There three main engine types in production.  The 4 stroke engine, the Turbine and the lesser produced Wankel rotary engine.  A key measure in the cost effectiveness of an engine is efficiency, with 100% efficiency representing the unthinkable, perfect engine, 86% representing the theoretical scientific limit and 73% representing the working limit.  A 30% efficient engine means that for every $1.00 you spend in fuel, you only get 30 cents worth of power.  The remaining 70 cents is lost as heat and non-combusted fuel.  All three engines have their pros and cons in sight of individual applications.  The Split Power Engine has incorporated within its design, features which are similar to the pros in each engine.  These include, the self contained, cylindrical combustion chamber of the 4 stroke engine, the single shaft, free spinning nature of the turbine, and the multi-engine stacking feature of the Wankel rotary engine.  The single drawback of all 3 of these engines is the less than 90 degree power angle.

Engine Comparison

4 Stroke Engine
The 4 stroke engine has development roots going all the way back to 1801.  The engine has numerous elements which contribute to its average 30% efficiency, with  2 reasons dominating.  The first reason is that the majority of this low efficiency comes from the angle of the connecting rod relative to the piston head and crankshaft, not being a constant 90 degrees.  The first angle is between the crankshaft in a horizontal position during expansion (half stroke) and the connecting rod, and is about 70 degrees.  This angle represents maximum torque in the rotation.  Using 100 as a basis, max torque is 100 sin 70 = 100 x .9397 = 93.97 lbs or %.  We can also see that the angle between the connecting rod and piston head is also 70 degrees, so power must additionally be reduced by 100 sin 70 = 1 - (100 x .9397) = 6.03 lbs.  Thus we have a power loss of 6.03 + 6.03 = 12.06 lbs or %, for a max power of 100 - 12.06 = 87.94 lbs or % .   Because zero power is created when the crankshaft is vertical (piston head top dead center) the average between 0 torque and 87.94 is 87.94 / 2 = 43.97 lbs or %.     The second reason is that since the force on the piston follows the gas laws, at bottom dead center when the piston head is at its lowest, over 14% of combustion power, relative to the average stroke power (head travel distance), remains unused due to the fact that the pressure has not decreased back to 14.7 psi, atmospheric pressure.  In all, only (43.97 lbs - 14 lbs) = 29.97 lbs or % of the power stroke is utilized.  Once the devices connected to the belt, such as the a/c compressor, steering pumps, etc., engine block heat loss and unbalanced cylinder against wall friction are subtracted, a final 25%+/- efficiency can be expected. 

Turbine Engine
Turbine engine development roots goes back to 1939.  The turbine engine is primarily used in aircrafts and for electricity generation by utilities, trains, ships, gas compressors and tanks.  The turbine engine is the most efficient of the three engines, having an efficiency range of 30 to 40%, simple cycle.  Simple cycle means that the exhaust heat is not utilized for building heating, etc.  Combined cycle engines (non aircraft) have achieved 64% efficiency.  There are 3 primary reasons for this engine being limited to under 40% efficiency.  The first is that the turbine is connected to the compressor.  The faster the turbine turns, the faster the compressor turns.  At some point during this increase in rotational speed, the turbine blades can only process so much compressed air before backpressure to the compressor starts to become unsustanible and an engine stall event occurs.  If we say that the compressor provides 100 lbs or % of air force against the turbine blades, then the shaft experiences 100+ lbs of anti-torque (the + due to the radius of the compressor).   The second is that air moves parallel  to the shaft but perpendicular to turbine rotation.  The blades of the turbine section are generally at 45 degree angles.  Air hitting this angled blade has a sine of .707 and a cosine of .707.  This means that only 70.7% of the air’s force is transferred into rotation.  70.7 is also applied as blade bending stress on the shaft.  As one can see, the 100+ lbs of anti torque would in general stall the engine because it is greater than the 70.7 lbs, but air is compressible, the turbine blade radius create a moment arm and thus more torque due to the combustion chambers being located at turbine blade perimeter, and the hot fuel-air mixture is expanding thus providing more torque on the shaft than the anti-torque of the cooler compressed air and blade angle losses.  The third factor is that the air from the compressor is fast moving and must mix with the fuel while simultaneously forming a combustion event thus creating unburnt fuel.  None of these events are individually controlled and thus there is a small rpm window where the engine operates at its greatest efficiency.

Wankel Rotary Engine
The Wankel rotary engine is said to be conceived in 1929 and a working engine developed in 1951 .  Its use is in limited quantities but is the 3rd most popular engine of the three.  It has a very low efficiency ranging from 15% to 25%.  It is also a 4 phase engine like the 4 stoke and turbine engine, having an intake, compression, combustion-power and exhaust phase in sequence, but the motion is axial and not reciprocating like the 4 stroke.  There are 3 primary reasons why the rotary engine has low efficiency.  The first is because the combustion gas pressure acts against the continuously moving and curved surface of the rotor, and curved surface of the housing.  (The highest angle force, 100%, that can be achieved is from a tangent force, which is a 90 degree angle to the radius). 

 If a 100% efficient, perfect engine were to exist it would mean that the engine was a perfect insulator which means that no heat would escape and the temperature of the surface of the outside of the engine would equal the outside environment temperature.  It would also mean that the exhaust temperature would be equal to the environment temperature and that the only byproduct would be carbon dioxide and water (minus the other elements like nitrogen which makes up 78% of air by volume and gas additives).  Scientific research says the greatest theoretical efficiency is 86%.

In summary, although certain elements can be improved upon in each engine type, the core design of each engine cannot change.  It is this fixed core design which permanently limits these engines within their respective efficiency ranges, with the greatest limiting factor being power angles.

Efficiency Explained, and Why it Matters

Although calculus needs to be used to identify the final net angle out of the many angles formed, a 40 degree average is a good top end estimate given the geometries.   This means that out of a 100 lbs of pressure, 100 sin 40 = 100 x .6428 = 64.28 lbs or % is generated or 100 - 64.28 = 35.72 lb or % loss.  The second is that the engine actually acts against itself. This is due to the fact during the entire combustion event, i.e. power phase, its combustion force acts on both sides of the centerline relative to the fixed stationary gear.  You can see in rotary drawings how the half moon combustion event is on both sides of the stationary gear’s centerline..  The original design of the Wankel had only one spark plug, but because it was in line with the stationary gear, rotation problems occurred so a second, lower plug was incorporated.  The upper spark plug being the weaker (in terms of geometry) within the combustion event and the lower one being stronger due to the rotor’s rotational direction, rotor inertia, and spark plug’s offset position from the stationary gear which creates a greater torque moment arm.  Such elements offset to a percentage, this counteracting gear pivot design.  The third is that the lower spark plug is almost in line with the exhaust.  This means that at 1/4 rotor turn after the combustion event happens, the exhaust event occurs and the result is loss of power, and unburned and incomplete burned fuel exiting the exhaust.  Thus 1/4 x 73 = 18.65 lbs or % loss.  Devices connected to the belt can represent an approximate 5% loss, but because there are 3 power pulse rotor rotations for every full shaft rotation 5% / 3 = 1.66% loss.  So 73% - (35.72 + 18.65 + 1.66) = 16.97% final efficiency which is in line with rotary engine mpg fuel data.  Although many focus on the fact that the rotary has more power density (more power for the size)  than the 4 stroke engine, when fuel efficiency is taken into account, it actually has less power density.

Table of sin (angle)

The Importance of the Power Angle

If you have read the data above you would have noticed that all of the engines have one thing in common.  They all lack the 90 degree power angle.  The 90 degree power angle is important because it determines how much of the combustion power is converted to rotational torque and how much is converted to friction.  The table to the left shows clearly that when the power angle is reduced, the torque is also reduced, the sin being representive of such % of reduction..  Such reduction is embodied in the equation (Force sin angle degree).  Using 100 pounds as the force, you can see that 100 sin 90 is equal to 100 x 1 = 100 lbs.  This shows that 100% of the force from the combustion event is applied to shaft rotation.  Likewise if the angle is at 72 degrees, then 100 sin 72 = 100 x .9511 = 95.11 lbs or 95.11%.  At 40 degrees, 100 sin 40 = 100 x .6428 = 64.28 lbs or 64.28%.  Thus a force at 90 degrees shows no loss , at 72 degrees 1 - .9511 = .0489 or a 4.89 lb. loss, and at 40 degrees 1 - .6428 = .3572 or a 35.72 lb. loss.  This loss should be applied to the greatest possible efficiency given the fuel type and environment temperature.

Looking at the angle diagram you can see that a force at an angle is composed of a x and y component.  If the force was pure y component then there would be no loss of combustion force because the angle would be 90 degrees from the x component.  Therefore the equation would be, 100 lbs sin 90 = 100 x 1 = 100 lbs.  Thus we can see if the combustion gas force is acting against the cylinder head/rotor/turbine blade at an angle of 70 degrees then only 100 lbs sin 70 = 100 x .9397 = 93.97 lbs of pressure is applied in the y component direction although 100 lbs of force from the air-fuel mixture is used.  Thus 100 - 93.97 = 6.03% of the fuel is wasted along with 6.03 lbs of power being lost.  The continuously changing connecting rod angles of the 4 stroke engine, the perpendicular directional air force change of the turbine and the continuously changing relative angle between the curved, rotor and housing, of the Wankel rotary engine, will always create fuel and power losses.  Additional power and fuel losses occur due to friction from the x component of the head/turbine/rotor against the cylinder walls/turbine shaft/rotor housing.  This loss is calculated using the cosine of the 70 degree angle which is .3420.  Thus the pressure exerted to the side which creates friction is 34.20 lbs.  Since oil is used for lubrication its friction coefficient is about .05 so the actual friction pressure is .05 x 34.20 lbs = 1.71 lbs.  This side pressure wears down seals and creates uneven pressure and wear on metal parts which for circular cylinders makes them oval over time, thus reducing power due to reduced vacuum and combustion force and allowing exhaust particulates to contaminate the oil in the oil pan sump.  Because these designs are intrinsic to each engine, these losses are permanent and cannot be made up elsewhere in the engine.  Efficiency is further reduced by a variety of factors such as seal friction, shaft friction, the engine material heat transfer properties, combustion event time, fuel to air ratio, spark timing, exhaust and intake bottlenecks, exhaust backpressure, mass of rotor/crankshaft/turbine, rotation counterforces, rotational speed, load, additional devices on shaft or belt, etc.

The Split Power Engine utilizes 100% of the combustion power due to its ability to throw gases at a continuous 90 degree angle throughout the entire gas expansion process, perpendicular to the radius of the rotor.  

Engine Comparison

So if we take 73% as the max reasonable efficiency in sight of octane burning at 1,500 degrees in a 70 degree Fahrenheit environment, for every $1.00 spent on gas a maximum of 73 cents can be used.  Keep in mind that if a fuel burns at 2,500 degrees Fahrenheit (1,644.26 Kelvin), then the max efficiency goes to 1-(294K/1,644.26K) = 82.2% or 82.2 cents used for every $1.00 spent on fuel.  

Average U.S. octane consumption per passenger car in 2018 is about 25 (EPA) miles per gallon.
Average annual miles is 18,858 for 35-54 males (USDOT).  If we round up to 20,000 , then 20,000/25mpg = 800 gallons per year or an average of 15 gallons per day.  As of 2019 the average cost of mid grade gas is about $2.65.  800 gallons per year x $2.65 = $2,120.  Going from a 25% efficiency engine to a 50% engine would allow roughly 400 gallons of fuel to be saved per year along with $2,120 x 50% = $1,060 in retail fuel cost savings.

The Split Power Engine with its 50% efficiency target design has many factors that make it the go to engine for vertical takeoff aircrafts and flying cars, hybrid gas-electric, road vehicles and aircrafts, and utility, backup and portable electricity generation.  Other than fuel and fuel cost savings, pollution, noise, maintenance and applications must be looked at when investing in new engines which are tabled at the bottom of this page.