How the Efficient-Mileage car rating system works:
A few notes before we begin:
Force: The product of mass and acceleration.
Torque: The product of rotational force
Work: The product of force applied over a
Power: The rate of doing work or the rate
of using energy.
Efficiency: The ratio of power output to
Accuracy: The extent to which a given measurement
agrees with the standard value for a given measurement. A good metrology
tool is at least ten times more precise than it is accurate.
Precision: The extent to which a given set
of measurements agree with their average. A machine can be inaccurate
and very precise.
The Efficient-Mileage rating system
was developed to rank cars by a single number that represents efficiency.
It isn’t an absolute measurement of efficiency.
Fuel Conversion Efficiency may be the most ideal way
to measure efficiency. The Fuel Conversion Efficiency measurement
begins with measuring the specific fuel consumption (sfc). This
is the measure of mass fuel flow rate per unit power output. This
measures how efficiently the engine is using the supplied fuel to
do work: sfc = (mass fuel flow per unit time)/(power output). There
are, however, problems concerning sfc measurements in relation to
the intention of the efficient-mileage rating system. There is no
engine that runs at a constant speed at a constant load. Load and
engine speed constantly change. As these change so does the sfc.
A complete sfc measurement would result in a chart that looks like
a topographical map. Measurements would need to be taken at many
intervals of engine speed and many intervals of a given engine speed
at an interval of load. This would give a very detailed view of
engine efficiency. Comparing relief maps of engine efficiency is
only helpful to an engineer interested optimizing an engine's efficiency.
Fuel Conversion Efficiency is ratio calculated from the sfc dimensional
value. The Fuel Conversion Efficiency (nf) is the ratio of the engine
output to the heating value of the fuel used (QHV).
nf = (work per cycle)/(mass fuel used x heating value
nf = (Power)/(mass fuel flow rate x heating value
nf = 1/(sfc x heating value of fuel)
The heating value of gasoline is on average 43 megajoules
(MJ) per kilogram or about 18,500 BTU per mass pound. A mass pound
is the same value as a pound with the understanding that it is a
measure of mass instead of weight, where weight is really force.
The heating value of diesel fuel is on average 47 MJ per kilogram,
about 9% more energy than gasoline. The diesel vehicles in the chart
were adjusted for the greater energy content in diesel. On the specific
diesel vehicle web pages the gain in rating that would occur if
the adjustment wasn't made is shown in order to portray the benefits
of using a fuel with greater energy density.
The best way to measure fuel consumption is by measuring
carbon balance. The total mass of fuel used must be equal to the
amount of carbon that exits the exhaust. The EPA measures this by
driving specified drive cycles. This type of test is not intended
to be an accurate measure of fuel consumption (although recent efforts
by the EPA have increased the probability of accuracy). The EPA
test is intended to be a precise measurement. This means that every
time the test is performed on the specific vehicle, the measurement
will be the same. My primary complaint is that the measurement is
not reported to the first tenth of a mpg.
The new EPA measurements are a wonderful source for
fuel consumption even if there is controversy over the accuracy.
The EPA mpg ratings are very precise. Cars can easily be ranked
by fuel consumption. And the real world mpg numbers average out
very closely to the average of the EPA numbers which does support
the argument that EPA numbers are accurate. The EPA mpg numbers
also represent what cars use in practical daily driving.
Due to the impracticality of measuring the carbon
balance of every car at every engine speed in relation to a variety
of engine loads an alternative method of calculating efficiency
was derived: efficiency = (work done)/(energy used). What? That's
the same thing written above? Maybe I should clarify. What is needed
is a measure of practical efficiency. Absolute efficiency is impractical
for comparison because it is specific to an engine speed and load.
In the place of efficiency there is practical efficiency. Why practical?
It is practical because it based on the energy used in practical
street-legal driving. The equation would be rewritten as: Practical
Efficiency = (work done)/(energy content in average EPA mpg). But
miles-per-gallon isn't a measure of mass fuel. Gallons-per-mile
is a step closer. Europe measures fuel consumption by liters per
100km. Gallons per mile is written as 10miles/mpg. The equation
would be written: Practical Efficiency = (work done)/((10/average
mpg) x 2754.67 x 43)). One gallon of gasoline has a mass of 2754.67
grams. The heating value of the gasoline is 43MJ per kg. Diesel's
heating value is 47MJ per kg (about 9% more than gasoline).
The final part of the equation is measuring what work
is done. The required work to move a car changes depending on weight
(passengers or cargo), rate of acceleration, inclines, gear ratio,
drag, friction in the drivetrain, lateral acceleration, wheel and
tire mass, etc. What work can a car do to produce a precise measurement
of work that would be helpful for comparing the work done between
two or more vehicles? The answer is as simple as it is old: a drag
race. A drag race is for time and speed within a given distance
(a straight and level quarter mile). This provides the potential
work a car can do. The ratio of potential work to the energy consumed
in practical daily driving is a useful number for comparing a meaningful
idea of efficiency. Calculating the work is simply: mass x acceleration
x distance. Work = Mass x (0.25 mile speed/0.25 mile time) x 0.25
miles. With English to metric conversions: Work = (weight x 0.45359)
x ((0.25 mile speed x 0.447)/0.25 mile time) x 402.336.
We're not done quite yet. What this gives us a practical
way to measure efficiency of an engine. Part of the total work done
by the engine is moving the mass of the car. An engine can pull
a lot of weight efficiently, but that doesn't mean a heavy car is
efficient. So we haven't yet arrived at a way to measure practical
efficiency. But we're close.
The whole thing:
Engine Efficiency = ((weight x 0.45359) x ((0.25 mile
speed x 0.447)/0.25 mile time) x 402.336) / ((10/average mpg) x
2754.67 x 43))
The next step is to write a second equation that quantifies
a given acceleration for a given amount of fuel. This will be called
Vehicle Efficiency. The equation is a simple variation on the engine
efficiency. The weight is neglected and the result is multiplied
by a handicap factor. The handicap factor is useful for giving the
Vehicle Efficiency rating an equal weight and distribution when
compared to the Engine Efficiency.
Vehicle Efficiency = ((((0.25 mile speed x 0.447)/0.25
mile time) x 402.336) / ((10/average mpg) x 2754.67 x 43))) x 1500
The Efficient-Mileage rating is simply the average
of the Engine Efficiency rating and the Vehicle Efficiency rating.
Efficient-Mileage rating = (Engine Efficiency rating
+ Vehicle Efficiency rating) / 2
The term ‘rating’ is used to bring attention
to the fact that these efficiency numbers do not represent absolute
engine efficiency measured in a dimensional value or percent. A
rating is like a score on a test, which this is. Outside the test,
the rating value has no meaning or use. But it is a powerful tool
Due to variation in driver ability on the quarter
mile, and variation in the accuracy (not precision) of the EPA measurements
there is a degree of uncertainty that can be described as +/- 1
Efficient-Mileage rating points. Any vehicle may move up or down
within a single rating point. Any car is probably equal to other
cars up to +1 rating point or down to -1 rating point. This also
means that the variation on the Engine Efficiency rating and the
Vehicle Efficiency rating is +/- 1 rating points. A difference of
2 points between cars is significant.
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