Quote:
Originally Posted by saadswb.ct
Hey,
I found the "Aerodynamic & rolling resistance, power & MPG calculator" extremely useful. I was wondering if if it would be possible to obtain the formulas that allowed the MPG figures to be generated on the results table.
Cheers.
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Just now seeing your post from April.
I don't have the workbooks I need to guarantee completeness, but I'll get you started, and will be back next Monday ( I only do this twice a week ).
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What we've been doing is, begin with a specific vehicle's Road Load ( the power absorbed by both rolling resistance, and aerodynamic drag ), at a given velocity, then work backwards through the powertrain, to the engine, adding parasitic accessory losses, to arrive at the engine's brake-horsepower, then, factoring for the brake specific fuel consumption ( BSFC ) of the engine, the mass of the fuel actually consumed, plus the heating value of that fuel, on, say, a British Thermal Unit ( Btu ) per Pound basis, we can arrive at the brake thermal efficiency of that vehicle.
* Standard, Society of Automotive Engineers/ ISO 'Atmospheric conditions' for mass per unit volume air are used.
* That mass, divided by the 'standard' acceleration due to gravity yields the 'Standard Air Density' (rho),which is use for all aerodynamic calculations ( more on that later ).
* A known, or estimated power absorption coefficient for the vehicle's tires is used along with the actual test weight of a vehicle to calculate the rolling-resistance portion of the Road Load.
* Argonne National Laboratory has provided current data on engine accessory loss percentage of total brake power, and powertrain losses ( a percentage of total transmitted power, used in reverse-engineering brake-horsepower.
* The American Petroleum Institute provides heating values for gasoline, gasoline-ethanol alcohol blends, and diesel fuels, 'Winter' / 'Summer'.
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* Test course conditions presumed:
- Paved surface
- Straight course
- Level course
- Dry
- Calm, to 'allowable, monitored & recorded wind conditions.'
- Fully-warmed vehicle ( thermal-equilibrium )
- Standard SAE dry-bulb temperature, or monitored actual / recorded, for post-test data reduction and normalization to standard conditions.
- Elevation, if other than sea level.
- Barometric pressure.
- Relative humidity ( RH ).
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We ignore the 'critical Reynolds number' calculation. For the subsonic, incompressible flow we'll experience driving at 'normal' posted speeds, and the 'size' of production automobiles, above 20- miles per hour, we presume a fully-turbulent boundary-layer, and a 'fixed' coefficient of aerodynamic drag ( Cd ).
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All published drag coefficients reflect 'standard air density ( rho ) conditions,' which for US units of measure are 60F dry-bulb temperature, sea level, 29.92-inches Mercury- barometric pressure, 0.0765-pounds per cubic foot of dry air specific mass, and 32.2-feet per second per second gravitational acceleration constant (g).
Air Density ( rho ) = air specific mass, divided by g
or, 0.0765 / 32.2 = 0.0023757
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Aerodynamic drag ( D ) is 'dynamic pressure' multiplied by the vehicles drag coefficient ( Cd ) , times it's projected frontal area ( A ).
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Dynamic pressure = [ 1/2 times ( rho ), times velocity-squared ].
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So, from algebra, D= ( 1/2 rho Cd A v-squared )
( You may here about a car's drag varying by the square of the velocity. The dynamic pressure formula is the source of this relationship )
'Doubling' your 'speed' causes the drag to increase by a factor of 'four', not two! ( 2X2=4)
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Since we're interested in how many horsepower, or kilowatts will be required to propel the car against the force of the wind, we need to enter some factor which relates the time-rate-of-work the engine or motor is accomplishing per unit time elapsed.
In US units, the horsepower is equivalent to the work required to lift, 550-pounds of mass, one-foot, each second,
or, 550 pound-feet/second.
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In US units, velocity is expressed in feet per second.
*A mile is 5,280-feet.
*A mile per hour ( mph ) = 5,280 feet per second, times 60-seconds per minute, times 60-minutes per hour.
* 60 X 60 = 3,600-seconds
* Mph X 5,280 / 3,600 = 1.4666 feet/second
* For instance, 62.1-mph ( 100 km/h ) = 62.1 X 5,280 / 3,600 = 91.08 feet/sec.
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Then, 'power' (P)= v/550 X ( 1/2 rho Cd A v-squared ),
which indicates for the 'velocity-cubed' relationship of power to air velocity, or conversely, road velocity in 'calm' air.
When you 'double' your 'speed' the power required to overcome aerodynamic drag goes up by factor of 'eight', not two.
( 2 X 2 X 2 = 8 )
You're hitting twice as much air, twice as hard, twice as often!
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Rolling-Resistance drag power absorption is only 'linear' in relation to velocity.
If you 'double' your 'speed', your rolling -resistance power requirement only doubles.
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If you know the power absorption coefficient of your car's tires ( Cfr ) , the rolling-resistance drag is the product of the test car's total mass, multiplied by the Cfr.
In US units, Dr-r ( pounds ) = ( pounds X Cfr )
The power requirement to overcome the rolling-resistance must also include the time-rate-of-work factor.
In US units, the power to overcome R-R ( Pr-r )= v/550 ( total weight X Cfr )
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Road Load = the sum of the car's Aerodynamic & Rolling-Resistance power requirement.
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Once you have the Road Load, you must factor in the powertrain mechanical efficiency losses to arrive at the power that was available from the engine/motor.
* Battery-Electric Vehicles have been assigned a 'mechanical' efficiency of 98% for their majority, single-speed transmission.
* Internal combustion-powered vehicles will demonstrate losses as a function of the amount of transmitted power through transmissions, auxiliary transmissions, propellor-shaft(s), differentials.... increasing, as the amount of power increases the amount of contact area between lubricated mating surfaces: 1/4-ton, 1/2-ton, 3/4-ton, 1-ton, ........... up to 40-tons rating, involving mechanical cooling fans in the heavier equipment.
* A typical ICE passenger car with overdrive transmission/transaxle would exhibit a mechanical efficiency of 92%.
Presently, ICE vehicles are also attributed with 2.2% engine accessory losses.
What's left over constitutes the car's 'brake-horsepower', or, brake-kilowatts.
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* Electric motor efficiencies are reported as high as 97%.
* Diesel engines and some Atkinson-cycle engines can achieve up to 42% thermal efficiencies, within a proscribed rpm window of their specific brake specific fuel consumption ( bsfc ) maps.
* 'Aggregate, overall, 'In-car' thermal efficiencies of internal combustion vehicles are reported in the range of 25%. 'Well-to-wheels' thermal efficiency = around 15%.
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Since so many United States metropolitan areas are out of compliance with EPA Clean Air Act standards, residents have access to only oxygenated gasoline fuels and low-sulfur diesel.
* Reformulated Regular Unleaded E10 gasoline weighs 6.138-pound/gallon, contains 111,836- Btus chemical energy, and has a thermal coefficient of expansion of 0.00069/ degree-F.
* Diesel fuel weighs 7.1089 pounds/gallon, contains 136,775.23 Btu/gallon, and has a thermal coefficient of expansion of 0.00046 / degree-F.
* 33.705-kWh of battery capacity has been assigned an equivalency to 1-gallon of gasoline.
* 40.108-kWh is assigned equivalent to 1-gallon Diesel fuel.
* There are 3412 Btu/kwh.
* 2546 Btu/horsepower.
* 745.7 Watts/ horsepower.
* Gallon = 3.785306-liters
* Horsepower = 745.7-Joules
* Horsepower = 745.7-Watts, or, 0.7457-kW
* Newton = 0.22480894-Pounds
* Newton-meter = 0.73756215 lb-ft.
* Meter-squared = 10.76391-square-feet
* 2.2046-pounds = kg
* Inch = 25.4mm
* 39.37-inches = Meter
* Mile = 1.609347- km
* MPH = 1.609347-km/h
* 32-feet/sec/sec = 9.81-meters/sec/sec
* @ 70-F, SAE automotive equilibrium temperatures are:
- coolant - 203-F
- engine oil - 214-F
- transmission fluid - 188-F
- differential lube- 159-F
* Standard ISO air density = 1.22 kg/ meter-cubed
* Mechanical efficiencies :
- Single-speed planetary transmission = 98%
- 1:1 manual or lockup transmission & driveline = 94% ( 1/2-ton )
- Overdrive manual or lockup transmission = 92%
- Regenerative-braking = 81.1% ( Emissions Analytics )
These values are used in the MPG-e and visa-versa calculations/comparisons used to compare ICE & BEV vehicles.
These values are important to the EcoModding mathematics.
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NOTE: What we do here at EcoModder.com has absolutely nothing to do with any official, government - regulated testing protocols, from any continent.
It's up to the individual to ascertain a 'baseline' performance datum for their vehicle, from which after-modification results may be compared, from which 'quanta', or trends may hopefully be attached under similar conditions.
* Automatic transmissions might experience damage if slipped into neutral, and engine idle during coastdown testing, so one would want to investigate this hazard before arbitrarily doing that type of test.
* Outdoor testing is rife with challenges ( one year, MIRA reported that for the entire year that, only eleven ( 11 ) days existed in England that would allow for outdoor testing to be undertaken ).
* A vast majority of automobiles have 'governed' top speeds, eliminating them from top speed testing ,one of the few methods that would actually produce useful drag data.
* Official rolling-resistance data for tires is sparse. California attempted to pass legislation which would mandate that tire manufacturers provide this data to consumers, something that would have helped millions. It was shot down, killed in the crib.
* While we might get a drag coefficient out of a manufacturer for a specific vehicle, we might never get an official frontal projected area for it.
* Some vehicles exhibit very close correlation between 'computer-mpg readings' and tank-mpg, providing high confidence during road testing.
* The University of California, at Davis, uses a dedicated auxiliary fuel tank, weighed at high precision, for closed-course road tests, allowing an accurate measurement of fuel 'mass' consumed over a measure distance.
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