2 Cylinders V 3 Cylinders

I've had a few comments about a posting on this subject by me that appeared on the L1 thread. I thought that it was worth expanding on this but in a more appropriate place.
There is a belief that 3 cylinder locos are better at starting than 2 cylinder ones as they cannot 'stick on centres'. The reality is different and I've produced some tractive effort curves for 2 and 3 cylinder locos to try and explain it. I have been unable to find examples of locos that were otherwise identical; except in the number of cylinders so, to overcome this I have used a Black 5 for the 2 cylinder example and created a virtual 3 cylinder Black 5. This 3 cylinder version has exactly the same nominal tractive effort (25,455 lb) and cylinder layout. The cylinder diameter has been reduced to 15.1" and the piston rod diameter to 2.25" to compensate for having 3 cylinders and the cranks are at 120° but everything else is the same, including con rod length.
Diagrams 1 & 2 show the two tractive effort curves for one revolution of the driving wheels for both types. The effort for each cylinder is shown, together with the combined total tractive effort. The curves are not symmetrical because of angularity and the effect of the piston rod on the return stroke. An allowance for expansion of the steam beyond 75% has also been made. It will be seen that the peak TE of the 2 cyl loco is just less than 33000 lb (compared with the nominal TE of 25455 lb) and that of the 3 cyl loco just underr 30,000 lb. Both locos exhibit a tractive effort curve that is above the nominal for the majority of a wheel revolution. The 3 cyl loco has a much smoother tractive effort curve.

So far, so good, there is nothing revoluntionary in this. However, if we now look at the tractive effort available at the moment of starting, a different picture emerges. A cylinder will only receive steam if the appropriate port is uncovered and I have based this on 75% cut off so, for one quarter of its stroke, any one cylinder will contribute nothing to providing starting force. The variation in tractive effort of the 2 cylinder loco is quite large, depending on theactual wheel position but the loco will still produce a peak tractive effort of about 33000 lb. However, the maximum starting tractive effort of the 3 cyl loco is only just about 28000 lb for three short peaks and, for much of the wheel revolution, it is below even the nominal tractive effort. The 3 cyl loco only starts to produce a reasonable tractive effort once it gets its train on the move and is admitting steam to all three cylinders.

What I haven't done in these diagrams is include for lead steam. This makes the situation even worse. The lead steam on a Black 5 starts to be admitted at about 93% of stroke and this will oppose any tractive force applied. Obviously, with 3 cylinders, there are six places in each wheel revolution where this has an effect. (I haven't included for this as I haven't worked out how to factor it in to the spreadsheet!)
Harry Holcroft certainly appreciated this problem with 3 cylinder locos, realised when investigating why Schools class locos struggled to start trains that their lesser and less powerful 2 cylinder cousins could start with ease. Gresley probably didn't because his 3 cylinder locos were originally limited to 65% cut off as he thought that long cut offs was unnecessary with a 3 cylinder loco and this makes starting even worse. It's only post war that they were modified to give a longer available cut off.

 

Cool, its easy to see from these diags that having one of two bigger cylinder working to its full output range out muscles three smaller cylinders non of which peak at the same time
Is finding sufficient TE just to start the train... ie a heavy train and an adverse gradient a common problem these days
Is the two cylinder loco not more likely to lose adhesion from applying this higher effort? than three cylinder with less force though applied more evenly ?

 

Most interesting, thanks!

 

They are not quite equivalent in TE, but the Maunsell moguls had 2 and 3 cylinder variants that were near identical to each other: N (two cylinder) / N1 (three cylinder); U (two) / U1 (three) and the K (two) / K1 (three) tank engines.

While I can understand the argument that a two cylinder design gives a higher peak TE on starting, there is a counter argument that the more even torque of a 3 cylinder design means a higher TE can be generated from a loco of given adhesion without risk of slipping. This point was made by James Clayton (personal assistant to REL Maunsell) in a discussion of Gresley's paper "The three cylinder high pressure locomotive" at a meeting of the Institution of Mechanical Engineers in 1925. (Quoted in OS Nock's book "The locomotives of REL Maunsell").

Incidentally, a side-benefit of the three cylinder N1 design was that the smaller outside cylinders meant it was narrower than a conventional two cylinder N class, with the result that it was permitted to run on the Hastings Line, long a bane of operating departments due to the severely restricted tunnels!

It is also interesting to look at the Lord Nelsons. Unlike a conventional 4 cylinder design, these had the cranks set at 135deg rather than 90deg. A conventional design would have a torque curve identical to a two cylinder loco (e.g. with large variation between peak and average torque). Whereas in the Lord Nelsons, the 135deg cranks gave eight beats per revolution, such that the torque curve is much smoother: in fact even smoother than a 3 cylinder design with cranks at 120deg. However, one loco - 865 "Sir John Hawkins" - had the crank setting at 90deg. The idea was that with this setting (and hence increased peak torque) would accelerate a train more rapidly. However, experience showed no difference in acceleration or starting performance.

Tom

 

A 3 cylinder loco does indeed have a smoother torque curve and can have a higher adhesion factor but I was setting out to show the disadvantage when starting and a 3 cylinder cannot benefit from the smooth torque curve until it has got its train on the move.
with regard to the Nelsons, accelerating a train is not going to be by peak torque alone. It is going to be by the average torque over the wheel revolution and that is going to be independent of crank positions, all other things being equal because you are simply adding up the torque of four cylinders in all cases. Four at 90 is probably going to give you a better chance of starting, than four at 135, though. Need to draw out the torque curves for both but not tonight!

 

Hang on a minute, a normal Black 5 has two 18.5 x 28" cylinders. Three 21.2" diameter cylinders is a considerable increase.

 

Did I put that?! Nobody else has spotted it so well done. I don't know why; a mental aberration is my excuse. The calcs were done on a cyl dia of 15.1".

I must say that there's been a sudden resurrection of interest in these long written MIC posts, which is all good, IMHO.

 

If you are wanting power and efficiency you go for 3 cylinders. However the outside cylinders have a crank setting of 90 degrees and the inside cylinder is set at 135 degrees to the outside cylinders. It is important to note that this arrangement has proved to be very successful with high starting tractive effort, little tendancy to slip and very high power output at all speeds. It also provides a robust design that can be engineered to deliver 6000+ ihp.
Yes, this locomotive will be a compound. Why 3 cylinders and not 4? Designing an adequate crank axle is a significant problem given the limitations of space.

 

I don't think that was an accidental side benefit, I think it was the whole point.

 

A (late) friend who was a goods guard on the Southern Region in the 50s told me that one of his regular trip workings was a heavy coal train which they took to Tonbridge yard. The usual loco on that working was an 'N' class (2 cyl.) The tricky bit - especially in winter with dew on the rails - was backing the train into a siding which went through a rather sharp reverse curve, and also up a significant gradient. Harry said that when their train got clear of the point, and the 'N' tried to set back, if there was any significant dew on the rails, the engine very often slipped to a stand, and was unable to get the train moving again.

They would then send for one of the Maunsell 'Z' class shunters which worked at Tonbridge, and that would shunt the train into the siding every time, with no fuss. Now, I grant you that the 'Z' class had 4 foot 8" driving wheels, as compared to the 5 foot 6" driving wheels on the 'N'; and the 'Z' was an 0-8-0, designed for heavy shunting, as compared to the 'N', a 2-6-0 mixed traffic engine - but Harry said it was very noticeable the way that the power came in so smoothly on the 'Z' that the driver could apply power gently, rather than it coming in with a bit of a rush, as it did with the 'N'.

A comparison which may be relevant is old British trials bikes. For those not familiar with them, trials were courses laid out over the most appalling ground available; axle deep mud, going through the rocky beds of streams, climbing incredibly steep slopes - and the point was for the riders to be able to get through each section without the bike coming to a stand, and without the rider touching his feet on the ground. Do a net search on images from the Scottish Six Days Trial, and you'll see what I mean.

Now, obviously those bikes had to be able to find grip to be able to apply enough power to keep moving, even up slopes as steep as 45 degrees or worse; so how were they built?

With massive heavy flywheels, and very low compression; they also had exhaust valve-lifters which the rider could use to let some compressed mixture leak out of the compression chamber, and an ignition control lever which allowed him to retard the ignition - which enabled them to drop both power and torque even further. All of these put together meant that the engine could generate low power - much lower than equivalent tourers, let alone racing bikes - and low torque, too. So what was the secret of their grippiness? No big pulses of high torque.

That suggests to me that Steve may be wrong on this point:

(my emphasis, J.E.)

It seems to me that where a 3 cylinder scores over a comparable 2 cylinder at starting in slippery conditions is simply because the available torque is less! Yes, you need a given amount of torque to start a train, but - as Steve has shown on his plots - the torque peaks are significantly higher on a 2 cylinder than they are on a comparable 3 cylinder. A 2 cylinder is therefore more likely to apply enough torque to the driving wheels to overcome the available friction - and spin the wheels.

Note that I stress the word 'comparable' in the above paragraph. In one of his posts above, Steve says:

(my emphasis, J.E.)

If I'm right, the reason those 'less powerful' 2 cylinder cousins could start those trains more easily than the 'Schools' was precisely because they were less powerful - and generated less torque!

My conclusion is that, if enough grip is available at the tyre / rail interface, a 2 cylinder can get a train moving more easily than a comparable 3 cylinder - but where grip is marginal, a comparable 3 cylinder engine may perform better at that task, as it's less likely to pick its wheels up.

But feel free to counter argue, by all means - and I very much appreciate Steve doing the work involved and posting it on here!

With best regards,

Jack

 

Exposing my lack of engineering knowledge, two things occur to me that have not been mentioned. Firstly, 3 cylinder designs put inherently less stress into the frames as each power surge is smaller; with there being scope for smaller cylinder diameter and/or stroke the piston speed can be reduced and the reciprocating / circulating weights reduced. Secondly, a 4-cylinder design like the Lord Nelsons would be taking steam from the steam chest more evenly; is there not some advantage there?

 

The basis of the argument that 2 cylinder locos have the advantage over 3 cylinder locos relates to the moment of starting. i.e, when the loco is stationary. Once on the move the 3 cylinder has the advantage when it comes to keeping the torque more constant.

 

As long as the applied torque is insufficient to overcome the friction at the tyre / rail interface, I agree; but the fact that a 2 cylinder loco can exert more torque than a comparable 3 cylinder loco means that if the maximum torque is applied, it's more likely to overcome the friction in marginal conditions, and result in wheel-slip.

 

The Z class had an adhesive weight of 71 tons 12 cwt compare to the 52 tons 4 cwt for the N, with an adhesion factor of 5.4 compared to 4.5. I believe this would make the Z much more sure footed. The Z also did not have a superheater which gives better response to the regulator. The valve events of the N were biased towards forward running which may have made the torque in reverse more uneven. I do not know what the valve events on the Z were like but knowing the quality of the design team they were most likely optimised for shunting duties.

 

Indeed, it would be more surprising if a Z class had not been better at shunting than an N!

The Z was a very clever bit of design using "off the shelf" components, as it were. From memory, one of the reasons stated by Holcroft for choosing three cylinders over two was to minimise noise, particularly at night, for a loco designed to be used in marshalling yards that were surrounded by residential property. It also used the LBSCR C2x boiler, which was a design known to have relatively high steam volume but a fairly small grate area, which was ideal in both economy and minimising noisy blowing off for a loco designed for periods of high intensity interspersed with periods of inactivity.

Tom

 

With any loco (two, three or four cylinders), if the applied force is greater than that of the limiting coefficient of friction, it will slip. However, it is a fundamental that, if you don't provide sufficient force to move the train, it won't move. That's the weakness of a three cylinder loco. For much of the wheels position, a three cylinder loco will not produce as high a starting torque as an equivalent two cylinder loco.

 

Out of curiosity - have you ever (hint) plotted the equivalent curves given in your original post for a Lord Nelson, i.e. comparing the majority (4 cylinder, 135deg crank angles, 8 beats per revolution) with the one-off No. 865 (4 cylinder, 90deg crank angles, 4 beats per revolution). Maunsell was evidently interested enough in the theory to have the one-off built with conventional phasing of the cranks, but as I understand, there was little to choose between them in practical use. I can picture the continuous TE curve in my head, but not what the starting TE curve would look like!

Tom

 

No and as I'm going on holiday, you can do this for your homework, if you want. (Changing times, homework is now optional!)

 

I ignored connecting rod angularity and it's only over 180 degrees, but here's a 2-cyl, 3-cyl and an LN superimposed. The y-axis is dimensionless, and the area is the same under all three curves.