OPTICAL POWER OUTPUT OF AN UNIDENTIFIED HIGH ALTITUDE LIGHT SOURCE
by Bruce Maccabee (c) 2000 by B MaccabeeABSTRACT
A Royal Canadian Air Force pilot while flying at an altitude of about 11 km saw and photographed a very bright, disc-like object that was remaining stationary near a thunderhead. An analysis of the photograph suggests that it would have been radiating in excess of a gigawatt of power within the spectral range of the film.
INTRODUCTION
At about 7:20 PM, MDT (about 20 minutes before sunset), on Aug. 27, 1956 a Royal Canadian Air Force pilot was flying nearly due west over the Canadian Rockies near Ft. MacCleod, Alberta (49.5 degrees latitude, 113.5 degree longitude). He was flying at 36,000 ft (about 11 m) in the second position (far left side) of a formation of four F-86 Sabre jet aircraft. While approaching a large thunderhead (cumulonimbus) at a ground speed of about 400 kts (740 km/hr) he saw, at a much lower altitude, a "bright light which was sharply defined and disc-shaped" or "like a shiny silver dollar sitting horizontal" (see Appendix 1 below). As he continued westward the sighting line to the object rotated backward to an “eight o’clock low” position before he lost sight of it, indicating that it was stationary in the lee of the anvil of the thunderhead at an altitude considerably below the plane. (Note: his recollection of the object being at his left side conflicts with the direction to the sun as determined from the photo; see below). It was below the upper layer of clouds but above the lower layer of clouds which, according to the pilot’s weather report, were at 10,000 to 13,000 ft (3 to 4 km). The object, which was viewed against the dark purplish background of the lower cloud layer, appeared to be "considerably brighter than the sunlight." As he flew past he decided to take a photo of the object. He had to “quarter- roll” the aircraft in the direction of the object in order to take the photo. The exact direction to the object at the time of the photo is not known. However, it probably was more than 30 degrees north of the direction to the sun (276 deg. azimuth, 8 deg. elevation) because the sun was apparently to the left of the left edge of the film which in turn, was about 28 degrees to the left of the object. (This latter statement is based on the locations of shadows on clouds made by other clouds at the lower left side of the photo). The pilot estimated the sighting duration at between 45 sec (2) and 3 minutes (1). After pointing the object out to the flight leader the pilot took a photograph of it (Figure 1). (Appendix 1 provides further details of the sighting.) The photograph, a 35 mm color slide (Kodachrome), is the subject of the analysis presented here. This is a scan of an excellent print made from the slide by the Jet Propulsion Laboratory.
A few minutes later, because he had his camera out or its container, he decided to take a picture of his flight. Figure 2 confirms his location relative to the other planes.
ANALYSIS
The exact nature of the object has not been determined. An initial suggestion that it was merely a brightly illuminated small cloud (1) has been ruled out for two reasons. The first is that it is just as bright on the right (east) side as it is on the left side whereas clouds in the photo are noticeably darker on their right sides, a fact that is consistent with the sunlight coming from the west. The second reason is that portions of the object were brighter than the brightest clouds. Klass (2 ) has suggested that the object was a plasma or something akin to ball lightning and Altschuler (3) included a discussion of the object in an article on ball lightning. Whatever the nature of the object, it would be of interest to have order of magnitude estimates of its radiance (watts/steradian/cm^2 or w/st/cm^2), radiant emittance (w/cm^2) and total power output within the spectral range of the film. (Note: the symbol ^ as used here means exponentiation or "raised to the power of".) The radiance in the direction of the camera can be estimated from the film density of the image combined with published film characteristics and with suitable assumptions about the camera settings and the range to the object. By also assuming the object to be a Lambertian radiator with constant emittance over its surface one can estimate the total radiant emittance and the total radiated power within the spectral range of the film. The radiance is found by solving a standard photographic equation (4), corrected for the effects of atmospheric attenuation (5) as shown in Appendix 2:L = (4/p)E(f#)^2 e^[(b-a) /cos(A)]/Tcos^4(B) 1)
whereE = H/t. 2)
and where e is the natural base, 2.71828. In these equations L is the radiance of the object in w/st/cm^2, E is the irradiance on the focal plane of the camera lens in w/cm^2 and f# is the ratio of the focal length to the lens diameter (set by the operator of the camera). The factor e^[(b-a)/cos(A)] corrects for atmospheric attenuation along the slant path, at angle a, relative to vertical from the object to the camera. In this correction factor, b is the optical thickness of the atmosphere from the ground to the altitude of the plane and a is the optical thickness from the ground to the altitude of the object. T is the transmission of the optics (lens, aircraft window), B is the angle between the optic axis of the camera and the direction to the object, i.e., the angle corresponding to the offset of the image from the center of the photo, H is the film exposure level in j/cm^2 at any particular location within the image and t is the shutter time in seconds. The quantities which go into Eq. (1) and (2) are not definitely known. However, reasonable estimates have been made in order to carry out the calculations. Based upon the camera settings that are recommended for the film (Kodachrome ASA 10) when used under the known lighting conditions (bright daylight) it is estimated that f# = 8, although it could have been one stop above or below this (i.e., either 5.6 or 11). A camera is designed so that an increase in f# by one stop increases the aperture area by two and a decrease in f# by one stop divides the aperture area by two. Therefore an uncertainty of one f-stop setting corresponds to a factor of two (or 1/2) uncertainty in the lens area and ultimately in the calculated radiance. The values of b and a in the attenuation correction factor depend upon the particular altitudes and are weighted averages over the spectral range of the film. From attenuation data (5) for a clear atmosphere the difference b-a has been determined for the airplane altitude in combination with two assumed altitudes of the object. The values of b-a and angle A have been estimated in the following two ways. The first way of determining b-a and the zenith angle makes use of the statements by the pilot that (a) the object looked like a horizontal coin (i.e., a thin disc with its axis vertical) seen from an angle to its axis (the zenith angle) and (b) he guessed the distance was about 3 nautical miles (5.5 km). Statement (a) implies that the image of the object would have a roughly elliptical shape. The aspect ratio of the ellipse (minor / major axis) would provide an estimate of the angle between the line of sight and the plane containing the disc (the complement of the zenith angle). The brightest central part of the image does have a roughly elliptical shape which is moderately consistent with the shape of a thin disc viewed obliquely (6). A good overall fit to the image is obtained with a 70 degree ellipse (i.e., a circle viewed at an angle of 70 degrees from the axis of the circle or 20 degrees from the plane of the circle) with a major axis of the image being 1.28 mm long. Thus the depression angle of the line of sight from the plane to the disc would be about 20 degrees, assuming that the disc itself was horizontal. The pilot stated that he had to roll the plane a bit in order to take the picture through the canopy indicating that the depression angle may well have been about 20 degrees or greater. Assuming again that the disc was in a horizontal plane, then the angle from the vertical axis to the airplane, A, was about 70 degrees. The 20 degree depression angle combined with the approximate 6 km range to the object yields an altitude of (11 km - 6 km x sin 20) = 9 km. The difference b-a is found for an optical path from 9 to 11 km by roughly averaging the optical thickness of the atmosphere over the sensitive spectral band of the film using tables in ref. 5. One finds that (b-a) is approximately 0.03. Combining this with A = 70 degrees, (b-a)/cos A = 0.09 and e^0.09 = 1.09. A second estimate of the attenuation correction is obtained by using the same angle a as found above but using a lower altitude for the object. The justification for using a lower altitude is based on two considerations: (a) the distance estimate given by the pilot was only a guess; the distance could have been greater than 6 km, and (b) the film imagery seems to show that the object illuminated the clouds just below it. (Note: the illuminated clouds are below the bright horizontal linear structure which is just below the elliptical image.) This would place the object relatively close to the lower cloud layer, which was at an altitude of about 3 to 4 km. Obviously the exact altitude of the object is unknown, but for the purposes of this second attenuation calculation it has been set equal to 4 km. At this altitude the range to the object is about 20 km and (b-a)/cos(70), as found from data in ref. 5, is about 0.29. The attenuation correction factor is e^0.29 = 1.34. Each of the attenuation correction factors quoted above was calculated for clear air. Although there was water vapor in the nearby clouds, it is probable that the vapor between clouds was not sufficient to make the attenuation correction factor much larger than the largest value listed above. The optical transmission, T, of the camera lens and airplane window is estimated to have been about 0.7 due to glass surface reflection losses (about 4% loss at each surface), although it might have been slightly greater. The shutter time is less certain. It may have been 1/125 sec, which, along with f/8, is the value recommended by the manufacturer (Kodak) for ASA 10, film under daylight conditions. However, it may also have been as long as 1/60 sec or as short as 1/250 sec. For these calculations t = 1/125 = 0.008 sec = 8 x 10^(-3) = 8E-3 sec (note the definition of exponential notation, 1E1 = 10, 1E2 = 100. 1E-3 = 1/1000). The angle b in Eq. (1) is only about 9 degrees so the cos^4(B) factor is about 0.95 The only remaining quantity to be determined is the average exposure, H, over the image. H is related to the optical densities within the image of the three color forming emulsion layers which make up the film. (Density is inversely related to the brightness of an image. In the case of slide film the density is the negative of the logarithm to base ten of the transmission factor of the film image.) Since the slide is color reversal film, image density decreases as the exposure increases. The image of interest appears quite overexposed and white (i.e., devoid of color). The color of the image of the object is the same as that of the images of the brightest white cloud areas which are also overexposed. Since the image of the object is white one may assume that all three color forming layers were exposed to approximately equal amounts of energy. The minimum neutral density at several locations within the image is about 0.11, which is only slightly larger than the density of completely overexposed film. This density is also about 0.03 lower than the density of the brightest (white) cloud area. Because lower density corresponds to greater exposure, certain portions of the object were brighter than the clouds. The average density over much of the image is approximately 0.12 (see Figure 3).
An order of magnitude estimate can be made of the value of H which could create a density as low as 0.12. The estimate is made by combining the exposure curves [film density vs log(H)] with the spectral sensitivity curves that are published by Kodak. The spectral sensitivity curves indicate how the monochromatic sensitivity varies with wavelength for the three emulsions, where sensitivity is the inverse of the energy density in j/cm^2. The sensitivity values are given for a decrease in film density of 0.3 units from the maximum density which is between 3.2 and 3.5 units. Using the integral form of the van Kreveld addition law (7) one can determine the sensitivity of a film to a continuous spectrum of light. Assuming for simplicity a flat spectrum over the spectral range of each emulsion one finds that the shorter wavelength emulsion (blue-violet to green, 350-500 nm wavelength) is roughly three times more sensitive than the mid range (green to red-orange, 500-600 nm) or long wavelength (red-orange to deep red, 600-700 nm) emulsion. Assuming that the object radiated a spectrum that would cause equal density changes in the three layers thus producing a white image, the approximate energy density needed to produce a film density decrease of 0.3 units would be 1E-7 j/cm^2. The exposure curves for the three emulsions indicate that to produce a film density decrease of about 3.2 units, i.e. to cause the film density to decrease to a value comparable to that of the image of the object, the energy density would have to be about 1000 times greater. Therefore an order of magnitude estimate of H is lE-4 j/cm^2, corresponding to the average image density of about 0.12. Inserting the above values into Eq.(1) and (2) yields a radiance of about 1.7 w/st/cm^2 if the object were at 6 km distance and about 2.1 w/st/cm^2 if it were at the 20 km distance. (The difference in the calculated radiances arises because of the atmospheric attenuation correction.) These values are so close to each other that the radiance will be approximated as 2 w/st/cm^2 regardless of the assumed distance. If the object were a Lambertian radiator then the radiant emittance, W = pi L, would be about 6 w/cm^2. This value of W can be produced by a 2450K blackbody with emissivity of 100% since it radiates about 3% of its total 200 w/cm^2 emittance within the bandwidth of the film (8). However, the color balance of the film suggests that at that temperature the image would have a distinctly reddish hue. On the other hand, a 3200K greybody with an emissivity of about 10% would provide approximately the same radiant emittance in the bandwidth of the film, but the color temperature would be high enough to produce a white image. A 10% emissivity is typical of some polished metals (8) which, even though hot enough to radiate, might give the visual appearance of a "shiny silver dollar sitting horizontal." It is possible to estimate the total power output of the object within the spectral range of the film by assuming a specific shape for the object and also that it was a Lambertian emitter with constant emittance over its surface. For simplicity the following calculations have been done assuming that the object was a cylinder with a length l/l0 of its diameter. Assumptions of other shapes will yield comparable or higher power outputs. The diameter of the cylinder is estimated from the major axis of the ellipse fitted to the image length (0.00128 m) combined with the focal length of the camera (50 mm = 0.05 m) and an assumed distance to the object. Using the simple imaging relation established by the camera lens, if the object had been 6 km distant then its diameter would have been (6000 m/0.05 m) x 0.00128 m or about 150 m. The total radiating surface area (top, bottom and the cylindrical surface) would have been about 42,000 m^2 = 4.2E+8 cm^2. Multiplying this by the emittance, 6 w/cm^2, yields about 2.5E+9 w within the spectral band of the film. If the object had been at 20 km distance the diameter would have been about 500 m, the surface area about 4.7E+9 cm^2 and the power output would have been about 3E+10 w within the spectral band of the film. Of course, the total power emitted over all frequencies might be much greater. A second method of estimating the total power, a method which treats the object as a “point” source emitter and which requires an estimate of the total energy deposited on the image, is presented in Appendix 2. This second method yields powers of 1.8E+9 w (instead of 2.5E+9) and 2.4E+10 w (instead of 3E+10). Since both methods require assumptions about the data it is difficult to decide which is more likely to be correct. However, the rather close agreement suggests that, at the very least, the numerical results to be calculated by either method for any chosen set of values for the f#, the shutter speed and the distance to the object would be acceptably accurate. The radiation power levels calculated here make it difficult to sustain the argument that the object was a plasma as ordinarily understood. Neither the origin of such a plasma, its size, its duration nor its total power output seem consistent with known plasma phenomenology. Its location near a huge thunderhead suggests that some transient electrical effect of the storm (e.g. lightning bolt) might have created it, but this would not explain its duration of many tens of seconds. Assuming a minimum estimated sighting duration of 45 sec and a minimum estimated distance of 6 km the energy radiated would have been on the order of 1E+11 j (about two orders of magnitude greater than the energy in a typical lightning stroke3 ) and the volume energy density of the assumed (cylindrical) plasma would have been about 4E+5 j/m^3. An energy density this great could be attained with single ionization of a portion of the air at 9 km altitude (3). However, the recombination time for a plasma is very short, typically 100 ms or less. Therefore energy storage (ionization) during a transient event (e.g., a lightning bolt) followed by relatively slow energy release during recombination could not account for the sighting duration. This implies that there must have been a continuous power source either within or outside the plasma. To determine whether or not such a power source exists would require theoretical and speculative analyses which go beyond the scope of this paper. An alternative phenomenon which may be considered is ball lightning or "kugelblitz." Ball lightning has some characteristics of an ordinary plasma but it exists for much longer periods of time and therefore must have some (unknown) energy storage mechanism "built in" or else it is continually powered in some (unknown) way by an external power source. According to independent surveys by McNally and Rayle totalling 627 sightings (see ref. 1, pgs. 32 and 35-38 for details) observers of ball lightning usually report sighting durations on the order of seconds. although about 8% have reported durations exceeding 1/2 minute and about 2% have reported durations greater than two minutes. Therefore, because of the duration of this sighting one might consider the possibility that the photographed object was a ball lightning. However, typical ball lightnings are roughly spherical blobs with diameters on the order of tens of cm, although about 4% of the observers have reported sizes greater than 1.5 m and at least one observer (a pilot, see ref. 3) has reported diameters up to 30 m. Since the photographed object was well over 100 m in diameter (depending upon the assumed distance), at the very least this object was a highly unusual example of ball lightning. Unfortunately there is no good theory that explains how even a typical ball lightning could exist. Therefore there is no way to scale predictions for ball lightning from the typical size under 1.5 m up to the size of the photographed object and to thereby determine whether or not it was ball lightning. By way of comparison with the radiation of this object (1E+9 to 1E+13 watts for 45 seconds or more), lightning radiates 1E+13 watts for 1E-4 sec, 1 kiloton of TNT “radiates” 1E+13 watts for 1E-3 sec, the Grand Coulee Dam power station generates 1E+10 watts, a nuclear rocket can generate exhaust power at a rate of about 1E+10 watts and the Saturn space rocket generates 1E+11 watts at maximum thrust. I thank J.F. Herr for supplying useful technical information and C. Spring for photographic help. I also thank Dr. Peter Sturrock, Philip J. Klass, Dr. David Fryberger and the two reviewers for helpful comments. This work was supported in part by the Fund for UFO Research.