The Toplis Level Luffing Crane- a mathematical quandary

[Pacific231G]

This came from our topic on slide rules and trigonometry. It was rather off-topic for that discussion but since it seemed to attract a high proportion of RMWeb's mathematicians I thought I'd try to get an answer. . 

 

This is a question that's been bugging me for years and though there are plenty of descriptions I've never found a satisfactory explanation. 

I know how this device works but I've never seen a satisfactory explanation of why it works.

 

Creative Commons

 

This crane is one of four preserved in Bristol but almost any model of a tradtional British port needs at least one or two of them. It's a dockside crane built by the Bath company Stothert and Pitt  using their Toplis Level Luffing system. Though this is quite a large one smaller versions were to be seen at places like channel ferry ports, to handle the gangways,mail and baggage, but anywhere where general cargo was handled and there are still a good number of them in Southampton Docks.

 

When a crane's jib is raised and lowered- "luffed"-  to bring a load towards or away from the crane it also moves up and down.  With the dericks on board a ship that's no real problem as you can simply hoist  the load to a suitable height and then swing the derrick round to bring it on or off the ship. For a dockside crane though, designed to handle cargo as quickly as possible,  you really want to bring the load as directly as possible between the ship's hold and the quayside. Level luffing means that as the jib is raised and lowered the load remains at the same level which makes handling far easier and so faster. Outside of Britain and in more modern cranes the horse head system seems to be more commonly employed and it is based on simple geometry.

 

The Toplis system  seems to have been patented in 1914 by Claude Toplis, Stothert and Pitt's Chief Engineer, applied for his patent in October 1912 and you may be able to see from the photo that it works by having pulleys at the end of the jib and also on a pylon above the cab where the machinery is housed  The load is on a hook at the end of a single hoist cable but, instead of that cable being run straight out from the hoisting drum, it first passes over a pulley on the tower to a pully on the end of the jib then back to another pulley on the tower before finally returning to a second pulley at the end of the jib and down to the hook. The hoisting cable is therefore tripled between the two sets of pulleys. This diagram is based on one in an old Meccano guide with only the hoist cable shown (in red) The ratio between the height of the pylon above the effective base of the jib T  and the length of the jib J is critical if the hook is to remain level but I've never seen a mathematical description of the system.

 

 

The principle is simple. As the jib is lowered or raised the distance between the two sets of pulleys increases or decreases and that pulls in or pays out enough cable to compensate for the rise and fall of the jib. What I can't figure out is the maths that determines that the hook is completelly level and what range of jib movement it works over. Anybody got enough maths to figure it out?

The diagram is very simplified and real dockside cranes normally had counterweighted jibs and, because the load didn't rise or fall, luffing required little power and was often driven by an arm connected to the jib rather than by a winding drum and cable. This also made operation much faster.

 

The other thing I never understood was why, when dockside cranes like this were a familiar sight in almost every port or quayside large or small up and down the country,  Airfix produced a kit for a "dockside crane" (now I think in the Dapol range) that was completely different and so untypical that model railway quaysides that used them never looked quite right..

.

Edited November 20, 2015 by Pacific231G

[34theletterbetweenB&D]

Sticking 'Topliss level luffing patent' into Google turned up this link which my primitive browser refused to open. http://www.linkapedia-architecture.com/topics/construction/level-luffing-crane/18028833   There was mention of patent 4606469, which may be the one. It may be quicker just to go to this, because I think the operating principle would have to be made explicit as key to granting the patent.

[Flying Pig]

US patent 460649 appears to refer to a variant of the horse head design: http://www.google.co.uk/patents/US4606469

 

This Meccano model may be of interest: http://www.alansmeccano.org/models/pic12.htm Sadly, Meccano omitted to mention how the system works, but it does seem to be a passive feature of the geometry.

[Pacific231G]

Sticking 'Topliss level luffing patent' into Google turned up this link which my primitive browser refused to open. http://www.linkapedia-architecture.com/topics/construction/level-luffing-crane/18028833   There was mention of patent 4606469, which may be the one. It may be quicker just to go to this, because I think the operating principle would have to be made explicit as key to granting the patent.

Thanks 34C & Simon.

US patent 460649 is a way of mounting the operator's cab on a horse's head crane so that it's close to the end of the jib. It looks pretty terrifying for the crane driver but I suppose they're used to being suspended in mid air. 

Cranes and the Toplis system in particular have long been a favourite with adult Meccano enthusiasts and somewhere I've got the plans for a simple (ish) demonstration model that allows you to adjust the height of the fixed pulleys to investigate the optimum ratio. I think though that I now know why none of those articles really explain why the Toplis system works.

 

Thanks to an article in The Engineer, from 1960 which finally gve me the date and number of the original 1912 Toplis patent application, I now have that patent and if anyone's interested it is  United Kingdom Patent 1912 22704-A (http://patent.ipexl.com/GB/191222704-a.html ).

 

The application describes the principle in very general terms and there is none of the complex trigonometry that a full mathermatical description of the system would require so I suspect that the precise relationship between the jib length and the height of the fixed pulleys was arrived at by a certain amount of trial and error (or empirically if you want to be posh about it) 

What is odd is that the basic arrangement of four pulleys is so simple that you wonder why every ship's bosun since Sinbad wasn't already completely familiar with it. I rather suspect they might have been. 

 

However, analysing it completely is a rather different matter and while it would be an interesting exercise for anyone with a real grasp of this sort of maths it's well beyond my ability. The equations derived in the April 1960 article in The Engineer (pp 735-738) by Dr. E Lightfoot and M. Girgraph MSc.are fiendishly complicated and even then they used an empirical equation supplied by one of the crane manufacturers. They applied a computer (not easy to get time on in those days) actually a Ferrranti Pegasus, to find the best pulley positions by number crunching the variables to produce a graph that would show the optimum values.

 

If anyone is interested the 1960 article is available online from Grace's Guide to British Industrial History  which includes scans of The Engineer from 1856-1960. However, if you're interested in engineering I must warn you that once you go in there you may never be heard from again !!  http://www.gracesguide.co.uk/Main_Page

Edited November 16, 2015 by Pacific231G

[MarkSG]

I can't answer the substantive question, but having now looked at an Airfix/Dapol crane I can see why they're wrong. Which is now annoying me, as it offends my more purist instincts

 

Maybe a more accurate dockside crane is something that could go on the future wishlists. It would fit into either the Skaledale or Scenecraft ranges.

[Pacific231G]

I can't answer the substantive question, but having now looked at an Airfix/Dapol crane I can see why they're wrong. Which is now annoying me, as it offends my more purist instincts

 

Maybe a more accurate dockside crane is something that could go on the future wishlists. It would fit into either the Skaledale or Scenecraft ranges.

Chris Mead has  a couple of rather large dockside cranes on his Overlord layout based on Southampton at the time of D-Day but I'm pretty sure they were scratchbuilt. Scale Link do have a N scale fret for a dockside crane which might be level luffing but I could only find the fret and no pictures of the assembled model on their site.  There are some European models from I think Faller and Artitec but they're either horsehead or in the case of Artitec (in 1:160 scale) something that looks rather like an articulated  horsehead jib but is actually fixed.

 

The Airfix crane annoyed me as a kid as I bought one, assembled it and realised it had little in common with any dockside travelling crane I'd ever seen. 

Edited November 17, 2015 by Pacific231G

[Andy Hayter]

I wonder if the working of the mechanism is related to the tower being roughly one third the height of the jib (looks like that to me at least), and the haulage line running from the tower to the tip of the jib three times. 

[unravelled]

If anyone is interested the 1960 article is available online from Grace's Guide to British Industrial History  which includes scans of The Engineer from 1856-1960. However, if you're interested in engineering I must warn you that once you go in there you may never be heard from again !!  http://www.gracesguide.co.uk/Main_Page

I spent many hours at college reading old copies of the Engineer, when I should have been doing other things. Many thanks for the link.

 

Dave

[Flying Pig]

I failed miserably to understand the problem in analytical terms so plugged the numbers into Excel instead (see attached).  Having chosen a rough value for the ratio between jib and tower, it's relatively easy to calculate the resulting load height for various angles between the two (I used 5 degree increments between 5 and 70 degrees) with nothing more than the Cosine rule. The range of heights obtained can then be reduced to a single value.  Minimising this value by tweaking the jib:tower ratio gives the optimum proportions for the crane (I use the Excel solver to do this).

 

For a line running 3 times between tower and jib, it turns out that optimum ratio of jib:tower is 3.602:1 at which total variation in load height is about 7.7% of the height of the tower (or about 23cm with a 3m tower and 10.8m jib).  Interestingly, the best result for a single run of the line is 12% of the tower and increasing the runs to 5 only gives a slight improvement to 6.7%, which is no doubt why the prototype stuck with 3 runs.

 

That was my evening.  Andy Hayter reached the same conclusion much more quickly

 

Crane.xls

 

Edited January 3, 2023 by Flying Pig
Replaced attachment

[Pacific231G]

I wonder if the working of the mechanism is related to the tower being roughly one third the height of the jib (looks like that to me at least), and the haulage line running from the tower to the tip of the jib three times. 

Hi Andy

In principle yes though as Simon has calculated it's not quite so simple. Toplis' original patent actually suggested that you could achieve the same result with different numbers of lines. The key ratio is between the variation in length between the two sets of pulleys and the vertical rise and fall of the jib head. For three lines (and I've not come across any other number actually being used) that would only equate precisely to the ratio between the tower height and the jib lenght if the jib was vertical so for the nornal range of jib angles the best ratio seems to have been found empirically. I had assumed that Toplis had come up with a set of solvable equations to describe his system but I don't think he did and assume he actually found the best tower height graphically.

The 1960 article in The Engineer also mentioned two other level luffing systems one patented by Mannock in 1922 and the other by Walls in 1928. I'll now try to find those. 

 

Simon, congratulations on your evening's work, it's more than I managed in weeks of head scratching and scribbling in notebooks on the Tube but I was looking for an analytical formula when I clearly should have been seeking a numerical solution.

Edited November 17, 2015 by Pacific231G

[rockershovel]

Most Victorian and Edwardian engineering depended on empirical refinement of generic designs. Design calculations were in considerable part, a function of the under-paid and much put-upon draughtsman.

[PatB]

I spent many hours at college reading old copies of the Engineer, when I should have been doing other things. Many thanks for the link.

 

Dave

 

Indeed. One of a number of reasons I failed (quite spectacularly, I must say) my second year Physics exams, way back when, was my discovery of the university library's bound collections of The Engineer and Automotive Engineering. Fascinating reading. It's also notable how many ideas and theories which we would now consider, quite rightly, ludicrous, were quite seriously held. It's a while ago now but ISTR the speculation following the fall of the Tay Bridge to have provided a particularly rich seam of weirdness.

[Pacific231G]

The 1960 article in The Engineer also mentioned two other level luffing systems one patented by Mannock in 1922 and the other by Walls in 1928. I'll now try to find those. 

 

 

I've now found Thomas Mannock's patent application (1922 GB196450A) and he used a single line between the fixed pulley and jib head I tnink using equilateral triangles but  his diagram should make it clear. I don't know if the luffing is quite as level as it is in the Toplis system.

 

 

This has advantages for heavier loads in that it puts less wear and tear on the hoisting line which only passes over two pulleys rather than four and is far simpler if multiple lines are needed at the hook.

 

I'm still trying to figure out how such simple types of rigging were ever patentable. 

Edited November 17, 2015 by Pacific231G

[rockershovel]

Very large crawler cranes often have luffing jibs, but the control systems are electronic these days

[34theletterbetweenB&D]

 [complete tangent]

... One of a number of reasons I failed (quite spectacularly, I must say) my second year Physics exams, way back when, was my discovery of the university library's bound collections of The Engineer and Automotive Engineering. Fascinating reading. It's also notable how many ideas and theories which we would now consider, quite rightly, ludicrous, were quite seriously held. It's a while ago now but ISTR the speculation following the fall of the Tay Bridge to have provided a particularly rich seam of weirdness.

That's a real education on the sound principle of putting lots of bright young things in close proximity to a lot of books. If there's one vital thing to learn, it is a healthy scepticism toward the most assertively declared 'received truths' of science, both pure and as applied in fields such as engineering. I still consider myself privileged to have experienced a live example in the field of geomorphology. After many years being taught 'orogenic uplift' as a foundational doctrine in the field, it was discarded overnight for 'plate tectonics'. It had only taken 60 years from Alfred Wegener's observational insights to finally overcome the weight of oppostion: mainly from academics whose entire careers were going into the dumpster due to riding a dead horse.

 

If you want closure on the Tay Bridge, the re-discovered failed girder now prominently displayed in Edinburgh at the National Museum of Scotland is most informative.

 

 [/complete tangent]

[edcayton]

 

The Airfix crane annoyed me as a kid as I bought one, assembled it and realised it had little in common with any dockside travelling crane I'd ever seen. 

 

Very much agee with that, but I had no idea why until this thread.

 

Ed

[PatB]

 [complete tangent]

That's a real education on the sound principle of putting lots of bright young things in close proximity to a lot of books. If there's one vital thing to learn, it is a healthy scepticism toward the most assertively declared 'received truths' of science, both pure and as applied in fields such as engineering. I still consider myself privileged to have experienced a live example in the field of geomorphology. After many years being taught 'orogenic uplift' as a foundational doctrine in the field, it was discarded overnight for 'plate tectonics'. It had only taken 60 years from Alfred Wegener's observational insights to finally overcome the weight of oppostion: mainly from academics whose entire careers were going into the dumpster due to riding a dead horse.

 

If you want closure on the Tay Bridge, the re-discovered failed girder now prominently displayed in Edinburgh at the National Museum of Scotland is most informative.

 

 [/complete tangent]

 

One of my few claims to fame is that one of my 1st year Physics courses was delivered by Professor "Rocky" Runcorn who was, I am led to believe, one of the main drivers of plate tectonics .

[Tiffy]

One of my few claims to fame is that one of my 1st year Physics courses was delivered by Professor "Rocky" Runcorn who was, I am led to believe, one of the main drivers of plate tectonics .

I'll bet he eats three Shredded Wheat for breakfast.

[Lady_Ava_Hay]

Proportional movement of the hook in relation to the jib is acheivable with most cranes. I drove a Jones 38ton wheeled crane at a boatyard and was quickly used to the idea of jibbing out and hoisting in at the same time. Although the movement of the hook was present it was relatively inches within the range of the jib.

 

Perhaps the luffing crane had other attributes that made it suitable for dockside use. For a  start, it would be important to realise that the actual lifting capacity of these cranes was limited. I have heard that three tons was about the maximum but the saving in winding machinery to have independent jib movement would save time and money.

 

My 38 tonner was designed to lift that weight more or less vertically but the numbers plummeted as the jib ( 70 feet ) went outwards.

[Pacific231G]

 

 

Perhaps the luffing crane had other attributes that made it suitable for dockside use. For a  start, it would be important to realise that the actual lifting capacity of these cranes was limited. I have heard that three tons was about the maximum but the saving in winding machinery to have independent jib movement would save time and money.

 

My 38 tonner was designed to lift that weight more or less vertically but the numbers plummeted as the jib ( 70 feet ) went outwards.

I think Stothert and Pitt generally called them high speed level luffing cranes so I guess the clue is in that. The economy in electricity consumption of not lifting the load when luffing in was one of the main attributes claimed in the various patents and the direct crank linkage for the jib movement would have been a lot quicker than a luffing drum . There was an interesting variation on that in the Toplis' lifeboat davits (for multiple lifeboats) as used on the RMS Arundel Castle for about half of its boats (qv The Engineer  May 13 1921) Here, the lower power needed to winch the boats out could have been vital if the ship's main generators had been disabled as they likely would in a sinking. The davits could be powered by a small emergency generator on the boat deck or even manually. 

The cranes were always associated with manual cargo handling yanking bags and boxes in and out of the holds or baggage, post and even cars on and off ferries. I'd like to know what was the smallest such crane they supplied as that would probably be the best subject for a model.

Edited November 17, 2015 by Pacific231G

[rockershovel]

Nominal lifting capacity for cranes is often something of a red herring, it's usually the radius or maximum uplift that is more important in operational terms. Sparrows used to have (probably still do have) a 1000 tonne rated mobile that never lifted anything like that weight, but it was always busy.

[Fat Controller]

Nominal lifting capacity for cranes is often something of a red herring, it's usually the radius or maximum uplift that is more important in operational terms. Sparrows used to have (probably still do have) a 1000 tonne rated mobile that never lifted anything like that weight, but it was always busy.

The Principle of Moments, if my memory of 'O' level physics serves me correctly; 'The Moment of Force about a point is the product of the force and the perpendicular distance of its line of action about the point. So the 1000 tonne crane could only lift that weight if the jib was upright; if the load was 10 metres from the base of the jib, I think I'm correct in saying the maximum load would be 1/10th of the maximum, so 100 tonnes.

[Andy Hayter]

So, if the Patent for the luffing crane was applied for in 1912, what was around before then?

 

Is there still a model life for the Airfix/Dapol dockside crane on Pre WW1 layouts?

[PatB]

I'll bet he eats three Shredded Wheat for breakfast.

 

More like rather a lot of the distilled product at lunchtime in the late, lamented Haymarket as I recall . I believe Prof Runcorn is equally late and lamented these days as he was getting on a bit way back then.

[Arthur]

So, if the Patent for the luffing crane was applied for in 1912, what was around before then?

 

Is there still a model life for the Airfix/Dapol dockside crane on Pre WW1 layouts?

I would think so Andy, post WW1 as well. The level luffing type of crane was relatively expensive and probably only justified at busy ports. There were no doubt simpler survivors at quieter docks.

 

Not quite the Airfix model but with the same jib arrangement, common to caterpillar track mounted cranes too.

 

http://www.canstockphoto.com/images-photos/dockside-crane.html