 20hp less than an X3/X5.
Well done
Thank you for the kind words, plymjack.

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Originally Posted by pokerface View Post
Very true. My brother has a 328 f30 and while the weight is somewhat within throwing distance, the fuel consumption is very different due to the upright shape of the X3.
Indeed, and if BMW can lower our Cd as it apparently did with its new X5, we might see a marked improvement in our mileage numbers at higher speeds.

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Originally Posted by clivem2 View Post
Is the graph for CdA, not Cd? It seems like it is (and it should be).
Apologies, Clive, as I'm not familiar with the singular term of 'CdA'. I didn't come across that in my search to learn about this, as all of the sites which recorded the 'Drag Coefficient' reported it as simply 'Cd'. The formula does indeed multiply the Cd by the 'A' (the frontal surface area of the car), so these are usually shown together in the formulas as CdA, but my understanding is those are two separate variables. My graph and its associated equations does factor in 'Cd', 'A', the estimated 'Friction roll', and the 'Speed' as variables.

A question I still have regarding 'HP vs Speed' - what percentage of a car's total rated HP is actually available to generate these speeds (and isn't lost in the transmission/tires etc)? [It seems from looking at the top end speeds listed for models at some 'reference' sites, and then comparing those speeds to this graph, that it would be about 78%, but since I know my graph isn't real world accurate I wasn't sure if anyone has a better grasp.]

Since the 28i series curves are almost identical (the weight differential is negligible effectively), one would then just have to stop around the 78% HP mark of your respective car's curve to see what top end speed (if not limited) might be, and same for the 35i series.

I have the data for the other models (the 40i and 50i series) which I can also graph if folks are interested.
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      06-30-2014, 05:13 PM   #6
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Quote:
Originally Posted by Max Well View Post
Apologies, Clive, as I'm not familiar with the singular term of 'CdA'. I didn't come across that in my search to learn about this, as all of the sites which recorded the 'Drag Coefficient' reported it as simply 'Cd'. The formula does indeed multiply the Cd by the 'A' (the frontal surface area of the car), so these are usually shown together in the formulas as CdA, but my understanding is those are two separate variables. My graph and its associated equations does factor in 'Cd', 'A', the estimated 'Friction roll', and the 'Speed' as variables.
Hey, I'm no expert on this and you're doing a great job! What I believe is the case is that if you have a 3 series and X3 with a Cd of say 0.33 then the X3 will have the greater wind resistance due to it's frontal area. Yes CdA is simply the normal shorthand for Cd * A.
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      06-30-2014, 07:06 PM   #7
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Quote:
Originally Posted by clivem2 View Post
Hey, I'm no expert on this and you're doing a great job! What I believe is the case is that if you have a 3 series and X3 with a Cd of say 0.33 then the X3 will have the greater wind resistance due to it's frontal area. Yes CdA is simply the normal shorthand for Cd * A.
Thanks, Clive.

I have almost completed the graph for all models, but given the higher HP max for the upper echelon power types, I will need to zoom the scale at different speed intervals (low, medium, and high) to show the differences more clearly. The next question, depending upon how compulsive one wants to be, would be to figure out the fuel usage of one HP - for if that variable is known, one could almost construct a usage chart for mpg/mph for each type. That seems way beyond the scope of this inaccurate model, but would still be a reasonable concept if so inclined. I have to think that what seems like even small differences, such as 20 HP, at constant speed probably does make a big difference in the mpg differences seen between types.

Also, I will produce a(n) 'X3-only' graph showing how changes in our X3's Cd, 'A', weight, and combinations thereof can lead to prominent changes in the 'HP vs Speed' curves.

What I am surprised about, is that the 'M' series are not necessarily groomed to be 'clean'. It seems their Cds are higher than some of the base models, which now is making more sense, for at the speeds some of these models are capable of reaching (if not limited), they would probably begin to have too much lift (thereby reducing friction and power/performance ability, and become unsafe at top-end speed, hence the need for modifications to keep them earthbound, which by definition, must induce a degree of drag).

Good stuff, and must make coming in to work each day as a BMW designer a joy.
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      07-01-2014, 03:24 AM   #8
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I've always thought of MSport aero as a styling exercise which results in worse aero. Most MSport models across the range have larger (often dummy) cooling ducts which increase the frontal area. Couple this with the wider tyres standard on MSports and you have more aero resistance.
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      07-02-2014, 01:18 AM   #9
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Very interesting work. well done!
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      07-02-2014, 05:46 AM   #10
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Quote:
Originally Posted by clivem2
I've always thought of MSport aero as a styling exercise which results in worse aero. Most MSport models across the range have larger (often dummy) cooling ducts which increase the frontal area. Couple this with the wider tyres standard on MSports and you have more aero resistance.
I believe dummy ducts are actually better for aero than open grills (which simply create turbulence).
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      07-02-2014, 10:09 AM   #11
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Quote:
Originally Posted by clivem2 View Post
I've always thought of MSport aero as a styling exercise which results in worse aero. Most MSport models across the range have larger (often dummy) cooling ducts which increase the frontal area. Couple this with the wider tyres standard on MSports and you have more aero resistance.
That is a good point, maybe not so much as increasing the frontal area but potentially changing the Cd? I've often wondered why those insets are placed on the front bumper (unless just for looks) as they do seem like they should function as aerodynamic 'cups' in a way, trapping air, rather than having a smooth, rounded bumper. I have no idea, though. On the other hand, because many of the BMWs are such high performance on the top end, could these be inserted purposely to cause a 'downward force' on the front end of the vehicles, much like the wings on a Formula 1? Way over my head, but intriguing to think about.

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Originally Posted by slyfox View Post
Very interesting work. well done!
Thanks

Quote:
Originally Posted by cSurf View Post
I believe dummy ducts are actually better for aero than open grills (which simply create turbulence).
That may also be true, cSurf, for unless the open grills are purposely channeled so that the flow may then become smooth (as the 'Air Curtains' and 'Air Breathers' allow), one would expect turbulence I would think.

I have now completed the general analysis of selected BMW models and am including the following graphs: 1). Overall view at speeds 20-200mph; 2). Focused view at speeds 20-65mph; 3). Focused view at speeds 65-110mph; 4). Focused view at speeds 110-155mph; and 5). Focused view at speeds 155-200mph.

Numbers two-five allow for more clarity in the differences given the expanded view. I have also estimated 'usable HP' as 80% of rated and provided reference lines so a quick glance can be used to find your model's curve and its potential top-end speed if unlimited. I was unable to find any reference to support that number, but by observing the rated top-end speeds if not limited which is available online, it seems that is a pretty reasonable estimate (at least for this purpose). Since weight seems to have minimal effect on this simple algorithm, curves for the same model with a different engine size are almost superimposed, which is why you may not see your engine size on the graph. Just find the model and follow the curve to your engine's HP effective max.

I used to think that speeds were electronically limited for law enforcement reasons, but I suspect now it is more due to induced lift at the higher speeds which make them become less stable. As an example, look at the rocket ship of a ride the 550i's curve suggests it would be capable of reaching!

Next up, when I get the time, will be a focused study on just the X3, analyzing how changes in Cd, A, wt, and combinations thereof affect the curve.
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      07-04-2014, 12:08 PM   #12
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One gallon of gas will give you 45 HP for one hour

FYI, according to http://en.wikipedia.org/wiki/Gasoline_gallon_equivalent one gallon of gas will give you 45 HP for one hour. And gas engines are about 25%-30% efficient at delivering mechanical work, for a net of about 13 HP/hour. Diesel engines can produce about 17 HP/hour for a gallon, so about 30% more efficient.
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      07-05-2014, 05:50 PM   #13
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Quote:
Originally Posted by wrp View Post
FYI, according to http://en.wikipedia.org/wiki/Gasoline_gallon_equivalent one gallon of gas will give you 45 HP for one hour. And gas engines are about 25%-30% efficient at delivering mechanical work, for a net of about 13 HP/hour. Diesel engines can produce about 17 HP/hour for a gallon, so about 30% more efficient.
Thanks for the comment, wrp. I've worked some more on this project. Long story short, vehicle weight in this simple analysis does have an effect on HP requirements, but much less than frontal area and Cd, so in essence, one can follow the curve of a respective model as a rough idea for all engine sizes it houses, essentially independent of weight.

The Area and Cd seem equally relevant in the equations, with 10% drops in either causing each curve to superimpose, and having definite (almost equal effects) at higher speeds. So I manually arrived at more accurate area numbers (instead of just using the generic 85% - which is surprisingly close, though). But as already discussed, designers aren't going to be able to do much with the frontal area for specific models, except perhaps saving about 100 sq inches in the side mirrors someday if cameras become realized. The inner box of what the car is designed for (how many occupants, type and size of load, etc), seems to set that variable pretty hard. So that leaves the Cd. And to that point, I saw a new X5 at the mall today, and the 'air curtains' and 'air breathers' are amazingly simple, yet it seems based on the data, remarkably effective. It would seem likely that we will continue to see technological advances from the aerophysics engineers centered on the Cd. Then the designers have to make those ideas attractive to the buying market.

I'm now trying to get a simplistic mpg chart set up for constant speeds at 45mph to 100mph for the models, but this becomes difficult as the 28i, 35i, and 50i engines have different efficiencies per unit Hp, and I don't know what those numbers are. I've come up with rough estimates based on models which come in the 28i, 35i, and 50i versions, which looks like the 35i engine is about 90% as 'efficient' as the 28i, and the 50i seems about 83% at HWY. Probably most important for this basic analysis, though - engine efficiency is not constant, as it appears it peaks around 75% of rated engine power near the range of greatest engine torque, so this attempt at producing a rough mpg chart for each model at varying speed is probably a lost cause, but it has broadened my understanding of the great cars we drive.
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      07-05-2014, 06:10 PM   #14
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Quote:
Originally Posted by cSurf View Post
I believe dummy ducts are actually better for aero than open grills (which simply create turbulence).
Ditto.
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      07-09-2014, 03:12 PM   #15
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Researching online, it seems each 'model/engine' pairing has its own unique 'mpg vs speed' curve, and there are way too many variables to allow a graph to be simulated accurately. Although a fair number of 'mpg vs spd' curves can be found for eco models from other manfrs, very few could be found for BMWs.

So I looked up ways to better understand the X3's engine, performance, and consumption, and just realized that apps are now available for mobile devices which allow connection wirelessly via Bluetooth or WIFI with a car's OBD through a simple connector. For less than $30 one can view on a mobile phone (or iPad etc) data from the OBD in real time, such as HP usage, mpg, water temp, air inlet temp, engine efficiency, engine torque, ... Many in this community may already know about this technology, but thought I'd share in case some did not. I've ordered mine and plan to see if I can derive a reproducible curve for the X3. Granted our display already shows mpg, but it is cumbersome while driving to reset the mpg for different speed tests while also recording the rpm and driving the car. Apparently these devices can store the data and even be downloaded into spreadsheets - we'll see.

While at the dealership yesterday I also took some close-up pictures of the X5's air breather and air curtain internal designs, which hopefully we'll see in the next gen X3.
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      07-14-2014, 05:09 PM   #16
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Now adding Performance and Consumption

Today was the first chance I had to try out the OBDII WiFi Adapter and 'Engine Link' app with my iPad. This was just a feasibility trial to see how it works and what it offers. Summary - simple connection process and real-time data easily obtained. As it connects directly with the OBD, I would think correction factors don't need to be factored in when viewing the data, but those with more expertise may have more insight.

Very easy to record, but you definitely need two people - one to drive responsibly and to assess level plane as best one can, and one to view the iPad and record the data.

I'll share some jpegs of today's short study (the first is the OBD adapter, the second is the iPad dashboard which can also be customized on subsequent pages, the third shows the graph with torque included, the fourth more zoomed to show the mpg more clearly). I can include a template I made to record, if anyone else wishes to share their own data. Understandably, unless one has access to well-constructed roads, very little traffic, and legal ability to exceed 70mph, the upper end of this analysis may never be realized. The other variable which will be difficult to factor, is altitude. In the equation for 'HP required', air density is assumed to be at steady state (and near sea level). Denver flat road results at 70mph won't be equal to sea level roads at 70mph, but with that caveat, if others wish to share their own data, I can add them into my database and develop averages (the more quality data points, the better).

From this expedited view, our 2012's 'sweet spot' is around 45mph. Note - in Park, the air conditioner increases the baseline HP usage of an idle engine from 3HP to 5HP. The original calculations curve for 'Required HP' parallels quite well if one factors out the AC. More refined real-time curves will assist.

This is an amazing community, and it wouldn't take much to develop some interesting (and reproducible) data.
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      07-20-2014, 05:10 PM   #17
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Updated to include the 2015 X3 xDr35i M Sport

I am now including an averaged graph with results obtained yesterday with our 2015 model. The graph changes some, but there will be significant (operator-dependent) variability with such a small number of data points (n=2). The main difficulties in obtaining real-time data is making sure the road is on level plane (how does one do that without a test track or the Salt flats), and to insure speed is maintained while minimizing aggressive accelerator changes. If more can post their results, the curve will certainly become more accurate, but at least this is a start (picture 1).

Which then leads to how can our X3 become more aerodynamic, which was the impetus for this thread? If we as consumers set the cabin box dimensions for our X3 as is, then the frontal surface area will not be able to change much. I like the X3 so I can haul 1200 lbs and large items when needed (without having to have a hitch an pull a trailer). A few weeks ago we took one of our old 55" widescreen Tvs to a relative 300 miles away. We didn't have a box, and it is so thin I was concerned about laying it flat. It fit fine. Not many in this mid-size SAV category would be able to do that. So while there may be 'sportier' SAVs out there, for a true comparison, it seems one must stay on point as to interior dimensions to insure apples are being compared to apples.

So, what is in store for the G01? Looking at the aerodynamics, the only thing the designers can do is either lower our height minimally, or make it longer. I'm including a graphic (picture 2) to illustrate (please forgive the simplistic example, but it makes the point) - if we have to push the cabin box in a wind tunnel, but we have the ability to extend the front and back like an accordion and make it more angled, it becomes clear which is more aerodynamic and easier to push.

(Picture 3) includes a review of the X5's and X3's evolution in a simple table. The X5 is our big brother, so it stands to reason that changes made in its evolution will ultimately trickle down to us. As one can see, length indeed is one of the big determinates in allowing the designers to decrease frontal angles to the wind, and despite the weight increase, the HWY mpg increases.

(Picture 4) shows our X3 in a measured format and a rough idea as to how just increasing the length by 6" (leaving the cabin dimensions exactly the same), would allow the designers a chance to improve the aerodynamics. I also show if one could change it 20" (impossible, just shown for effect) how aerodynamic it would become.

(Picture 5) takes our own 2015 X3 M Sport and with some simplistic Photo-editing (apologies here), what 4" on the front end, and 2" on the back end could accomplish. As I don't have (or know anything about) modelling software, I can't say what effects those changes on the Cd would be, but by the X5's example, it must be significant. Plus, with the new 'M' variant coming, it would seem the engineers would appreciate some more room in the front for a bigger engine.

In sum, it seems even though the 'size' may not change as Scott indicated (suspecting that implies internal cabin dimensions), it seems that there must be at least some change in the length (+/- wheelbase to go along with such) if signficant Cd improvements on that 40% which deals with the body design. Our X3 appears to have the worst aerodynamic profile of any of BMW's models, and given its popularity, alot of attention must be going into improving such (beyond just the wheels, wheel wells, underbody, and air vents) for the G01 (or so I hope).
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      07-27-2014, 02:53 PM   #18
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Potential Gas Savings with G01

In keeping with initial reasoning for researching this topic (how can the larger and heavier new X5 get better HWY MPG than our X3 does) - now that Scott has suggested all of those aerodynamic mods will be used in the G01 in 2017 ['Wish List for G01 (3rd Gen) X3 2017'], I ran some simple numbers.

In sum, as BMW produces roughly 120K X3s per year (est from the 9,941 units produced in Jun 2014 x 12), even if one only puts 10K miles on their car (and EPA estimates about 45% of that would be HWY miles), if the G01 can get 5mpg better (the X5 got roughly 4), then over one year 3.5M gal of gas might be saved once all have driven for a year. That is 188,000 Barrels of crude oil.

Amazing if it pans out (and we have the real world X5 suggesting it should), and really a testament to the aerophysicists, engineers, and designers at BMW.
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      08-01-2014, 11:34 AM   #19
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Templates for Data Gathering

In case anyone else wishes to record and share their X3's performance data, I'm attaching the following templates which might assist with the data recording. It would be interesting to see how the curves of the 28i and the diesel variants compare with the 35i. If you share the numbers, I'll graph them separately for each engine type, and will also produce a combined MPG curve for each of them as well.
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      08-03-2014, 04:05 PM   #20
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Updated and Corrected F25 X3 xDr35i Performance Curves

After yesterday's trip we had a number of stretches of level roads to document the 75mph numbers, so these averaged values have now been added. Additionally, and I must apologize to the community for this, upon adding these I double-checked all data once again. It appears in the previous 'X3 only' graphs I set up Excel to draw from the 5 series 'Required HP' calculated data on the master worksheet. That error has now been corrected.

Now, the HP 'Actual' superimposes almost exactly the 'Calculated' at 60mph and above. It seems to begin trailing a bit at 75mph, so undoubtedly the F'roll' needs to be a speed-biased value. With that said, it is fascinating for a stranger to this field of aerodynamics to see how science does blend with reality.

For completeness, I have now included the Torque (divided by 10 to maintain scaling) and RPM (divided by 100) curves so that we have a more complete picture of our F25 35i series data.
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      04-14-2016, 07:55 AM   #21
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Quote:
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...

Which then leads to how can our X3 become more aerodynamic, which was the impetus for this thread? If we as consumers set the cabin box dimensions for our X3 as is, then the frontal surface area will not be able to change much. I like the X3 so I can haul 1200 lbs and large items when needed (without having to have a hitch an pull a trailer). A few weeks ago we took one of our old 55" widescreen Tvs to a relative 300 miles away. We didn't have a box, and it is so thin I was concerned about laying it flat. It fit fine. Not many in this mid-size SAV category would be able to do that. So while there may be 'sportier' SAVs out there, for a true comparison, it seems one must stay on point as to interior dimensions to insure apples are being compared to apples.

So, what is in store for the G01? Looking at the aerodynamics, the only thing the designers can do is either lower our height minimally, or make it longer. I'm including a graphic (picture 2) to illustrate (please forgive the simplistic example, but it makes the point) - if we have to push the cabin box in a wind tunnel, but we have the ability to extend the front and back like an accordion and make it more angled, it becomes clear which is more aerodynamic and easier to push.

(Picture 3) includes a review of the X5's and X3's evolution in a simple table. The X5 is our big brother, so it stands to reason that changes made in its evolution will ultimately trickle down to us. As one can see, length indeed is one of the big determinates in allowing the designers to decrease frontal angles to the wind, and despite the weight increase, the HWY mpg increases. ...

In sum, it seems even though the 'size' may not change as Scott indicated (suspecting that implies internal cabin dimensions), it seems that there must be at least some change in the length (+/- wheelbase to go along with such) if signficant Cd improvements on that 40% which deals with the body design. Our X3 appears to have the worst aerodynamic profile of any of BMW's models, and given its popularity, alot of attention must be going into improving such (beyond just the wheels, wheel wells, underbody, and air vents) for the G01 (or so I hope).
As videos and photographs of camouflaged G01 prototypes are becoming increasingly available online, it appeared reasonable to consider if some of the considerations discussed in my post from 20 Jul 2014 can be answered. A side view photograph provided by Palbay which can be found online (Copyrighted, so out of respect for him and our Photography colleagues it will not be posted here) allows for a comparison of our current LCI (our 2015 X3 35i M Sport).

Although the camouflage inherently makes conclusions difficult (as size of protuberances and the markings may be purposely exaggerated to rightfully disguise), it would appear that the cabin seating area dimensions appear fairly similar externally from the side view. No doubt newer, thinner, and lighter materials on the inside are probably going to allow us more interior room, and as a front view analysis hasn't been done, it is possible it could provide more width as well.

It appears roughly 4" more length may be present in the rear window and upper bumper region which would further enhance the aerodynamic effects of the Kamm-tail as discussed in this thread, and might also provide us with more cargo room?

This is certainly an exciting time for those of us who enjoy the driving dynamics, size, and functionality of our X3s, and anticipation for the G01's arrival next year continues to grow. Much appreciation to those sharing some early glimpses of the G01 prototypes online, and to BMW for allowing them to be tested in locations amenable for such to be documented so as to at least whet our appetite until the main course is delivered.
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