Design>Manufacture>Test and Development
Second World War engines were designed and made just as they are today, except that the advent of the computer has enabled a lot of work to be carried out faster. However it has not fundamentally changed the approach.
Successful firms had to have a very expert staff, with only the most basic tasks able to be given to semi-skilled workers, and even then only after mass-production had been set up. Just as today, in the design office analysis staff and senior engineers would guide draftsmen to an overall concept to follow, and the designers would have to realise these goals in a way that could be manufactured.
An extremely high level of mathematics was required of the analysis staff, and only for unusual cases would consulting scientists and mathematicians be brought in from universities and government research labs to help. These would often be some of the most famous personalities in science of the day, in Britain perhaps engine expert Harry Ricardo, government scientist Sir Henry Tizard and Alan Griffith who helped lay the modern foundations of crack theory and metal fatigue.
The lack of computer facilities did not make WW2 designers give up on complex analysis of problems in three dimensions, it merely made it harder to achieve. (Some images and explanations follow in the other tabs).