I am not sure if this question is appropriate for this SE - Ideally this should be posted in Engineering SE but as far as I'm aware it does not exist! (I can only assume that the scope of engineering is far too broad for one sub-domain.)


In the 1960s and 70s computers such as the CDC-6600, and its successor the CRAY-1, were considered the pinnacle of computing power. Now, in my understanding of computers and FEA/CFD etc., the power of these computers (60-80MHz-ish) would be nowhere near powerful enough to perform FEA/CFD calculations within realistic time frames and to a reasonable degree of accuracy.

So what tools did NASA, and other entities with similar requirements (be it in construction, automotive, aerospace industries), use to perform their stress analysis, aerodynamics, engine fluid flows, pressures etc. before constructing and indeed launching their vehicles (, implementing their designs in general)?

As an engineer I can appreciate the importance of these steps in a design process so I'm truly stumped.

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    $\begingroup$ They used slide rules. $\endgroup$
    – GdD
    Commented Jan 16, 2015 at 14:57
  • $\begingroup$ Can you elaborate? $\endgroup$
    – Phizzy
    Commented Jan 16, 2015 at 15:29
  • 2
    $\begingroup$ At a guess, I'd imagine they'd do similar kinds of analysis "by hand" (i.e. with electronic calculators or early computers) over a much smaller number of elements ("assume a spherical cow of uniform density...") and look at flows in an analog simulator (i.e. a scale model in a wind tunnel). $\endgroup$ Commented Jan 16, 2015 at 15:39
  • $\begingroup$ amazon.com/Roarks-Formulas-Stress-Strain-Edition/dp/0071742476/… $\endgroup$
    – Erik
    Commented Jan 16, 2015 at 17:41
  • $\begingroup$ FEA is doable, and practical results can be obtained, using nothing but paper and pencil. If you ever take a finite elements course, you'll probably be solving out some problems by hand on the exams. I did, at least, and it was in this millenium :) $\endgroup$ Commented Jan 13, 2016 at 20:00

5 Answers 5


As an engineer who has used slide rules, logarithmic tables, calculators, computers and done designs on paper and using computers, in the paper design era engineers concentrated on the critical areas of designs.

These days, computers and mathematical techniques such as FEA & boundary element analysis, etc. allow engineers to consider a larger number of options and to consider a larger number of "what if" scenarios. These days, engineers can be bogged down in data, detail and decimal point accuracy.

In the pre computerized era engineers also used graphs that others had developed such as psychrometric charts and where they didn't know they did laboratory and larger scale testing, such as wind tunnels with smoke and streamer and hydraulic channels and dye for hydraulics and streamlining.

To test the streamlining of high performance cars, small streamers were placed all over the body to be able to view how the air flowed over the car.

One method used to envisage stresses and stress flow was to cut shapes into perspex sheets and to view the prismatic light patterns in the perspex when it was placed under different stress regimes (it was a bit like stress contours). It didn't give any numerical values but people could get a better idea of where adverse stress concentrations could occur and then alter the design accordingly.

Prior to the mid 1970s engineers had to know mathematics and hand calculation shortcuts, i.e. to approximate $\pi$ to 2 or 3 decimal places using 22/7; particularly for junior engineers.

Neil Armstrong & Buzz Aldrin took slide rules to the Moon as part of NASA standard issue.


Buzz Aldrin's slide rule (sliderulemuseum.com)
Buzz Aldrin's slide rule from Apollo 11 (courtesy of sliderulemuseum.com)

During the early part of the Cold War scientists and engineers in the West had access to powerful computers. In the Soviet Bloc countries scientists and engineers didn't have such access, they developed mathematical techniques to be able to get answers quickly.

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    $\begingroup$ +1. I have that very same Pickett slide rule, complete with black leather slide rule case! But somewhere along the way I lost my much better bamboo slide rule. $\endgroup$ Commented Jan 17, 2015 at 13:02

What sort of analysis was performed before “modern” computing and the invention of finite element analysis and computational fluid dynamics?

Techniques such as computational fluid dynamics (CFD) and finite element method (FEM) are older than you think and were used early on in the space age. Although CFD is very computationally demanding, CFD predates digital computers. The development of the finite element method post-dates the development of digital computers, but not by much. M. Jon Turner at Boeing is generally credited with being one of the key inventors of the FEM during the 1950s. Precursors to FEM also pre-date digital computing.

Below is a picture of a roomful of highly parallel computer processors from the pre-digital age. This image also depicts an old-style data storage system, the box full of nicely filed paper at the bottom right.

Human computers - "computers" used to be human

Prior to the widespread use of digital computers, analog computation provided an alternative to hand calculation computation. Analog computers were heavily used to simulate a number of physical processes, including engines and rockets. The next two images show Vannevar Bush's differential analyzer, a mechanical analog computer that could solve up to sixth order differential equations, and the Beckman Instruments EASE analog computer, which the Allison division of General Motors used to design jet engines. Until the 1960s, many saw analog computers as being superior to digital computers.

Vennevar Bush's differential analyzer

Beckman Instruments EASE analog computer

  • 2
    $\begingroup$ Fantastic pictures. I recall my boss and mentor for thermal analysis recounting that in earlier times (I'm not sure, the '60s or '70s perhaps) the organisation had a maths department who ran a room full of people whose job was to invert matrices as a service to other technical departments. $\endgroup$
    – Puffin
    Commented Jan 13, 2016 at 20:32
  • $\begingroup$ Note that the vast majority of human calculators In the photo were women. This is consistent with the portrayal in the film Hidden Figures. It makes me wonder... Did these women typically advance beyond the role of number cruncher to become research scientists? Or was the glass ceiling holding them back? $\endgroup$
    – Paul
    Commented Jul 1, 2020 at 22:28
  • $\begingroup$ @Paul - The Computer History Museum dates the photo in question to the 1920s. I don't think so, not from how the women are dressed. Other sites place the photo at Los Alamos (so no earlier than 1942), yet others at place it at NACA (no budget until WW II). I suspect from the style of dress and that almost everyone is female that the photo is from the WW II era. NACA hired female college graduates as subprofessional calculators and paid them \$1440 / year. NACA hired male college graduates (the few who weren't pulled into military service) as junior engineers and paid them \$2660 / year. $\endgroup$ Commented Jul 2, 2020 at 2:45
  • $\begingroup$ When the war ended, NACA continued the practice of hiring female college graduates who were adept at mathematics as subprofessionals (e.g., computer) while male college graduates who were adept at mathematics as subprofessional were hired as professionals (e.g., junior engineer). $\endgroup$ Commented Jul 2, 2020 at 2:50

You also had reference books like Formulas for Stress and Strain by Roark (and Young) and Stress Concentration Factors by Peterson. Prediction might not have been as strong as it is today but often enough comparison was possible.


A less noticed but very impactful branch of Computational Solid Mechanics was also developed during the 60's: model reduction techniques.(*)

These are basically about a reduction of the number of equations to be solved before starting the actual computation. Analytical simplifications are introduced into the mathematical model leading to a decrease of both complexity of the task and accuracy of the result. So, there is a trade-off between speed and reliability.

The method of Guyan condensation[ 1, 2 ] is one example. It was published in 1965 after being developed within the US aerospace industry.

I have heard but can't prove that it was used in the design iterations for structural parts of rockets. It's absolutely suitable for this purpose, as in the pre-design phase quick estimations are sufficient.

To name just one of the many follow-ups, dynamic condensation [ 3 ] is a related method for estimating critical frequencies of a structure that is subject to vibrations.

(*) I'm neither claiming that the development was initiated during that decade nor that it was or is limited to CSM.


You would be surprised how much of aerodynamics can be done by hand. Granted, you probably won’t get very detailed answers for complex bodies, but you can get order of magnitude estimates very easily using a combination of:

Idealized gas laws
Isentropic flow assumptions
Tables of values

Believe it or not, this is how aerodynamics is taught in college. Not with CFD or computers, but with tables of values that enable you to analyze a system. Look at any of the standard aero textbooks and you’ll find lots of appendices filled with tables of values. Stagnation ratio values, atmospheric values, theta-beta-M tables, etc... The analysis often reduces to multiplication Of several table values. It’s not perfect, but it gets pretty close to the right answer. The tables of values were either derived analytically or from experiments.

Remember that if you can get a certain order of magnitude estimate of a quantity of interest, applying an additional safety factor on top of that is usually enough to prevent failure in a design. Sometimes its better to think think of engineering as an exercise in managing uncertainties in approximations rather than getting the “exact answer” to a problem.

When more complex values need to be computed, they would be done iteratively and (preferrably) in 1D. A lot of codes from the 60’s began as 1D codes and increased in dimension as memory expanded. Since most interactions between a vehicle and the air occur through the boundary layer, boundary layer equations can be incredibly powerful. If you have inviscid streamlines, you can integrate the boundary layer equations over a streamline to obtain things like drag and heat flux. This effectively reduces the computation to an iterative integration in 1D.


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