Background of The internal combustion principles of DeRochas


1- A minimum boundary surface with a largest bore

The lower mechanical surface boundaries principle is meant to  decrease power loss from friction and inertia of the moving pistons, which increases dramatically at higher speeds. 

  • In our Relative-Motion  turbo charged version design, having  the four strokes accomplished in one reciprocating cycle, where fluid intake and compression hosted in a separate compartment behind a second piston, and completed at the same time of the power and exhaust  strokes, a required acceleration to perform similar conventional cylinder work is decreased to half, with lower piston speed that not only decreases the overall piston-to-cylinder surface boundaries  as a function of time, but also increases the upper speed  limits of possible power gain. 

2- A greatest initial piston speed

Any sacrifice of initial speed in a conventional cylinder would be a potential power loss. That is done, with conventional engines by initial combustion forces that could be thirty times higher than the load or resistance forces.

This principle has come under doubt since direct injection was applied, where some text books interpreted the advantages to be a result of higher compression ratios available with direct injection, and our interpretation concludes that better efficiencies with direct injection is a result of

1) Lower initial speeds  that allow a better equilibrium in transferring potential forces to piston  forces.

2) Lower average speed is helpful in ridding of the freeze zone at piston surface with more complete fuel burning.

  •  The new Relative-Motion combustion design is done with minimum acceleration required to maintain a working speed, which is optimized not only by the initial forces, but also by secondary forces of partial compression initiated behind the second piston, where  pressure is dynamically reflected as  forces applied to a crankshaft piston. 
  • The ratio of transmitting pressure forces to piston forces is enhanced by  the factor of decreased speed requirement.

3- A greatest expansion ratio

Designs intended to enhance expansion ratio were based on initial combustion conditions and allowance or limits of the negative driving force which starts about half way of the power stroke.

  • With the Relative Motion design, we can simply maintain positive driving forces toward the end of the power stroke, extending the mid distance, and as a result the expansion ratio, regardless of initial conditions. As a result, initial acceleration and fuel requirements can be cut by about two to three folds. 

4- A greatest initial combustion pressure


Simulation tests at similar compression ratios, show much higher initial pressure associated with premixed fluid but still with lesser performance.

  • one of the disadvantages of having higher initial pressure with sharper force decline, is the in-equilibrium of transmitting pressure forces to piston forces associated with higher piston speed in a conventional cylinder. 

  • Relative Motion design, having speed controlled, by initially exposing smaller piston surface, and not by initial pressure conditions, allows us to use earlier direct injection before the spark, for increased initial pressure, with yet better equilibrium of transmitting pressure forces to the piston.

Separating the compression compartment

Cylinder designs during the past century always committed to these principles,  with most advances based on the third principle of increasing the expansion ratio. 

The Relative Motion cylinder compares itself to a four -stroke conventional cylinder, but the intake and compression strokes are done in a different compartment than the power and exhaust strokes .

The Relative Motion Cylinder difference

The Relative Motion cylinder, can make a naturally aspirated engine with a piston configured for variable surface-to-pressure exposure during a power stroke, or can make a turbocharged engine with the four strokes split in two separate compartments, allowing one power stroke every cycle where torque pulses are further integrated in a uniform motion.

  • Engine air flow is limited by a choke point when a piston's average speed exceeds about 15 m/sec. This limitation is enhanced, by having a given piston speed of a Relative Motion cylinder, work at higher power output of comparable speed of a conventional cylinder.
  • As we increase the number of cylinders in a conventional cylinder engine, and the torque pulses get more closely overlapped, vibration is better handled and refined. Similarly, further improvement is accomplished by having every piston cycle become a power cycle.

  • Splitting chambers of the four strokes, and making every piston cycle a power cycle, can also double the shaft power of the engine at a given revolving speed: P (W) =2π N (Rev/s) *T (N-m), where T= torque applied twice more frequently in a Relative Motion cylinder at a similar revolving speed.

 Torque available at each operation speed is independently controlled by applying secondary forces, communicated from the turbocharge, to second piston, to crankshaft piston. "Enhancing potential-to-kinetic equilibrium with a power output improvement". Some studies claim that the nonequilibrium is responsible for rendering 50%-90% of the burned fuel, as non-useful. 

  • Also, In a conventional cylinder, forces for performing the intake-compression piston cycle, are borrowed forces from another cylinder working power. In a Relative Motion cylinder, a compression force borrowed, is a secondary working force transferred to a piston.

The clean exhaust advantage of Relative Motion Cylinder


Testing results included here ,were performed at higher initial pressure than ordinary working conditions to experience worst case of oxygen run out. More tests are being conducted, similar to average working conditions of a transport vehicle. Tests were always scalable and results were always in favor of an enhanced mean effective pressure in a direct injection method. 

  • Relative Motion cylinder however is not governed by the either-or choices, as we are now able to have triple the mean effective pressure and also use earlier injection because the piston speed is not anymore dependent only on initial pressure, but also on variable surface design. 


Relative Motion cylinder provided 300% higher mean internal pressure at comparable conventional fuel and cylinder volumes, however that is without increasing piston speed that causes fluid freeze and incomplete exhaust burning.

Increased internal combustion pressure resulted in ridding of non-manageable exhaust of CO and CH hydrocarbons, which decreased by 250% and 500% respectively, at a similar use of fuel volume ( CO and HC are called the unburned exhaust, and for that reason, they are considered the markers of the burning efficiency) . Mass fraction of other free radicals, which is the most damaging to human health was in one simulation decreased from 0.196% to 0.114%, that is before corrections of fuel savings.

Manageable gases like (NO2 and CO2) and H2O, were desirably increased, where such increase, is in expense of the non-manageable exhaust gases. 

After correction for fuel requirement to meet certain levels of torque and horsepower, the overall output of NO2 and CO2 were of comparable or lesser values under direct inject method of testing. A Relative Motion cylinder also, offers design controls that allow further increase of internal pressure by earlier fuel injection, without the suffering of increasing piston speed, and for that reason, emission controls became a great potential to further enhance the exhaust quality before reaching the filtering work for both NO2 and CO2.

The (NO) output was about the same, but was also reduced by about 50 % after correction for fuel requirements. It was almost eliminated with earlier injection time, and that can save on the need for expensive early filtration methods intended to convert NO to NO2.

Sizing of internal cylinder parts, under variable motion engineering controls of piston speeds, and cylinder internal combustion pressure, provided many choices of final designs to better address the needs of environmental and energy gain requirements. 

When adopted, direct injection offered a double work-energy availability. With a Relative Motion cylinder we will take another even bigger positive step, as to the size of improvements on both energy return and cleaner emissions.



Better exhaust output


Reduced hydrocarbons

H12C23 tests showed 500% reduction of non-manageable hydrocarbons where mass fraction in comparable direct injection parameters decreased from 2.13% to 0.39% with Relative Motion.


Reducing the non manageable exhaust


Non-manageable exhaust CO was reduced by 250%

due to increased combustion pressure with modified piston speed.  CO mass fraction at comparable direct injection test parameters was reduced from 4.43% to 1.76%. earlier injection promised even much better numbers, as testing is not completed yet.

Usually, combustion complete burning efficiency is associated with lower Co, Hydrocarbons.

Enhancing Work Energy


more work energy availability offers higher torque-horse power output or lower fuel requirements

Similar graph enhancement was historically realized after discovering the benefits of direct injection.  This graph, can self-audit itself, showing less work energy available at the first 15% of the expansion stroke, due to having pressure applied to smaller surface, while the remaining 85% of stroke, work energy is doubled. Also the graph is informative of how bigger initial acceleration results in a bigger waste of energy.

Calculating useful energy by deducting friction losses, will further increase the benefits of the Relative-Motion, where compression forces calculated as a loss in one cylinder, is simultaneously recovered at another by increasing the second cylinder mean effective pressure.

Powerful & vibration refined Relative Motion engine


Force per time graph

Like a bad driver, ordinary cylinder seems in this graph to be wasting so much energy on sudden acceleration followed by non-useful sharp force decline, and according to Newton, forces and energy are used only during acceleration. In a Relative Motion cylinder, motion is stabilized around a given motion baseline, requiring minimum acceleration changes, and as a result a minimum fuel requirement. 

  • This graph shows enhancement of a first combustion principle offering minimum motion boundaries as a function of time. 
  • Third & Forth principles, are to be adapted to Relative Motion kinetics, having the initial combustion force minimized, & compensated by a force enhanced during the rest of stroke. 
  • While a conventional torque graph turns negative around half distance of the power stroke, it extends beyond that in a Relative Motion cylinder with a bigger average of torque magnitude and torque impulse time where power is proportionate to such changes.

Graph shows no force jerking of the piston motion in the new design as long as we do not apply secondary force suddenly after the power stroke starts

Contrary to history of about 20% energy recovery efficiency of conventional supercharging methods, we anticipate with the use of a turbocharger along with a Relative Motion cylinder that the energy recovery would be about 70-80% efficiency.

Increased cylinder mean internal combustion pressure with Relative Motion.


Increased cylinder mean internal combustion pressure.

Using comparable direct injection fuel volume and cylinder size, mean effective pressure behind a piston was more than doubled. 

A Relative Motion engine performance can be effectively measured as:

Performance = work per cycle /volume displaced

  • (Work= mean pressure* crank rev per cycle/ Engine Revolution per sec). that is 2-3 times bigger pressure in a Relative Motion cylinder.
  • Volume displaced is about 1/2 in the presence of space occupier (floating piston).

Simple calculation provides over 300% improvement, at lower resisting loads and over 400% enhancement at higher resistance where mean pressure further improved and work graph difference is increased, all being done within our Relative Motion operational engine cycle. 

On the window sticker of a vehicle, these performance calculations mean that an 18 miles per gallon of a conventional vehicle, shall improve its overall performance to about 70 miles per gallon ability, when using our Relative Motion enhancements, which will not only help the consumer, but also can secure the energy market. 

  • This pressure enhancement, is before calculating effects of secondary forces,  or potential exhaust recovery at about 70%, using a turbocharger, or extending the expansion ratio, and also before calculating changes of friction losses, where boundaries area decreased. 

For all these above reasons, an average of 400% power output enhancement, is what we expect from the new Relative Motion method, over a conventional cylinder, and that is how we obtain a 70 miles per gallon potential result.