Relative Motion as a Function of Time

The Relative Motion Cylinder

 Unlike two pistons sharing a cylinder, and expanding in opposite directions, our same direction acceleration did not cause that the second piston shares or deducts its kinetic energy from the first piston power. 

Expansion stroke is completed by the first crankshaft piston, while 

second piston, created the higher-pressure field of Relative-Motion, competing for cylinder space, creating a combustion space-void of a negative mass, and a  relative-distance requiring less energy to do work.

Are we exaggerating the performance claims?

  • This video is a working visualization, to solve for the design-to-function relational goals. The OTTO's principles, treating the physics of a working  piston like a bullet is dropped for the purpose of using better equilibrium of transferring combustion forces to a piston work. 

Functions and physics need to be reviewed by using new principles we introduced at our American Physical Society presentation, for fellows to accept that we are not trying to break valid rules while we link our functions to the new design.

ANSYS simulation tests, were repeated by SOLIDWORKS and some key graphs were posted hereunder for those capable of repeating such tests, are able to verify. 

We did not take any confirming step, before working many simulation tests. Some fellows having business background, were able to communicate feedbacks, that is helping us to better choose our presenting words for credible statements, and beyond any advertising techniques.

Performance equation, was imbedded in the design video presentation, for those who prefer to build on theoretical base, before advancing a verification plan. While simulation tests show about 200% work/time enhancement, the 400% figure of claimed performance, was based on known engineering equation that can be verified in textbooks. We based our calculations on a well-known reference " Internal Combustion Engine Fundamentals - Second Edition -Chapter 2, Engine Design and Operation Parameters" for John B. Heywood.

on theoretical level we remined our readers, of the following:

While DeRochas-Otto principles recommend highest initial piston speed, John B. Heywood, reminds us that speed is what limits the engine breathing, and decides energy spent on acceleration.  This issue is solved in our Relative Motion design, where a relative motion established by a lesser acceleration control method.

Torque is what measures engine ability to do work, and Power measures the rate of work done per second. On both measures, our Relative-Motion cylinder doubled the performance, with every stroke is a power stroke and with our force graph doubling the distance before it goes negative.

Our second floating piston, is not applying any negative power consumption to the crankshaft drive, being mechanically separate from the crankshaft, and being floating inside the cylinder, with all valves are closed, while it is competing with the combustion fluid for space, creating a negative combustion Pascal mass,  and decreasing volume of displacement, with the crank shaft piston is the only Pascal output surface.

BackgrounD The 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 as of August, 2019 show that the main reason of adopting the direct injection solution, was about 40% better fuel efficiency and 70% lower CO2 output. The premixed fuel, in conventional cylinder had a cleaner output of C12H23, NO and NO2.

  • 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 CH hydrocarbons, mass fraction was decreased by about ten folds from ( 6.59% to 0.067% in direct injection method with compression ratio of 18.3:1) However using premixed fuel and air, the hydrocarbon output was similar (about 0.0002%). This preferred cleaner carbon output, which is along with (CO) a marker of complete burning, was sacrificed for two reasons, first for the increase of CO2 output associated with the premix (from 5.7% to 16.9% ) and second, for the lower efficiency of the premix, meaning the 16.9 % will be calculated per mile as 25%.

 The mass fraction of exhaust markers, like C12H23, NO,NO2  were improved with the new Relative-Motion design, at initial compression ratio of 18:1,  however CO and CO2 were increased in parallel with the decrease in O2 mass fraction. 

CO output increased in comparable fuel volume from 4.71% to 7.98% direct inject and 6.77% premix. Per mile output we had similar mass fraction output in direct injection, and 20% less with premix.

CO2 in conventional cylinder, decreased between premix and direct injection, for similar fuel volume from 16.93% to 5.72%. calculating per mile the numbers are about 500% enhancement difference accomplished by the direct injection, and that what explains the regulations of prohibiting the use of the premix fuel. in the new design, we can have 15% output per similar volume if used as a premix, but we can have about similar or better output per mile, when using a partially premixed fluid. Also the combination of CO+CO2 can be similar using a premix fuel in the Relative motion design, compared with direct injection in conventional cylinder. Higher compression ratios will further decrease the output of CO, example we had 250% lesser mass fraction output of CO at 30:1 theoretical compression ratio.

 A Relative Motion cylinder, offers design controls that allow further increase of internal pressure by earlier fuel injection, without the suffering of increasing piston speed, or the loss of efficiency, and for that reason, emission controls will have more variable control tools, for better exhaust of all markers, and not only CO2 .

The (NO) output was about the same, but was also reduced by about 50 % after correction for fuel requirements per mile. However 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.  

IN summary, the new Relative-Motion design, by increasing the mean effective pressure, along with controlling the piston speed with partially premixing the fuel, and within the limits of accepting about 20% enhancement on CO2, it can allow ten folds enhancements on CH, NO and 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 at 30:1 compression ratio, and from 6.59% to 0.67% at 18:1 compression ratio.

the premix option will eliminate this black material output of exhaust down to 0.00024%, which is a 1000 times less than it is in the direct injection method.

The premix, can be partly used in the Relative-Motion Cylinder, with controlled CO2 level, while in a conventional cylinder it would increase CO2 by 500% to levels prohibited everywhere.


Reducing the non-manageable exhaust


Non-manageable exhaust CO was reduced by 250% at compression ratio of 30:1

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% at 30:1 theoretical compression ratio. at 18:1 we may loos such advantage, however that can be managed by partially premixing fluid, which provided better results.

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 effective pressure


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.