Optimum connecting rod length

Not wishing to Hi-jack another thread in which this matter has been mentioned, I have to ask Is There One? obviously shorter rods are not as heavy as longer rods, therefore less reciprocating weight, making higher revs possible, but the centre of gravity will 'rotate' in a nearer to circular motion, So more 'up and down' forces(?) and angularity differences acting on cross head/slidebar/glands. Plus of course 'Length' is relative to stroke, I'd guess that valve gear, such as Joy may also have an effect, So Over To You.

 

I think that it is like a lot of things in engineering in that it is mostly compromise.

 

As you say Shorter connecting rods will result in larger forces acting on the slide bars.....so I agree with the compromise rather than optimise.

 

Is there such a word as comprimum?

 

I suppose since I jumped on it in the other thread, I should comment. I thought that since I had cited kinematics, I should bring numbers, especially if they were going to prove me wrong, and had a nice little pair of examples lined up, which I thought would perfectly illustrate the trade offs. For those unfamiliar, the SAR 15E 4-8-2 and 16E 4-6-2 are basically two versions of the same machine, same boiler, same 24" x 28" cylinders, same look. If you've seen a 15F (surely) then the 15E is that, only with rotary cam poppet valves, and the 16E is the 15E as a 6'0" Pacific instead of a 5'0" 4-8-2. I'm using these rather than LNER Pacifics as examples because I happen to have drawings...

The 15E has 7'5" connecting rods driving the second axle, while the 16E has 9'0.25" rods. I checked the drawings and found that, contrary to expectation, the 16E has lighter connecting rods. It seems some smart person in the drawing office thought that it would be worth keeping the rod weight down on a fast Pacific, so had the big end carefully relieved to remove material, and gave a slightly more involved profile to the middle of the rod with both a straight and tapered section of fluting. Very inconsiderate of them, but also understandable as to why you wouldn't want this level of manufacturing complexity for every rod on every mixed-traffic 4-8-2 as well. Anyway, I was a bit puzzled by some inconsistencies regarding weight on other drawings, and did a model of the 15E rods just to be sure. So, here are the points of interest:

The 15E rods weigh 360 lbs (16E rods are about 20lbs lighter). However, the fluted main section of the rods comes in at approx 23 lbs/ft, and if you multiply that by 7'5" you get a mere 169 lbs. So the weight of the rods are very heavily influenced by the big and small ends, rather than the length. Pushing them out to 9'0.25" while keeping the 15E details gets you up to 396 lbs, but the percentage increase in weight (10%) is much less than the percentage increase in length (22%). Yes, you might need a deeper section to avoid buckling, but actually stiffness for buckling resistance goes with the fourth power of section dimensions, whereas susceptibility to bucking only goes with the square of length, so you can get a lot more stiffness for not too much material. I'd say that the extra weight of longer rods is probably not hugely significant. I'm therefore going to pretty much ignore the dynamic differences, you can probably design down to the weight you need somehow. As a final note for comparison, the rods for a GMA Garratt are 12' long and 470 lbs, although the section is different, the 23 lbs/foot scaling from the 15E rod isn't that far out.

As for angularity and slidebar loads, the short version is that both classes have a piston thrust at full boiler pressure of 95000 lbs. A little bit of Pythagoras gives a maximum vertical reaction at the slide bars of 15132lbs (6.76 tons) for the 15E and 12391lbs (5.53 tons) for the 16E, or about 22% more for the 4-8-2. I'm not going to calculate the reactions at each wheel, because frankly I've probably gone slightly too far on this already, but you get the idea. The fluctuation in load on the wheels of the driving axle will be of a similar order on an outside cylinder engine, so quite a substantial fraction of the individual wheel loads.

Finally, for the effect on valve events, since these engines have rotary cam valves we can probably assume that if set at 50% cut off, the valves will be closing with the crank at 90 degrees to dead centre. On the 15E with short rods, that means 46% and 54% in the front and back half of the cylinder respectively, for the 16E it's slightly more even at 46.8% and 53.2%

To cut the rambling short, I'd suggest that connecting rod length does have an influence. Longer rods are kinematically preferable (see the reaction forces and equality of valve events) and the weight penalty is less than might be expected, although obviously all else being equal shorter rods will be lighter. However, their main job is to connect cylinder A to crank B; once the axles and cylinders have been laid out in a reasonably sensible fashion, the connecting rod can be whatever is required, within reason, as demonstrated by two perfectly successful examples above. You wouldn't make an engine longer just to make the rods longer, but you might change the driven axle on an 8-coupled engine (see the GMA).

 

One of Durrant's books on Garratts (sorry, can't recall which) commented "longer coupling rods have a stabilising effect on large narrow gauge locomotives" (my emphasis). I suspect 'narrow gauge' is the key term, given what passed for speed on Cape Gauge freight workings was some way south of what we might consider particularly fast.

Drive to the second coupled axle wad used on the 1927 Kenya-Uganda Rly class EC1 8 coupled Garratts (EAR Classes 50/51), where just two years later, the superb SAR 4-8-2+2-8-4 Class GL, whose design was entrusted entirely to BP, drove onto the third coupled axle, which thereafter always seemed the preferred default for 8 coupled units.

Regarding Cape Gauge speeds, just to provide some context, one specific comment, in 'Steam in Africa' (A. Durrant. ISBN: 9780600349464 Pub Octopus 1981) I recall was 140Kph max, or just shy of 87mph, mentioned in respect of a later SAR express 'pacific' (IIRC class 16E of 1935).

 

Thanks for some actual figures. Those that I find the most interesting are the vertical forces on the slide bars and, correspondingly, on the cranks. I have a picture of GWR 5101 on my wall and I have always wondered how much the forces from its short connecting rods alter the vertical loads on its middle driving wheels. I don't have a drawing to take dimensions from, but I think the answer must be Quite a lot. We tend to think about hammer blow, due to the use of rotating balance weights to provide some compensation for the reciprocating masses, but the static changes on wheel loading due to the angularity of the connecting rods would seem to be of comparable magnitude, especially at low speed, long cut-off, when there is close to full boiler pressure halfway through the piston stroke.

 

One aspect of connecting rod design that I am not sure about, is how the big end oil space is created? Obviously it is machined into the forging but then a top must be put on with the screwed tube for the oil cork.....but there doesn't seem to be any sign that the top is welded in place when I have looked closely......or is it so well done and blended in, that it is invisible?

 

Just well done and blended in. On most locos, that is. I can think of some Greek and Polish locos where that is not the case.

 

Although there are a lot of considerations like preferred driving axel, overal engine length. Motion weights, slide bar forces, cylinder position and so on. In piston stroke relative to the angle of mid stroke the longer the better. This is part of defining even power out of the two ends of the cylinder. The quoted ideal is up to 5 times the piston stroke. In practice that is not always posible.

 

Thanks Steve.

 

Quite clearly, the connecting rod in the photo is of the optimum length.

 

I agree, it's just long enough to reach from the gudgeon pin to the crank pin.

Andy.

 

This should help.

 

Thanks std tank......another mystery solved!