John Knowles

Steam loccomotive resistance and information on its values

Locomotive resistance (LR) is the sum of the several sources of friction imposed by the running of the locomotive, as a vehicle and as a machine, or what is lost of the work done in the cylinders to achieve the work done at the drawbar.

What for?

To estimate the power of steam locomotives from records of runs.

Why Study Now?

When railways were operated by steam locomotives, precise LR was not a crucial piece of information, or at least it did not have to known with precision, and indeed it was not precisely known.
The nominal tractive effort in the cylinders was calculated according to a well known formula, and a modest but inexact reduction made for various resistances to give the tractive effort at the coupled wheel rims. If the resulting tractive effort was high for the adhesion available, the tractive effort was taken as a quarter of the adhesive weight. There were various formulae for the vehicle resistance of the locomotive, from which the tractive effort at the tender drawhook could be obtained. With the resistance of the vehicles to be hauled and the gradients and curves en route, the maximum loads which could be moved on a slow goods train could be calculated. From this, the weight of the locomotive itself was deducted to give the trailing load.
In making this calculation, a further modest percentage reduction might be made to the tractive effort or the resulting load, so that the engine was not asked to work to its maximum on every up gradient. These calculated loads were often then subject to test. If it was found from experience that the engines were not able to haul the calculated load satisfactorily, reliably or in the usual or necessary time, the load was reduced. It might, with experience be increased slightly, especially if the kinetic energy of a moving train could help on short climbs. Alternatively, a certain class of locomotive might be tested on each section, and the loads for other classes related to it through their tractive efforts and own weights. The loads to be hauled at high speed for which the extent of boiler power was the determining factor were almost always subject to test.
That is not to say that LR was not of interest. A lot has been published about it, including alleged values, but a lot is not sensible, or at best is far too simple, often the result of poor analysis of the way LR arises, poor data and poor analysis of the data. Probably about three quarters of the information can be dismissed. Even after analysis of what is sensible as data and/or is sensibly expressed, it has been necessary to go back to first principles to determine LR, especially the machinery resistance.
Indeed, a lot of what appeared was far from conclusive. On 22 April 1904, some figures of the ihp and dbhp of Great Northern Atlantic 251 (70 tons locomotive only) at four speeds, appeared in The Engineer and an editorial asked what is the source of such high internal resistance. The CME of the line H G Ivatt believed that internal resistance increased with cylinder size, and suggested more smaller cylinders (which he thought reduced resistance in cylinder friction and improved balance), and avoidance of large throw of coupling rods. There were only two responses: one that there was even less realisation in the USA of internal resistance, and one which mentioned friction from the inertia of the moving parts. No one analysed the figures and showed whether they were sensible from first principles. There was no separation of the vehicle and machinery components of LR. As it happens, for a given ITE the length of the piston rings meeting cylinder walls, an important component of machinery resistance, is greater with more smaller cylinders, not less.

Aims of this Paper

To set down the principles of how LR arises, examine the many references in the literature for likely helpfulness, consider the data available, and try to establish what might be satisfactory general values for the components of LR, for all sizes of steam locomotive, and how they might be assembled into the resistance for a particular locomotive under particular circumstances. Further and important aims are to spur further thought on what is said here and in the literature, uncover evidence not currently known, and encourage obtaining new evidence.

This is a work in progress. Various incomplete items will be found in the text.

This work existed on the Intenet in late October 2013, but it has not been possible to transcribe the address onto the index page for steamindex.

The literature citations contained herein are given in a somewhat shorthand style: nevertheless as many key figures not listed in staaemindex so far are mentioned (and their work is described) reference will be made to this document in the hope that a more satisfactory address my eventually by found.

Steam Locomotive Resistance and Information on its Values A paper by John Knowles setting out how this resistance arises and what can be said about its values. Author's copyright.

June 2013 Version.

Comment is encouraged, and can be made direct to the author at the email address of johnk.pb 15 (first part) (second part), the two parts joined by the at sign. It is intended to add a summary of comments to the paper.


1 Introduction, reasons to study steam locomotive resistance (LR), definitions and abbreviations, and summary of conclusions


2 Initial observations


3 A note on lubrication


4 Likely values of vehicle resistance


5 Likely behaviour and values of machinery resistance; observations on: compounds; small coupled wheels; low boiler pressure; four, eight and ten coupled; poor port and valve dimensions


6 How can evidence of LR be obtained, interpreted and analysed?


7 Problems of estimation and with data


8 The experimental method, and analysis of experimental results


9 British LR Data
9.01 .Class 5 44764


9.02 Rugby Testing Station


9.03 Declared values - 46225, the BR Testing Method, LI09 and L116, 71000, King, Merchant Navy, WD engines


9.04 Test Bulletins


10 German LR Data


11 Other LR data


12 Literature references to LR and its components 93
13 Information needed to determine LR


14 Obtaining MR by Iteration


15 Using locomotive characteristics to estimate MR from known MR of other locomotives


16 Calculation of locomotive output on a particular run


17 Acceptable approximations in determining VR and MR


18 The reasonableness of the estimates


19 Conclusions


20 Further work


Appendix Data underlying Part 11