Aero / Thermodynamic Energy Balance Protocol

[aerohead]

Cd requested this, so I'll begin it today, and by this coming Wednesday, we should have at least one complete example in the bag.
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This energy balance allows for a complete snapshot of a vehicles baseline performance, such that, when a single variable is introduced ( streamlining ), one can reverse-engineer the new coefficient of aerodynamic drag, based upon the new performance.
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The procedure is courtesy of Chrysler Corporation, circa 1934, from an SAE Paper published about Carl Breer's streamlining of the 1934 DeSoto Airflow test mule, finally published near the time of the Pearl Harbor attack in December, 1941.
It's primarily a book-keeping exercise which captures all pertinent data required for the engineering of a new Cd. It's not sexy. It's tedious.
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The following are some of the components required ( in US units ):

Vehicle width
Vehicle height
Tire width
OEM Cd
OEM projected frontal area
OEM CdA
Test weight
Air temperature
Test velocity ( constant ) mph
Test velocity ( constant ) feet/ second ( @ 5280-feet/mile)@ 3600 = 95.333 feet/second
Engine rpm: constant
Local air density
Wind: calm ( data-log if not )
Windows 'up'
Accessories: 'OFF'
Actual mpg
Fuel type
Fuel mass per unit volume
Fuel mass per unit distance/time
British thermal units ( Btu ) per unit volume
Btu per unit time
Gross-horsepower per 2,546-Btu/HP
Engine thermal efficiency % ( published or estimated )
Brake-horsepower per thermal efficiency ( derived )
Engine accessory losses %
Powertrain efficiency %
Road Load horsepower
Rolling resistance force & power absorption
Aerodynamic force and power absorption.
Brake Specific Fuel Consumption ( optional )
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Test Route:
Concrete surface preferred, due to uniform rolling resistance capability ).
Straight ( to eliminate introduction of curve drag ). If not straight, Interstate highway ( as they're designed for 100-mph travel, with vary large curve radii ).
Dry, no precipitation of any kind is permitted.
Level ( so as not to introduce elevation effects ). If not, drive a 'loop' to cancel out one-way variability.
Traffic: not allowed. If traffic, keep a distance so as not to introduce 'drafting', convoy' effects.
Fully-warmed, prior to testing ( to stabilize thermal hydrodynamic, and rubber rolling resistance variability ).
Preserve all calculator values in register to minimize 'rounding-errors' over the dozens of calculations, beginning to end.
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SAMPLE calculation : Think Flight V1 & V2, 2022 Subaru Impreza Wagon, OEM Baseline -to - #4 Configuration :
* Width-70.1-inches ( 1780.54mm )
* Height- 57.3-inches (1455.42mm )
* Ground clearance- 5.1-inches ( 129.54mm )
* Tire width- 205mm
* Tire sidewall height- 112.75mm
* Coefficient of aerodynamic drag, Cd 0.29 ( from online )
* Af ( estimated @ 85.5% of gross area ) approx. 23.8153-sq-feet ( 2.215 meters-squared )
* CdA- approx. 6.9064-sq-ft ( 0.64162558-meters-squared )
* Dry-bulb temperature- 72- F
* Air density ( rho ) approx. 0.00232568323-slugs
* Curb Weight- 3050-lb ( 1380-kg )
* Test weight- approx. 3250-lb ( 1470.5-kg )
* Fuel type: REGULAR UNLEADED Reformulated E10
* Fuel mass: 6.138-lb/gallon
* Fuel energy content- 111,836 British Thermal Units ( Btu ) / gallon
* Engine thermal efficiency- approx. 40%
* Engine accessory losses ( 2.2% [ Argonne National Laboratory )
* CVT transmission mechanical efficiency- 87.71% ( National Labs )
* 2546-Btu/ horsepower
* 3412-Btu / kWh
* 745.7-Watts / horsepower
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Think Flight's V1 road test:
* 182.5-miles ( 293.7-km ) loop, with return leg to original fuel pump
* 5.12- gallons consumed
* 35.644-mpg indicated
* Time-to-distance : 2.807692-hours roundtrip
* 1.8235618-gallons/ hour
* X 6.138-lb/gallon = 11.930226- lbs /hour
* = 203939.857-Btu / hour ( gross )
* X 0.40 ( thermal eff. ) = 81575.9429- Btu - hour ( NET )
* divided by 2546-Btu/HP= 32.04-Brake-Horsepower ( bhp )
* X 0.978 ( 2.2% accessory loss ) = 31.33512-hp
* X 0.8771 ( CVT transmission loss ) = Road Load Horsepower = 27.484-hp *
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Solving for rolling resistance:
And using the aerodynamic power formula:
* Aero HP = 95.333/ 550-lb-ft/second ( 0.5 X 0.00232568323 X 0.29 X 23.8153 X 95.333-squared )
= 12.65148-hp ( aero )
THEN: 27.484-Road HP minus 12.65148- aero hp = 14.833669-hp * ( a constant )
AND: 14.833669-hp =[ 95.333/ 550-lb-ft/second X ( 3250-lbs X Cfrr )]
simplifying : 14.833669 = 0.173332727 ( 3250 X Cfrr )
with algebra: [ (14.833669/ 0.17333272) = ( 3250 X CFrr )
then: 85.57916243 = ( 3250- Cf )
with algebra: 85.5791643/ 3250 = CFrr= 0.02633205
Divided by 4-tires = Cf 0.0065825 / tire ( a constant )
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Solving for the V2 video, #4-configuration Cd:
Scaling off an enlarged photo-reproduction of #4, I 'guestimated' that the addition of the airdam increased the frontal area of the Impreza to Af- 24.4394-sq-ft ( 2.270494644-meters-sq )*
At 43.0971-mpg, the Impreza is now consuming only 3.73806-gallons over its 161.1-mile loop.
Time to distance was 161.1/ 65 = 2.478461538- hours.
65/ 161.1 X 3.73806 = 1.508193660-gallons/ hour
X 111,836 = 168,670.3471-Btu / hour ( gross )
X 0.40 ( thermal efficiency ) = 67,468.13884-Btu/hour (NET )
divided by 2546 btu/hp = 26.49966176-bhp*
X 0.978 ( accessory loss ) = 25.9166692-hp
X 0.8771 ( transmission loss ) = 22.7315-hp Road Load*
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22.7315 - 14.833669-hp rolling resistance ( constant ) = 7.897841-hp aero*
Solving for the new coefficient of aerodynamic drag:
7.897841 =[ 95.333/ 550-lb-ft/sec ( 0.5 X 0.00232568323 X ? X 24.4394 X 95.333-squared ) ]
Simplifying:
7.897841 = 0.173332727 ( 258.2840466 X ? )
from algebra: 45.5646267 = ( 258.2840466 X ? )
from algebra : Cd 0.1764*
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From any test, and any results, the estimations are maintained. 'Constants' remain as such.
If frontal area is changed, it must be reflected in the math.
As 'new' official data comes to light, they can be inserted into the calculations in order to 'accurize' the results.
Any change in vehicle weight for what we'll be doing during these 'cardboard and duct tape' and 'foamboard and duct tape ' modifications will be statistically meaningless.
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Let me know if you think I've made any glaring mistakes or omissions. I'm just mimicking what Chrysler did.
It's because that there are no requirements for automakers to share the specifics of their products that we're forced to make these 'guestimations'.
It does get us in the ball park.