Time for some maths…

5th June 2011
I have been writing Dunrobin’s Conservation Management Plan, which includes a summary of all main dimensions and statistics. It was therefore interesting to note it’s tractive effort was a very modest 7,183 lbs. Maybe I should explain…
Tractive effort is the expression of the pulling (or pushing) effort of one object against another and is commonly used in locomotive descriptions in preference to perhaps more familiar terms such as Horse Power (HP) or Brake Horse Power (BHP). The basic formula for its calculation is:

Tractive effort = 0.85 x Boiler Pressure x Cylinder bore (squared) x cylinder stroke

Divided by driving wheel diameter (in inches)
Thus, by this equation, Coffee Pot No.1 with its 6×12 inch cylinders, 120psi boiler and 30 inch driving wheels tops the TE register at 1,469 lb s! This doesn’t allow for the effect of 3:1 gearing of this engine however…
The figure of 0.85 is a statement of boiler efficiency (so the formula is calculated at 85% of potential), which was widely used but not entirely accurate. Some UK industrial locomotive builders used 0.75 in their calculations (75%), feeling this better reflected reality, certainly for industrial applications with indifferent coal and perhaps less requirement to steam the boiler to its maximum potential. Adhesion is another important factor to consider, and there are numerous developments of this basic study that one can find online if it is of interest.
So why is Dunrobin so interesting to me in this regard? Well, compare our 0-4-4T, weighing in at 25 tons (of which only 16 tons is available for adhesion, with the bogie under the cab taking a large proportion of the available tractive weight) with some other locos that might be considered of comparable diminutive size:
Lancashire & Yorkshire Railway ‘Pug’ 0-4-0ST 11,335lb
Southern Railway (and predecessors) ‘Terrier’ 0-6-0T 10,695lb (in later form)
South Eastern & Chatham Railway ‘P’ class 0-6-0T 7,810lb (the most similar in power)
Hunslet ‘Jazzer’ 0-6-0T 15,940lb
Great Western Railway 57XX 0-6-0PT 22,515lb
NER Y7 0-4-0T (such as No.985 which we operate) 11,640lb
For further comparison:
Flying Scotsman 32,910lb (with a superheated boiler)
Duchess of Hamilton 40,000lb
US Union Pacific Railroad ‘Big Boy’ 4-8-8-4 135,375lb!!!!
Even the narrow gauge Penrhyn Quarry ‘Main Line’ 0-4-0STs (Charles, Linda and Blanche) were 6,320lb – though the latter two have been much rebuilt and must have a higher TE rating. The smaller ‘Quarry Hunslet’ is just under 3000lb.
So why is Dunrobin so small in TE terms – well, a large part of this is the size of the driving wheels, which are 4 ft 6 in (54 inches). Look back to the formula and imagine it with, say, 36 inch driving wheels – you can see how this would change things… It would come in at about 10,774lb. However, Dunrobin was built for stately progress at a reasonable speed, not for shunting or freight work where high tractive effort was valued over speed and less wheel revolutions over a given distance. It therefore shows that in every way, including its picnic baskets, Dunrobin really was the perfect ‘gentleman’s sporting locomotive’!
So endeth the lesson!