A TURN FOR THE BETTER by Dave Skertchly
Thwarted in his plan to build the Festiniog Railway’s Dduallt loop, “Mad Professor” Dave Skertchly, sets out to calculate the minimum turning radius for a garden railway.
It was when building the teardrop loop on my line, that I noticed a similarity with the famous spiral at Dduallt on the Festiniog Railway. I did some sums and found that, to scale, the spiral is actually larger than the whole of my garden railway, with a radius of about 65m (213’), which would scale to 3.4m (11’3”) in the garden. When I asked “The Wise Old Men of Garden Railways” about the minimum radius of a garden railway, I got the answer that the minimum is about 2’6”, but why is this?
The narrow gauge wheel standards presented by the Association of 16mm Narrow gauge modellers appear to give us all the information we need to set the wheels and check rails, but alas little else. An Internet search suggests that the wheel standards may be based on pre-1940s commercial coarse O gauge standards and that, in turn, probably means a bit of a guess.
It seems that track radius is determined by the limitations of tin plate track assembled on the hearth rug in front of a roaring coal fire. In those days, Hornby trains were grown-up toys, and functionality, not finescale, was the priority. Since there is no mention of minimum track radius, I set out to work it out from first principles.
As always, it is best to start at the beginning and a good place is by measuring the radius of our curves. A length of string might do, but a pair of rules to measure the width and height of the arc can enable the radius to be calculated using geometry. I used a free program available on the web to do the calculations.
You will have noticed that the wheels of a train are solidly fixed, so when going around a corner, the outside wheel has to travel further than the inside wheel. This is a bit of a problem, effectively twisting the wheel off the axle. A Facebook friend, however, reminded me that train wheels are not flat, they are tapered, by 3-degrees or so it is said,
this is called the coning angle.
As a pair of wheels enter the curve, they try to go straight on, this is nothing to do with inertia but geometry, which causes the outer wheel to climb to the top of the taper and the inner wheel to run on the bottom of the taper. Each wheel is now rolling on a different diameter so they turn towards the smaller one, and that’s towards the inner wheel. The train will also conveniently lean into the corner.
I am rubbish at sums, so I set up a spreadsheet to do the maths, a trick known as “Newton’s method” or ”the method of successive approximations”. The spreadsheet calculated the circumference of the inner and outer path covered by the wheel sets and then the radius. I noted that the minimum radius would be the one case when the difference in track radii was equal to the track gauge. Surprisingly, I found that the track radius is dependant on wheel diameter, and in all the cases, it was much greater than the apocryphal 760mm or 2’6”.
The alternative to the wheels gliding almost frictionless around curves is to have them shoved around by the flanges, just listen to a full-size train on a tighter than standard corner. It screams as the wheels slip, the flanges rub and steel slivers are ground off the rails, to alleviate this, flange lubricators are fitted to the track.
The flange makes contact on a chord determined by the core diameter of the wheel. The maximum gap between the flange and the track on the centre line is 1mm derived from the design of the wheels and track. The line extended from the contact point through the maximum gap allowed by the specification to the point at which it intersects with the same line extended from the other pair of wheels when separated by the wheelbase, plus a bit of geometry gives us the two parameters we need to calculate the turning radius with our internet calculator.
The table shows the turning radius for trucks carriages and locomotives having different wheelbases and wheel diameters. The wheel diameter seems to be pretty well irrelevant, so it is all down to wheelbase. We can see now that the “Wise Old Men of Garden Railways” are absolutely right, the minimum turning radius is now about 760mm (2’6”) but only for trucks and locomotive having a wheelbase of less than 40mm (1.5”). I guess that this is what Robert Fairlie and James Spooner found out when they developed the articulated Fairlie locomotive.
I was just about to order a pint of fine Auld Phagbutt when I suddenly wondered about the radius of curves on my railway. Using the Internet calculator, I found that two of my corners are just 2’3” while one is unintentionally even less, down to 650mm (2’1”).
Before I could get to that pint, I wondered whether I could measure the effect of wheelbase and bearing type on the train? It so happens that I have short wheelbase slate wagons, long wheelbase coal wagons and long wheelbase carriages. By coincidence, I also have three matching carriages made many years ago on which the wheels are free to rotate on the axle.
In GR 313 Sep 2020, you will recall that I made a dynamometer truck to measure drawbar loads and this truck was retrieved from its box. All the trucks/carriages were ballasted until they weighed roughly the same, even though weight makes little difference. Each rake was connected to the dy
namometer and in turn, hauled by the works HGLW shunter. The drawbar load was noted on the straight and in the positions around my tight curves. The drawbar load on the straight was then subtracted from that measured on the curve to ensure that the results reflected track friction not bearing friction. The results were spectacular.
The slate wagon has small wheels and a 40mm wheelbase, which our theory tells us should be almost friction-free and, as predicted, it does indeed have the lowest drawbar load. Next best is the carriage with a 100mm wheelbase but with wheels that can freewheel on the axle. The fixed axle trucks and carriages with the 100mm wheelbase take almost three times the drawbar load as the slate wagons having the same weight. The eagle-eyed among you will note that I seem to have a problem at Lost’n Bodge and this will need attention from the track gang!
So, I can now explain why the larger, more powerful locomotives with four or sixwheel drive and a long wheelbase can haul less than the tiny Penelope the Gas Works Peckett. Friction is wasting energy on the tight curves. My large locomotives, using six or more batteries, will run for an hour or so,
but my smaller locomotives will run all afternoon on just two batteries.
As I sit on my rustic park bench outside the Sheep Shearers Arms I sip at my pint of fine Auld Phagbutt and consider how it is that our track standards have always been a bit of a guess. I recall when dad smoked a pipe while we sat and shivered in shorts and watched patiently while dad played with our trains in front of the roaring coal fire. The logic of those rail standards may indeed now be lost in the mists of time but as “Elizabeth Mary” the diesel hauls a rake of theoretically-oversized trucks through the tight turn at Rainbow Rock and past the flowers adorning the cutting, I realise that maybe they got it right after all. Cheers.
Editor: If you would like to look into this further, we will make the original spreadsheets available for download from the Garden Rail March section of Rmweb.co.uk ■