Railway Performance Society Magazine - Milepost

Horsepower and average gradient calculator

After recording details of a train journey, it is possible to calculate the drawbar horsepower delivered by the locomotive over sections of the route. Traditionally this is done for the approaches to the major summits on the route travelled. It is possible to compare classes of locomotives or indeed locomotives within the same class using this tool from the blue coloured tab

There is also an average gradient calculator to assist in horsepower calculations (on the yellow-coloured tab). As most RPS distance charts now hold gradient data in great detail, the maximum number of changes in gradient in this calculator is only five, and may be restrictive. A block calculator is now available (on the red coloured tab) which allows members to copy the four columns from the relevant section of the distance chart, and paste to the block calculator, and the average gradient should be calculated automatically,

Download Horsepower and average gradient calculator

For those interested in the subject, below is an explanation by Michael Rowe of some of the concepts of the calculation of horsepower, which appeared in the Society magazine in April 2022

DRAWBAR HORSEPOWER (DBHP). The power (i.e work done) in moving the train - the power at the tender coupling (or equivalent) 

Some simple equations, assuming steady speed and constant gradient:400-ton train, 130-ton locomotive, 50mph, 1/200 gradient (Imperial units) 

WDAR (Work done against resistance) = m x V x R divided by 550 

m = the load of the train in tons 

V = speed in ft/sec  50mph in ft/sec = 50 x 5280 (ft in mile) / 3600 (secs in hour) = 73.3  

 R = resistance in lbs/ton. (In this example: assume Mark1 stock, BR published test results give 8.0lbs/ton with wind speed of 7.5mph at temperature of 45F. (This factor varies, dependent upon speed)

One horsepower is the work required to lift 550 lbs one foot in one second. i.e. - mVR/550 =400 x 73.3 x 8.0 / 550 = 427 HP 

WDAG (Work done against gradient) =2240 x m x V divided by 550 x gr

Train weight in lbs 

gr = gradient e.g. 1/200 

V = Maintained Speed in ft/sec  

i.e    2240mV/550gr  = 400 x 2240 x 73.3 / (550 x 200)    = 597 HP   

DBHP = WDAR + WDAG = 427 + 597 = 1023 

EQUIVALENT DRAWBAR HORSEPOWER (EDHP) EDHP = DBHP plus work by the locomotive against a gradient. i.e WDAGloco  As above i.e. 130tons at 50mph on 1/200 

WDAGloco + 130 x 2240 x 73.3 / (550 x 200) = 194 

EDHP = DBHP + WDAGloco  = 1023 + 194 = 1217 

Any calculation, even as simple as these, is dependent on the quality of the available data  In the modern era speeds and train weights are routinely within +/- 1% accuracy; historical data is often less reliable. Resistance R involves many variables including at the rail/wheel interface (e.g. long welded rail, wear, super elevation, curvature etc}, wind direction and speed, stock geometry etc.. Potential errors are unlikely to be less than +/- 5% 

{DBHP = EDHP on absolutely level track } 

Referring to Justin's query Why two different standards. Apart from the ˜tongue in cheek" comment that enthusiasts like larger numbers EDHP does offer some comparison between heavier and lighter trains e.g., as per the example below whilst the DBHP figures are similar in practice the locomotive on the lighter train is developing a higher EDHP 

A comparison between the previous 400-ton train climbing the 1/200 at 50 mph with a 250 ton train travelling at 68 mph 

400 ton train, 130 ton loco, 50mph DBHP = 1023 EDHP  = 1217  250 ton train  130 ton loco, .68mph  DBHP = 1018 EDHP  = 1281 

INDICATED HORSEPOWER (IHP)

The power produced in the cylinders. IHP = EDHP + WDAR for the locomotive. IHP includes the work done in overcoming the locomotive resistance to the air, at the rail/wheel interface and internal locomotive mechanical/frictional resistance. This is a complex, and on occasion contentious subject, witness the extensive contributions to locomotive resistance on the RPS website  

As a personal thought, and almost certainly oversimplifying; DBHP is the available power to work a train, the information a planner/timetabler requires. EDHP, at times adds to any evaluation of how hard a locomotive is working. IHP values assist in assessing overall locomotive efficiencies and for enthusiasts which locomotive has earned maximum bragging rights 


 

 


 


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