See this page for:

• Calculated Performance Predictions (undertaken by David Wardale as part of the 5AT Fundamental Design Calculations);
• Computer Simulation Performance Predictions (using Prof Bill Hall's Software);
• Predictions of Actual Operational Performance (prepared by Dr David Pawson).

Calculated Performance Predictions

The "Deltic" performance predictions for the 80 tonne 5AT locomotive are astonishing when compared to similar sized locomotives of the "steam era". It is hard to believe that a locomotive no bigger than a Standard Class 5 would be able to produce performances far superior to any British Pacifics of the steam era. Yet such predictions are based both on detailed engineering calculations and on the actual performance of "The Red Devil", the sole member of the SAR Class 26 4-8-4 locomotive, as modified by David Wardale in the 1980s using the theories and practices developed by Ing. L.D. Porta in Argentina.

The calculations on which the performance predictions for the 5AT are based are referred to as the "Fundamental Design Calculations" or FDCs and were undertaken by David Wardale during 2002-2004, of which Part 1 is presented on this website. These calculations are split up into five sections:

• FDC 1.1 - "Determination of the Target Power and Tractive Effort vs. Speed Characteristics", in which the "target" indicated power, indicated TE, drawbar power and drawbar TE are established;
• FDC 1.2 - "Determination of Target Load vs. Speed vs. Gradient Curves", in which the drawbar TE values are compared to train resistance estimates to derive the maximum gradients that can be climbed over a range of constant speeds when hauling a 400 tonne train;
• FDC 1.3 - "Preliminary Basic Calculations" in which the axle loads, driving wheel size, cylinder stroke, boiler pressure, superheat temperature, adhesion limits and tender size are defined, from which the cylinder diameter is determined, steam and fuel consumption rates, operating range, indicator diagram, and exhaust emissions are estimated, all based on the target maximum indicated and drawbar power outputs..
• FDC 1.4 - "Tractive Effort Diagram" in which wheel-rim tractive forces are determined for each 15^o rotation of the driving wheels at speeds of 113 kph and 125 kph in order to verify that slippage will be controlled under all normal operating conditions.
• FDC 1.3.F - "Preliminary Basic Calculations (Final Version)" - As stated in Note 1 of this set of calculations: "These calculations are the original calculations [FDC 1.3.] with data from other FDCs substituted for the original figures where it is different."

Computer Simulation Performance Predictions

Having (manually) completing the full 17 sets of Fundamental Design Calculations, Dave Wardale undertook an independent verification of the 5AT's performance using a computer-based steam loco performance simulation software package created by the late Professor Bill Hall. Bill Hall wrote two simulation programs: a "basic" package called "Perform" in which simplified valve events are assumed, and a more sophisticated package called "Perwal" in which actual valve events are predicted. Dr David Pawson, a retired industrial chemist, undertook a substantial amount of work (in association with Bill Hall) in calibrating the software packages by comparing their outputs with records from the BR stationary testing plant at Rugby and the GWR testing facility at Swindon, and from documented reports on various locomotive road tests in the 1950s and early '60s. Since Bill Hall's death, David Pawson has taken on the role of advocate for his software and can justifiably claim to be its leading exponent.

In the Introduction to his final set of Fundamental Design Calculations, FDC 18 "Performance Predictions", Dave Wardale describes both the overall methodology and the Perwal software package that he used to verify the 5AT's performance, while noting his reservations about the applicability of the software for simulating SGS (Second Generation Steam) locomotives. He writes as follows:

• The accurate prediction of (locomotive) performance requires an indicator diagram for each chosen condition to be estimated: this has been done in Figs. 1.3.1. and 1.3.1.F. for the estimated conditions obtaining at maximum drawbar power. The production of such indicator diagrams is laborious and not justified other than for particular conditions of interest, such as maximum power. Computer programs are however now available that predict the indicated power – speed – evaporation – cut-off relationships from relevant data about the locomotive. Two such programs, developed by the late Prof. W. Hall, are ‘Perform’ and ‘Perwal’. The former makes an approximation to the locomotive’s valve events, whereas the latter links ‘Perform’ to the program used for determining the valve motion given by Walschaerts valve gear, i.e. Walschaerts, Ref. [14] of FDC.5, and is thus more accurate as it is based on a precise determination of the locomotive’s valve events. For this reason the present calculations are made using the Perwal program.
• As there is no transparency in the computer programs, their validity cannot be directly verified. They require the use of data, such as discharge coefficients, that has to be estimated, and however good the theory behind the programs, the results are clearly only as accurate as the estimation of this data. Good correlation between performance figures obtained from these programs and test results for B.R. locomotives is said to exist, depending on the values used for the various coefficients (i.e. the coefficients have been chosen such that there is agreement between calculation and test). This would point to an indirect verification of the programs’ validity when applied to First Generation Steam (FGS). However when using them to predict performance where there are no test results available for comparison, as in the present case, there is no way of confirming that any estimated input data is correct.
• Although, with the reservation given above, the programs appear applicable to FGS, this does not necessarily guarantee applicability to SGS such as the 5AT, where engine design shows a number of advances over that of FGS designed to improve steam flow and reduce heat transfer, i.e. to make the power generation process approach closer to the isentropic ideal. Such advances are, however, at least partly accounted for in Perwal by the input data (in respect of such items as discharge coefficients, expansion and compression indices, valve motion and cylinder cover temperature). Steam flow and heat transfer processes in an engine are complex, and there must be doubt that any analytical approach is better than an approximation. However as the calculations concerned are not design calculations, which of necessity must be accurate, a degree of uncertainty can be accepted, i.e. the present work can be taken as giving at least a reasonable guide to the expected 5AT performance. It also follows that any error will tend towards under-estimating performance of SGS, i.e. the 5AT should perform as well as or better than Perwal predicts.

Wardale's conclusions about the results of the simulation are as follows (with minor abbreviations):

"Good agreement is seen for all results except for cut-off and indicated thermal efficiency. The cut-off discrepancy is not too great and is of no consequence for the FDC’s: it is because of differences in the estimated indicator diagrams, Fig. 1.3.1.F. and that given by Perwal (which can be compared), the former being better in that it predicts a lower cut-off for the required mean effective pressure. The reason for the discrepancy in indicated thermal efficiency is discussed below. Agreement on the important parameter of cylinder indicated power is within 0,4%, and as the locomotive’s rolling resistance is the same for either method, a similar agreement applies to the drawbar power, i.e. Perwal confirms the cylinder and drawbar powers used as the basis for the FDC’s. However due to the different shape of the two curves of maximum continuous indicated power vs. speed, Perwal predicts a slightly higher maximum drawbar power than [1.3.F.(1)] at slightly lower speed.

The difference in maximum drawbar power predicted by the two methods is within the accuracy of the calculations. Although Perwal's prediction of speed at maximum horsepower is is somewhat less than that estimated in FDC 1.3, the drawbar power vs. speed curve derived from Perwal is very flat in this vicinity, varying only from 1,920 kW up to 1,925kW then down to 1 900 kW over the range 90 to 110 km/h. Only a slight variation in the indicated power vs. speed curve would therefore be needed for the speed at maximum drawbar power to deviate significantly from Perwal's prediction.

The probable reason for the discrepancy in indicated thermal efficiency is because the denominator in the expression (cylinder work ÷ heat in steam to cylinders) is different depending on whether ‘heat in steam to cylinders’ is taken as the total heat transferred to the tender water or the heat transferred in the boiler only (i.e. that heat which comes from the fuel), which is less than the total when exhaust steam feedwater heating is used. Taking the former as the basis, the 5AT indicated thermal efficiency corresponding to FDC 18 [127] would be ([1.3.F.(82)] ÷ ([1.3.F.(77)] – [1.3.F.(117)])) = 16.3%, which is only 2.5% higher than the Perwal figure of 15,9%, i.e. there is acceptable agreement if the same basis for efficiency is used."

It is hoped that it will be possible for copies of the programs Perform and Perwal to be made available through this website once documentation for them is completed.

Predictions of Actual Operational Performance

Dr David Pawson has prepared several performance predictions for the 5AT operating over two rail routes in the UK. These predictions are presented in spreadsheet format, one covering Crewe to Carlisle (over Shap Summit) and the other from Kings Cross to Grantham (over Stoke). Each shows four 5AT runs hauling loads of 375 and 500 tonnes gross at maximum speeds of 90 and 110 mph. The results are summarized as follows:

David Pawson offers the following commentary on his spreadsheet model:

"There are two separate parts to the simulations: the times and speeds; and the consumption estimates. The times and speeds are broadly a combination of:

• Newton's laws,
• (largely) accepted locomotive and coach resistance values, and
• known gradient profiles.

These are therefore pretty reliable illustrations of what the application of around 3000 IHP to the trains will deliver in terms of times and speeds.

The consumption figures are less exact. They are based on theoretical models that are inherently sound, but do not take into account all sorts of factors that would likely pertain in the real world. They should therefore be viewed as ‘preliminary indications’ of what might be achieved in ideal circumstances."