After getting my certificate in Aeronautical Engineering from the
Curtiss-Wright Technical Institute of Aeronautics, I started my work
life in 1941 April in a general novice training program at Douglas
Aircraft in Santa Monica, California -- Dept. 66. One of the work stops
was the lofting department, where contour design was done. That is, the
3-view patterns in full size that defined the shape and structure of an
airplane. When I arrived, these "lines" were cut into, not drawn on, a
thin aluminum sheet, but one could still visit the hard maple flooring
where the original lines of the DC-3 were cut. A famous airplane.
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
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
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
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- 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
- 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.