Get email productivity tips!  
  Home    Up Contact Legal Stuff  

          A calculator hidden in a book

The intriguing Cornell F.24 aerial photography calculator

    At first glance the book “How many?”, by Charles Cornell, seems like any of the small hardcover books common a century ago. But when you open the cover you see it’s just a carefully padded box that contains a strange calculating device, bearing the title “F.24 Photographic Calculator”, and the name of C. H. Cornell.
Cornell F.24 calculator case  Cornell F.24 calculator in case
Click a photo to enlarge
    The calculator would pass for a “slide chart”, that inexpensive poor relation of a slide rule, if it weren’t much thicker and sturdier, and much more complex. To add to the fun, its two faces are entirely covered in low-altitude aerial photographs!


    The F.24 is a two-sided device, and measures 14.5x9.0x1.4 cm. counting both sides there are ten windows with hairlines (made from actual taut threads), through which scales on the inner parts can be read.

Cornell F.24 calculator - front  Cornell F.24 calculator - back
Click a photo to enlarge

    There are five moving parts: two sections of the faces that slide horizontally, two vertically sliding inner strips that are visible through cutout windows in the sliding and fixed sections, and a rotatable disc visible through two windows on the front side. You can see the possible motions in the photos below.
Cornell F.24 calculator - moving parts - front  Cornell F.24 calculator - moving parts - back

    The whole thing is built from a stack of thick (2 to 5 mm) pieces of board in many shapes, which together form the faces, slides, channels, tongues and grooves that allow the moving parts to slide around. This thick board material is in turn made from glued thinner strips of cardboard about 1 mm thick. All printed surfaces are coated in some glossy cellophane-like film.
    The top part of the back side became unglued, which allows its removal to show you how this construction looks on the inside and in cross section.

Cornell F.24 calculator - construction detail
Click photo to enlarge

What does it do?

    This device came with no documentation of any kind, only mysteries: What does it do? Who built it, and when? And lastly – why put it inside a fake book?!
    The answer to the first question is easy to come by, because of the captions on the various scales, and the choice of photos to decorate its faces and the cover of the “book”. This is a calculator for planning aerial photography flights. It helps you figure, given the flight height, speed, film size and lens f-number, how to time your photo shooting to ensure proper coverage of the desired land area while allowing for the required overlap between successive frames. Below I explain the full details.

When was it made, where, and by who?

    Dating the F.24 calculator is tricky. Absent any reference to it anywhere I can find, I can’t give an accurate answer. Still, there are some hints:

  • The look and feel of this device are definitely not military, at least not in the modern sense. By the time of WW2 military stuff looked just that – gray, robust, and definitely marked as government issue. This calculator’s case is more reminiscent of 19th century craftsmanship. Perhaps it is a prototype, or a survivor from a small hand-assembled batch (though so far I haven’t heard of another exemplar).
  • The altitude and speed scales go up to 20,000 ft. and 210 MPH. Assuming these parameters were feasible at the time, this can help put a lower limit on the date of the F.24’s design. Airplanes reached 20,000 ft. fairly early – by 1916 – but no plane flew at 210 MPH before 1922. Thus, this device would have been designed for airplanes available not earlier than that year.
  • After WW2, conventionally structured slide rules that served the same function were available. An example is the Pickett model N700-T, seen in the photo (alongside its very sensible leather case – no mystery books here!). Their availability would have rendered the F.24 obsolete.
Pickett model N700-T aerial photography slide rule
Click photo to enlarge
    So... looks like the F.24 calculator comes from the 20s or 30s, basically the period between the two world wars. As for country of origin -- the use of inches, feet and miles place it in the UK or its (current or past) dominions, including the US.
    Who produced it remains a mystery. Quite possibly it was the Charles H Cornell named on the device and “book” cover, but if so, we have yet to learn who he was; and since the book is a fake -- I can find no record of any book by that name -- there is no certainty that its author wasn’t imaginary as well.

Operation details

    It took me a while to figure out how the calculator works: I had no instruction manual, some of the readout windows lack captions, and it took a while to notice that someone before me had inserted one of the slides in backwards. Thus it is with some measure of pride that I report the successful reverse-engineering of the F.24. Here is the essence of the missing instructions, then:


Flight parameters:
h = altitude above ground
v = flight speed
Camera parameters:
Df = film frame length
f = lens focal length
Ground parameters:
L = Length of ground
   strip to be covered
Dg = ground frame length
Overlap% = length shared
   betw. successive frames
Dgnet = ground frame
   length excluding overlap
Other parameters:
Scale = ratio of feature
   size betw. Ground & Film
N = number of photos
   required to cover L
Texp = time interval
   between exposures

Aerial photography geometry

    The planning of aerial photography is governed by basic geometry and kinematics. The formulas involved are as follows (assuming a sensible, i.e. Metric, system of units):

= h / f         Dg = Df * Scale = (Df * h) / f         Dgnet = Dg * (100% –Overlap%)

   N = L / Dgnet = L / (Dg * (100% –Overlap%))               Texp = Dgnet / v

    Of course this calculator is not based on Metric units, but its scale design takes care of both the calculation and the unit conversions needed to effect these formulas in Imperial units.

Example problem

    An airplane flying 13,000 feet above the ground, at a speed of 160 MPH, needs to photograph a strip of land 3 miles long by snapping a sequence of exposures using a camera with a focal length of 10 inches and a film frame length of 5 inches. The exposures need to overlap by 60%.  [Note: the F.24 is designed to only work with a 5” film and a 60% overlap.] Find the scale of the resultant photographs, the length of each frame on the ground in feet with and without overlap, the number of exposures needed, and the time between successive exposures.

Solution procedure (blue numbers refer to the photos below):

  • Scale: On the front side, rotate the disc to set the altitude (13,000 ft) next to the focal length (10”) in window <1>. Read the scale factor (15,600) at <2>.
  • Dg (ground frame length): With the disc set as above, read Dg (6500 ft) at <3>.
  • Dgnet (ground frame length excluding the overlap): With the disc set as above, read Dgnet (2600 ft) at <4>.
  • N (number of exposures): On the front side, set the horizontal slide to the run length (3 miles) at <5> ; set the vertical slide in either window’s left readout (in this example, <6>) to Dgnet (2600 ft) ; read N (6) in the respective window <7>.
  • Texp (time interval between successive exposures): On the back side, set the horizontal slide to the flight speed (160 MPH) at <8> ; set the vertical slide in the corresponding lower window (in this example, <9>) to Dgnet (2600 ft) ; read Texp (11 sec) in the respective upper window <11>.
Cornell F.24 calcualtor - example - front  Cornell F.24 calcualtor - example - back
Click a photo to enlarge

And why the fake book?

    The unusual book-like case inevitably conjures romantic notions involving spies, smugglers, resistance fighters or prisoners of war. These notions, however, don’t survive close scrutiny. For one, if you wanted to smuggle a calculator to someone behind enemy lines, you’d use a real book and make a hollow in some glued pages, rather than a decorative but obviously fake box. Besides, POWs and partisans could use a code book or a map atlas, but they’d hardly have a need for planning reconnaissance flights!
    The book format could still be useful for storing the calculator among books on a shelf, and I can only assume that Mr. Cornell (if it was he) got a kick out of packaging his creation in this original manner.

Exhibit provenance:
    Found this one on eBay, from a seller in the UK. Unfortunately he got it from an antique merchant who had no further information.

More info:
    For the principles and formulas that govern aerial photography planning, you can check for example this presentation.

Back Index Next

Home | HOC | Fractals | Miscellany | About | Contact

Copyright © 2016 N. Zeldes. All rights reserved.