You'll understand everything about Atkinson, Miller and Otto cycle engines after watching this video

Автокөліктер мен көлік құралдары

A typical four stroke engine or an Otto cycle engine does intake, compression, combustion and exhaust. The Atkinson cycle and the Miller cycle engines also do intake, compression, combustion and exhaust, however they differ in a small but very important detail which allows them to be significantly more efficient than the Otto combustion cycle. And in this video we will dive back into the history of engines in order to see and learn about the evolution of the combustion engine and the difference between four stroke Otto, Atkinson and Miller cycle engines .
The Otto engine as we know it today was invented in 1876 by German Nicolaus August Otto.
Although it doesn't seem that way the 1876 engine has many of the elements we see on engines today and is Otto's first true four stroke engine. There's a crankshaft, a connecting rod and even a camshaft. Inside we have a piston and the engine does intake, compression, combustion and exhaust just like any modern engine.
Of course Otto's first engine was an instant commercial success and of course Otto patented the design. Now this, the patent, is what brings us to Mr . James Atkinson, who like many of his contemporaries, after seeing the commercial success of the Otto engine, started developing his own engine. Now the catch is that in order to be commercially viable such an engine had to be different enough from Otto's design in order to not infringe on the patent rights.
Now Atkinson decided that the compression stroke of the Otto engine was actually something that could be improved upon, and that was to be done by reducing the length of the compression stroke in relation to the length of the combustion stroke, or the expansion stroke as some call it. In other words the engine would spend more time making power than wasting power on compressing the air fuel mixture.
In 1957 US engineer Ralph Miller patented the Miller Cycle engine. Now the Miller Cycle engine relies on the same concept as the Atkinson engine and that is to reduce the power sapping effects of the compression stroke. The big deal is that Ralph Miller chose a much simpler and much more elegant solution compared to the extremely complicated set of rods and linkages from Atkinson's original design.
And the solution is this: keep the intake valve open longer. That's it. The construction of the engine stays absolutely the same as that of a conventional Otto engine, the only thing that differs is the valve timing. A conventional Otto engine closes the intake valve before the compression stroke begins. This is done in order to ensure that the entire length of the cylinder is used to store and compress the air fuel mixture leading to optimal power output. The Miller engine doesn't close the intake valve when the compression stroke begins. The intake valve is kept open during the first 20-30% of the compression stroke. An open intake valve of course means that the upward motion of the piston simply pushes some of the air fuel mixture back into the intake manifold. The piston can't compress anything until the intake valve closes.
In fact in the late 90s Mazda put this exact concept into practice with their KJ-ZEM engine which they installed into the Mazda Millenia / Xedos 9 /Eunos 800. The KJ-ZEM was a supercharger 2.3 V6 running the Miller Cycle.
Right after the Mazda Millenia was discontinued Toyota revived the concept behind the Atkinson/Miller cycle. Toyota's foray into this field started in 1997 with the very first generation of the Toyota Prius and it's 1NZ-FXE engine. But this time instead of a supercharger we have an electric motor which is used to make up for the lack of torque and responsiveness. As we know electric motors produce instant torque and they don't sap the power of the engine like superchargers do which means that hybrid drivetrains and the Atkinson cycle are a match made in heaven which was put into practice in all of Toyota's hybrid vehicles. Now another advantage that modern technology has brought is variable valve timing or VVT. This makes it possible to run the engine in the Atkinson cycle only when this is desirable, which reduced load conditions such as highway cruising.
Now Toyota's usage of the Atkinson cycle is perhaps the most popular to date, but Mazda definitely hasn't given up and they employed the Miller cycle yet again in a fashion similar to what we have seen in the Mazda Millenia. This time it bears the name Skyactiv-X and in addition to a small roots supercharger and the Miller cycle the Skyactiv X is also the first ever commercial engine to have Spark Controlled Compression Ignition or SCCI.
A special thank you to my patrons:
Daniel
Pepe
Brian Alvarez
Peter Della Flora
Dave Westwood
Joe C
Zwoa Meda Beda
Toma Marini
Cole Philips
00:00 The road to compression
08:15 Atkinson
14:05 Miller
18:04 Mazda and Toyota
#d4a #atkinson #enginebootcamp

Пікірлер: 1 500

  • @d4a
    @d4a Жыл бұрын

    100 cars that changed the world: amzn.to/3DGXDf6 Stem engine model: amzn.to/3Y5iZLv 1-2-3 count with Car parts: amzn.to/3jxP7Z6 Patreon: www.patreon.com/d4a

  • @jububoobaroo67

    @jububoobaroo67

    Жыл бұрын

    Thank you for explaining how single attribution neglects credit to what is often a long collaborative effort. Michelson, Lorentz and Poincare should always be mentioned when Einstein is for example. He gave them no credit and stole their works as his own.

  • @NickShl

    @NickShl

    Жыл бұрын

    You look on Atkinson engine only from one point of view. Thinking that it reduces intake stoke is wrong. Have you touched exhaust pipe? Hot, right? That is because there some energy left. What if we will be able to catch this energy somehow... may be we can make power stroke longer, give exhaust gases more space to expand? But wait! That exactly what Atkinson engine does!

  • @Danger_mouse

    @Danger_mouse

    Жыл бұрын

    Thanks for another great video 👌 19:15 I was lucky enough to be working for a Mazda dealer in Australia where we were Eunos agents. We had several Eunos 800Ms that we serviced and they were amazing cars to drive, and also for the owners. They were beautifully made, nothing went wrong, ever... We just serviced them as per the service schedule and sent them back out on the road. Mazda claimed of them back in the day, more power and torque than the 3.0 JE V6, better fuel economy than the KF 2.0lt. Our owners certainly reported they were good on fuel. I actually loved the Eunos range, the little 30X hatch with the 1.8 V6 was great fun, and the 500 hardtop was a nice looking contemporary car for the time, very unique. Maybe you could do a video on the Japanese luxury era with the RISE of Lexus, Eunos, Acura and Infinity... 🤔

  • @Danger_mouse

    @Danger_mouse

    Жыл бұрын

    @@NickShl He mentioned that, however the fact remains that part of the compression stroke is lost and power is reduced.

  • @Tetraden-a

    @Tetraden-a

    Жыл бұрын

    Wait a second... Why do you look almost like Nicolaus Otto? O_O

  • @seanlovi8798
    @seanlovi8798 Жыл бұрын

    I can't believe am getting this education for free, it's almost illegal.

  • @makantahi3731

    @makantahi3731

    Жыл бұрын

    then donate some money to be legal

  • @jcorkable

    @jcorkable

    Жыл бұрын

    Please, don’t give the government any ideas.

  • @orangejjay

    @orangejjay

    Жыл бұрын

    @@jcorkable lol big bad "the government" better watch out! They'll get ya!

  • @litutheking6646

    @litutheking6646

    Жыл бұрын

    Illegal😂

  • @pickipanfil6042

    @pickipanfil6042

    Жыл бұрын

    Selling education should be illegal...

  • @ozfugs
    @ozfugs Жыл бұрын

    This probably won't mean much to anyone else but I remember finding a Japanese guys personal university webpage back in the mid 1990's. I'm not sure if he was a professor or a student but it was like an encyclopedia for Japanese car technology of the time. He had excellent technical explanations and diagrams for all kinds of things. You could tell the guy loved the topic and loved sharing how it worked. That was part of my introduction to the Internet and even though the site is long gone I still have fond memories. And this channel reminds me of that. It's the same kind of intelligent and passionate effort. The same kind of enthusiasm. And it's cool to see how the delivery format has evolved from basic text to full on edited videos with 3d animations. I really enjoy this channel and appreciate the work that goes into it.

  • @d4a

    @d4a

    Жыл бұрын

    Believe me, it means a lot to me. Btw I have very fond memories of the early days of the internet too

  • @demef758

    @demef758

    Жыл бұрын

    AND, he can pronounce all of the funny foreign names that none of us can!

  • @robertgift

    @robertgift

    Жыл бұрын

    Why is the site gone?

  • @Thinkle911

    @Thinkle911

    Жыл бұрын

    @@demef758 He is indeed doing it very well! It's not the ususal "wet" and "sloppy" American/english interpreatiation of letters, but pretty much to the point normal german or french, only "Yougene Langen" was a bit off, it should have been Oigen Langen, Like in oil and a G like in graphics.

  • @Videoswithsoarin

    @Videoswithsoarin

    Жыл бұрын

    have you tried finding it on the way back machine???

  • @chiefdenis
    @chiefdenis Жыл бұрын

    I dont think I've ever seen a bad video from this guy, been here almost/roughly 3 years, and this guy is the GOAT of mechanical KZread school, no one explains things quite like him, and I've seen everything.

  • @sallehsallehnewton3258

    @sallehsallehnewton3258

    Жыл бұрын

    The naked engine is a bad video

  • @chiefdenis

    @chiefdenis

    Жыл бұрын

    @@sallehsallehnewton3258 eh, i beg to differ

  • @hoganfan924
    @hoganfan92411 ай бұрын

    Good video. Ralph Miller’s original idea was to close the intake valve well before BDC to increase efficiency. He wrote about this (as I recall) in a 1948 ASME paper. I read his paper 25 years ago while working on VVL/VVT concepts for Chrysler. This works very well for low load efficiency (up to about 8% improvement), due to virtual elimination of the pumping loop by running unthrottled, and is what BMW Valvetronic and Fiat does Multi-air to run “unthrottled.” A guy at GM named Don Stivender did research on extremely low lift cams in the 60’s, and another GM guy named Tuttle made very short duration cams (with more normal lifts) in the early ‘80’s, testing Miller’s original concept. Tuttle also ran very long duration cams to control load (testing the later miller approach) Stivender claimed a 5% improvement in efficiency, and Tuttle around 8%. Stivender called his very low lift the STIVE cycle (Sonic Throttling Intake Valve Engine). Very clever! I built some very short duration cams with moderately low lifts to verify the blended “Stivender & Tuttle/Miller” with the very early intake valve closing concept in our 1.6l “Tritec” engine in 1999/2000 and verified the concept could deliver about 6-8% lower BSFC unthrottled. Most folks (even engine guys) didn’t understand how this works, but the evidence is right in the P-V diagram, and the virtual elimination of the pumping loop. Here’s are links to Tuttle’s 1980 & ‘82 SAE papers(I couldn’t find Miller’s): www.sae.org/publications/technical-papers/content/800794/ www.sae.org/publications/technical-papers/content/820408/ Here’s Stivender’s paper: www.sae.org/publications/technical-papers/content/680399/

  • @jackreacher7183

    @jackreacher7183

    6 ай бұрын

    Great message and refences.

  • @tomconner5067

    @tomconner5067

    6 ай бұрын

    Let me begin by stating that your comment obviously indicates an impressive understanding of the compound processes and coordinated functions of internal combustion engines and the incentives behind the R&D by engine manufacturers. There are other viewers that demonstrate an understanding of the mechanical action, and some guys are on point, but this is the first time someone commented and there was no tunnel vision, or inaccuracy, without an air of bias or disapproval.

  • @tomconner5067

    @tomconner5067

    6 ай бұрын

    I see that some information sources shoot the concepts in the foot from the sidelines and do not back up their claims with any evidence, but rather stand behind the concept that they are correct if they can not be proven to be incorrect, or the opposite of what they state can not be proven ( it’s a form of industrial censorship backed by astrophysicists to make outrageous claims that make you either wonder if they’re jerking your chain or need a vacation at an inpatient behavioral research facility yet you must accept their subjective input if there’s no sound evidence against it, or no accepted standard or understanding exists to debunk the authenticity of their nonsense. It appears to be a blackloophole. A system of abstract speculative skepticism, used as a snubber by sandbaggers.

  • @hoganfan924

    @hoganfan924

    5 ай бұрын

    @@tomconner5067 Thank you for the kind comment. The engine development work I did at Chrysler from ‘97-2000 was the most technically challenging, mentally stimulating and rewarding work of my 35 year career in the auto industry, and I had a lot of tough, innovative and interesting projects. I loved doing advanced side projects like the VVT/VVL studies. I authored a white paper on that work, that I hope had an impact and laid the groundwork for future development.

  • @DC-rn1fc

    @DC-rn1fc

    2 ай бұрын

    Wait a second ... what sort of engine guy doesn't understand dethrottling? The highload-benefits are a tad harder to grasp, and only work really well with boosted engines. There, one could see the concept outsource a part of compression without impacting expansion. Outsourced to the compressor (be it attached to a turbine or driven by the crankshaft), cooled inbetween, thereby lowering p and T, yet having the same amount of charfe inside. That way, knock is countered, and that allows to either collect an improved efficiency at high load, or to increase the geometric compression ratio, thereby expansion ratio, thereby efficiency. But, as stated, this only applies to boosted engines - naturally aspirated ones, would lose a great deal of torque and power, if run on that mode, ... fits some applications, like Toyota's hybrids, but, there, these engines only are so successful because nobody really took them on - a similar drivetrain with a higher-tech ICE would outperform a prius in any regard. Anyway, the mid-load region is the only one where you won't benefit much from a variable valvetrain, be it two or three steps with a lobe each, or continuously like BMW made it ... the nicest VVT I found so far is Nissan's - I've had the very same idea, but came across it in a book that sums up a converence on VVTs (there were annualy ones when this was considered one of the three major promising paths - Downsizing, Stratified load and dethrottling by variable valvetrain), and thought ... cool, some dude in Japan had the same idea and actually made it happen. Nice! Got a more complex, but still better one up my sleeve any day, that could even spare an intake cam phaser, if some parameters match up. Anyway, I get that understanding the concept of outsourced compression and inbetween cooling may be a bit un-intuitive, but dethrottling, while sometimes hard to apply in reality, the basic principle is fairly easy to grasp...

  • @_monti142
    @_monti142 Жыл бұрын

    i needed this video so much, nobody explains engines better than you on youtube, many thanks :D

  • @ddegn

    @ddegn

    Жыл бұрын

    I'm not a "motor head" myself but I love the videos on this channel.

  • @IllusionSector

    @IllusionSector

    Жыл бұрын

    @@ddegn I'm gonna close my eyes and picture the words coming out of Christoff Walz's mouth.

  • @ralphwarom2514

    @ralphwarom2514

    Жыл бұрын

    This video reminds me to not take forbgranted what we have now. Its crazy how gold stuff I today compared to the early days of the ice

  • @tarstarkusz

    @tarstarkusz

    Жыл бұрын

    What is in this video is wrong and right, but more wrong. You absolutely need compression to get high thermal efficiency. Compression is why diesel engines are so much more efficient than gasoline engines. Large expensive diesel engines powering things like container ships or desiel locomotives can reach 50% thermal efficiency Compression does not merely improve power, it improves efficiency.

  • @ddegn

    @ddegn

    Жыл бұрын

    @@tarstarkusz "You absolutely need compression to get high thermal efficiency." I thought the need for compression was stated in the video? The question is how this compression is achieved. The compression can be achieved using a supercharger rather than using the entire compression stroke. I don't know why compressing using a supercharger has advantages but I doubt Mazda would add this complication without having a good reason.

  • @jimosborn390
    @jimosborn390 Жыл бұрын

    Excellent explanation. When I was learning I was taught efficiency is related to compression ratio. Later I discovered it is really a matter of expansion ratio. Atkinson/Miller cycles let you have an expansion ratio much larger than an Otto cycle.

  • @makantahi3731

    @makantahi3731

    Жыл бұрын

    it can be monitored on 2 ways: 1. burning efficiency-higher pressure, higher efficiency, and 2. expansion efficiency: as nearer to atmospheric pressure/temperature as more efficient, so max eff will be if both are high: high pressure on the end of compression(start of combustion) and longest/expansion to the lowest temp/press on the end of expansion stroke

  • @ahobimo732

    @ahobimo732

    Жыл бұрын

    Thank you! I finished the video, and for the life of me, 8 couldn't figure out why a supercharger wouldn't just cancel out the increased efficiency of a Miller cycle engine. Your comment finally cleared it up for me. 👍

  • @keithyinger3326

    @keithyinger3326

    Жыл бұрын

    @@ahobimo732 that's what I couldn't wrap my head around either. Sure the Atkinson cycle is sucking in air and then expelling some of it, but if you add in a supercharger and crammed even more air in there, then wouldn't that higher pressure charge of air be harder to compress than the usual charge of air? I would think that extra force it takes to compress the tire pressure charge of air would cancel out the benefits of having a shorter compression stroke.

  • @ahobimo732

    @ahobimo732

    Жыл бұрын

    @@keithyinger3326 I think the key is what Jim already said: it's not reduced compression that matters, it's increased expansion. The supercharger can raise the compression and the engine will still acheive improved efficiency, IF it has a longer expansion stroke.

  • @ferrumignis

    @ferrumignis

    Жыл бұрын

    Both things are true, thermal efficiency is linked directly to compression ratio, but having an expansion ratio greater than the compression ratio also benefits efficiency.

  • @kristianhermann5971
    @kristianhermann59719 ай бұрын

    On efficiency, it's worth mentioning the added power with Otto allowed for engine downsizing too - so on a HP-to-HP basis, added efficiency with an Atkinson required a larger engine - awesome history lesson!

  • @zazugee

    @zazugee

    24 күн бұрын

    efficiency is thermodynamic efficiency and it's related to the type of cycle, it have nothing to do with the downsizing the generan efficiency is real world one and you can impact it by reducing weight ...etc

  • @ishtiaquehussain2265
    @ishtiaquehussain2265 Жыл бұрын

    Thanks a lot, man! You are unbelievably good at explaining complex engineering topics. Please know that we really really appreciate your channel, your videos and everything that you do for us. Wish you all the best for the future!

  • @that1guyonpoint213
    @that1guyonpoint213 Жыл бұрын

    Another great video. As a mechanical engineering student you've taught me way more than any class ever could!

  • @DuaneKerzic

    @DuaneKerzic

    Жыл бұрын

    You really need to pay attention in thermodynamics as this guy got it all wrong.

  • @eli6394

    @eli6394

    Жыл бұрын

    @@DuaneKerzic What did he get wrong? In my thermodynamics class we analyzed the Otto and Diesel cycles within a control volume and neglected energy loss, energy in and out, and mass in and mass out . We solely focused on the changes in temperature and pressure within the control volumes to keep things simple. The video doesn’t go into depth about the chemistry and thermodynamics but his approach is realistic and applicable. I didn’t notice anything wrong about the information in this video but I could have missed something. 🤷🏽‍♂️

  • @DuaneKerzic

    @DuaneKerzic

    Жыл бұрын

    @@eli6394 In my thermodynamics classes, we learned how to analyze the Carnot, Otto, Diesel, Stirling, Ericsson, Atkinson, Miller, Brayton, Rankin, 2 cycle internal combustion engines, along with the effects of turbo and super charging (with and without intercooling), economizers, super heat, reheating, and much more. He got the linkages correct. But the linkages aren't why an engine makes power. They make power by extracting heat from a gas due to the expansion of those gasses. As we know efficiency of an otto cycle is proportional to the compression ratio of the engine, the compression stroke doesn't rob power from the engine. In the case of the Atkinson and Miller cycles the efficiency closer to the expansion ratio of the engine. The reason these cycles were developed was to allow greater expansion ratios while still using externally mixed low octane fuels to control knocking and preignition which is limited by the compression ratio. The 'super charger' in the Miller cycle wasn't replaced by an electric motor. There were naturally aspirated Miller engines in constant speed use before Toyota and Mazda. Which is basically how they are used in hybrids with generators and CV transmissions. The reason for the electric motor is to allow for a lower power, lighter, smaller displacement, high efficacy engine that runs at a constant speed and constant power most of the time. An auto only needs full power for very short periods of the drive cycle such as starting from a stop, climbing steep hills. I could go on.

  • @magnusgustavsson6475

    @magnusgustavsson6475

    Жыл бұрын

    @@DuaneKerzic I agree with you point on thermodynamics, It is the longer expansion cycle that gives a more complete combustion. About Toyotas hybrids, I think he meant that the supercharging is replaced by the electric drive at low rpms of the engine.Basically, the engine i an hybrid can work on a single rpm so there is no need for a responsive and low torque engine there.

  • @DuaneKerzic

    @DuaneKerzic

    Жыл бұрын

    It has nothing to do with how complete the combustion is. In our regular gas engines we aren't allowing unburned fuel to be exhausted. We just aren't expanding the gas after heating it as much.

  • @eTiMaGo
    @eTiMaGo Жыл бұрын

    I guess Toyota didn't want people to think "It's Miller time!" about their engines :D Seriosuly though, thanks again, I knew the basic conceptual differences between these engine types, but you have brought me a new level of understanding :)

  • @jasperrodrigues7026
    @jasperrodrigues7026 Жыл бұрын

    Goodness GRAVY! You are unbelievably good at explaining and illustrating things. I can only imagine how much time and work you put into honing your skills and knowledge. Thank you so much for posting your videos and sharing your knowledge with the rest of us. - Jasper

  • @reneneron2971
    @reneneron2971 Жыл бұрын

    Great video. Not all Toyota hybrids use the Atkinson cycle engine in their hybrids; the 3MZ hybrid engine does not. Further, Toyota will often increase the base compression ratio on an engine used in the Atkinson cycle model so that the effective compression ratio is similar to the Otto cycle version (an example being the hybrid 2AR-FXE versus the standard 2AR-FE). The camshaft profiles and valve timing are different as well. With proper engine management, the 2AR-FXE can be operated as an Otto cycle engine to gain power with a loss of efficiency with higher octane fuel. There is still a loss of power with the Atkinson cycle compensated for by the electric motor, but improved efficiency. Detonation (and octane) limits the practical compression ratio of any gasoline ICE engine.

  • @chicken29843

    @chicken29843

    Жыл бұрын

    It should also be noted that these engines are not actually driving the wheels in the hybrids.

  • @-Jethro-
    @-Jethro- Жыл бұрын

    I’ve always thought of this more as increasing the power stroke length to extract more usable energy, rather than decreasing the compression stroke. It’s really the same thing, but I believe it better expresses the intent of increasing efficiency. Thanks for the video! Good stuff.

  • @crezychameau

    @crezychameau

    Жыл бұрын

    I also like this way of explaining the concept better :) It is litteraly the concept behind 5 strokes engines

  • @kilura1

    @kilura1

    Жыл бұрын

    Yeah, this is quite important. See, If you have less mass of air + fuel mixture in the end of compression stroke, the pressure and temperature of gasses will be smaller in the end of combustion stroke (compared to OTTO cycle). This can be also achieved by throttling air intake during suction stroke (basically, this is what happens when you release gas pedal, gasses outlet temperature drops down). But this will strongly increase intake manifold resistance => efficiency will be less. Also Mazda's Skyactiv engines are designed to have very big Compression ratio. This allows you to maintain Pc (compression pressure) same as in OTTO engine. (In general, increasing Compression and Combustion pressure leads to increasing of efficiency). Marine Diesel Engines now have gigantic stroke of up to 3.5 meters(!). In order to expand gasses as much as possible thus utilizing as much of energy as possible.

  • @allanallansson9532

    @allanallansson9532

    Жыл бұрын

    Agree! This increase power extraction even overcomes some of the thermodynamically unavoidable losses due to lower compression. Part of the efficiency of diesel engines is their high compression ratio and ethanol mix in in gasoline makes for higher efficiency due to higher octane value which allows higher compression ratio without knock.

  • @chrissmith2114

    @chrissmith2114

    Жыл бұрын

    Pumping losses are the problem with petrol engines, diesel does not suffer from them.

  • @ferrumignis

    @ferrumignis

    Жыл бұрын

    @@chrissmith2114 Even diesel engines suffer pumping losses,they are just lower because they are not usually throttled (though some diesel engines are). The additional pumping losses on a petrol engine occur when the engine is throttled upstream of the intake valves, so the piston is expending energy working against the partial vacuum in the intake manifold/plenum. This can be eliminated by not throttling in this way, instead using adjustable valve duration like the BMW Valvetronic system or Fiats Multiair.

  • @pontifier
    @pontifier Жыл бұрын

    In high school I independently came up with the miller valve timing idea for increasing efficiency of four stroke engines. My reasoning was not to reduce the energy of the compression cycle, but realizing that a combusted fuel takes up much more space than it did before, the power stroke should be longer to allow the piston to reach atmospheric pressure before the exhaust stroke starts.

  • @hitanshupatel2519

    @hitanshupatel2519

    5 ай бұрын

    This is exactly what I was thinking as I watched the video. It is impressive that you thought of that in high school. Did you have formal thermodynamics education?

  • @pontifier

    @pontifier

    5 ай бұрын

    @@hitanshupatel2519 No, but I'm fairly good at making accurate mental models of things and seeing how they behave as parts move and interact. That includes pressures and forces, and I sometimes I can see how and where fluids will flow and things will break. My dreams are accurate enough that I had a dream about driving backward and had to learn how to drive quickly by looking in the rear view mirror. When I woke up, I found that I was able to use what I learned to drive very quickly backward in a real car.

  • @zazugee

    @zazugee

    24 күн бұрын

    yes, i had the same thought when i heard of Atkinson cycle, i never thought it was about reducing compression.

  • @zazugee

    @zazugee

    24 күн бұрын

    thought for natural aspirated it's straight forward, but when you're using a supercharger, it's like you're combining a renkin cycle on top of oto/atkinson-cycle

  • @bravo_cj
    @bravo_cj2 күн бұрын

    ngl I’m totally impressed by the Miller cycle. Such a genius, simple yet effective idea! It’s absolutely beautiful!

  • @ISHQEAMEEN381
    @ISHQEAMEEN381 Жыл бұрын

    This type of video i was waiting for Thank you so much bro Keep it up

  • @jhaluska80
    @jhaluska80 Жыл бұрын

    I have been enjoying the history and engineering lessons you provide on engines. It really helps me understand and appreciate them more.

  • @mikejohnson4617
    @mikejohnson4617Ай бұрын

    Wow, I learned something today! Thanks. Spent 30 plus yrs in engine engineering labs as a technician on Otto engines. As a retiree, have been curious about these other cycles and have never grasped the differences until now.👍 Subscribed.

  • @KO-pk7df
    @KO-pk7df Жыл бұрын

    I have known of these engines for a long time but now I actually understand the difference between them! Thanks.

  • @PaulThomas-qo9vy
    @PaulThomas-qo9vy Жыл бұрын

    Thank you for the BEST comparative explanation of these 3 piston engine cycle types! Very clear & precise!

  • @scampilover00
    @scampilover00 Жыл бұрын

    Would be good to hear more about the sky active technology from this channel, your explanations are unmatched

  • @jackrichards1863
    @jackrichards1863 Жыл бұрын

    This is the most revealing story of engine types I never heard before. Thanks Mr.

  • @maccaberry1041
    @maccaberry1041 Жыл бұрын

    Awesome homage to the internal combustion engine. It's not dead yet and we owe our modern quality of life to this ingenious invention. Thankyou.

  • @AnthonyCelata
    @AnthonyCelata10 ай бұрын

    This is legit the best and most educational youtube channel on the interwebs

  • @tunebyaotphilippines2546
    @tunebyaotphilippines2546 Жыл бұрын

    Learning at its best! 👌🏻

  • @SONO4B11T
    @SONO4B11T Жыл бұрын

    I never bothered to learn these different cycles, cause where i'd read about them, they just made it sound complicated. This video on the other hand, was fun and informative. And who doesn't like a bit of history!

  • @xxw379k
    @xxw379k Жыл бұрын

    Nothing is as meditative as KZread videos about technology. Namaste! 🙏

  • @Raj-nh3fc
    @Raj-nh3fc Жыл бұрын

    Wow, once again thanks. You are raising our knowledge and understanding of IC engines almost vertically. We want more!

  • @patrickfargie1146
    @patrickfargie1146 Жыл бұрын

    My dude, it's 7am here in Tennessee. You can't be posting videos this late 😂 Nevertheless, I'm always here for it.

  • @phatwayne
    @phatwayne Жыл бұрын

    Thanks for yet another topic brilliantly explained.

  • @karlplasser1314
    @karlplasser1314 Жыл бұрын

    Thank you very much! I finally understand how my Ford Galaxy Hybrid can have an Attkinson motor without having funny rods. Your lesson was extremly revealing.

  • @eskiv9505
    @eskiv9505 Жыл бұрын

    I just realized with your vidéo that we French people are the only ones to talk about "Beau de Rochas cycle" rather than "Otto cycle" :). Thanks for the video, high quality explanation as always

  • @francoistombe

    @francoistombe

    Жыл бұрын

    The Brits were adamant that a compression engine like Diesels design was built a decade earlier by a fellow called Ackroyd Stuart. They refused to say diesel and would use compression ignition instead.

  • @charliefoxtrott1048
    @charliefoxtrott1048 Жыл бұрын

    Wow! Just wow! Thank you 4 this!

  • @dimikraa1135
    @dimikraa1135 Жыл бұрын

    as a Owner of a Mazda KL engine, this video makes me happy😊very good content as always!

  • @tommentrak4982

    @tommentrak4982

    Жыл бұрын

    Make me want to go find one of those Milllennia S in a boneyard and grab all the necessary parts and drop it in my old Probe. Way too late by now, but definitely would be a kick in the pants for the old girl.

  • @CheeseFriesAndCoffee
    @CheeseFriesAndCoffee6 ай бұрын

    I'm so happy I found this channel. Your explanations are both easy to follow and interesting.

  • @deano3580
    @deano35805 ай бұрын

    Tried a couple of videos looking for this explanation. This guy has thoroughly nailed it and was by far the best. Clear, to the point, no waffle, good, appropriate graphics

  • @zaidkidwai7831
    @zaidkidwai7831 Жыл бұрын

    Fantastic work my man. Love your videos, explained clearly and concisely.

  • @georges3799
    @georges3799 Жыл бұрын

    Very well presented. I especially enjoyed the historical aspects of engine designs. Would you please, explain how these engines are lubricated? What is happening to the oil in the engine?

  • @abbarasheed8599

    @abbarasheed8599

    Жыл бұрын

    Also to add to your plea, how the engines are cooled too with liquid cooling

  • @liorm2877
    @liorm2877 Жыл бұрын

    Guys totally love watching your reviews. Bought a car (unrevoewed) a few months back, still watching with joy, but this was so super brilliant and I am so happy to see it. Loved it all, but Jim's bit had me in stitches!

  • @c.a.r.s.carsandrelevantspecs
    @c.a.r.s.carsandrelevantspecs Жыл бұрын

    Another fantastic video! I especially appreciate how you differentiate between the Atkinson and Miller cycles and how you explain that in modern engines they are essentially the same in concept and practice. Thanks again! 😃

  • @ericsalmazo481
    @ericsalmazo481 Жыл бұрын

    Unbelievably good content. Thank you for your work.

  • @SwervingLemon
    @SwervingLemon Жыл бұрын

    You're awesome. I was wondering about this last week. Your animations make the concepts very clear.

  • @blairkinsman3477
    @blairkinsman34778 ай бұрын

    Great video identifying the Otto and Atkinson/Miller I was taught that the Atkinson/Miller benefit was two-fold: one was the reduction of waste in compression, but the other was the extension of the expansion stroke which allows more of the pressure created by combustion to be converted to work. 17:02 you draw a horizontal line as the cylinder moves upward and point out the reduction of compression waste by ~20% .. and we have that .. but if we reference the datum at start of compression instead of start of upward motion, what we also have is ~ 20% greater extension of the power stroke allowing the pressure in the chamber to work longer. At 8:55 the diagram showing Atkinson having shorter intake stroke and same length power stroke is actually Miller. Atkinson would have both blue squares the same size and a resulting longer red square, illustrating the extension of the power stroke. Traditional kpi such as power per cubic inch displaced (the same size red square) show Atkinson as lower, but power per cubic inch compressed (and therefore power per amount of fuel consumed - the same sized blue square) show Atkinson higher. As you said, with car engines being mobile, weight matters and pure Atkinson requires a larger chamber. As engine material technology improves, that gap in weight becomes less. As you said, the addition of the electric supplementary motor corrects the “low responsiveness” feeling - lower power per cubic inch displaced - of the Miller. New engine designs are looking to alternate mechanisms besides reciprocating pistons to obtain the benefit of Atkinson expansion. In the big picture, the 150 years of reciprocating pistons is a short time in human history.

  • @gregroles5638
    @gregroles5638 Жыл бұрын

    Considering buying a Skyactiv CX-5 turbo for the missus, and had my head around Miller cycle a bit, but wow, this has to be the best and most visually perfect description I've yet seen. Kudos!!

  • @jakemartin4305
    @jakemartin4305 Жыл бұрын

    This is amazing ive always believed that knowing how something has evolved over time helps you understand the current technologies and even helps is repairs of those technologies as well love this channel 👏👏👍

  • @kevinpulver4027
    @kevinpulver4027 Жыл бұрын

    You taught me something! I have castings for a model Atkinson Cycle engine. But I didn't realize that the compression and power stroke lengths differed. I know some guys in Nebraska who have working examples of Otto's "Schumm" engine referenced in your video. For those who want to read more about the history of engines, "Internal Fire" by Clessie Cummins has a lot to say.

  • @francoistombe

    @francoistombe

    Жыл бұрын

    Clessie was the founder of Cummins ( and has his own autobiography ( pun unintentional)). His son wrote Internal Fire. He used the name Lyle Cummins, but as C Lyle Cummins so I guess he is Clessie junior.

  • @tdsdl1
    @tdsdl1 Жыл бұрын

    This is one of the best series on You Tube. Wonderfully presented and understandable. Thank you.

  • @AlandGalvez
    @AlandGalvez10 ай бұрын

    Just wow. Been watching videos for an hour trying to understand what this guy does so clearly. Thanks a lot. Glad I found this video.

  • @olavl8827
    @olavl8827 Жыл бұрын

    Great video as always. Personally I'm not much of a car person and I drive just a cheap old boring car, which serves my needs. But I love learning about technology and engineering in general and this explanation was just fantastic.

  • @Trendyflute
    @Trendyflute Жыл бұрын

    Good video, I enjoy when you look at the different types of one thing and explain the similarities, differences, and history! I thought the Miller Cycle Mazda Millenia S was so cool back in the day (as a comfy sedan goes). A video like this on the history and variety of variable valve timing systems would be neat. Or even maybe before that, just valvetrains in general?? I feel like I know most of this stuff but you always manage to slip in a few new bits of info.!!

  • @rkc62
    @rkc62 Жыл бұрын

    This is amazing - thanks for posting! The explanation graphics are excellent as always, but the Otto history graphics are exceptionally entertaining.

  • @Tom-Lahaye
    @Tom-Lahaye Жыл бұрын

    Excellent explanation! Essentially the development of the ICE followed the same route as that of the steam engine. First steam engines as developed by Thomas Newcomen in 1712 were atmospheric, the engine would suck steam at atmospheric pressure into the cylinder at the downward stroke of the piston, the valve would close and the steam allowed to condense as the cylinder wall was cooled by water. The condensation of the steam would create an under pressure wich sucked the piston back upwards. These engines also had poor efficiency and low power output, 5hp for an engine that filled a building, they were used to drive pumps at coal pits. Then someone got the idea of using steam created in a boiler under higher than atmospheric pressure, and using the expansion of the steam trying to equalize it's pressure to atmospheric pressure, and not to condense. Power output and efficiency raised dramatically, steam engine became small enough to power vehicles on rails and road. So a very similar story thus, and I think the development was a continuation of the development made in steam technology, and the idea after the ICE at that time was to drop the steam generating boiler with its thermal losses and space requirements.

  • @tommywallbanger
    @tommywallbanger Жыл бұрын

    Love your videos they are incredibly informative but explained in a way that is easy to understand.

  • @jozsefizsak
    @jozsefizsak Жыл бұрын

    Thank you so much! This was interesting and informative but also uplifting, due to how wonderfully well you explain things.

  • @TheGinger1
    @TheGinger1 Жыл бұрын

    Great video as always. I love the way you present such dry subjects in ways that make them genuinely interesting and entertaining. Keep it up.

  • @MrMarty77
    @MrMarty77 Жыл бұрын

    That was the best explanation of these 3 different cycles that I've heard so far.

  • @wadeepperson6906
    @wadeepperson69069 ай бұрын

    It was kinda cool to learn how vw’s new 1.5 was a Miller cycle combined with a turbocharger to reduce the power lost with the shorter compression stroke. I always thought they were supercharged but it’s the same approach with no parasitic loss.

  • @GablesDude
    @GablesDude Жыл бұрын

    This was excellent! Very clear chronology and explanation.

  • @AH-mu5iq
    @AH-mu5iq Жыл бұрын

    Very good video, though I'd like to say; that closing the inlet valve later part way up the compression stroke can actually increase the amount fuel/air mixture entering the cylinder and therefore increase cylinder pressure 'at higher rpm's'. As the negative pressure of the gases drawn in during the inlet stroke are still trying equalise to atmospheric while the piston is starting its compression stroke. So there is an optimum timing for this dependant on the engine speed.

  • @omniphoriusvcf907
    @omniphoriusvcf907 Жыл бұрын

    Love how there's no yelling on this channel, just great explanations.

  • @nickrider5220
    @nickrider5220 Жыл бұрын

    Very well described sir ! and extremely fascinating 👍

  • @jgfjfgjfhjf
    @jgfjfgjfhjf Жыл бұрын

    I'm sure the title is correct

  • @fuzzycuffs
    @fuzzycuffs Жыл бұрын

    This was so amazingly informative. I linked so many previously known concepts and practices about motors together after this video.

  • @laura-ann.0726
    @laura-ann.0726 Жыл бұрын

    We own two Toyota hybrids: a 2019 Prius Prime, and a 2020 Corolla Hybrid. They both get phenomenal fuel economy: 58 mpg in the Corolla, 65 in the Prius Prime. Both have the same 1.8l VVT Atkinson cycle engine. The Prius Prime has a larger 8 kw-hour lithium ion battery and this can store more recaptured energy from regen braking, than the small 1 kw-hr NIMH battery in the Corolla, so it's fuel economy is better. My personal opinion is that plug-in hybrids are the most versatile vehicles ever developed. Depending on battery size and weight limits, it should be possible to build a 5-passenger sedan or 7-passenger Mini-van that would have up to 100 mile EV range. Pair that with an Atkinson cycle engine (1.5 liter in a sedan, 2.5 liters for a Mini-van), and a 16 gallon fuel tank, and you would then have 600 mile range for those long road trips that Americans love to take. For people living in areas with very cold winter climate, having an ICE lets you run the heater full blast without significantly reducing driving range, and running the ICE for a few minutes can warm up the traction battery far more quickly, so that it can accept a faster charging rate if you do stop somewhere at a DC fast charging station. I Loved this video! It's the best explanation and best graphics I've ever seen to explain just how Atkinson's crank linkage and Miller's VVT valve timing concepts actually worked. The Atkinson engine with the complex linkages would probably have never worked well in a passenger car: too complex and too bulky. But the way Toyota uses a Miller/Atkinson hybrid cycle (VVT, naturally aspirated) works amazingly well in the Toyota Hybrid Synergy Drive. In the Prius Prime and Rav4 Prime, most of the propulsion power comes from the electric motor, unless you are climbing a steep hill, or the traction battery is depleted, in which case the ICE comes on-line. Thanks for the video!

  • @loganpe427
    @loganpe427 Жыл бұрын

    Very, very interesting video! I was retiring as a mechanic at the time Mazda announced it's SkyActive engine, I heard about it but didn't pursue any research, I had no idea it was based on the Miller cycle! Thank you, great information as always!

  • @szymoniak75
    @szymoniak75 Жыл бұрын

    Your videos are always interesting, great explanation

  • @muha0644
    @muha0644Ай бұрын

    12:53 Sarajevo! This is where i live! I immediately recognized it.

  • @rocka07
    @rocka07 Жыл бұрын

    one of the best and most underrated channels on YT

  • @johngray5360
    @johngray5360 Жыл бұрын

    I had to do head gaskets on a Mazda millenia s about 10yrs ago and what a nightmare! There are sooo many vacuum lines, plastic tees and check valves under and around the supercharger that break just looking at them!🤯🤬 Great video and can't wait for an update on the MR-2

  • @BB-lm7cs
    @BB-lm7cs Жыл бұрын

    Fun fact: Some of Cat's ACERT diesel engines (BXS and MXS for example) also used a miller cycle. Boost close to 60psi was provided by series turbos. I think there was a variant of Cummins' big cam engines using the miller cycle too.

  • @Ceedub3406

    @Ceedub3406

    Жыл бұрын

    ACERT is Miller cycle. Helped meet EPA07 by reducing NOx production in cylinder. Pretty cool stuff. Basically reverse Jake brakes

  • @bradferguson4943

    @bradferguson4943

    Жыл бұрын

    You're right. And it's switchable. There's a brake-like device on the intake rocker called an IVA that can hold it open longer. It can be turned on as needed.

  • @mrpetit2

    @mrpetit2

    11 ай бұрын

    ​@@bradferguson4943 If it didn't have that it probably would be impossible to start.

  • @bt1097
    @bt1097 Жыл бұрын

    We take engines for granted. I love engineering, its truly amazing.

  • @kimkeam2094
    @kimkeam2094 Жыл бұрын

    I was not fully aware of the differences between the type of cycle but really appreciate the information you have provided for us. Thanks!

  • @BlackStar250874
    @BlackStar250874 Жыл бұрын

    As usual, a very impressive educational demonstration, or could you say a broadside. Five stars! ***** Greetings from Finland from one hybrid user with an Atkinson-cycle ;)

  • @pirat87pl
    @pirat87pl Жыл бұрын

    I needed this explanation really badly ever since I was at a Lexus showroom and they boasted having 'Atkinson cycle' engines, but none of the salespeople could explain how it works. It was driving me nuts. Google only had general explanations that always felt incomplete.

  • @mrpetit2

    @mrpetit2

    11 ай бұрын

    Salespersons usually aren't techies. A good salesperson would get a mechanic from the shop to explain that for him.

  • @pirat87pl

    @pirat87pl

    11 ай бұрын

    @@mrpetit2 I don't care. If someones selling me something they don't understand - I'm not buying it. If they can't even explain things that are on the sticker then how am I supposed to believe anything they say?

  • @samrodian919
    @samrodian919 Жыл бұрын

    Fascinating video. Thank you that was so informative and I had no idea about Mr Millers engine design, and the VVT was the reason behind its introduction in so many manufacturers engines. I myself had a Toyota 1300 cc VVT engine in my Yaris from 2001.

  • @heinpereboom5521
    @heinpereboom552110 ай бұрын

    You are still my favorite technician! Wonderful explanation of the development of the engine with the important details!

  • @AlexandreNegrao
    @AlexandreNegrao Жыл бұрын

    I'm always learning something new watching your videos...thank you! Would you please make a video about Toyota's M20A engines? Here in Brazil Toyota sells the FKB version, wich is called"flex" because it can run on petrol or ethanol (from sugar cane).

  • @NukeTshernobyl
    @NukeTshernobyl Жыл бұрын

    You can also supercharge Toyota's Atkinsion engines. It was totally interesting, when I saw a supercharged CT200h on a car show. This thing made just above 300hp, and was a menace on the track.

  • @asharma9345
    @asharma9345 Жыл бұрын

    Dude, This is Excellent Video. Full of Information.

  • @CautelousOne
    @CautelousOne Жыл бұрын

    First time ever seeing one of his videos. Instant Subscribe. Details without tedium. Perfection.

  • @fabiopereira9113
    @fabiopereira9113 Жыл бұрын

    The goal is not to reduce the amount of energy wasted during compression, but to increase the expansion stroke. Just look at a PV diagram.

  • @jpsother1183
    @jpsother1183 Жыл бұрын

    I get the feeling Toyota uses "Atkinson" instead of Miller for branding reasons. Their method is more Miller without the charger than Atkinson's differing length of piston movement. A true Atkinson would do best in a stationary and/or very low rpm situation and that is more what it was designed for, than use in a mobile situation.

  • @RyanAumiller

    @RyanAumiller

    Жыл бұрын

    The electric motor functions as the "supercharger" in this case, it just makes up for volumetric efficiency by acting as a variable geometry flywheel. there's really nothing "atkinson" about the toyota version I call "miller cycle 2, electric boogaloo" because it does nothing to vary stroke geometry/displacement like say... the infiniti VC-Turbo engine that utilizes bellcranks similar to an actual atkinson engine to vary the stroke geometry and instead makes up for its lack of volumetric efficiency with a more direct power-adder. I see anything that utilizes changes in cam geometry to control volumetric efficiency for the cycle as "miller" and anything that utilizes changes in crank geometry to physically change the displacement as "atkinson" especially since examples of both exist... I don't agree at all with toyota calling their hybrid synergy drive an "atkinson" based cycle when it does nothing to make displacement a variable.

  • @jpsother1183

    @jpsother1183

    Жыл бұрын

    @@RyanAumiller "miller cycle 2, electric boogaloo" made me guffaw. Also it is very appropriate for the situation.

  • @wjanis1
    @wjanis1 Жыл бұрын

    You are a genius who can simplified the complex.

  • @massmanute
    @massmanute10 күн бұрын

    Maybe it's just an alternative but equivalent explanation to the one you proposed, but I thought that the reason Atkinson and Miller engines are more efficient comes down to harvesting more energy from the power stroke. Here's why I say this. In at Otto cycle engine there is still a lot of pressure in the cylinder when the piston is at the bottom of its stroke. If the stroke could be extended then more energy could be extracted compared to an Otto cycle engine. From an energy balance point of view, shortening the intake stroke is equivalent to extending the power stroke. I think the difference in the intake stroke length compared to the power stroke length is the key reason why Atkinson and Miller engines are more efficient. Of course, in a mechanical sense the stroke lengths in the Miller engine are the same as in an Otto engine. However, because of the valve timing, a Miller engine acts like an engine with a shorter intake stroke.

  • @guglegugle8075
    @guglegugle8075 Жыл бұрын

    Bardzo dziękuję👋 W zaledwie 20 minut pozyskałem sporo wiedzy świetnie zobrazowanej i bardzo logicznie przedstawionej 👌👍

  • @xXVintersorgXx
    @xXVintersorgXx Жыл бұрын

    My dad had one of those millennium's. It was a great car until the super charger self destructed. The major problem with it was actually that it required high octane gasoline

  • @magnusgustavsson6475

    @magnusgustavsson6475

    Жыл бұрын

    Would be perfect then on E85!

  • @xXVintersorgXx

    @xXVintersorgXx

    Жыл бұрын

    @@magnusgustavsson6475 I think it needed 91 octane according to the manual

  • @Truetoself3838
    @Truetoself38383 ай бұрын

    Your video is pretty amazing. So much history intertwined with the basic science of how the engines work... thank you...

  • @catingloves
    @catingloves Жыл бұрын

    Excellent. Now I know what it meant by Atkinson cycle in a Prius. Great education.

  • @velvetsmack2645
    @velvetsmack2645 Жыл бұрын

    Great explanation and video. Learned quite a lot. I actually owned a Mazda Millenia with the miller. I truly miss it. What's interesting about this tech is that we're now looking at the new age of electric, which ultimately means (or will mean) times almost up on this piece of engineering. Hydrogen may save it for a while, but I see a driven world with less engineering complexity - which would maybe lead to its ultimate demise.

  • @willemmaas9813
    @willemmaas9813 Жыл бұрын

    Thank you for this detailed explanation of the different cycle engines.

  • @waelal-zubieri5358
    @waelal-zubieri5358 Жыл бұрын

    I believe more modern engines can switch their VVT even at low RPM since they are electronically controlled rather than controlled by oil pressure like older Hondas. I believe pretty much any modern turbo charged today uses the miller cycle to save on gas. It's why these engines get excellent highway efficiency but the moment you are driving in the city in stop and go situations, efficiency drops significantly. In my car, I can easily get 30+ MPG even at relatively high speeds, but in the city can only achieve 16-20 MPG.

  • @d4a

    @d4a

    Жыл бұрын

    Yes but there's still a catch. When you can switch to Miller at very low rpm the engine ends up being in Otto most of the time and the number of scenarios when you're actually running Miller is very much reduced. It's impossible to be responsive at low rpm and be in Miller at the same time, maybe that's how I should have phrased that part.

  • @ferrumignis

    @ferrumignis

    Жыл бұрын

    The Honda VTEC is electronically controlled, but it electronically controlls the flow of oil to actuate the valve timing system. This is the same as the vast majority of other manufacturers VVT systems. The only examples I can immediately think of that don't use oil pressure are BMWs Valvetronic (electric motor directly drives a mechanical system to control valve lift) and the koenigsegg free valve system. There may be a few others but they are in the minority.

  • @georgewashington938
    @georgewashington938 Жыл бұрын

    I am biased in favor of the Otto engine

  • @kerrylewis2581
    @kerrylewis2581 Жыл бұрын

    I may still be seated, but I'm giving your explanation a standing ovation. Fantastic video

  • @TheArtikFoxx
    @TheArtikFoxx Жыл бұрын

    Amazing video, thank you for creating this and putting it on KZread for everyone.

  • @fellspoint9364
    @fellspoint9364 Жыл бұрын

    Wow, very well done. You covered a lot of technical ground in a clear and concise manner.

  • @pavelbratchenko3885
    @pavelbratchenko38859 ай бұрын

    Dude, this is incredible. You doing such an amazing job at explaining this!

  • @iHuffDiesel
    @iHuffDiesel Жыл бұрын

    I really appreciate your channel. You have helped me in so many aspects in life. Not only in engines and physics but in the willing to learn and aspire to gain every bit of knowledge I can. Thank you🙏🏼

  • @d4a

    @d4a

    Жыл бұрын

    I'm overjoyed to hear that. Thank you.

  • @ColoTJ7
    @ColoTJ7 Жыл бұрын

    Thanks. Best explanation I've heard and now fully understand.

  • @keithartworker
    @keithartworker Жыл бұрын

    Well done! So many questions elegantly answered.

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