Wardale's fundamental design calculations for the 5AT conclude with FDC 18 titled "Class 5AT 4-6-0: Performance Predictions". Here, Wardale used Prof. Hall's software packages Perwal and Perform to predict the 5AT's performance and compare the outputs with his own hand-calculated estimates.
It should be noted that both Perwal and Perform use imperial units. In fact, Professor Hall, being a professional engineer, undertook all his calculations and modelling in metric units, however because his software was intended for the use of the steam enthusiast fraternity which habitually favours imperial units, he converted his software to use those units.
The method of use is as follows:
- Open the Perwal program.
- Select OK to Load Walschaerts Program. Two windows will open: a Command (cmd.exe) window and the Walshaerts gear - Data Entry window (see below).
- Close the Command window. This should cause two Perform windows to open. These will be used later - see below.
- Enter the valve gear data. Here the 5AT's valve gear dimensions are shown (after conversion to imperial units).
- Click on Save Current Engine. Note: In most cases the numbers are entered to three decimal places, however when storing these dimensions, Perwal reduces them to two decimal places. Thus for consistent outputs, the third decimal number should be manually reinserted when the data is recalled.
- Click on Get Results to open the window shown below.
- Enter an angle for the Lifting Arm. In this case 5.2 degrees is chosen. Then press the Go button to generate the results shown below. These include Front and Back Valve Events and a Piston vs. Valve position diagram. As may be seen, the average cut-off is approximately 20% (the exact figure is 19.9%)
- Turn to Perform's "Define the Engine" window (below) and enter the engine data - in this case, the 5AT's data is used, once again converted to imperial units.
Note: (1) The cylinder cover temperature must be chosen. In this case, Wardale has chosen a value that is higher than the saturation temperature for the steam entering the cylinder. Wardale justifies this for the 5AT by "the factors used to minimise heat transfer, such as high superheat temperature, optimum cylinder insulation and the use of thermal barrier coating".
(2) The values for steam temperature and steamchest pressure are calculated by simple pro-rata formulae based on data recorded by Wardale on the Red Devil. For the 5AT, the steamchest pressure is calculated by the formula: Psc ≈ Pb – (2.32 x 10-7 x ms2) in kPa (divide by 6.895 to get to lbf/in2), where Psc = steamchest pressure in kPa; Pb = boiler pressure in kPa; and ms = steam flow to cylinder in kg/h. Also, for the 5AT, steamchest temperature is calculated by the formula: T ≈ 383 + (4.1 x 10-3 x ms) oC, where ms = steam flow to cylinder in kg/h. These formulae would need to be adjusted for other locomotives.
(3) In the case of the 5AT, the piston diameter is adjusted to take account of the fact that contrary to UK practice, the 5AT is fitted with piston tail rods. Wardale assumed that Perform was designed for locomotives without piston tail rods.
- Click on Save Current Engine.
Note: Perform saves some data to three decimal places and other data to one decimal place. For consistent results, the correct figures needs to be manually added whenever the data is recalled - in particular the Blast Discharge Coefficient which only saves to one decimal place.
- Turn to the Perform: Performance window (below) to read off the output figures including:
Steam Consumption; Indicated Power; Indicated Efficiency; Blast Pipe Pressure; Mean Effective Pressure and Indicated TE. An Indicator Diagram is also produced.
- The process is repeated using different values for speed over a range of cut-offs. In each case, the steam flow, steamchest pressure and temperature need to be determined by a process of iteration (easily done on a spreadsheet).
- The results can be combined to generate a Maximum Indicated Power vs. Speed curve for the locomotive as produced (manually) by Wardale, below. Above approx 35 km/h, maximum power output is limited by the steam flow rate - i.e. boiler capacity.
Comparison between Perwal and Perform Outputs
Perform is the simulation package that produces estimates of steam consumption, power and tractive effort. When not run in conjunction with Perwal, it assumes a simplified valve gear for calculation of valve events. When run in conjunction with Perwal (as in the methodology described above), Perwal uses the valve events calculated by Perwal based on specified valve gear dimensions. Thus, if the specified valve gear dimensions are correct and accurate, Perform should produce a more accurate simulation than when using its own simplified valve events.
A comparison between the outputs produced by Perform when run on its own and when run in conjunction with Perwal using 5AT data and dimensions, shows differences ranging between 3% at full cut-off up to nearly 10% at low cut-off, lower power outputs being generated when Perform is run using its own estimate of valve events. It would therefore appear that Perform is a useful tool for making preliminary estimates for a tentative locomotive cylinder and valve arrangement.
A comparison table listing the two sets of outputs for the 5AT can be downloaded by clicking here.