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Computation for Speed of Optimal Mileage
Name: Muthu
Status: Student
Grade: 9-12
Location: Outside U.S.
Country: India
Date: Winter 2009-2010
Question:
How does an engineer calculate the ideal speed to get
high mileage in a car or other vehicle?
Replies:
Hi Muthu,
The short answer to your question is "he doesn't!" Basically, there
are far too
many variables and unknowns to be able to calculate exactly what speed will
give maximum mileage. Among the parameters that must be known are the
following: Engine, transmission, and differential efficiencies at all speeds,
detailed knowledge of aerodynamic drag at all speeds, rolling resistance of
the tires and wheel bearings at all speeds, and so on.
As you can imagine, in order to attempt to accurately calculate the optimal
speed for minimum fuel mileage, this quickly turns into an impossibly
complex problem. As a result, engineers do not attempt to calculate this.
Typically with most cars the speed that results in minimum fuel consumption
is between 50 to 60 MPH (80 to 100 km/h). This is generally the speed
where the engine runs most efficiently, and the speed just before air
resistance (or "drag") starts to exponentially increase. To determine the
answer to a greater accuracy, actual tests are made.
Regards,
Bob Wilson
It is complicated, and much of it is not actually calculated, but
determined from experiments. The efficiency of a car moving at
constant speed depends on many things, including engine design,
drag (wind resistance), and friction from many sources. Let us
just look at engine efficiency and drag, because their variation
with car speed is significant.
A car's engine is optimized for a limited range of speeds, and
geared so that the engine can stay mostly in that range. Above
some engine speed, there is not enough time for the gas/air mixture
to get into the cylinders and fill them optimally, or for the exhaust
to get out optimally, so the efficiency drops. Below some engine
speed, the pressure increase of ignited fuel in a cylinder is not
well matched to the speed at which the moving piston increases
the cylinder volume, so again the efficiency drops. (There are
other factors, including precisely when the cylinders should best
be ignited, that vary with engine speed. I mostly do not know what
they are or how they vary with engine speed.)
In short, there is an optimal (most efficient) engine speed, and this
means there is a different optimal car speed for each transmission
gear.
Drag, on the other hand, increases steadily with car speed, but it is
so hard to calculate accurately that wind-tunnel experiments are
performed to measure the drag at different speeds. Experiments have
shown that drag is negligible at low speed, and increases rapidly as
speed increases.
Because drag increases with car speed, the best gas mileage should
be achieved at some fairly low speed in first gear. (Nobody would
actually drive at that speed, because they would hear honking and
observe nasty gestures.) As the car speed increases, the efficiency
will decrease because of engine inefficiency until the car is shifted
to second gear. As the car's speed increases through the range of
second gear, the efficiency will increase to a maximum and then begin
decreasing. All the while the car speed is increasing, drag is
increasing, so each gear's optimal speed will be lower than engine
efficiency alone would suggest.
Tim Mooney
Muthu
There are two approaches, 1) by calculation; and 2) by measurement.
By calculation you can calculate the miles per gallon at different speeds
By measurement you actually measure how many miles per gallon a car gets at
a given speed.
This measurement is actually determined for aircraft so if pilots have an
engine failure in flight, they will know what speed they need to fly at for
maximum range.
Sincere regards,
Mike Stewart
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Update: June 2012
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