We’re all aware
of the digital revolution permeating our lives. The
automotive industry applies computers to manage the
operation of their reciprocating engines. The
result is that the hundred year old design is somewhat more
efficient. What we need is a paradigm shift to a true
digital engine that is both fuel-efficient and very green.
Such an engine would go a long way to solving our energy,
pollution and economic crises.
This is
the first in a series of digital
energy conversion systems with direct application to
vehicles. This engine is modularized so each function
in the conversion process is handled as as a separate
entity. The engine uses different fuels with simple
module changes. Each module connects with the next
module by digital interface. The digital interface is
both mechanical and computerized. The result is that
each module converts energy under optimum conditions. This
produces a small engine that is very green and does not
require a transmission for typical automotive and light
truck applications. One of the most dynamic features
of the engine is that the combustion gases are allowed to
expand over 160 times, using thousands of logic steps per
revolution instead of approximately 8 for the standard
automotive engine. This allows clean
combustion and dramatically increases fuel economy.Usable torque is produced at zero RPMs.
It’s inexpensive to build and truly
robust.This 64 lb engine is capable
of producing 250 horsepower (scalable) and will produce fuel
efficiencies of over 100 MPG in a vehicle. The thermal
expansion ratio of this engine is astounding.
THE ADVANTAGES OF LARGE THERMAL EXPANSION RATIOS ON FUEL
EFFICIENCY
Problem:
Reciprocating engines require a proper air to fuel mixture
in order to burn fossil fuels efficiently.The octane rating of the fuel sets the maximum
efficient compression ratio. Once the compression ratio is
set, the expansion ratio for the hot gases is also set.Diesel engines have a higher compression ratio;
therefore they have a higher expansion ratio resulting in
higher fuel efficiency than gasoline engines. Standard
gasoline and diesel reciprocating engines require a central
shaft with other fixed parameters noted above which dictate
their general fuel efficiency. The effects of Hybrid
technologies are not considered in this paper. Given these
conditions, production automobiles cannot be expected to
achieve fuel economy of 100 MPG.
Solution:
If an internal combustion engine can be designed where the
central shaft no longer dictates the other parameters then
the fuel efficiency of the engine is not constrained.The expansion ratio is the largest single effect on
fuel efficiency.Gasoline reciprocating engines usually have an
expansion ratio of about 8/1, while the expansion ratio for
diesel reciprocating engines is about 17/1.By removing the central drive shaft, one could
separate out the four cycles of the internal combustion
engine, which are intake, compression, power and exhaust.The power stroke happens after the air to fuel
mixture is ignited and the hot gases force the piston toward
bottom dead center.In a modularized engine, the power stroke could be a
separate module where the expansion ratio can be set by a
computer.In practical design criteria the expansion ratio of
100/1 is optimum.Expansion ratios over 100/1 introduce more friction
than the horsepower produced by the extra expansions (law of
diminishing returns).
This paper will demonstrate the effect of thermal expansion
on fuel economy through the use of Charles' Law and Boyle's
Law shown below.We are also including a basic formula for determining
the horsepower required to compress air.We are going to be comparing four models of internal
combustion engines to show the relationship that the
expansion ratio has on fuel economy when all other factors
are held constant.
With a modularized internal combustion engine, the intake
and compression is done with one module, known as a
compressor. The output of the compressor is fed into a
second module. The second module is the combustion module
which mixes the proper air fuel mixture and ignites it so
the mixture is burned with optimum efficiency. One of the
advantages is that the combustion process can be operated
100% of the time. The output from the second module is fed
into a third module, the torque converter. The design of the
torque converter can be similar in design to the compressor
module with greater volume. The torque converter has a
volume per revolution that would allow 100/1 expansion of
the hot gases.The torque converter in a modularized engine is
positive displacement, therefore producing torque at zero
RPMs.Horsepower can then be added to get to the desired
RPMs with a given load.In the standard reciprocating engine, about 20% of
the RPMs are required for the engine to overcome its own
friction prior to producing any usable output torque.The net result is that a modularized engine does not
require a transmission to adjust the torque to the
rotational requirements.
A standard reciprocating engine, whether gasoline or diesel,
can be used as a hot gas generator to drive a modularized
torque converter. In this case, the reciprocating engine is
not connected to the drive shaft.Instead, the hot exhaust gases are fed directly into
the modularized torque converter. The reciprocating engines
will still have 8/1 to 17/1 expansion ratios, but in
addition the torque converter would multiply these expansion
ratios to achieve 100/1 expansions. In order for an engine
to be run in this fashion, some of the hot gases in the
combustion cylinder will not be exhausted and will be
recycled into the next combustion cycle. This recycling of
some of the exhaustion gases has been extensively studied by
automobile manufacturers and they have found that this will
further improve fuel efficiency.
Parameters for Comparisons:
1.
The basic example will be a reciprocating engine with 1/1
expansions. This will be compared with a reciprocating
gasoline engine with 8/1 expansion ratio, a hypothetical
gasoline engine with 17/1 expansion ratio and a modularized
engine with 100/1 expansion ratio.
2.
Gasoline octane ratings have different British Thermal Units
(BTU) ratings, but in these comparisons they will be
considered equal by stating the combustion pressure without
reference to how it was generated. The burn cycle will be
considered instantaneous. The only factor that changes is
the expansion ratio and the resultant Final Volume. All
other factors are the same.The emphasis will be solely on the expansion ratios
to show how they affect the fuel economy.
3.
All comparisons will have 1000 PSI generated by the initial
combustion process, 20 cubic inches (CI) in volume of the
initial combustion gases and 1000 Revolutions per Minute
(RPM).
Formulas:
HP = Theoretical Horsepower to Compressed Air
Q = System air flow rated in cubic feet per minute
PSI = Outlet gage pressure in pounds per square inch
CFM = Cubic Feet per Minute
K = Temperature in Kelvin's
MPG = Miles per gallon
CI = Cubic inches
CF = Cubic inches in a cubic foot as 1728 CI
Conditions: Dry air at sea level, atmospheric pressure =
14.7 PSI and single stage adiabatic compression (without
heat loss to cylinder wall).
Boyle's Law:Initial Pressure / Final pressure = Final Volume /
Initial Volume
Charles Law: Initial Volume / Initial temperature K = Final
Volume / Final temperature K
Charles Law is shown to demonstrate that pressure is
directly proportional to temperature when the absolute
temperature scale is measured in Kelvin's. In this example,
as the hot gases expand they become cooler. The hot gases,
after expansion, are exhausted to the atmosphere which sets
the lowest pressure. The pressure here is stated as the
pressure above sea level of 14.7 PSI.
Theoretical Horsepower to Compressed Air: HP = .2267 Q [ (
{PSI /14.7} + 1).238 - 1]
Reference for formulas:POCKET REF, Glover, Thomas J.
GASOLINE
RECIPROCATING ENGINE with 1/1 THERMAL EXPANSIONS
Initial Pressure = 1000 PSI
Initial Volume = 20 CI (volume of compressed air fuel
mixture just prior to combustion)
RPM's for all three comparisons = 1000 RPM's
Thermal Expansion Ratio = 1/1
Initial Pressure / Final pressure = Final Volume / Initial
Volume, which can be restated as Final pressure = Initial
Pressure x Initial Volume / Initial Volume x the Expansion
ratio
Final Pressure = 1000 PSI as Initial Pressure x 20 CI as
Initial Volume / Final Volume is 20 CI as Initial Volume x
1/1 Expansions = 1000 PSI
Final Volume as generated in one minute as the Q = Initial
Volume x the expansion ratio x RPM / Number of CI in a Cubic
Foot (CF)
Final Volume as the Q = 20 CI x 1000 RPM's / 1728 CI / CF =
11.57 CFM
Initial Theoretical Horsepower (used for all three
comparisons):
HP = .2267 x 11.57 CFM [ ( { 1000 PSI / 14.7 + 1).238
- 1 ] = 4.56 HP
GASOLINE RECIPROCATING ENGINE with 8/1 THERMAL EXPANSIONS
Initial Pressure = 1000 PSI
Initial Volume = 20 CI (volume of compressed air fuel
mixture just prior to combustion)
RPM's for all three comparisons = 1000 RPM's
Thermal Expansion Ratio = 8/1
Final Pressure = Initial Pressure x Initial Volume / Initial
Volume x Expansion ratio
Final Pressure = 1000 PSI x 20 CI / 20 CI x 8/1 Expansions =
125 PSI
Final Volume generated in one minute as the Q = Initial
Volume x the expansion ratio x RPM / Number of CI in a Cubic
Foot (CF)
Final Volume as the Q = 20 CI x 8/1 expansion x 1000 RPM's /
1728 CI / CF = 92.59 CFM
Final Theoretical Horsepower: HP = .2267 x 92.59 CFM [ ( {
125 PSI / 14.7 + 1).238 - 1 ] = 14.88 HP
CONCLUSION: With 1/1 thermal expansions the engine produced
4.56 HP, but with 8/1 thermal expansions the engine produced
14.88 HP or 3.26 times more HP with the same amount of fuel
expended. This would equal the reciprocal or 3.26 more MPG
with all other conditions being equal. The improvement in
the MPG is directly attributed to the 8/1 thermal expansions
versus 1/1.
MODIFIED GASOLINE RECIPROCATING ENGINE with 17/1 THERMAL
EXPANSIONS
At the present time gasoline engines cannot reach 17/1
thermal expansions because the compression ratio is
proportional to the expansion ratio. The 17/1 would cause
pre-ignition and damage the engine. Diesel engines do have
expansion ratios of 17/1 but diesel fuels have a different
burn rate and BTU rating. Gasoline engines could be modified
to get the 17/1.
If the intake valve was to remain closed for a
period of time during the intake stroke, then less air is
compressed, but if the compression ratio was reset to
perhaps 10/1 then the thermal expansion could be increased
substantially. The problem is that the net HP will drop
dramatically. This is not practical because the standard
reciprocating engines are designed for the worst case when
the pressure of the combustion takes place. Therefore all
parts need to be capable of accepting those conditions. With
a modular engine the compressor would need to be designed
for 150 PSI, not 1000 PSI, and the temperatures would be
proportionally less as per Charles' Law. All seals and metal
needed to constrain 150 PSI are considerably less, so the
weight and cost is reduced.The same can be stated for the torque converter and
the cost and energy savings of not having a transmission
cannot be overlooked.
Initial Pressure = 1000 PSI
Initial Volume = 20 CI (volume of compressed air fuel
mixture just prior to combustion)
RPM's for all three comparisons = 1000 RPM's
Number of Thermal Expansions = 17/1
Final Pressure = Initial Pressure x Initial Volume / Initial
Volume x Expansion ratio
Final Pressure = 1000 PSI x 20 CI / 20 PSI x 17/1 Expansions
= 58.82 PSI
Final Volume generated in one minute as the Q = Initial
Volume x the expansion ratio x RPM / Number of CI in a Cubic
Foot (CF)
Final Volume as the Q = 20 CI x 17/1 expansion x 1000 RPM's
/ 1728 CI / CF = 196.76 CFM
Final Theoretical Horsepower: HP = .2267 x 196.76 CFM [ ( {
58.82 PSI / 14.7 + 1).238 - 1 ] = 20.83 HP
CONCLUSION: With 1/1 thermal expansions the engine produced
4.56 HP, but with 17/1 thermal expansions the engine
produced 20.83 HP or 4.57 times more HP with the same amount
of fuel expended. This would equal the reciprocal or 4.57
more MPG with all other conditions being equal. This
modified Gasoline Reciprocating Engine with 20.83 HP when
compared to the standard gasoline engine with 8/1 expansions
and 14.88 HP, is 1.40 times more fuel efficient with all
other factors being equal.
MODULARIZED GASOLINE ENGINE with 100/1 THERMAL EXPANSIONS
Initial Pressure = 1000 PSI
Initial Volume = 20 CI (volume of compressed air fuel
mixture just prior to combustion)
RPM's for all three comparisons = 1000 RPM's
Thermal Expansion Ratio = 100/1
Final Pressure = Initial Pressure x Initial Volume / Initial
Volume x Expansion ratio
Final Pressure = 1000 PSI x 20 CI / 20 PSI x 100/1
Expansions = 10 PSI
Final Volume generated in one minute as the Q = Initial
Volume x the expansion ratio x RPM / Number of CI in a Cubic
Foot (CF)
Final Volume as the Q = 20 CI x 100/1 expansion x 1000 RPM's
/ 1728 CI / CF = 1157.41 CFM
Final Theoretical Horsepower: HP = .2267 x 1157.41 CFM [ ( {
10 PSI / 14.7 + 1).238 - 1 ] = 34.37 HP
CONCLUSION: With 1/1 thermal expansions the engine produced
4.56 HP, but with 100/1 thermal expansions the engine
produced 34.37 HP or 7.54 times more HP with the same amount
of fuel expended. This would equal the reciprocal or 7.54
more MPG with all other conditions being equal. The
Modularized Engine with 34.37 HP when compared to the
Gasoline Engine with 8/1 expansions and 14.88 HP is 2.31
times more fuel efficient. The Modularized Engine with 34.37
HP when compared to the modified gasoline Reciprocating
Engine with 20.83 HP is 1.65 times more fuel efficient.
The most fuel efficient EPA rated mass-produced gasoline
automobile is the "Prius" which claims 50 - 60 MPG or an
average of 55 MPG. If we compare the Modularized
Gasoline Engine with the Prius, the Modularized Engine
would be 2.31 times more efficient or have an EPA rating
of 55 MPG x 2.31 =
127 MPG if all other factors are equal.
Thermal expansion is the most important factor when
trying to improve efficiency.
A L L D I G I T A L
INTRODUCTION
We’re all aware of the digital revolution permeating our lives. The automotive industry applies computers to manage the operation of their reciprocating engines. The result is that the hundred year old design is somewhat more efficient. What we need is a paradigm shift to a true digital engine that is both fuel-efficient and very green. Such an engine would go a long way to solving our energy, pollution and economic crises.
This is the first in a series of digital energy conversion systems with direct application to vehicles. This engine is modularized so each function in the conversion process is handled as as a separate entity. The engine uses different fuels with simple module changes. Each module connects with the next module by digital interface. The digital interface is both mechanical and computerized. The result is that each module converts energy under optimum conditions. This produces a small engine that is very green and does not require a transmission for typical automotive and light truck applications. One of the most dynamic features of the engine is that the combustion gases are allowed to expand over 160 times, using thousands of logic steps per revolution instead of approximately 8 for the standard automotive engine. This allows clean combustion and dramatically increases fuel economy. Usable torque is produced at zero RPMs. It’s inexpensive to build and truly robust. This 64 lb engine is capable of producing 250 horsepower (scalable) and will produce fuel efficiencies of over 100 MPG in a vehicle. The thermal expansion ratio of this engine is astounding.
THE ADVANTAGES OF LARGE THERMAL EXPANSION RATIOS ON FUEL EFFICIENCY
Problem:
Reciprocating engines require a proper air to fuel mixture in order to burn fossil fuels efficiently. The octane rating of the fuel sets the maximum efficient compression ratio. Once the compression ratio is set, the expansion ratio for the hot gases is also set. Diesel engines have a higher compression ratio; therefore they have a higher expansion ratio resulting in higher fuel efficiency than gasoline engines. Standard gasoline and diesel reciprocating engines require a central shaft with other fixed parameters noted above which dictate their general fuel efficiency. The effects of Hybrid technologies are not considered in this paper. Given these conditions, production automobiles cannot be expected to achieve fuel economy of 100 MPG.
Solution:
If an internal combustion engine can be designed where the central shaft no longer dictates the other parameters then the fuel efficiency of the engine is not constrained. The expansion ratio is the largest single effect on fuel efficiency. Gasoline reciprocating engines usually have an expansion ratio of about 8/1, while the expansion ratio for diesel reciprocating engines is about 17/1. By removing the central drive shaft, one could separate out the four cycles of the internal combustion engine, which are intake, compression, power and exhaust. The power stroke happens after the air to fuel mixture is ignited and the hot gases force the piston toward bottom dead center. In a modularized engine, the power stroke could be a separate module where the expansion ratio can be set by a computer. In practical design criteria the expansion ratio of 100/1 is optimum. Expansion ratios over 100/1 introduce more friction than the horsepower produced by the extra expansions (law of diminishing returns).
This paper will demonstrate the effect of thermal expansion on fuel economy through the use of Charles' Law and Boyle's Law shown below. We are also including a basic formula for determining the horsepower required to compress air. We are going to be comparing four models of internal combustion engines to show the relationship that the expansion ratio has on fuel economy when all other factors are held constant.
With a modularized internal combustion engine, the intake and compression is done with one module, known as a compressor. The output of the compressor is fed into a second module. The second module is the combustion module which mixes the proper air fuel mixture and ignites it so the mixture is burned with optimum efficiency. One of the advantages is that the combustion process can be operated 100% of the time. The output from the second module is fed into a third module, the torque converter. The design of the torque converter can be similar in design to the compressor module with greater volume. The torque converter has a volume per revolution that would allow 100/1 expansion of the hot gases. The torque converter in a modularized engine is positive displacement, therefore producing torque at zero RPMs. Horsepower can then be added to get to the desired RPMs with a given load. In the standard reciprocating engine, about 20% of the RPMs are required for the engine to overcome its own friction prior to producing any usable output torque. The net result is that a modularized engine does not require a transmission to adjust the torque to the rotational requirements.
A standard reciprocating engine, whether gasoline or diesel, can be used as a hot gas generator to drive a modularized torque converter. In this case, the reciprocating engine is not connected to the drive shaft. Instead, the hot exhaust gases are fed directly into the modularized torque converter. The reciprocating engines will still have 8/1 to 17/1 expansion ratios, but in addition the torque converter would multiply these expansion ratios to achieve 100/1 expansions. In order for an engine to be run in this fashion, some of the hot gases in the combustion cylinder will not be exhausted and will be recycled into the next combustion cycle. This recycling of some of the exhaustion gases has been extensively studied by automobile manufacturers and they have found that this will further improve fuel efficiency.
Parameters for Comparisons:
1. The basic example will be a reciprocating engine with 1/1 expansions. This will be compared with a reciprocating gasoline engine with 8/1 expansion ratio, a hypothetical gasoline engine with 17/1 expansion ratio and a modularized engine with 100/1 expansion ratio.
2. Gasoline octane ratings have different British Thermal Units (BTU) ratings, but in these comparisons they will be considered equal by stating the combustion pressure without reference to how it was generated. The burn cycle will be considered instantaneous. The only factor that changes is the expansion ratio and the resultant Final Volume. All other factors are the same. The emphasis will be solely on the expansion ratios to show how they affect the fuel economy.
3. All comparisons will have 1000 PSI generated by the initial combustion process, 20 cubic inches (CI) in volume of the initial combustion gases and 1000 Revolutions per Minute (RPM).Formulas:
HP = Theoretical Horsepower to Compressed Air
Q = System air flow rated in cubic feet per minute
PSI = Outlet gage pressure in pounds per square inch
CFM = Cubic Feet per Minute
K = Temperature in Kelvin's
MPG = Miles per gallon
CI = Cubic inches
CF = Cubic inches in a cubic foot as 1728 CI
Conditions: Dry air at sea level, atmospheric pressure = 14.7 PSI and single stage adiabatic compression (without heat loss to cylinder wall).
Boyle's Law: Initial Pressure / Final pressure = Final Volume / Initial Volume
Charles Law: Initial Volume / Initial temperature K = Final Volume / Final temperature K
Charles Law is shown to demonstrate that pressure is directly proportional to temperature when the absolute temperature scale is measured in Kelvin's. In this example, as the hot gases expand they become cooler. The hot gases, after expansion, are exhausted to the atmosphere which sets the lowest pressure. The pressure here is stated as the pressure above sea level of 14.7 PSI.
Theoretical Horsepower to Compressed Air: HP = .2267 Q [ ( {PSI /14.7} + 1).238 - 1]
Reference for formulas: POCKET REF, Glover, Thomas J.
GASOLINE RECIPROCATING ENGINE with 1/1 THERMAL EXPANSIONS
Initial Pressure = 1000 PSI
Initial Volume = 20 CI (volume of compressed air fuel mixture just prior to combustion)
RPM's for all three comparisons = 1000 RPM's
Thermal Expansion Ratio = 1/1
Initial Pressure / Final pressure = Final Volume / Initial Volume, which can be restated as Final pressure = Initial Pressure x Initial Volume / Initial Volume x the Expansion ratio
Final Pressure = 1000 PSI as Initial Pressure x 20 CI as Initial Volume / Final Volume is 20 CI as Initial Volume x 1/1 Expansions = 1000 PSI
Final Volume as generated in one minute as the Q = Initial Volume x the expansion ratio x RPM / Number of CI in a Cubic Foot (CF)
Final Volume as the Q = 20 CI x 1000 RPM's / 1728 CI / CF = 11.57 CFM
Initial Theoretical Horsepower (used for all three comparisons):
HP = .2267 x 11.57 CFM [ ( { 1000 PSI / 14.7 + 1).238 - 1 ] = 4.56 HP
GASOLINE RECIPROCATING ENGINE with 8/1 THERMAL EXPANSIONS
Initial Pressure = 1000 PSI
Initial Volume = 20 CI (volume of compressed air fuel mixture just prior to combustion)
RPM's for all three comparisons = 1000 RPM's
Thermal Expansion Ratio = 8/1
Final Pressure = Initial Pressure x Initial Volume / Initial Volume x Expansion ratio
Final Pressure = 1000 PSI x 20 CI / 20 CI x 8/1 Expansions = 125 PSI
Final Volume generated in one minute as the Q = Initial Volume x the expansion ratio x RPM / Number of CI in a Cubic Foot (CF)
Final Volume as the Q = 20 CI x 8/1 expansion x 1000 RPM's / 1728 CI / CF = 92.59 CFM
Final Theoretical Horsepower: HP = .2267 x 92.59 CFM [ ( { 125 PSI / 14.7 + 1).238 - 1 ] = 14.88 HP
CONCLUSION: With 1/1 thermal expansions the engine produced 4.56 HP, but with 8/1 thermal expansions the engine produced 14.88 HP or 3.26 times more HP with the same amount of fuel expended. This would equal the reciprocal or 3.26 more MPG with all other conditions being equal. The improvement in the MPG is directly attributed to the 8/1 thermal expansions versus 1/1.
MODIFIED GASOLINE RECIPROCATING ENGINE with 17/1 THERMAL EXPANSIONS
At the present time gasoline engines cannot reach 17/1 thermal expansions because the compression ratio is proportional to the expansion ratio. The 17/1 would cause pre-ignition and damage the engine. Diesel engines do have expansion ratios of 17/1 but diesel fuels have a different burn rate and BTU rating. Gasoline engines could be modified to get the 17/1. If the intake valve was to remain closed for a period of time during the intake stroke, then less air is compressed, but if the compression ratio was reset to perhaps 10/1 then the thermal expansion could be increased substantially. The problem is that the net HP will drop dramatically. This is not practical because the standard reciprocating engines are designed for the worst case when the pressure of the combustion takes place. Therefore all parts need to be capable of accepting those conditions. With a modular engine the compressor would need to be designed for 150 PSI, not 1000 PSI, and the temperatures would be proportionally less as per Charles' Law. All seals and metal needed to constrain 150 PSI are considerably less, so the weight and cost is reduced. The same can be stated for the torque converter and the cost and energy savings of not having a transmission cannot be overlooked.
Initial Pressure = 1000 PSI
Initial Volume = 20 CI (volume of compressed air fuel mixture just prior to combustion)
RPM's for all three comparisons = 1000 RPM's
Number of Thermal Expansions = 17/1
Final Pressure = Initial Pressure x Initial Volume / Initial Volume x Expansion ratio
Final Pressure = 1000 PSI x 20 CI / 20 PSI x 17/1 Expansions = 58.82 PSI
Final Volume generated in one minute as the Q = Initial Volume x the expansion ratio x RPM / Number of CI in a Cubic Foot (CF)
Final Volume as the Q = 20 CI x 17/1 expansion x 1000 RPM's / 1728 CI / CF = 196.76 CFM
Final Theoretical Horsepower: HP = .2267 x 196.76 CFM [ ( { 58.82 PSI / 14.7 + 1).238 - 1 ] = 20.83 HP
CONCLUSION: With 1/1 thermal expansions the engine produced 4.56 HP, but with 17/1 thermal expansions the engine produced 20.83 HP or 4.57 times more HP with the same amount of fuel expended. This would equal the reciprocal or 4.57 more MPG with all other conditions being equal. This modified Gasoline Reciprocating Engine with 20.83 HP when compared to the standard gasoline engine with 8/1 expansions and 14.88 HP, is 1.40 times more fuel efficient with all other factors being equal.
MODULARIZED GASOLINE ENGINE with 100/1 THERMAL EXPANSIONS
Initial Pressure = 1000 PSI
Initial Volume = 20 CI (volume of compressed air fuel mixture just prior to combustion)
RPM's for all three comparisons = 1000 RPM's
Thermal Expansion Ratio = 100/1
Final Pressure = Initial Pressure x Initial Volume / Initial Volume x Expansion ratio
Final Pressure = 1000 PSI x 20 CI / 20 PSI x 100/1 Expansions = 10 PSI
Final Volume generated in one minute as the Q = Initial Volume x the expansion ratio x RPM / Number of CI in a Cubic Foot (CF)
Final Volume as the Q = 20 CI x 100/1 expansion x 1000 RPM's / 1728 CI / CF = 1157.41 CFM
Final Theoretical Horsepower: HP = .2267 x 1157.41 CFM [ ( { 10 PSI / 14.7 + 1).238 - 1 ] = 34.37 HP
CONCLUSION: With 1/1 thermal expansions the engine produced 4.56 HP, but with 100/1 thermal expansions the engine produced 34.37 HP or 7.54 times more HP with the same amount of fuel expended. This would equal the reciprocal or 7.54 more MPG with all other conditions being equal. The Modularized Engine with 34.37 HP when compared to the Gasoline Engine with 8/1 expansions and 14.88 HP is 2.31 times more fuel efficient. The Modularized Engine with 34.37 HP when compared to the modified gasoline Reciprocating Engine with 20.83 HP is 1.65 times more fuel efficient.
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