Continuous Springy Beams without tears.

The following was first published in Scalefour News 194.

Continuous Springy Beams (CSBs) have, over the last ten years or so, have proved themselves to be an elegant solution to the problem of providing a suspension system for finescale locos. However Foe many people there is a fundamental problem with them in that the placement of the anchor points that hold the spring wire is non-obvious. This has lead to the use of complicated spreadsheets determine these points, which is of putting to many people. I have long held the belief that what was needed was a simple rule of thumb method where the anchor point positions could be calculated with nothing more sophisticated than a calculator. Now after an afternoon of displacement activity, when I should have been working on something else, I have found the answer[1].

Magic Numbers

The problem that CSBs poses mathematically is that there are an infinite number of solutions. While we can discount many of these, for instance where the outer anchors lie outside the frames, there are still many other possible combinations of anchor that will give similar solutions. However there is one special case that gives a ‘magic number’ that will help with a more general solution.

CSB four coupled

If we use the case of a four coupled loco, it is obvious that if the centre anchor is placed midway between the axles and the outer anchors are arranged symmetrically the bottom of the curve that the spring takes up will occur at a point midway between the axles, i.e. at the central anchor point (Fig 1 A). Now if we move the outer anchor points, so that they stay symmetrical, there will be a point where the top points of the springs curve will be above each of the axles (Fig 1 B). From experience this point is about 0.3 of the wheelbase outside the axles. This relationship will remain true for all wheelbases that we are likely to use and it is also true however many axles there are. So 0.3 is are ‘magic number’ which we can use in future calculations.

The Plot Thickens

CSB test graphic

What I did was to take a symmetrical frame, in this case 8′ x 8′ (32 x 32mm), and built a plot using the spreadsheet to produce a range of wheelbases where the centre axle was progressively offset by 6” (2mm), while the outer anchor points were kept constant. This is shown in Fig 2. I occurred to me that, given I had not been too careful about choosing the ‘best’ outcome, that there were two relationships that were worth pursuing. One was that the lefthand inner anchor was a constant distance from the lefthand axle and that there was a relationship between the position of the righthand inner anchor and the offset of the centre axle. I went back to the spreadsheet and proved my conjectures by plugging in the calculated positions. After then testing the calculations on another wheelbase (6′ x 6′), I felt confident enough that the conjectures were correct to spent time finding all the edge cases to produce this:

CSB Matrix

This is a matrix of all the wheelbases where the rule of thumb gives an acceptable result. The shorter wheelbase is plotted on the vertically, while the longer wheelbase is plotted horizontally. A green block represents a wheelbase where the maximum and minimum weights on the axles are within about 2% of each other. The yellow blocks represent wheelbases which lie just outside the 2% limits or where they could be inside or outside the limit depending on how values are rounded. Looking at the matrix I think that most loco classes will well within the green part of the plot [2], but I would be glad to hear of any that are in the yellow blocks or even the uncoloured parts to the top right hand.

The Rule of Thumb

CSB Universal

Answers

Does this mean that I don’t have to use the spreadsheet?

Not really, since the spreadsheet will give you information on the best size of spring wire to use and the position of the centre of gravity which will help to balance the loco. Also there may well be occasions where the calculated positions of the anchors coincide with some part of the structure of the frames, brake hangers in particular, then you will have to resort to the spreadsheet. You will, however, have a set of starting points for the anchors that will take ease finding a correct solution.

[1] Or maybe just one of many answers

[2] I have not counted any early French or Belgian locos in this.

A little closer

Prompted by a mega thread on RMweb (and an enthusiastic customer) I’ve completed the drawings for a set of loco frames that, it’s hoped, will make like much easier for those who want rarer locos but who don’t enjoy assembling etched brass kits.

The renderings represent a MR 1F 0-6-0T which is part of a batch of MR and S&D Johnson kits that will be put into production in the first half of next year. The main part of the frames is cast in brass and the keeper is sintered nylon. Etched phosphor-bronze strips are attached to the keeper to for the pickups. This particular set of frames is a test piece to test the fit of the keeper, it is intended that the frames that are included in kits will have the footplate and splashers included in the cast. With luck this set will be ready before Christmas and then work can start on the production frames.

Constructive comment welcome.

MR 1F 0-6-0T cast frames.

Components of cast frames for a MR 1F 0-6-0T

Loco Bodies

There has been a discussion of 3d printed loco bodies in this thread with interesting contributions from Atso and Atlantic 3279. Experience with the O4/5 body has shown that, not only will a raw 3d print be expensive and need a lot of finishing, but that the machines which these prints are made on are not always consistent in what they produce. I have come to the realisation to the best way to produce loco bodies is to cast them in resin from 3d printed patterns. This will give major advantages e.g.

Lower prices and/or better margins.
‘Ready to paint’ finish.

However there are some disadvantages.

Longer lead times.
Batch sizes will be larger.
The holes for fixing handrails have to be drilled by the modeller.
Some parts e.g. backheads, cab fittings and possibly smokebox fronts will have to be made separately.

In view of the need to order resin castings in batches I am going to need some, maybe 12-15, pre-orders before they are put into production.

However this is all in the future, as most of my design time of the next few months will be directed towards producing drawings of frames for the loco and loco frame kits that have already been announced, together with some others that have been promised but not announced on the website. In all I am aiming to have about a dozen done by Christmas. Renderings of these drawings and forthcoming wagon and coach kits will be posted on my Newsletter as they are finished.

To sign up for the newletter, if you haven’t already, go to this page

New Stuff

Instead of scratching my head trying to thing something clever to write, i’ve decided to take the easy way out and just post pictures of things I’ve been working in recently.

Bridge Plates

Bridge Plate Rendering

These are for a skew bridge on a customer’s new layout. The dimensions are 35 x 7 x 2 scale feet (140 x 28 x 8 mm in 4 mm scale) They are being produce at the moment an the price will be £64 for a pair.
Similar bridge plates can be produced with different dimensions. Please ask for details.

LNER O4/5 Boiler
BLK0500/5 LNER O4/5 boiler/cab 4
BLK0500/5 LNER O4/5 boiler/cab 3
BLK0500/5 LNER O4/5 boiler/cab 2
BLK0500/5 LNER O4/5 boiler/cab 1
This is a complete replacement for the boiler/cab unit on a Bachmann Robinson O4 2-8-0. This on will produce the O4/5 variant of which there were 9 examples lasting from 1932 to 1959. These boilers can be produced with or without firebox hand holes and washout plugs and with or without vacuum ejectors.
The prototype drawing is finished and will be sent for production shortly. The expected price will be about £50.
Other replacement units are contemplated, both for the Robinson O4 and other Bachmann locos.

All the pieces on this page will be supplied unpainted and direct from the manufacturers.