The fundamental design calculations (FDCs) are the starting point for any locomotive design, without which the engineering drawings cannot be made and the locomotive cannot be built. They are the foundation of the present scheme to build a highperformance steam locomotive.
In the past these calculations have been based on design "standards" or "rules", such as those of the Association of American Railroads (AAR). In the UK the "big four" railway companies had their own design rules, which were inherited by BR. Such rules are summarized in publications such as Steam Locomotive Design: Data and Formulae by Phillipson and The Locomotive Engineer's Pocket Book. They are a mixture of basic engineering principles and empiricism, the latter often resulting in "design ratios" which relate dimensions or parameters in one component to those in another (for example free gas area through the boiler tubes as a % of the grate area). In some areas of design, more especially for simple mechanical problems, these former design rules are still appropriate. However they are in general wholly inadequate for more sophisticated mechanical and thermodynamic design.
To obtain the performance level which the Class 5AT 460 will be capable of these former design methods cannot be used  to do so would result in performance being not markedly better than that already achieved with steam traction. Instead a more rigorous and refined engineering design methodology is required, making use of more sophisticated engineering data and calculations in such areas as stress analysis, heat transfer, fluid flow, etc. Chapelon's disciple, Ing. L. D. Porta, has adapted this principle to locomotive design, and the writer is one of the few people who have had access to the resultant methodology and become familiar with it, using it perhaps more extensively than any engineer except Porta himself, when putting it into practice in his work on steam locomotive development projects in South Africa and China.
Porta evolved a method whereby the calculations start from known or fixed parameters, e.g. desired levels of performance or limiting dimensions, temperatures or pressures, and work through the appropriate theory stepbystep until all the important dimensions defining the component or assembly concerned are arrived at. This stepbystep approach makes the calculation procedure extremely easy to follow.
An important feature of this technique is its holistic approach, each component being seen as part of a dynamic whole, being influenced by and influencing other parts of the locomotive.
As the procedure is in principle the same for all Stephensonian locomotives, it can be used for any design by simply changing the numerical values to suit. Thus, for example, a lightweight piston valve is designed by carrying out a stress analysis on each part of the valve to determine its section. The starting parameters might be the valve diameter, the maximum steam chest pressure, the release steam pressure, the maximum steam temperature, the distance between the inlet edges of the valve liner ports, the port widths, the valve steam and exhaust laps, the required lead, the type of coupling to the valve spindle and of the spindle to its crosshead, whether or not a valve tail rod and inlet and exhaust diffusers are to be fitted, the maximum cutoff and valve travel, the maximum rotational speed of the engine (allowing for overspeed when slipping if necessary), the materials and construction methods to be used, and the permissible stress levels in the various parts of the valve. Given these, all valve dimensions can be calculated to give the lightest possible valve (minimum weight being essential for optimum tribological conditions in service and for minimum loading on the valve gear), of the best thermodynamic design, and in which stress levels are always within those allowable. The work sheets will show the whole development of the calculations from these fixed parameters for the Class 5AT design, but by simply inserting the different starting parameters applicable to a different locomotive, the whole process can be repeated for any design. The calculation process is therefore "universal' in scope.
The following is a list of areas where such cardinal design calculations, based on fixed parameters such as the required power output, maximum operating speed, permissible axle load, permissible overall dimensions, etc., are required for the Class 5AT 460.

Complete locomotive. Prediction of overall performance and efficiency, and fuel and water consumptions and operating range at defined operating conditions. Production of predicted maximum power and tractive effort  speed curves, maximum torque  crank angle curves, and train loadspeedgradient curves.

Boiler and superheater. Calculations to determine the required boiler evaporative capacity. Heat generation, heat transfer, and gas and steam flow calculations giving all important dimensions of the boiler and superheater, the overall boiler and superheater performance and efficiency, the steam temperature at exit from the superheater, the boiler gas flow resistance (for use in the exhaust system calculations), the steam pressure drop through the superheater, etc.

Boiler strength calculations. To be made according to a recognized boiler code or codes, approved by the potential boiler certifiers and insurers, to define all important constructional details of the boiler.

Feedwater and combustion air preheaters. Fluid flow and heat transfer calculations to specify the heater dimensions and predict heater performance (i.e. final feedwater and combustion air temperatures, required exhaust steam flow rates, and pressure drops through the heaters) and stress calculations to specify important constructional parameters.

Exhaust system. Thermodynamic calculations to give the critical blast nozzle and chimney dimensions and to predict exhaust system performance.

Engine unit. Thermodynamic and fluid flow calculations to predict cylinder performance. Stress calculations to define the form of and all important dimensions of the cylinders and steam chests, cylinder and steam chest covers (the former provisionally of special thininnerwall insulated type), pistons and rings, piston rods and tail rods, piston valves and rings, and valve spindles. Fluid flow and heat transfer calculations to give the form and dimensions of any valve and cylinder liner cooling passages which may be used.

Driving gear. Stress calculations to give all important dimensions of the crossheads, slidebars, connecting rods, coupling rods, knuckle joints and crankpins (of critical importance to items (4.6) & (4.7) is that all reciprocating components shall be as light as safely possible). Roller bearing load calculations to specify the roller bearings for the crossheads (or connecting rod small ends) and the crankpins, and to predict bearing life.

Running gear. Stress calculations to give all important dimensions of all axles. Roller bearing load calculations to specify all axle roller bearings and to predict bearing life.

Balancing. Calculations to determine the optimum balancing of the locomotive's rotating and reciprocating parts and to specify the form, position and size of the balance weights in the driving and coupled wheel centres. Prediction of all outofbalance forces and couples in horizontal and vertical planes, and vibration analysis to predict the effect of these.

Spring gear. Calculations to predict the total engine sprung mass (mass calculations will be made individually for each item being considered in the overall calculations process) and its longitudinal centre of gravity, and the unsprung masses, and hence to specify spring design and the dimensions of the equalizing beam system to give the desired axle loads.

Walschaerts valve gear. Calculations to determine the dimensions of the valve gear components to give the specified valve motion. Stress calculations to determine all critical sections of the valve gear components, and load calculations to specify all valve gear roller bearings and to predict bearing life.

Leading bogie. Calculations to specify the bogie lateral displacementrestoring force characteristic, to define the form of the roller centring device, and to predict the locomotive's vehicular stability.

Brake gear. Calculations to specify the brake rigging for the required braking force.

Mainframe. Mainframe design is still largely empirical: plate frames are mandated by the deep firebox and will be based on postwar German and French allwelded mainframe design. Fundamental calculations for the frame will be made.

Proprietary equipment. Proprietary equipment to be used on the locomotive will be precisely specified.

The calculations give references to all material used in their production, and are presented in tabular format according to Porta's method, i.e.: Item No., Description of item, including equations, etc. Unit Used, Numerical Value.
The calculation sheets are presented in Microsoft Word format. Deleting the numerical data for the Class 5AT will give sheets which can be completed for any other design.
The calculations have not been produced in program format. It is considered essential for the future of steam traction that the knowledge they represent is understood and learnt, and the way to do this is for them to be gone through and understood item by item. If presented as computer programs, in which data is inputted and answers simply come out, the intervening engineering will not be understood, and this is a sure way for the knowledge to become lost in due course. Computerization can, of course, be applied in the future, if desired.
The calculations are largely in SI units. These are superior to all other systems of units and the writer has always used them in his design work. We are looking forward and a break must be made with Imperial units: this is a good time to do so as far as steam locomotive engineering is concerned.
The calculations summarized above form the basis of the Class 5AT highperformance 460. They are the starting point of its design, without which the project cannot proceed or succeed. They will also be a starting point from which to spread the necessary wider knowledge of Porta's technology, and are an important means of assuring that Porta's knowledge does not become lost. They can be used as the basis for any other advanced Stephensonian locomotive project. Specific parts of the calculations can also be used in isolation where it is desired to improve just a part of an existing design, say the piston valves. As such the calculations themselves should be of considerable interest and value to the steam locomotive fraternity worldwide.
See also Wardale's summary of the work written after its completion.