While it is nice to know that fixing the CofG centrally over the driving wheels will produce a good working chassis, what about those occasions when this is easier to say than to do. This covers loco’s with weight bearing carrying wheels, and 0-n-0 locos which, for what ever reason, don’t naturally lend themselves to a centrally placed CofG.
To try and keep the arguments simple, its better if we start by thinking about 0-n-0s chassis.
A question of balance and adhesion, the 0-n-0 chassis.
If a loco doesn’t naturally suit a CofG centrally over the driving wheels, wouldn’t it be better to design a CSB which allows for a more convenient balance point? Isn’t the fact that, to date, our method for setting out the fulcrum points doesn’t want to work that way a bit of a constraint?
Also, the implications of having a design location for your loco’s CofG is that, if the finished loco doesn’t conform to the design there have to be consequences. It is certainly true that a CSBed loco with the CofG out of place will not sit as level as it should, and, while this may not be all that visible there can be implications for its running. See the 04 story. So, isn’t having to be careful about the balance of the loco an extra complication implied by the use of CSB?
First of all I’m happy to say that we now have Alan Turners new fulcrum calculation tool which he has posted on the Abstruse CSB Theory thread. This does enable us to work with a chassis where the CofG isn’t central, and it also tells us how much weight is being placed on each axle.
But even given that we can now design a chassis with the CofG off centre, I’m not convinced there is any real value in doing it unless it is truly unavoidable.
This is all down to adhesion.
Beyond a certain, fairly light, weight, a well balanced CSBed loco should run OK. Additional weight is only required to enable you to pull a worthwhile train. We need to remember that, for a chassis with any pretensions to similar loads on each axle, adhesion is limited by the lightest loaded axle. This is why we want the axles to be as equally loaded as possible, and this is only possible with the CofG central on the chassis. Moving the CofG away from the chassis centre means that, while the axle at the end nearest the CofG will be more heavily loaded, weight must come off the axles the other side of the CofG. This implies that adding weight off centre may well mean you loco has less pulling power! Therefore it makes more sense to weight the loco less, and get the CofG central, than to just load it up as much as possible and living with an off centre CofG!
So yes, we do need to be careful in weighing and balancing our CSB loco, but before you call this a good reason for not considering a CSB chassis, just have a think about the alternatives. The adhesion limit being set by the most lightly loaded axle isn’t just a sprung chassis issue, it applies to any loco. The fact that you may not have considered how the weight distribution of your compensated loco affects is adhesion doesn’t mean it doesn't have an effect, and very few compensated chassis will allow the sort of even weight distribution we are designing for with a CSB. See digest sheet 41 The Principles of Model Locomotive Suspension, Worked Examples
So while CSB chassis design does mean you need to be aware of where you loco’s CofG is:-
- 1. it isn’t difficult to know where the CofG is (for one method see here)
- 2. because we know just loading weight isn’t the answer, weighting to set the CofG by putting relatively small weight at the extreme ends of the loco is a lot easier than trying to get lots of weight in just anywhere.
The upshot is that the designing a CSB with the CofG central isn’t just a convenient design assumption, it actually is going to give you the best available performance from your chassis.
A question of balance and adhesion, CSB chassis with a load bearing bogie
So having got our head round the balance implications for a chassis which just has driving wheels all supported by the CSB, what about including carrying wheels, and in particular bogies, which don’t easily lend themselves to inclusion under a CSB.
To sort out this problem, firstly you need to realise that one key quality of a CSB chassis is that it sits level when the load it is carrying is applied at a given location, normally the centre the wheelbase. When considering the 0-n-0 chassis, this has been synonymous with the loco CofG, but when a loco has other load bearing wheels this is no longer true. None the less if the chassis is sitting level under load, then that load is still balanced over that design point, which in future I shall refer to the “Centre of Load” (CofL).
Next we need to remember a little school boy physics, and in particular, the Principle of Moments. While up to now it has been convenient to assume that all the loco’s weight is located at it’s CofG, the principle of moments tells us we can consider it as if it was divided into number of separate bits who's weights are distributed about the loco. Viewed this way, the weight times the distance from the CofG of all the pieces to one side of the CofG will exactly equal the weight times the distance from the CofG of all the bits on the other side. In particular we can divide the loco’s weight into two parts, one over the CSB CofL, and one over the bogie CofL.
For a loco putting some of its weight on a bogie, this tells us the actual CofG of the loco will be somewhere between the CSB CofL and the CofL of the bogie, which could well be a little CSB based chassis in its own right. We can chose how much weight is carried by the driving wheels , and how much is carried by the bogie, by deciding where the actual CofG is located.
Once you’ve got that, this diagram should summarise it all nicely..
From there on in all that is necessary is to decide how much of the loco weight you want to carry on the bogie, and arrange the CofG location accordingly. So,if you wanted, say, 10% of the loco weight on the bogie, the CofG will need to be 1/10th of the distance from the drivers CofL to the Bogie CofL, and you can see that the maths here isn't going to be to challenging. At this stage I’m not going to comment on what a reasonable weight distribution between drivers and bogie actually is. Mostly because I haven’t got any practical information on what works and what doesn’t. Perhaps others could lend there collected experience at this point.
As to getting the thing to sit level, your choices are as follows.
- 1. Design the chassis to sit level for a given deflection of the CSBs (presumably 0.5mm) on both drivers and bogie. You still get the option to play with the CSB wire sizes to suit the actual finished loco weight, and even to adjust the level if it still isn’t quite right. I was planning to release a 4 wheel version of the old spread sheet so you could calculate the required wire size on the bogie for a given load and defection, though it is possible Alan might get there first. However until then, or because there are a number of variables in play here which may not stack up as expected, one might still want to consider one or other of the following as well. Or even in stead.
- 2. Fitting an adjustable bogie rubbing plate so that you can adjust it up or down until the chassis sits level. Useful if your design proves imperfect and changing the wires will not produce a sufficient change in deflection to level up the chassis.
- 3. Adjust the loco CofG position for or aft until the loco chassis sits level. This changes the balance of load between drivers an bogie and hence their relative deflections.
If you’ve read the CSBs and the Single Bogie thread, you will see that I have just generalised the argument I developed to deal with the C12 discussed there. It was option 3 I chose on that occasion.