Here is a spreadsheet calculator for working these out. I don't know if something like this is already available here somewhere. If it is and it's better please say so someone and I'll erase this.
As I know nothing about maths, computers, etc, I can't help if anyone has any questions. My son put it together for me; he has the grey matter I lack. Hopefully it still works from being downloaded to my phone and uploaded here.
I find it useful to know in advance for example whether drain cocks are going to be clouted by a pony wheel on a 4ft curve, and how much they need to move out if so.
Although he has labelled it a sideplay calculator this has nothing to do with sideplay of the wheels within the rails. Sideplay will vary according to the Back to Back and any gauge widening; this spreadsheet makes no allowance for those things.
Bogie and pony wheel swing calculator

 Posts: 981
 Joined: Sat Jan 09, 2010 11:33 pm
Bogie and pony wheel swing calculator
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 20170919  leading_trailing sideplay.xlsx
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Re: Bogie and pony wheel swing calculator
Just looking at the diagram, accompanying the Excel spreadsheet, isn't there a variable missing to cater for a bogie rather than a pony truck  2 axles rather than one? The mathematical model, shown, will work for a pony truck and the trailing wheels of a four wheel bogie.
The coupled wheelbase chord a. is depicted as touching the bogie wheelbase chord b which will work for a pony truck where b represents the distance between the leading driving axle and the pony truck axle. In most locomotives there is a space between these two entities which is the separation of the bogie/pony wheels from the coupled wheels. This separation effectively increases the deflection of the bogie/pony truck, the more separation there is.
For a bogie, an additional chord needs to be added to the model (chord c. which adjoins chord b.) representing the wheelbase of the bogie.
On a locomotive with a four wheel bogie, the front wheels of the bogie will deflect more than the rear wheels, so a v(i) and v(ii) measure is required being the respective deflections of each pair of bogie wheels.
I had a discussion on RMWeb, quite recently, about the problems of an rtr B16/1, which has a large separation between the coupled wheelbase and the rear of the bogie wheebase (7' 8" or 30.66 mm in 4mm scale) and a 6' 6" (26 mm in 4 mm scale) wheelbase bogie, such that on typical rtr curves (I took 18" radius as a representative), the bogie wheels would foul the backs of the cylinders.
This also comes into play on those locomotives which do not have bogie wheel cutouts in the mainframes. The LNER D20's and G5's (to name but two) employed pinching in of the mainframes (by around 1.5" each side) to handle the bogie wheel deflection, which is fine on the 4 mm equivalent using 8' radius curves but doesn't work for much below 4' 0" radius.
Cheers
MIke
The coupled wheelbase chord a. is depicted as touching the bogie wheelbase chord b which will work for a pony truck where b represents the distance between the leading driving axle and the pony truck axle. In most locomotives there is a space between these two entities which is the separation of the bogie/pony wheels from the coupled wheels. This separation effectively increases the deflection of the bogie/pony truck, the more separation there is.
For a bogie, an additional chord needs to be added to the model (chord c. which adjoins chord b.) representing the wheelbase of the bogie.
On a locomotive with a four wheel bogie, the front wheels of the bogie will deflect more than the rear wheels, so a v(i) and v(ii) measure is required being the respective deflections of each pair of bogie wheels.
I had a discussion on RMWeb, quite recently, about the problems of an rtr B16/1, which has a large separation between the coupled wheelbase and the rear of the bogie wheebase (7' 8" or 30.66 mm in 4mm scale) and a 6' 6" (26 mm in 4 mm scale) wheelbase bogie, such that on typical rtr curves (I took 18" radius as a representative), the bogie wheels would foul the backs of the cylinders.
This also comes into play on those locomotives which do not have bogie wheel cutouts in the mainframes. The LNER D20's and G5's (to name but two) employed pinching in of the mainframes (by around 1.5" each side) to handle the bogie wheel deflection, which is fine on the 4 mm equivalent using 8' radius curves but doesn't work for much below 4' 0" radius.
Cheers
MIke

 Posts: 372
 Joined: Sun Jul 20, 2008 6:27 pm
Re: Bogie and pony wheel swing calculator
I had this problem recently when constructing a C.R. 440 (A Dunalastair 1).
I first worked out for the coupled wheelbase the tightest radius before the flanges began to bind.
Then I worked out how much sideplay I could allow on the bogie, having first decided on how much I could narrow the frames at the front, and making assumptions about whether the bogie would be pivoted at the middle, or 1" off the middle, as the CR did, or near the rear axle, leaving all the movement to be on the front axle, or the other way round.
Then I had a dram
What assumptions can be made in any calculations, bearing in mind that the relationship between full size track and full size wheels is not the same as the relationship between P4 wheels and P4 track
Then I thought the bogie pivot should not be fixed, but should have spring controlled sideplay, as the prototype did. So how much sideplay should I allow, and how was I going to control it?
Then I had another (large) dram.
Then I thought "how am I going to spring this thing"...……..
I'm not showing them here, but I did cover pages in calculations. A lot of data is available. But I built the thing according to what seemed possible and reasonable, and mostly ignored the calculations. And it runs beautifully round my far from perfect track, with radius down to 39".
Incidentally, in my experience any P4 wheel that doesn't carry sufficient weight will carry straight on at the first bend!
Allan F
I first worked out for the coupled wheelbase the tightest radius before the flanges began to bind.
Then I worked out how much sideplay I could allow on the bogie, having first decided on how much I could narrow the frames at the front, and making assumptions about whether the bogie would be pivoted at the middle, or 1" off the middle, as the CR did, or near the rear axle, leaving all the movement to be on the front axle, or the other way round.
Then I had a dram
What assumptions can be made in any calculations, bearing in mind that the relationship between full size track and full size wheels is not the same as the relationship between P4 wheels and P4 track
Then I thought the bogie pivot should not be fixed, but should have spring controlled sideplay, as the prototype did. So how much sideplay should I allow, and how was I going to control it?
Then I had another (large) dram.
Then I thought "how am I going to spring this thing"...……..
I'm not showing them here, but I did cover pages in calculations. A lot of data is available. But I built the thing according to what seemed possible and reasonable, and mostly ignored the calculations. And it runs beautifully round my far from perfect track, with radius down to 39".
Incidentally, in my experience any P4 wheel that doesn't carry sufficient weight will carry straight on at the first bend!
Allan F
 grovenor2685
 Forum Team
 Posts: 3447
 Joined: Sun Jun 29, 2008 8:02 pm
Re: Bogie and pony wheel swing calculator
For a bogie, an additional chord needs to be added to the model (chord c. which adjoins chord b.) representing the wheelbase of the bogie.
Not really, just do the calculation seperately for each wheelset using 'b' as the distance from wheelset concerned to the driving wheel.
And if you want the sideplay required at the bogie pivot do it a third time using the distance from drving wheel to bogie pivot.
Regards

 Posts: 981
 Joined: Sat Jan 09, 2010 11:33 pm
Re: Bogie and pony wheel swing calculator
Mike I was relieved (and grateful!) to see no less an authority than Keith give exactly the answer that I was going to do.
What I can't, after further thought, get my head round is this. My first 044 wouldn't get round a 4ft curve when the bogie pivot was as designed centrally above the bogie. There was not enough sideplay on the inner driving wheel. But moving the pivot inwards to a point halfway between bogie and inner driving wheel solved the problem even with the bogie still fixed to the arm from that pivot.
Allan's alcohol fuelled practical experience proves too that an ounce of practice is worth a ton of theory. I'd love to see a pic or even video to cheer us up Allan! Such a beautiful prototype. And to have a dram when we next meet!
So it seems to me the calculator is more useful for pony trucks than bogies. But it may be useful as a general warning light that there may be problems that require creative solutions when thinking about, for example, getting a beautiful A1 round a 3ft curve!
What I can't, after further thought, get my head round is this. My first 044 wouldn't get round a 4ft curve when the bogie pivot was as designed centrally above the bogie. There was not enough sideplay on the inner driving wheel. But moving the pivot inwards to a point halfway between bogie and inner driving wheel solved the problem even with the bogie still fixed to the arm from that pivot.
Allan's alcohol fuelled practical experience proves too that an ounce of practice is worth a ton of theory. I'd love to see a pic or even video to cheer us up Allan! Such a beautiful prototype. And to have a dram when we next meet!
So it seems to me the calculator is more useful for pony trucks than bogies. But it may be useful as a general warning light that there may be problems that require creative solutions when thinking about, for example, getting a beautiful A1 round a 3ft curve!
Re: Bogie and pony wheel swing calculator
Julian Roberts wrote:Mike I was relieved (and grateful!) to see no less an authority than Keith give exactly the answer that I was going to do.
What I can't, after further thought, get my head round is this. My first 044 wouldn't get round a 4ft curve when the bogie pivot was as designed centrally above the bogie. There was not enough sideplay on the inner driving wheel. But moving the pivot inwards to a point halfway between bogie and inner driving wheel solved the problem even with the bogie still fixed to the arm from that pivot.
Allan's alcohol fuelled practical experience proves too that an ounce of practice is worth a ton of theory. I'd love to see a pic or even video to cheer us up Allan! Such a beautiful prototype. And to have a dram when we next meet!
So it seems to me the calculator is more useful for pony trucks than bogies. But it may be useful as a general warning light that there may be problems that require creative solutions when thinking about, for example, getting a beautiful A1 round a 3ft curve!
I had exactly the same quandry on the G5 044's that I built. The bogie etching, in the kit, had a pivot hole in the stretcher, around 2mm from the bogie centre, towards the rear driving wheel. With that arrangement and with no allowance for sideways movement of the bogie/stretcher, only rotation, then the bogie wheels nearest the rear drivers would tend to turn outside of the curve and the ones furthest from the drivers inside of the curve.
The problem was sorted by making the hole in the stretcher into a slot such that the bogie pivot point can actually move into the curve as well.
As Keith points out, your mathematical model can be used to calculate the width of the slot necessary to allow the correct sideways movement of the bogie stretcher and hence the actual deflection of the pivot point of the bogie.
Of course, the acid test was trying the whole chassis on a curve of the minimum radius on the layout.
I think this is the same solution as Alan used but I missed out on the dram; I resorted to Shiraz.
Cheers
Mike
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