A thorny maths problem

[devondynosoar118]

Ok, this is probably going to sound like a maths test paper so here it is.

Tom (a maths dunce) is measuring the outline of a long lost engine shed from a map. The scale is 1 inch to 40 feet.

He measures the bar of the scale and discovers it is only 94% of its correct length or 1/16th inch short. This means the map is not its full size either.

 

How does tom convert what he measures from the map into 2mm to the Foot scale without his brain running out his ears?

 

For an extra 5 marks, write a moron proof formula where X is the measurement from the under scale map and Y is the dimensions he should cut from his plasticard for a 2mm scale model!

[Guest jim s-w]

To correct the map times all measurements by 1.064

 

to convert to 2mm scale times mm by 3.15

 

Or to keep it simple times all measurements on the map by 3.35

 

HTH

 

Jim

[Nick Holliday]

I realise that this is extreme nit-picking and won't affect the final result, but by my calculations the plan has ended up being reproduced at 1:512 - the original scale (1:480) times 16 over 15, although this is dependent on the accuracy of the measurement against the scale bar. Since 2mm scale is a ratio of 1:152, every measurement on the plan has to be multiplied by 3.37! However this does assume that the distortion is the same in both directions across the whole of the plan.

What I would suggest to Tom is that he lets us know which long-lost shed he is interested in, and maybe someone can come up with more accurate dimensions. I think that the dimensions of almost every GWR shed, together with much of the ancilliary buildings, are given in the two volumes by Eddie Lyons, and I suspect that this info is available for many other lines as well.

[Kris]

I would guess that it is the Kingsbridge shed, Nick.

[devondynosoar118]

It is Kris. Thank you for giving me a clear formula Jim, bonus marks to you. Nick I will check the Library database and Amazon for those books as well as they sound like an exceptionally useful resource.

[Guest jim s-w]

No Worries

 

Id probably use Nick's figure of 3.37 though as he seems more knowledgeable than me. The 0.02 wont make any real difference but may as well use the right numbers.

 

Cheers

 

Jim

[devondynosoar118]

I must have a much reduced version of the plan! My scale length shed is 28mm long. I am guessing that I will have to go to the cookworthy museum and see the original, if it is there. Unless anyone has the book mentioned above. Its going to cost me £16 I don't have.

[Kris]

Having done a quick and dirty bit of measuring I think that you will end up with a building in the region of 70 - 75 scale foot long. This does strike me as being a little on the large size and I wonder if the map that I have just scaled this off has included the water tower as part of the engine shed structure as this does not show separately. If you take this off the length then you would end up with a shed about 55 - 60ft long which sounds more reasonable.

[Nick Holliday]

According to Eddie Lyons, Kingsbridge shed was "approximately 100 ft x 21 ft." Sadly this is not one of the more accurate dimensions that appear elsewhere in his book. Your shed would then be roughly 200 mm x 42 mm. However, scaling off the drawing in the book, the shed comes out more like 78 ft x 23 ft, and this is roughly confirmed working off the www.old-maps.co.uk 1:2500 OS map for 1938. This would make the model 156 mm x 46 mm. I suggest you have a go at taking images from old-maps and superimposing them on a modern satelite view which can be scaled, to get your own plan.

[devondynosoar118]

Thank you very much gentlemen. Unfortunately the shed in question has been demolished so I cannot put Nick's suggestion int practice. Given the proportions you have given me I will go with the measurements you have given me. Thanks again Kris for using your excellent database again. Nick that sounds about right looking at the pictures. The GWR map of the original plan has the shed separate from the water tower. I am starting the carcass this week if I can. Also is there any mention of windows? From the views I have it looks like only roof lights are present and that there is a row of vent chimneys along the roof. Rather annoyingly most photographers seemed to stand with their back to the shed when they took pictures!

[Kris]

Looking at this photo I would say that there were not any windows (at least towards the front of the shed), both from the poor view of the side of the shed and the lack of light in showing in the shed its self (obviously the loco in there would block out some of the light).

[devondynosoar118]

Gosh, 2 engines on shed! A busy day on the branch. I agree, I have not found anything to suggest windows on either side. In the 1890's views in the branch book you can see almost the whole side of the shed. It is quite long and there are clearly no windows on the platform side. Thanks again for more detail Kris. Those drawings of the station doorways and detail were really useful too. Do you think the platform facing is brick or stone? I thought brick but this view looks more like stone. The main platform face is certainly stone.

[Kris]

The main platform face was stone for part of the length. If you have the Vic Mitchell & Keith Smith's book and look at photo 101 you can see that the stone facing ends maybe 20 - 30ft beyond the end of the bay. After this the main was brick faced. Image 106 from the same book also shows that the bay platform side was brick faced at the station end and photo 111 shows the brick facing at the far end. Photo 109 shows the other side of the bay and this also appears to be brick faced, this photo also gives a very good view of the inside of the engine shed clearly showing that there were no windows on the hill side of the shed nor at the end of the shed. The light in the shed appears to be coming entirely from the roof lights.

If you have Ken Williams and Dermot Reynolds's book (2nd edition) there is a cracking side on photo of the engine shed on page 75, this confirms that there were no side windows on the station side.

Going back to the platform I suspect that originally the whole length was stone faced but I suspect that the brick faced section was a result of the platform extension. If this is the case it suggests that when the platform was extended they also remodelled part of the existing section giving that a brick face at the same time.

[devondynosoar118]

I don't have the Mitchell and Smith, I will have to get a copy. Thanks on photo info, Will do a mixture as suggested but I'll get the book 1st. I have seen the pic of the shed you mention and its a cracker. I have been formulating a method for the vents, I am thinking brass box section and soldered wire or guitar string, depending on thickness.

[Kris]

I think that they have it in harbour books, so you could at least have a look to see if it is worth purchasing.

[devondynosoar118]

I still am not having any joy despite Nick's excellent plan which has however resolved a few issues I had with where things go around the buffer stops. I have resolved to go with the dimensions Nick has calculated from the old maps and take Kris' advice on the finishes and window detail. Am starting the carcass tonight!

[devondynosoar118]

The shed is now an almost completed shell, just the smoke channel and chimneys to put in plus the roof and chimneys. Will post some pics as soon as I can. Thanks to all, I recon it looks pretty close to the original.

[Guest jonte]

Please for give me for chipping in with the men, but if I'm to understand that you've measured the length of the building as 28mm on the map, this equates to 44 feet in real life.

 

This is how I arrived at my answer:

 

As Nick quite rightly calculates, a scale of 1 inch to 40 feet, is equivalent to 1:480.

However you say that the scale measures 15/16" and that the map has been adjusted accordingly.

 

To arrive at my answer, therefore, I simply used ratios (Just as Nick and Jim did), although I arranged mine as follows:

 

1 : 480 : : 15/16 : X

 

Therefore, X = 450" (480 x 15/16)

= 37.5 feet

 

In other words, for every 15/16" on the map, this represents a distance of 37.5 feet.

 

So, if I'm right in assuming that you've measured the length of the building on the map as 28mm, this converts to approximately 11/10", therefore:

 

15/16 : 450 :: 11/10 : X

 

X = 528 "

= 44 feet.

 

If I've totally misunderstood you, then please just ignore, however, perhaps you might find my method of some use.

 

Jonte

[devondynosoar118]

Thank you Jonte- All contributions welcome. Seeing the working out is helpful. I have now built the carcass of the shed, pics to follow but I am sure I will need the above for the next few buildings!

[Guest jonte]

Thank you Jonte- All contributions welcome. Seeing the working out is helpful. I have now built the carcass of the shed, pics to follow but I am sure I will need the above for the next few buildings!

 

Hi devondynosoar118

 

I'm glad to help and I hope you can follow my workings. If you need any further assistance and you think I can be of help, please don't hesitate to PM me.

 

Out of interest, I had a look at the photo of the shed that appeared in a previous post and I think the angle of the photo makes the building appear longer than it is/was, although I'm certainly no expert with a lens.

 

Best wishes,

 

Jonte

[Nick Holliday]

Jonte, I hate to be nit-picking but there is a fundamental flaw in your argument.

First of all, we have to assume that the scale bar on the drawing was intended to be 1 inch long, on the basis that the drawing was supposed to be 1†to 40’. However, on the print this one inch bar was actually only fifteen/sixteenths of an inch, (94%) which would imply that the drawing had been reproduced slightly under scale. However, the scale bar would still represent 40’ (assuming that is the correct scale for the drawing). This therefore means that every 15/16 inch measured would represent 40 feet; hence 1 inch on the print would now represent 42’ 6â€, at a scale of 1:510.

If we understand the 28 mm measurement to be taken off this reduced print, that would then represent roughly 47 feet on the ground.

 

However, by whatever calculation that is used, an engine shed of around 45 feet long is unusually small, and the available evidence would seem to suggest that a figure between 75 and 100 feet is more likely. I can only conclude that the original drawing was either not 1†to 40’, perhaps 1:1250, and the scale bar represented 100 feet, which would lead to an overall length for the shed of 110 feet (rather more than the figure that Eddie Lyons quoted) or the drawing was 1†to 40’ but has been reduced rather more than by 94% and we have misunderstood the significance of the scale bar

 

Playing with the figures, light has just dawned. The scale bar on the plan (15/16†or 23.8 mm) actually represents 1 chain, or 66 feet, which is the standard unit for surveying. Taking the 28 mm measurement and dividing by the scale bar length and then multiplying by 66 gives the answer 77’ 6â€. This is fairly close to the size I scaled off old-maps and passed to the enquirer. This means the scale of the drawing is approximately 1:850, which would mean that the 2mm scale dimension would be 850/152 the plan dimension, or a multiplying factor of 5.65, making the length of the engine shed roughly 158 mm. Sorry if this has come a bit late, I might have been inspired earlier if only I had been able to find the copy of a 1†to 40’ plan in my possession which is currently buried somewhere in my loft!

[Guest jonte]

You sound as though you know what you're talking about so I shaln't argue

 

As I wrote in my post, I was also working on an assumption; an assumption that the map had been amended in proportion to the scale hence the method I chose. Knowing very little about maps, is it possible that could that be the case, or would that simply not be? I'm not bad with Admiralty charts though

 

Perhaps the engine shed was merely for overnight stabling purposes (Sidmouth?), anything more serious requiring a visit to an MPD - if that's the correct term? Apologies, I'm afraid I'm more of a modeller than a train buff

 

Best wishes,

 

Jonte

[Kris]

Perhaps the engine shed was merely for overnight stabling purposes (Sidmouth?), anything more serious requiring a visit to an MPD - if that's the correct term?

 

 

The shed was only for overnight stabling Jonte, normal maintenance of the lines locos would have been carried out at Laira (Plymouth).

 

 

[devondynosoar118]

I think the map in question has been substantially reduced, I also think that I may have been incorrect in my initial measurement of the scale bar. Dad has sent me two corrected plans he got off the web with a description of the scaling. With the goods shed I can simply run a tape over it and then scale it down. The huts are all fairly small but I wanted the shed, station, motor goods shed and (eventually) goods shed to be as good as I could get them. Will get the pics pf the engine shed next Monday.

Anyone have any idea as to the internal detail? I have assumed that the roof joists were similar to those in the Station building but wondered if there was a smoke channel along the ridge, connecting to the chimneys visible in the roof, or weather these were simply supported on the purlins without a channel, the vents just being of the hole in the roof type?

[Kris]

There was a channel below the level of the joist tie beams that collected smoke steam etc from the loco. I would assume that this was likely to have been connected to the chimneys. This channel appears to have run the full length of the shed and appears to have been 3-4ft wide with straight sides at least a foot (maybe 2) deep.