Midland Railway Company

[Compound2632]

There was a typical comment on the LNWR Facebook group, re. the Precursor Tanks (a class of non-superheated 4-4-2T engines derived from George Whale's 4-4-0s): "I do wonder how the LMS could classify these locos as 2P, Midland prejudice perhaps?" I had to point out that in terms of the key factors entering into the tractive effort calculation, compared to the LMS Standard 2P, the Precursor Tank had identical-sized cylinders and lower boiler pressure, with only its smaller wheels being in its favour. The 2P and the 483 Class from which it was derived were of course superheated engines with piston valves. It's not a question of prejudice but mathematics. But of course nominal tractive effort cannot tell you everything about a locomotive's effectiveness.

[Dave Hunt]

The power classification wasn't based on starting tractive effort anyway. Somewhere I have the details of how it was calculated and when I get a round tuit I'll post them.

 

Dave

[bbishop]

A very cogent argument, Dave.  It is worth reading both volumes of Eric Langridge's "Under 10 CMEs", especially where he designes the motion for the Class 4 tanks.  Bill

[Compound2632]

1 hour ago, Dave Hunt said:

The power classification wasn't based on starting tractive effort anyway. Somewhere I have the details of how it was calculated and when I get a round tuit I'll post them.

 

Dave

 

TE at 50 mph for passenger engines, I understand. But I've not discovered the formula for that, only starting TE.

[Dave Hunt]

OK, having found a spare round tuit in the workshop I can now offer the following on power classes, which I hope will not be too boring.

 

Although the basis of the power classification system used by the LMS and later by BR can be said to have originated on the Midland, there were distinct differences. The Midland’s system started in 1889 when passenger locomotives were grouped into three classes and tables of loads were drawn up a document issued in 1896. Initially the classifications were not constant throughout the Midland, though, as some locomotives were in one class for a particular route but a different class elsewhere. This anomaly was later corrected. At first, the most powerful engines were put into Class 1, the next into Class 2 and so on but each time more powerful engines were introduced the classes had to be rearranged so in 1905 the system was reversed with Class 1 the least powerful and Class 5 the most powerful. Thus classes could be introduced as engine power increased without rearranging everything else. Power classes 1 – 3 for goods engines were introduced in January 1905 and in 1906 the number of passenger classes was reduced from five to three. In 1908 passenger power class 4 was introduced for the Compounds and '990' Class 4-4-0s and in 1914 goods class 4 was applied to the 'Big Goods' 0-6-0s. Tank engines, however, remained unclassified.

 

The main purpose of using power classifications was so that the Traffic Department could stipulate which locomotives should be assigned to particular trains to maintain schedules and when by 1910 the Paget/Follows traffic control system begun in 1907 was in operation throughout the Midland, they were an essential feature. Maximum loads for a particular class over a given route were stipulated such that the poorest engine of that class could maintain section timings irrespective of its condition (providing it was actually serviceable) so controllers and shed foremen were better able to allocate suitable locomotives to duties. There is actually more to it than that but the above will suffice.

 

At the grouping the LMS decided (note – the LMS, not some mythical Midland ‘takeover’ faction as those making the decisions came equally from the LNWR/LYR as well as other constituents) that there was a strong case for adoption of the Midland’s traffic control system insofar as classifying engines by power and publishing maximum permitted loads based on those classifications. However, whilst the Midland had based its classifications on a combination of boiler and cylinder size this was then considered too simplistic. Using nominal tractive effort was rejected since the actual results obtained when running differed markedly from those suggested by the figures it produced due to various factors. A significant one was the mean effective pressure (MEP) in the cylinders, which depends on such things as sizes and streamlining of steam pipes, port openings, valve events and boiler capacity and falls off with increasing piston speed so any measure of tractive effort must be allied to the design speed range of the locomotive. The L&YR had calculated that MEP as a percentage of boiler pressure varied by up to 65% for piston speeds between 150 and 1,200 feet per second and Horwich Drawing Office produced a curve showing average MEP against piston speed that eventually formed the basis for the power classification adopted. Details were contained in an annexe to a document on various matters of locomotive policy issued on 23rd February 1923 as follows:

 

                                                    METHOD OF RATING ENGINES ACCORDING TO THEIR POWER

        The value of an engine as a means of hauling a train depends upon the drawbar pull it is capable of producing at the speeds at which the class of traffic for which it is designed normally runs.

        Strictly speaking, the drawbar pull depends not only on engine dimensions, such as cylinder volume, grate area etc. but also on the resistance of engine and tender as a vehicle, this depending on the weight and number of coupled wheels.

        It is suggested, however, that for the present purposes consideration of factors, such as engine resistance, are an unnecessary refinement and that for practical classification the value of an engine may be based on the simple tractive effort, neglecting friction and resistance as a vehicle. 

          It may be pointed out that the nominal tractive effort is not a satisfactory measure of the power of an engine at normal running speeds. For instance, a high nominal tractive effort may be due to a small wheel diameter, but since the mean effective pressure in the cylinder falls off as the piston speed increases, it follows that the tractive effort of an engine having a small driving wheel will fall off more quickly as the speed of the train increases than does the tractive effort of an engine with a larger wheel.

            The method suggested is to use a curve deduced from experiments on the L&Y Railway, which gives mean effective pressure (expressed as a percentage of the boiler pressure) for various piston speeds.

            The mean effective pressure for any piston speed depends, of course, not only on the size of ports, steam pipes, etc., but also on the ability of the boiler to supply the necessary quantity of steam. It is, therefore, necessary, after working out the tractive effort at the selected speeds in accordance with the above curve, to make sure that the boiler is adequate to supply the necessary steam.

              The speeds at which it is suggested that the tractive effort should be worked out are 25 m.p.h. for freight engines and 50 m.p.h. for passenger engines, the engines being rated according to the maximum T. E. they may be expected to develop at these speeds.

 

There was also a coefficient suggested for taking into account boiler power but this was omitted when the proposal was approved by the Traffic Committee and power classifications were applied to all locomotives, including tank engines. The figures for tractive effort of goods engines taken from the curve at 25 mph and those of passenger engines at 50mph, which were the the theoretical force at the rim of the tyres when new, were as follows:

 

  Class 1 goods 3,360 to 4,480 lbs. / 1.5 to 2 tons; passenger 6,384 to 8,064 lbs. / 2.85 to 3.6 tons

  Class 2 goods 4,480 to 5,600 lbs. / 2 to 2.5 tons; passenger 8,064 to 9,744 lbs. / 3.6 to 4.35 tons

  Class 3 goods 5,600 to 6,720 lbs. / 2.5 to 3 tons; passenger 9,744 to 11,424 lbs. / 4.35 to 5.1 tons

   Class 4 goods 6,720 to 7,840 lbs. / 3 to 3.5 tons; passenger 11,424 to 13,104 lbs. / 5.1 to 5.85 tons

   Class 5 goods 7,840 to 8,960 lbs. / 3.5 to 4 tons; passenger 13,104 to 14,784 lbs. / 5.85 to 6.6 tons

   Class 6 goods 8,960 to 10,080 lbs. / 4 to 4.5 tons; passenger 14,784 to 16,464 lbs. / 6.6 to 7.35 tons

    Class 7 goods 10,080 to 11,200 lbs. / 4.5 to 5 tons; passenger 16,464 to 18,144 lbs. / 7.35 to 8.1 tons

 

Note that although the most powerful LMS locomotives at that time were Class 6, the higher Class 7 was defined for both passenger and freight locomotives.

 

Originally, any locomotive with a tractive effort below Class 1 was simply unclassified but later a Class 0 was introduced for the small 0-4-0 saddle tanks. In October 1927 the P and F suffixes appeared when it was decided that simply having the Horwich Moguls in Class 4 did not reflect their true capabilities and when the large boilered Claughtons appeared in 1928, Class 5X was introduced as a ‘half way house’ between Classes 5 and 6.

 

The LMS system lasted into BR days with locomotives classified 5XP becoming Class 6 and Class 6 and 7 engines moved up one then a freight Class 9 was introduced for the Riddles 2-10-0. The system was known as Statistical Power Classification and was used by the Motive Power Department to indicate haulage capacity. It was displayed on all BR locomotives except those belonging to the Southern Region, which used the Operating Department system known as Loading Classification that included an estimation of braking power.

 

I hope that this is of some interest.

 

Dave

Edited July 9, 2020 by Dave Hunt

[jamie92208]

14 hours ago, Buhar said:

That was an interesting diversion in Early Risers, though it took some tracking back to follow it all.  I don't frequent that thread, so was a bit miffed to see serious railway discussion taking place.  

 

Dave, I don't think you can lay blame at Tuplin and Nock as being at fault for the continued view that the Midland had a "small engine policy".  I don't think David Jenkinson and Bob Essery would have been unafraid to re-appraise earlier thinking, but they reach the same conclusion despite both evidently having fondness and respect for the MR.  That said, I think they were thinking more of the effect of the Midland approach in the early days of the LMS.  There is no denying that the Compounds were good sized engines both when first built and when Deeley's full production started.  However, that was 1905 and 1907 and, apart from superheating them from 1909, that was it.  In terms of passenger locomotives the MR then continued it's programme of rebuilding the smaller 4-4-0s into the 483 Class 2P and reconfiguring 0-6-0s up and down power classes.  At the same time the fleet of 2-4-0s were still very active and over 250 came to the LMS.  The Midland just seems to have stopped locomotive development (beyond the drawing board) for itself after Deeley left.  The 4Fs were a 1911 design and didn't really meet the needs of a company with such substantial long-distance coal traffic.

 

Elsewhere similarly sized companies (and some smaller ones) were developing 2-6-0s, 4-6-0s and 0-8-0s.  Admittedly, there were not always a success, but they were addressing traffic needs.  Maybe it could be said that the Midland kept its traffic needs and locomotive design in balance (taking into account a desire to avoid expensive civil engineering works) and managed itself pretty well (apart from the London-bound coal traffic) but I think what irks and leads to folk like me teasing Stephen from time to time about MR motive power is the imposition of that thinking on the LMS.  The Compounds did consistently fine work on turns that matched their design brief, Euston to Wolverhampton for example, but were never going to be suitable as a WCML prime mover. The 4Fs, not withstanding Adrian Tester's attempt at rehabilitation, weren't big enough or sturdy enough to be the prime freight locomotive for the system as a whole and there were just too many 2Ps built.

 

On speed, I think there were quite a few free-steaming big-wheeled 4-4-0s dotted around that could probably get up to 85-90 mph in favourable conditions, the LY Flyers and the Dunalastairs leap to mind from other bits of the LMS.  That's not to decry the work of Midland engines in that regard; they ran freely, were very well looked after and I can't recall hearing of any Midland class having steaming problems at all, unlike a host of other designs.

 

Alan

You mean 4-6-0's like this I suppose.  This made a guest appearance on Lancaster Green Ayre a couple of weeks ago as part of a gauge 1 modellers meeting about 20 miles away.(It's a long story involving French and English and people booking a B & B for the wrong day.   Anyway to fill in time they came over and Eddie Castellaine who brought a rather nice Manson 4-6-0 that he scratch built 20 years ago.

It even had working inside valve gear.

We did give it a run with three Midland Clerestories and an L & Y tri Composite, which it handled with ease but never got chance to take any photos.   If I'd know what was coming I would have sorted out my M & GSW coaches.

 

Whilst I had trains set up for the visit I took this photo in the fiddle yard. It is a nice comparison of a 990 and a Compound

Left to right, 996 from a Gibson scratchbuilding aid built by me.

3182 a Mercian 2F scratchbuilding aid, built by me.

2215 A scratchbuilt Baldwin by Ray Clasper.

1004 by me from a Slaters kit.

 

Jamie

 

 

[Dave Hunt]

4 hours ago, bbishop said:

A very cogent argument, Dave.  It is worth reading both volumes of Eric Langridge's "Under 10 CMEs", especially where he designes the motion for the Class 4 tanks.  Bill

 

I've just amended this post as originally I'd stated that I once met Eric Langridge through my friend David Tee. That, however, is rubbish and was due to an age-related brain fade (not through smoking funny substances, honestly). The chap I was thinking of was John Powell and I met him through another friend, Dennis Monk, who used to work with him as a mechanical inspector. I did get some notes supplied by Eric Langridge from David Tee though and they have been invaluable for some of my writing. 

 

I think I'll go and lie down now.....

 

Dave

Edited July 9, 2020 by Dave Hunt
Brain fa*t correction

[Compound2632]

Ah, so to calculate the power class one needs the L&Y curve. Omission of any factor relating to the boiler other than pressure has the consequence that the Claughtons given large boilers from 1928 would have remained 5P, but 5XP was introduced as a fudge. This is unfortunate as it underminds my argument with my LNW friends that the LMS power classification was ruthlessly unbiased.

[John-Miles]

My dad was a mechanical engineer and knew Tuplin. He thought Tuplin was a bit of a showman at the expense of accuracy..

Edited July 9, 2020 by John-Miles
Ambiguity

[PenrithBeacon]

4 hours ago, Compound2632 said:

Ah, so to calculate the power class one needs the L&Y curve. Omission of any factor relating to the boiler other than pressure has the consequence that the Claughtons given large boilers from 1928 would have remained 5P, but 5XP was introduced as a fudge. This is unfortunate as it underminds my argument with my LNW friends that the LMS power classification was ruthlessly unbiased.

I thought the larger boilers where 225lb as opposed to the original 180lb and they were the same design as the Patriot's boiler hence 5XP. There was the occasional fudge due to the formula used being pretty crude so the Stanier 7F became 8F this being one example amongst others.

[Compound2632]

2 minutes ago, PenrithBeacon said:

I thought the larger boilers where 225lb as opposed to the original 180lb and they were the same design as the Patriot's boiler hence 5XP. 

 

OK, I'd forgotten to check that. 

[PenrithBeacon]

Easy done, been there.

[Dave Hunt]

5 hours ago, Compound2632 said:

Ah, so to calculate the power class one needs the L&Y curve. Omission of any factor relating to the boiler other than pressure has the consequence that the Claughtons given large boilers from 1928 would have remained 5P, but 5XP was introduced as a fudge. This is unfortunate as it underminds my argument with my LNW friends that the LMS power classification was ruthlessly unbiased.

 

The large boiler Claughtons also had the operating pressure raised from 175 to 200 psi.

 

Dave

[Crimson Rambler]

Dear All

 

The following is a copy of the LYR curve the Midland used for its final power scheme:-

 

 

It formed part of a series of articles on Locomotive Testing I wrote for a railway magazine - until the editor thought they were too technical and stopped it! The following explains how it was used:-

 

 

Crimson Rambler

 

 

[Compound2632]

Piston speed (or perhaps one should say velocity) was sinusoidal, so presumably the piston speed used is the maximum value?

 

Applying this in a hand-waving way to the Standard 2P vs Precursor Tank example, the latter's 6'3" drivers are smaller than the 2P's 6'9", so the piston speed at 50 mph will be 8% higher, since both engines have 26" stroke. The George the Fifth also has 6'9" drivers and 26" cylinder stroke, so it's easy to calculate the Precursor Tank's piston speed: 971 ft/min. From the graph, this gives mean effective pressure as 27% of boiler pressure. For the Precursor Tank, with 175 psi boiler pressure, this gives 47 psi; for the 2P, with 180 psi, 52 psi. This is in the ratio 1.1:1 in the 2P's favour, very nearly cancelling out the reduction in nominal TE from the larger drivers (greater distance travelled per piston stroke).

The Precursor tank had 7% greater grate area than the 2P - 22.4 sq ft vs 21.0 sq ft, but this is more than counterbalanced by the advantage in steam consumption for the superheated 2P. Thus it is evident that the LMS was entirely justified in putting the Precursor Tanks, and indeed the Precursors themselves in Class 2.

 

This sheds an interesting light on the "small engine" question. The Precursors were the first of the LNWR's "big engines", coming out in 1904. In contrast, the Midland Belpaires, introduced in 1900, had similar dimensions - 6'9" drivers, 19.5" x 26" cylinders, 175 psi boiler pressure - 180 psi and 200 psi in later batches. Cylinder volume and boiler pressure were just a little bit greater, enough to put even the non-superheated engines into Class 3 (I haven't tried the calculation yet.)

 

Also, as far as I can see, the reduction in driving wheel diameter from the Midland 483 Class - 7'0" - to the 2P had no effect on the power class calculation, as the increase in piston speed is offset by the smaller distance travelled per stroke. 

[1165Valour]

Right then, so is there an explanation somewhere of how to calculate the mean effective pressure and piston speed? It would seem that is all one needs to begin using the formula for themselves.

[Regularity]

51 minutes ago, Compound2632 said:

Piston speed (or perhaps one should say velocity) was sinusoidal, so presumably the piston speed used is the maximum value?

Probably average: something equivalent to RMS? Wouldn’t the velocity, which is directional, cancel out as the pistons will be double acting?

 

28 minutes ago, GWRSwindon said:

Right then, so is there an explanation somewhere of how to calculate the mean effective pressure and piston speed? It would seem that is all one needs to begin using the formula for themselves.

The MEP is derived from the graph: you only need the piston speed, which you can work out knowing the stroke and wheel diameter (in feet), with there being 5,280 feet in a mile, and whatever you wish to use as an approximation for pi.

[Compound2632]

55 minutes ago, GWRSwindon said:

Right then, so is there an explanation somewhere of how to calculate the mean effective pressure and piston speed? It would seem that is all one needs to begin using the formula for themselves.

 

As @Regularity says, the piston speed can be relatively straightforwardly calculated for a given speed - here 50 mph - the driving wheel diameter and the piston stroke. In fact @Crimson Rambler has given us a crib by quoting the speed for a locomotive with 6'9" drivers and 26" stroke cylinders:

 

piston speed = (stroke / 26") x (6'9" / driving wheel diameter) x 899 ft/min

 

The mean effective pressure is then the percentage for this piston speed (from the graph) of the nominal boiler pressure. The TE formula (for zero speed) often includes a factor of 0.85 which de-rates the nominal boiler pressure (an allowance for loss of pressure in the steam pipes to the cylinders) but I suspect this is factored into Mr Gass' curve already, since that is derived from measurements.

 

The formula for nominal tractive effort is:

 

TE = (2 x total cylinder volume x pressure) / driving wheel circumference,

 

assuming a coherent set of units: ideally SI but for British and American steam locomotives, if one sticks to putting all dimensions into inches and working in steam pressure measured in pounds per square inch, one gets the TE in pounds force, which in the LMS table is converted to (imperial) tons force by dividing by 2240 lb/ton.

 

The factor of 2 allows for steam being admitted to the cylinder twice for each revolution of the driving wheels (double-acting cylinders)and by total cylinder volume, I mean, calculating over all the cylinders: e.g. for a three-cylinder locomotive with 18" diameter by 26" stroke, 

 

total cylinder volume = 3 x pi x 9" x 9" x 26" = 19,848 cubic inches.

 

The driving wheel circumference is, in the absence of slipping, the distance travelled, so the formula can be rearranged:

 

volume x pressure = TE x distance travelled;

 

(change of) volume x pressure is the work done per cycle, so this is simply an instance of the well-known formula:

 

work done = force x distance moved.

 

Now, to replicate the LMS calculation, I suppose that for the value of pressure in the TE equation, I substitute the mean effective pressure for my piston speed, calculated from Mr Gass' graph and the nominal boiler pressure?

 

 

Edited July 12, 2020 by Compound2632

[Compound2632]

Just checking this out for the LMS Standard 2P:

 

Driving wheel circumference = pi x 6'9" = 254"

 

Total cylinder volume = 2 x pi x 9.5" x 9.5" x 26" = 14,743 cubic in

 

Piston speed at 50 mph = 899 ft/min, giving mean effective pressure = 0.29 x 180 psi = 52.2 psi

 

Giving:

 

Tractive effort at 50 mph = 2 x 14,743 in^3 x 52.2 lbf in^-2 / 254 in = 6,060 lbf = 2.7 tons force.

 

For the boiler power calculation, with superheated steam we take 40 hp/sq ft, with a grate area of 21 sq ft for the G7S boiler, giving:

 

Boiler capacity = 40 hp/sq ft x 21 sq ft = 840 hp. 

 

Both these figures put the 2P in passenger class 3 but if the TE is de-rated by the factor of 0.85 to 2.3 tons force, it's in class 2.

 

Checking the George the Fifth calculation:

 

Driving wheel circumference = pi x 6'9" = 254"

 

Cylinders 20.5" x 26"; total cylinder volume = 2 x pi x 10.25" x 10.25" x 26" = 17,163 cubic in

 

Piston speed at 50 mph = 899 ft/min, giving mean effective pressure = 0.29 x 180 psi = 52.2 psi

 

Giving:

 

Tractive effort at 50 mph = 2 x 17,163 in^3 x 52.2 lbf in^-2 / 254 in = 7,054 lbf = 3.2 tons force.

 

@Crimson Rambler's figure is 6,848 lbf, just 3% lower than my calculation, so not quite sure where I'm going wrong?

 

 

[Crimson Rambler]

Stephen your boiler pressure differs from mine - I think the Georges ran at 175lbs

 

Incidentally put at its simplest for a two-cylinder simple engine the tractive effort formula becomes:-

 

(cyl dia. x cyl dia x stroke x boiler pressure x factor from curve)/Driving wheel dia 

 

       all dimensions in inches - hence :-

 

(20.5 x 20.5 x 26 x 175 x 0.29)/81 = 6,846lbs = 3.06tons

 

And the power developed is 6,846lbs x 50mph/375 (a units conversion factor) = 913 indicated horsepower

 

Crimson Rambler

[Compound2632]

1 hour ago, Crimson Rambler said:

Stephen your boiler pressure differs from mine - I think the Georges ran at 175lbs

 

Aha. I got my number from Wikipedia. Talbot's book gives 175 psi as built. I wonder if, with reboilering, the pressure was increased?

 

1 hour ago, Crimson Rambler said:

Incidentally put at its simplest for a two-cylinder simple engine the tractive effort formula becomes:-

 

(cyl dia. x cyl dia x stroke x boiler pressure x factor from curve)/Driving wheel dia 

 

 

Yes indeed, with cancelling factors of pi and some numerical factors. I'd left those in in order to bring out the physics:

 

Work done = Pressure x change of Volume = Force x distance moved.

[1165Valour]

Sorry, I'm afraid I'm a bit slow on the uptake today - to calculate the piston speed of an engine with 28" stroke and 6'8" drivers at 50 mph, what should I do?

[Crimson Rambler]

GWRSwindon

At 50mph the engine will travel 5,280ft x 50mph  or 264,000ft but considered over a minute this is equal to 4400ft/min.

A wheel 6ft 8ins is equivalent to 6.666667ft diameter so the number of wheel revolutions made is given by (4,400/6.66667) X (113/355)  where (113/355) is equal to pi.

So the wheel is revolving at 210rpm.

In that time the piston makes two strokes each of 28ins each.

Hence piston speed is 210 X 28 x 2/12 = 980ft/min.

 

Hope this helps.

 

Crimson Rambler

 

 

[Compound2632]

I think that can be expressed slightly more simply. 

 

The distance travelled by the locomotive in one revolution is (pi x driving wheel diameter).

 

The distance travelled by the piston in one revolution is (2 x piston stroke)

 

Therefore:

 

Average speed of piston = [(2 x piston stroke) / (pi x driving wheel diameter)] x speed of locomotive.

 

To use the graph, the only further thing needed is to convert the speed in miles/hour to speed in ft/min:

 

1 mile/hour = 5,280 ft/hour = 88 ft/min

 

So for the George the Fifth example, with piston stroke = 26 in, driving wheel diameter = 81 in, and at 50 mph:

 

Average speed of piston = [(2 x 26 in) / (pi x 81 in)] x 50 x 88 ft / min = 899 ft/min.

 

Heigh-ho for the SI!

 

I'm still baffled why the calculation makes the LMS Standard 2P a 3P!

Edited July 12, 2020 by Compound2632

[1165Valour]

1 hour ago, Crimson Rambler said:

GWRSwindon

At 50mph the engine will travel 5,280ft x 50mph  or 264,000ft but considered over a minute this is equal to 4400ft/min.

A wheel 6ft 8ins is equivalent to 6.666667ft diameter so the number of wheel revolutions made is given by (4,400/6.66667) X (113/355)  where (113/355) is equal to pi.

So the wheel is revolving at 210rpm.

In that time the piston makes two strokes each of 28ins each.

Hence piston speed is 210 X 28 x 2/12 = 980ft/min.

 

Hope this helps.

 

Crimson Rambler

 

 

 

9 minutes ago, Compound2632 said:

I think that can be expressed slightly more simply. 

 

The distance travelled by the locomotive in one revolution is (pi x driving wheel diameter).

 

The distance travelled by the piston in one revolution is (2 x piston stroke)

 

Therefore:

 

Average speed of piston = [(2 x piston stroke) / (pi x driving wheel diameter)] x speed of locomotive.

 

To use the graph, the only further thing needed is to convert the speed in miles/hour to speed in ft/min:

 

1 mile/hour = 5,280 ft/hour = 88 ft/min

 

So for the George the Fifth example, with piston stroke = 26 in, driving wheel diameter = 81 in, and at 50 mph:

 

Average speed of piston = [(2 x 26 in) / (pi x 81 in)] x 50 x 88 ft / min = 899 ft/min.

 

Heigh-ho for the SI!

 

I'm still baffled why the calculation makes the LMS Standard 2P a 3P!

Thank you! The American public education system did a uniquely poor job teaching me physics.