February 20, 2001
Richard Gillespie, Executive Director
The International Group for Historic Aircraft Recovery
2812 Fawkes Drive
Wilmington, Delaware 19808
VIA: US MAIL FIRST CLASS AND FACSIMILE 302-944-7945
PRELIMINARY LETTER OF OPINION (WITH CORRECTIONS)
Dear Mr. Gillespie,
I am in receipt of two photographs from TIGHAR of Ms. Amelia Earhart standing on the left wing of her Lockheed Electra 10E. These are the same two photographs used for the heel length analysis which is described in correspondence to TIGHAR dated January 31, 2001 and February 20, 2001. I understand that both photographs are copies of the same photograph shot at different scales. I understand that you need to know the length of Ms. Earhart’s right shoe seen in the photograph.
It is my understanding that TIGHAR has in its possession parts of a recovered shoe from one of its expeditions, and that TIGHAR’s objective is to compare the length of the recovered shoe to the length of the shoe seen in the supplied photographs. I have no prior knowledge of the recovered shoe, and therefore I hereby certify and affirm that I do not currently know, nor have I ever known, any measurement information with respect to this recovered artifact.
The orientation of the shoe (‘object’) seen in the photographs with respect to the camera is complex: like the heel in the previous analysis there is minimal displacement of the object from the image y-axis, near maximum displacement from the image x-axis, and the object is rotated in all three dimensions. This complicates accurate analysis.
Analysis begins by establishing scale in the photograph. The methodology for this was previously described in the above referenced heel length correspondence. This analysis reuses results from the heel analysis including the ridge center-to-center spacing of 0.125 inch, or 3.175 millimeters.
The projection of the side of the shoe comprise 76.5 ridges. This measurement was made by projecting the front tip and rear heel of the shoe down to a ridge, and then counting the number of ridges between these two projected points. To minimize error, the counting was made in the same family of parallel lines as the scale.
This is not, however, sufficient information to establish the shoe length because of the oblique angle of the shoe with respect to the camera in the plane of the wing surface. The apparent length of the object is different than the actual length due to this oblique angle. It is therefore essential to accommodate this oblique angle to correct the object’s apparent length.
First, the height of the camera relative to the plane of the wing is low, and the error introduced by this height is negligible and can be ignored.
Second, when the heel is rotated by 11.3° as was established in the heel analysis, the right end point of the visible toe-to-heel diagonal moves along the perimeter of the heel half-circle (see previous letter for a description of this model) obscuring the actual end of the heel. Correspondingly, more of the tip of the shoe becomes uncovered and visible. The absolute value of the error introduced at both ends, one in the positive, one in the negative, is nearly the same, as both ends of the shoe have similar radii of curvature. Therefore, the obscuration effect is nearly cancelled out, becomes negligibly small, and can be ignored.
Finally, in the previous correspondence, the projected heel length of 17.35 ridges was found to correspond to the physical length of 55.1 millimeters. The projected shoe length measurement belongs to the same family of parallel lines as the projected heel length measurement, therefore ratiometric analysis may be applied. This effectively reuses anamorphic compression coefficients which are embedded in the heel ridge to physical length ratio. Therefore:
where x is the length of the shoe. Solving for x, the shoe’s length is 242.9 millimeters. I have not yet performed an error analysis to establish a confidence interval.
|Thank you for your continued interest in, and support, of PHOTEK.|
Jeff Glickman, PHOTEK