WAR AND PERSPECTIVE
(Airplanes, Perspective, and Computers)
(or - Douglas to Lockheed)

The manager, John Apalategui (it's a Basque name), thought I showed promise, so he cut short my Dept. 66 tour, and put me on permanent assignment in "the loft". We did much calculating work. Any curved lines, such as an airfoil cross section or the planform shape of a wing, were preferably defined as segments of conic sections (parabola, ellipse, hyperbola). It was a new method then, replacing the arbitrary curves of hand-fitted splines (flexible plastic straight edges that you bent and moved or held in place with big pieces of lead, called "ducks", that had little protruding hooks to fit in a notched rail on top of the spline). I am well aware that spline curves have come back into fashion with computers, and that they probably love the air flow better, but we had not that knowledge then.

The basic mechanism was a theorem of Pascal, which said that for a hexagon defined by any 6 points on a conic section, the points of intersection of the three pairs of opposite sides lay on a straight line. Thus if one defined two points and the slopes there, with another point that the conic was to pass through, any number of 6th points were definable by Pascal's rule. And so the full curve was defined.

This was all a part of projective geometry, and I taught classes in that at UCLA. Some great tricks could be done to lines via projective distortions.

Early in my work there I was given the task of designing a mechanical conic drawer, based upon this. I did so successfully, building it of very hard wood, with slotted arms moving on steel pins. After it worked, I was told that a former person with that same assignment had committed suicide over his failure! I was not pleased.

We used mechanical calculators for this work. The main brands were Friden, Marchant, and Monroe. My greatest proficiency was with the first (I still have one of those old Fridens in my garage!). Of course the engineers needed scale drawings in addition to the full scale layouts. But the complexities of aircraft parts and assemblies made visualization difficult, not only for the structure itself but also for the internal equipment (fuel lines, control cables, heat ducts, intercomm radio, etc.).

So I devised a method of perspective. It involved picking a theoretical eye point at an angle and distance to the plane, which was represented by a great number of identifiable points obtained from the 3-view drawings of the contour design. Then an imaginary flat screen was interposed. All of these points, in their X-Y-Z values, were connected theoretically to the eye point, and the 2-dimensional X'-Y' values of the points where these "rays" intersected the screen were given to the engineers. They then plotted them on drawing paper and connected them appropriately according to their identity, yielding a basis for perspective drawings. This was applied not only to entire aircraft views, but also to views as small as those of a single formed or machined part. I recall supplying such data to Donald Douglas, Jr., who had been a classmate of mine at Curtiss-Wright Tech in 1940-41.

Now imagine an intermission where I did aerodynamic calculations (still at Douglas), drew tract house plans, was a senior set designer at RKO (movie) Studios, built custom furniture for movie stars, found early computers at the RAND Corporation in 1949 March, moved to Lockheed's California Division in 1951, started and ran a computer department for Marquardt Aircraft, then another for Lockheed Missiles at Van Nuys. End of intermission!

At Lockheed Missiles (1954) I was given charge of two sections -- digital computers (which I knew something about), and analog computers (where I was nearly totally ignorant). For the digital side we had our own IBM 650s (and an IBM 701 at the main Lockheed plant at our disposal) for the digital work.

Included in the analog computer mission was reduction of telemetered data from flights of test missiles. Fortunately for the analog side we had a Bob Prince already there, and later I brought in Dr. Jack Sherman to head the section.

One task was to present the results of analog monitoring of test missile flights in some visual form. One of our pieces of equipment was a punch-card-driven plotter. Benson-Lehner, I think.

I remembered my success with perspective views at Douglas Aircraft during World War II. And while a set designer at RKO Pictures I had created a group of plastic overlay templates to represent camera angle capacity. These were movable on the set drawings to show the director what the camera would take in for different lenses, so shooting angles could be optimized. Common now, but not then.

So I ordered a topographic map of the White Sands Proving Grounds (or Missile Range), where these tests were flown. I selected a suitable eye view point in space, high up on the Southeast side, and determined the coordinate rotation by trigonometric means. Salient coordinate points on the map were rotated via the 650 through the transformation values selected. The new values (in 2-D) were plotted on a large art board. Then a real artist was engaged to paint a rendering of the range topography over it, using these points as his guide.

Thereafter, when a test flight was made, our analog equipment translated certain data to digital coordinates, mainly altitude, ground location, roll, and yaw. The 650 program took this data and created from it other data such as the intersections of vertical locations dropped from the flight path to meet the ground and levels of altitude at even thousands of feet. The IBM 650 put all these points through a rotation process identical to that of the map, and punched cards.

These X'-Y' coordinates on cards then drove a plotter that marked on a transparent plastic sheet that would then serve as an overlay for the painting of the missile range, giving a continuous curve of the flight, with a faint curtain dropping vertically to the ground. On this curtain were marked its intersections with the even-thousand-foot altitudes. The missile itself was shown by two lines, like the edges of a ribbon, so local roll and yaw movement could be seen. The plotter also marked the time points.

This presentation form was a huge success with U. S. Government brass. They were ecstatic. To my knowledge this was the origin (however crude) of computer-processed methods of dynamic (moving) perspective. I expect that these basic principles remain unchanged as the underlying methods for computer graphics and Star-Wars-type movies and videos. Holy Jurassic Park!

Fall-Out from this Knowledge

• Later at Douglas I moved to the Aerodynamics department. One task was to take two curves, thrust horsepower available and required, and find their maximum difference at what airspeed. The CalTech graduates all did as they had learned -- plotted them in ink on vellum, used dividers to plot the difference, inked that, and marked the maximum point. I did it differently, by knowing those conics. There was an easy formula for finding the maximum of a parabola through the three points farthest apart, and the desk calculator did it some 10-20 times faster. But the CalTech grads refused (for some 10 years) to acknowledge my method. That was not the way they had learned to do it, and I had not gone to CalTech anyway!
• At Lockheed California one task was using an IBM CPC to do the same type of contour design for a vertical-rising fighter plane. I computed cross sections every half inch for the length of the fuselage. An engineer needing to move a bulkhead didn't have to come back to me again. Just looked at the computer printout.
• While at IBM I gave, at the request of Vice President John McPherson, the conical lofting methods to an assistant chief engineer at Buick, for body design. And also to some shipbuilders, through Alex Bernstein (also a chess expert) at the IBM Service Bureau.