Rotary Displacement Calculation!

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The rotary engine is a 6 stroke internal combustion engine. I know, people will probably start screaming at me for this so let�s get into a little explanation as to why and how typical mathematical formulas for piston engines don't work.
First of all, lets get the terms "stroke" and "cycle" defined (Some of you get your heads out of the gutter!) since everyone commonly gets these terms interchanged. They are not the same thing. Every internal combustion engine whether it is a 2 stroke, 4 stroke, diesel, gasoline, propane injected, etc. is a 4 cycle engine. Why? All of these engines take in air (intake), compress the air (compression), ignite the air whether by spark plug or glow plug (ignition), and expel it out the tailpipe (exhaust). There you go 4 cycles. Simple isn't it.
The term "stroke" in this context refers to how many times the crankshaft or eccentric shaft makes a piston go up or down to complete the cycle. The connecting rods and pistons are just an extension of the offset lobes of the crankshaft. This is also true in regards to a rotor and eccentric shaft. When the lobe rotates upward, the piston goes up. When the lobe rotates down, the piston goes down. Every time it moves one way is considered a stroke. In a 2 stroke engine, all 4 phases or cycles of the combustion process are completed in only 2 strokes of the piston, 1 up and 1 down. This is only 1 complete revolution of the crankshaft. In a 4 stroke engine, it takes 4 strokes of the piston, up, down, up, down to go through the complete combustion process. This is 2 complete revolutions of the crankshaft.
It's all a very simple mathematical relationship. Now lets go look at the workings of a rotary engine. If we look at a rotary engine eccentric shaft and compare it to a piston engine crankshaft, we see essentially the same piece. Both have lobes and because of this both engines will have a stroke length, even the rotating rotary. It doesn't matter if it is a piston going back and forth or a rotor going round and round. The crankshaft motion remains the same. On a rotary engine, the rotors are spinning at exactly 1/3 the speed of the eccentric shaft. From the time that the air entering one chamber goes through the combustion phases to the time it leaves the engine from the same chamber (rotor face), the eccentric shaft has gone around 3 complete times unlike a 4 strokes 2 times or a 2 strokes 1 time. If we do the math we see that the lobes of the eccentric shaft must have gone up and down 6 times (up, down, up, down, up, down). Since it does this process the exact same way every time for every rotor face, it is a 6 stroke engine. That�s right the rotary engine is a 6 stroke! Do not confuse these strokes with the 4 internal cycles that every engine has!

Let's sum this up in a simple chart to visually explain how this works: 2 stroke engine (up, down) - 1 complete crankshaft revolution. 4 stroke engine (up, down, up, down) - 2 complete crankshaft revolutions. 6 stroke (rotary) engine (up, down, up, down, up, down) - 3 complete crankshaft (eccentric shaft) revolutions. See a pattern? All of these engines though are still 4 cycle engines! They are different stroke engines though so the amount of work they do per time is very different. A 2 stroke engine does twice the work per amount of time that a 4 stroke does. Don't believe me? Go race 2-80cc motorcycles, 1-2 stroke and 1-4 stroke and see who wins! This must mean that the rotary engine does the least amount of work per time than both other engine types. Yes it does. But, unlike a piston engine, it uses 3 sides of it's piston (rotor) at a time. In reality it makes no difference if we have 1 rotor with 3 usable faces or 6 rotors with 1 usable face each as in a piston engine.
Here's a little info on how to properly figure out displacement on a rotary engine. Everyone argues that it is really a 1.3 liter while others argue that it is really a 2.6 liter engine. They are both wrong! If we look at how a piston engines volume is calculated we arrive at a displacement based on total swept volume of every piston added together. It is not based on rpm. On a rotary, displacement is figured using one rotor face in one complete revolution then multiplied by 2. This only leaves the total for 2 combustion chambers though and the rotary has 6! Since the volume of a 13b rotary is rated at 1.3 liters (only 2 combustion chambers) it really adds up to 3.9 liters!!! I can hear it now, "...but we only have 2 rotors!" So what! Like I said it makes no difference if there are 2 rotors with 6 faces or 6 rotors with one face each. the total is always 6 and the base numbers are only based on 2 chambers. The rotary merely does 3 times the work in a package 1/3 the size. It's just a 3.9 liter engine crammed into a 1.3 liter body. Just so none of you start a fight over this, I will explain this later so don't chastise me yet!!! In case anyone is curious I did some math to determine what the 13B rotary would be sized at if it were a piston engine.
The results are pretty neat. First of all the rotary would be a 3.9 liter, 6 cylinder engine. It would be a 6 stroke. Each cylinder would be 6.54" across (damn big piston!) but the stroke length would only be 1.18" in length peak to peak. Not much there. Interesting isn't it. Now just imagine a way to make all this work with only 2 intake runners! In all fairness to the terms I have used, the word "stroke" can be interchanged with the word "cycle" since both technically have the same definition. The terms "periods", "quarters", or "phases" can also be used correctly. I merely wrote it the way I did to get a certain mental picture going. I have already dealt with why the rotary engine is really a 6 stroke engine and why displacement is really 3.9 liters and not 1.3 liters. Now I need to explain why the rotary engine doesn't have the torque or horsepower of a good 3.9 liter engine or why it doesn't get the gas mileage of a 1.3 liter engine. The world has always wondered so here's why. Remember that I stated that the true displacement of the rotary engine, if figured out according to the way piston engine volumes are calculated, is according to the total number of rotor faces and not the number of rotors, nor does it have anything to do with rpm. This added up to 3.9 liters for a 2 rotor 13B engine and not the published spec of 1.3 liters. They just crammed all 3.9 liters into a 1.3 liter body. If the engine is really a 3.9 liter engine then why doesn't it have the low end torque of a 3.9 liter engine? This has a very simple answer. Lack of leverage.
OK, what the hell does that mean? First of all we must figure out what a lever is. It is a device that multiplies mechanical advantage over an object to do the same amount of work with a smaller amout of effort. Another way to look at it is to do a greater amount of work with the same amount of effort. It's the same thing. Let's look at leverage differences as an example in a piston engine. What happens to a piston engine when we make it a "stroker"? Ignoring a host of other variables, it gains torque. It also gains horsepower but they are both a fixed mathematical ratio between each other and you can't increase or decrease one without the other. Why did it gain torque? Greater mechanical advantage or leverage over the crankshaft. The reason being is that on a �stroker� crankshaft as opposed to the stock crankshaft, the lobe centerline is farther out from the rotational centerline of the crankshaft. This increases the leverage that the piston has over the crankshaft. Don't believe me? Try this. Get a short pole and hold it at the end straight out away from your body. Attach a 10 lb weight to it exactly 1 foot away from your hands. The weight is exerting exactly 10 ft. lbs. of torque on your hands. Now move that weight out away from you to 2 feet away from your hands. Now the same weight is exerting 20 ft. lbs. of torque on your hands. You have just in essence made a "stroker".
Now let's get back to the engine. Now we know that the greater the stroke length, the greater the engine torque. As I stated, the rotary engine only has an effective stroke length of 1.18". My weed eater has that! There is not very much mechanical advantage over the eccentric shaft. This still doesn't explain everything though. Remember, I stated that if the 13B rotary were a piston engine it would have pistons 6.54" across. Now we just discovered another enemy of efficiency, flame front speed. When the spark plug ignites the mixture in the engine, it doesn't just ignite everything all at once. The spark ignites at the plug and then has to travel outward away from the plug at a certain rate of speed. While this only takes milliseconds, this amount of time gets more critical the higher the rpm gets due to the shorter amount of available time. The result is that as rpm's rise efficiency decreases. The larger the area of the piston, the farther the flame front has to travel and the greater the chance that all of the mixture does not get ignited when it should. Just can't go far enough fast enough. Today�s rotaries have 2 sparkplugs per chamber to help combat this problem. Varying their ignition time in relation to each other even helps somewhat with power and emission. That's right they don't necessarily fire together even though they are in the same chamber. This can get complex so I will not deal with it at this time. Some race engines even have 3 plugs per chamber to improve efficiency and ignition wave front speed. On piston engines, Mercedes has capitalized on this and uses 2 plugs per cylinder in some of their higher end cars. Do they know something others don't?

There is also one more aspect that affects it. Remember that the rotary is a 6 stroke engine. A 2 stroke engine does twice the amount of work per amount of time that a 4 stroke engine does. A 4 stroke engine does 50% more work per amount of time that a 6 stroke does. The rotary engine does less work per eccentric shaft rotation than your typical 4 stroke counterpart. All of these characteristics combine to make an engine that has relatively little low end power and needs to be revved up to be truly powerful. I make it sound like we should have less torque than a 1.3 liter engine due to the above reasons. This isn't true though. Remember that we still have a 3.9 liter engine even though it only uses 2 lobes on the eccentric shaft. We should not expect to develop the torque numbers of a 1.3 liter engine. It should settle in somewhere around 50% less than a 3.9 liter engine which would put it around equal to a 2.6 liter engine in power. These traits of the rotary engine are also why the engine gets worse gas mileage than your typical 1.3 liter engine. Hell it gets worse gas mileage than your typical 2.6 liter engine. Another aspect that affects this is port timing and duration. If we had a piston engine of 2.6 liters in size that had the same intake and exhaust timing as the rotary then it would get comparable gas mileage to the rotary. The 12A/13B rotary though have much more exhaust duration than intake duration due to the peripheral exhaust port location. This contributes to several factors which decrease efficiency. Exhaust gas dilution is one of them. For each stroke there is a small amount of overlap. The exhaust ports and intake ports are open to the same chamber at the same time for a short amount of time as measured in degrees of eccentric shaft rotation. The higher the rpm's the less important this becomes since air velocity will generally keep the gasses where we want them to go. At lower rpm's though, the intake and exhaust air velocity is not very high. This will cause some exhaust to go back through the combustion chamber again. When this happens volumetric efficiency decreases and there is less room for fresh air to fit inside the combustion space. Also this re-circulated exhaust gas is very hot. A hotter air molecule is larger than a cold one which means a fewer number of molecules can fit in the same area per amount of pressure exerted on them. Another aspect of the rotary's peripheral exhaust port configuration that contributes to less low end power and greater fuel consumption is its incredibly long duration or time it is open for. Unfortunately when we make the port bigger we also change it's timing. We don't have the luxury of being able to mill out a head to accept a larger valve while still being able to use the same cam. The timing is really only optimized for high rpm use. We are leaving it open for too long which gets back to the whole overlap problem. Again, all of this is just a generalization and can be affected by how well the intake and exhaust flow and how well they can scavenge. The affects of scavenging, intake design, Helmholtz effect, and proper exhaust design are all out of the scope of this article.
So just assume it is an even world. Luckily there is a cure for this. It is called Renesis! It is the new 13B based rotary engine in the new Mazda RX-8. The exhaust ports are no longer in the periphery of the chamber but have rather been moved to the side housings. This allowed the designers to more appropriately optimize the port timing duration. The location also allows more port area leaving the engine. So now we have more area to flow air out of faster. This new location also completely got rid of the port overlap. There is actually 64 degrees of dwell. This amount of dwell was originally greater in the early test engine called the MSP-RE since it had the intake timing of the '84-'91 n/a RX-7's 6 port engine. However dwell is only useful if you just have enough to get the job done but not so much that you are getting losses from it. Because of this Mazda engineers learned that they could open the intake earlier than previously and still maintain all of the other good aspects of the new exhaust layout. A bigger intake port = more time for air to enter and a greater CFM rating through the port. Less turbulence through the port as well. Less overlap gives us less dilution of the intake air and a cooler intake charge. More available room for incoming air. Volumetric efficiency increases. Since efficiency goes up, our use of gas gets more efficient. In other words it takes less fuel to do the same amount of work.
What�s the result? Better gas mileage. With today�s gas prices this is a very welcome thing. The efficiency increase also means that emissions characteristics are also improved -another bonus with today�s laws concerning air quality. So after reading this you are probably wondering why in the world anyone would want to use one of these engines. First and most obvious is size. They crammed a 3.9 liter engine, or more appropriately a 2.6 usable liter engine into a 1.3 liter body. Second, it is just such a simple design. There are only 3 moving parts. Fewer moving parts have less frictional losses. Also fewer moving parts have less chance statistically of failure. The more it moves the more chances you have for failure. Third, nothing moves back and forth. So what? A piston stopping and changing direction exerts a lot of stress on everything from the crankshaft to the connecting rods, to the pistons, to the wristpins, etc. Let�s not also forget the stresses on the valves for being slammed open and shut as well as the temperature extremes they see during the combustion cycle. A body in motion tends to stay in motion. It is a very unnatural act to change direction suddenly or at all for that matter. A rotary just spins away in the same direction. Yes the lobes of the eccentric shaft do see stress but remember that we don't have very much leverage over them. The rotors are also exerting some of their rotational stress on the stationary gears as well so some stress is never transmitted to the eccentric shaft from the rotors. The lack of stroke length and pure rotational motional do make it very naturally adapted to high rpm use. If we look at really high horsepower piston race engines, their stroke length has been shortened to reduce the stresses to all of the engine components at high rpms. The last and most important reason why the rotary engine is still a popular engine despite its shortcomings is because it is different.
There is always something to be said for individuality and uniqueness. If you own a piston engine it doesn't matter how big it is or if it is made by Chevrolet or Honda. It is still the same device. Just to shoot down right now any arguments on displacement think about this: The 13B rotary engine is a 1.3 liter. Yes. The 13B rotary engine is a 2.6 liter. Yes. The 13B rotary engine is a 3.9 liter. Yes. Notice that all of these statements are TRUE!!! That's right there is a truth to all of those statements. Go read the whole thing again. To understand why this is so, lets define truth. Truth can be defined in a couple of ways: Anything that is not false (none of those statements is) or it can be defined as: One's individual interpretation of presented facts. This herein is the source of our debate. We can't change the facts no matter how hard we try. Arguing won't do it. What is debatable however, is each individual's interpretation of facts. If your interpretation doesn't match someone else's, you argue about it. Here are the facts: The rotary engine as rated by Mazda is 1.3 liters because each individual rotor, following one face of one rotor through the complete cycle, has a swept displacement of 654cc or .65 liters. Multiply this times 2 rotors to achieve 1.3. Since this only accounts for 2 of the total of 6 rotor faces, we multiply our answer by 3 to get an actual displacement of 3.9 liters. However since the rotary engine is a 6 stroke engine and not a 4 stroke engine since it takes 3 complete eccentric shaft revolutions to fire all faces instead of the typical engine's 2, it only does 66% the work of a 4 stroke 3.9 liter engine. Calculating for this we divide 3.9 by 1.5 to get a total of 2.6 liters equivalent work to a 4 stroke piston engine. All of these, from a 1.3 liter in physical size package. No one can argue that this is not correct and any response saying otherwise will have been explained by what I just said. Any debate will only focus on one aspect and not the total facts. Just to put a cap on this whole thing: If at any time you try to calculate proper sizing for a turbo, intake manifold runners, intake plenum size, exhaust size, etc, and you try to use the 1.3 liter number in your equations, you will be way, way, way off!!!!!!!!! There are only 2 ways to flow more air: increase displacement or increase rpm. A 1.6 liter Honda engine doesn't flow anywhere even remotely near what a 13B (1.3 liter) flows per the same rpm. Just some food for thought.

Note: Fred "RotaryGod" Swain Published on http://www.myrotarycar.com.

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However

Another way to look at it is...

Rotary Displacement

As rotary engine enthusiasts, we all know the obvious, intoxicating charms of Wankel wonder. Unique, unusual, lightweight, compact, high revving, what�s not to like? One of the most commonly deliberated subjects is �what is the rotary engine�s displacement�? An excellent question. Here�s our best to make the case for the engine�s displacement.

Conventional reciprocating engines are the standard that most relate to. We all know that these engines are measured by measuring the area of the bore, multiply by the stroke and then multiply by the number of cylinders. Simple as that.

For simplicity, we�ll use the 13B engine as the standard we�re calculating. You can use these ideas and apply them to a 12A or 20B yourself. The rotary engine is obviously unique. The engine has two rotors shaped roughly like a triangle. This makes for three combustion faces per rotor and a total of six for a standard two-rotor engine. Each face has a �swept volume� or displacement of 40ci(654cc) and there are a total of six faces. With this known, the engine displacement should be 40ci(654cc) times six to equal 240ci(3.9L), right? In a way, yes, but that would not be a comparable displacement to the 4-cycle engine.

The key for comparing the displacement between the 4-cycle engine and the rotary engine is in studying the degrees of rotation for a thermodynamic cycle to occur. For a 4-cycle engine to complete every thermodynamic cycle, the engine must rotate 720� or two complete revolutions of the crankshaft. The rotary engine is different. The engine rotor rotates at 1/3 the speed of the crankshaft. On two rotor engines, front and rear rotors are 180� offset from each other. Each rotation of the engine (360�) will bring two faces through the combustion cycle (the torque input to the eccentric shaft). This said, it takes 1080� or three complete revolutions of the crankshaft to complete the entire thermodynamic cycle. Obviously, we have a disparity. How can we get a relatable number to compare to a 4-stroke engine? The best way is to study 720� of rotation of the two-rotor engine. Every 360� of rotation, two faces of the engine complete a combustion cycle. 720� will have a total of four faces completing their cycle. 40ci(654cc) per face times four faces equals 160ci or 2.6L. That�s a well-reasoned number and now gives us something to be able to compare to other engines. In addition, since four faces passed by in the comparison, it�s like a four cylinder engine.

Now we know, the 13B compare well to a 2.6L 4-cylinder 4-cycle engine.