BEAM HEIGHT FOR 'TRIBUTE IN LIGHT'
 --------------------------------
 John Pazmino
 NYSkies Astronomy Inc 
 nyskies@nyskies.org
 www.nyskies.org
 2012 September 12 
Introduction
 ----------
    On the afternoon of the collapse of the World Trade Center, 11 
September 2001, several civic leaders discussed ways to honor the 
2,800 deaths in that catastrophe. The ideas revolved around a device, 
illuminated or luminous, that recalls the Twin Towers. It would be 
displayed on the annual anniversary of the attacks. 
    I give here only a description of the present installation, 
skipping the history. Details of the display's development are well 
handled by New York City history sources. 
    Eventually the Municipal Arts Society set up a battery of xenon 
lamps to shine two parallel beams into the sky on each anniversary. 
This became the 'Tribute in light', sometimes mistakenly called 
'Tribute of light'. The beams were first displayed on the 6-month day, 
11 March 2002. Then after they were lighted on each September 11th 
thru 2012. 
    In summer 2012 Municipal Arts Society passed operations of the 
Tribute in Light to the National 9/11 Memorial and Museum. It will 
incorporate, by current discussions, the lamps into the memorial park 
at the south side of the new World Trade Center. 
Beam height
 ---------
    In one early plan for a 9/11 remembrance, the artist believed he 
could make two prisms of light to duplicate the size and shape of the 
Twin Towers. His diagrams showed the light dead-ending at 400 meter 
elevation, the roof of the late Twin Towers. He supposed the sky above 
would be dark. He thought light could be confined within a prescribed 
volume as if it was a liquid filling a vessel. 
    In lighting proposals and ideas other than for the 9/11 event the 
same effect is depicted. The false notion is rampant in advertising, 
cartoons, even lighting instructions. In such instances the beam thins 
out like the hairs of a brush with empty landscape beyond the beam. 
    A ray of light travels, given clear path, to infinity. It may 
weaken from dispersion or absorption along its way. Photons, once 
released from the source, do not spontaneously end their flight 
farther than some arbitrary downstream point. 
    You appreciate this in astronomy. We see the stars because photons 
from them pass thru tens, hundreds, thousands of lightyears to us. 
There is no such thing as a source that has a dofined zone around it 
within which you see it. The object would suddenly pop into view 
soonest you enter the zone of illumination. 
    The shafts of light from Tribute in Light do not, in spite of some 
illustrations, rise up to a certain elevation and then self-quench. 
They reach, litterally, to the stars. We see the shafts because some 
of their photons are scattered and reflected in the atmosphere, like 
any other light rays in an air filled with haze, aerosols, particles,  
moisture. If Tribute in Light was set up on the Moon, we would not see 
any rays shooting from the lamps. 
    When we admire Tribute in Light we marvel at how high is the 
apparent top of the beams. A thousand meters? A few kilometers? We can 
determine this from simple trigonometry and a street map. 
    There is an ultimate elevation ceiling for our vision. The air 
thins out with elevation. At some height there are just too few air 
particles to reflect back any beam photons. How high can that be?
Aviation traffic
 --------------
    The brilliance of the beams and their only occasional occurrence 
could pose serious hazard to aviation near the City. As luck falls 
out, Manhattan, where the beams are based, has many restrictions on 
overflight to prevent casually flying into the beams. 
    To be extra safe, aircraft temporary alerts and advisories are 
issued by the nearby airports about Tribute in Light. A typical one 
notes the geographic location of the lamps and a radius of avoidance 
centered on them. The advisory is for the full duration of the 
illumination, including the shutoffs for birds and testing. 
    There are no known dazzling, distraction, or other incidents 
relating to Tribute in Light. 
Cosmic sweep
 ----------
    As the photons pour from Tribute in Light the Earth rotates. The 
beam sweeps a circle in the celestial sphere, crossing over all stars 
with declination equal to the latitude of new York. The beams aim at 
the local zenith from approximate latitude of 41 degrees north. 
    Each second of shining creates a stream of photons, the segment 
length of the Twin Tower prisms, 300,000 kilometer long. Due to Earth 
rotation, the next second of photon stream is adjacent ot the first, 
not following directly behind it. We generate a spiral ribbon of 
photons for the tenish hours shining during the anniversary night of 
the display. 
    This ribbon radiates into space and only ONE instant of photon 
stream will hit a target in its way. The others miss to either side of 
it. When the lamps are turned off at dawn the final one-second photon 
stream is emitted to cap off the fan in the heavens.
    The ribbon flows outward, assuming perfect alignment, and spreads 
from the angular displacement of the lamps during its emission. 
    The diagram shows what's going on
              |--10.80 billion km (10 hour flight of 1st photons) 
              || 
               || 
                ||---\_ 300,000km (per second of emission) 
                 ||--/ 
                  | . . . |
                          || 
                           || 
                            || 
                             |-- just leaving lamps at Earth 
              ##### . . . #####-- successive place of lamps on Earth 
              |<--7,083km-->| (from 10 hour rotation of Earth) 
             >===direction of Earth rotation===> 
    Potential recipients of Tribute in Light are. from dusk to dawn of 
September 11-12, in constellations Lyra, Cygnus, Lacerta, Andromeda, 
Perseus. The beams sweep thru the planet-hunting field of the Kepler 
spacecraft and the Andromeda galaxy. Eventually, according as the 
distances in lightyears to the targets, Tribute of Light will shine on 
peoples now unknown and perhaps forever unknowable. 
Inverse-square law 
 ----------------
    Among the bigger screwups in science education is the application 
of the inverse-square law. Just about every body 'knows' light weakens 
with the square of the distance it travels. You may recall the diagram 
of a spreading beam of light intersecting one, tile, then four, then 
nine, and sixteen, at 1, 2, 3, and 5 units of distance. You may even 
know the correct way to derive the inverse-square law by an enclosing 
sphere around the light source. 
    All of this inverse stuff is correct, but ONLY for a source that 
radiates equally in all directions. We assume most celestial bodies do 
that, yet even there we know a planet radiates off of only its 
sunlighted side. The night side sends out almost no light. 
    The inverse relation fails completely with collimated or focused 
light. A torch focuses the emission of its lamp with a reflector. Its 
rays are sent out more or less in one direction. The weakening of the 
beam is orders less than inverse square. 
    It also fails completely for sources having large angular size at 
the receiving point of its rays. A ceiling panel, fluorescent tube, 
array of LEDs do not follow the inverse-square law. 
    Laser beams emit almost precisely parallel rays with very little 
weakening with downstream position. That's why we can send a laser 
beam to the Moon and see its reflection from mirrors placed there by 
spacecraft. And why lasers are under test to replace radio for 
interplanetary comms with spaceprobes. 
    Tribute in Light does not weaken with the inverse rule because its 
rays are forced to radiate in parallel paths with minimal dispersion 
or deviation.  
Design 
 ----
    The display consists of two square prisms of blue beams aiming 
verticly into the sky. The sides of the prisms are formed by close-
spaced parallel beams from 11 lamps. Only the sides are formed, the 
interior space within the prism is empty. The four sides and two 
prisms total 88 lamps. 
    The motif is to replicate the vertical columns of the late Twin  
Towers for those viewing the beams from nearby. Remote viewers see two 
uniform beams reaching above the skyline. The beams are so well 
collimated that the ribbed or fluted sides sustain themselfs for a 
significant distance above the ground. Eventually, at some great 
height, varying mostly on weather, the ribs blur and blend together. 
    Ideally the two prisms should rise from the base of the late Twin 
Towers. Perhaps they would be centered within the foundation being 
that the 14-1/2 meter width of the prisms versus the original 70ish 
meter width of the Towers. 
    This idea was never possible due to early rescue and recovery work 
and then construction of the 9/11 memorial. In it the base, 
footprints, of the towers became reflecting pools. 
    From 2010 thru now there was consideration to discontinue the 
Tribute in Light from lack of funds or after a respectable number of 
displays after 2001. Civic and social opposition got up the funds, 
about $500,000 per show. 
Lamps 
 --- 
    Each lamp is 7 kilowatt output and the size and bulk of a free- 
standing postal mailbox. It sits on its own mount by which it is 
collimated with the other lamps to form the flutted prisms. To check 
the collimation, observers from the crew are spotted at four sides, in 
Brooklyn, midtown manhattan, New Jersey, and Staten Island. They radio 
in any defect of alignment, calling for adjustment of the the errant 
lamp's base. 
    The lamps are arranged in two corner-facing squares, about 14-1/2 
meters and 11 lamps on the side. I'm not sure if the diagonals of the 
squares line up but they at least closely represent the orientation of 
the late Twin Towers. 
    The four sides and pair of squares total 88 lamps consuming about 
610 kilowatts. The electric is supplied by a gas-fueled trailer-
mounted generator parked near the lamps. 
    A crew of 30 takes a week to assemble the display, test it, run it 
for the one night, and take it down. After the show the equipment is 
packed for storage some where inside the garage. I don't know where 
the gear was kept in years prior to installation on the garage. 
    For the first several years, the lamps were carried on temporary 
platform on West St across from Ground Zero. As construction at the 
new World Trade Center advanced, this site was displaced. The present 
installation is atop the parking garage near Rector St and West St, a 
few blocks south of Ground Zero. 
Hours
 ---
    The display is tested on & off on the couple days leading to 
September 11th, giving the world a preview of the instant year's show. 
Among the tests is the exact alignment of the beams. Each lamp's beam 
must be precisely vertical and evenly spaced from the other beams, 
else the texture of the twin prisms is ruined. 
    To check the collimation, observers from the crew are spotted at 
four sides, in Brooklyn, midtown manhattan, New Jersey, and Staten 
Island. They radio in any defect of alignment, calling for adjustment 
of the the errant lamp's base. 
    On the 11th the lamps are turned on in evening twilight and left 
one until the morning twilight of the 12th. The run regardless of 
weather. On rainy days the beams are scattered into a blue corona with 
a hotspot on the underbelly of clouds. In clear sky the beams reach to 
amazingly high altitude, seemingly to overhead. 
    To lessen bird trapping, the display is shut off for 20-minute 
intervals several times during the night. In 2012 these are in the owl 
hours. The shutoff may be at any time the crew notices an increase of 
birds confused within the prisms and in risk of falling from 
exhaustion. 
    I do not hear of a lamp burning out during the show. I suppose 
this can occur but a single missing lamp per prism will be noticed 
only by viewers close enough to ee the individual beams. The aspect 
for remote viewers is unharmed. 
Astronomy
 -------
    For a battery of such powerful lamps the 'Tribute in light' is 
incredibly sky-friendly! I personally see observe stars right against 
the edge of the beams, like they were the tail of a comet, with 
minimal loss from increased sky background brightness. Other 
astronomers note that more than a few degrees from the beams, the sky 
remains a dark as can be for the instant night.
    A searing example of how benign the display was on 11 March 2002. 
On the very first show, six months after the attacks, astronomers 
gathered in Central Park at nightfall to watch comet Ikeya-Zhang. They 
enjoyed bare-eye views of it while the beams were shining. 
    Some low-level darksky advocates show off pictures of the twin 
beams spraying light al over the City. They are selected form photos 
taken under rain or cloud, when there's no stargazing feasible. 
    The sky-friendly design comes largely from the sensitivity of the 
Municipal Arts Society to the 'majestic darkness' aura of the City and 
the mindset of the people to keep obnoxious illuminations away. 
    The significant hazard in the sky is entrapment of birds. The 
display comes during the autumn migration of birds from north to 
south. When first operated, birds did fly into the prisms, get 
confused and disoriented by the luminous walls, then fall out of the 
sky from fatigue of aimless flying. It ws common during the takedown 
of the display on the 12th to find THOUSANDS of dead birds in the many 
blocks around the installation. 
    In 2011 and 2012 the Tribute in Light crew watched the beams with 
binoculars to monitor the birds. When the birds are too numerous, the 
lamps are turned off for 20 minutes. This gives the birds a clear dark 
surrounds to continue their southward flight. The shutoff occurs a few 
times during the night. 
    With this operation the bird fatality in 2011 was a mere one 
hundred or so. The 2012 figure as I write this piece isn't ready yet. 
Atmosphere probe 
 -------------- 
    With two intense collimated beams aimed to the local zenith, we 
have a chance to probe the mid and upper atmosphere. For one feature, 
the beam may light up layers of haze or thin cloud, otherwise not 
visible in darkness. The local weather offices inspects the beams for 
hotspots of these layers but do not collect measured information. 
    The layers block some of the upward rays, making the beam above a 
bit dimmer. This shortens the height. The beam may seem to end at the 
topmost hotspot with no discernible prolongation above it.
    The other feature is the full height of the beams in clear sky, 
with no interference by layers. Many astronomers asked, how tall are 
the beams? Or, how high into the atmosphere do they probe? 
Simple experiment
 ---------------
    You can measure the linear elevation of the beams by simple 
measurements, specially since as an astronomer you can measure 
altitudes of stars. When the beams are in clear sky measure the 
altitude of the apparent top of the beams. That's really the only data 
you need to take on the spot. The rest is done at your desk.
    The beam top can be diffuse and may feather into the background 
sky. Capture the elevation of the highest definitely visible beam. You 
may try hiding and not the beams with a card and see if they do 
contrast against adjacent sky. 
    If there are hotspots or beads from atmospheric layers, take their 
altitudes, too. The results from these should be almost the same for 
all observers, but the full height of the beam could differ due to 
perspective effects. 
    The other datum you need, gotten from  street-level maps, is your 
distance from the lamps. For this as at 2012 you may site the lamps at 
Rector and West Streets on Manhattan. If your map shows structures on 
Manhattan, put the lamps on the garage at the approach ramp of Battery 
Tunnel on West Street. 
    The lamps are about 18 meters above see level. If your elevation 
is substantially different from this, note it, also perhaps from your 
maps. For almost all of us in the City we can let the two elevations 
be equal. Only if your on a tall building or in high hills will you 
want to correct for differential elevation. 
Calculation
 ---------
    This is easy with a sci/tech calculette.
    (height) = (distance from lamps) * (tangent of altitude) 
Any elevation correction is added to this height. Say you are in hills 
200 meter above sea level. The correction is (your elev) - (lamp elev) 
= (200) - (18) = (182 meter), which is added to the height found from 
the equation. You'll find that for almost all heights you obtain this 
is a very small correction and can usually be neglected.
My observations 
 -------------
    I watched the Tribute in Light last night, 11 September 2012, at 
about 21:30 EDST. The sky was generally clear but no where as dark as 
the preceding night of the 10th. There was no chance of seeing the 
Milky way, now that we are in the 2012 autumn sighting season.. 
    I measured the altitude of the top of the beams and also of a 
hotspot along them. The top was at altitude 72 degrees. The hotspot 
was at 34 degrees. This was done by fist & finger. I repeated the 
measurement three or four times and took an eyeball mean. 
    My house is quite 11 kilometers from the beams. I am also pretty 
much at the same elevation as the lamps generating the beams. 
    The geometry ignores the curvature of the ground. Unless you're 
viewing the prisms from very far, a hundred or more kilometers, away 
you may assume a flat ground. A person inspecting the beams that far 
away may see the top only a couple degrees altitude. The tilt of the 
beams rom the observer's vertical may be smothered in the precision of 
the altitude measurement. COnsidering just the geometry of the Earth's 
globe and a beam top at 40 kilometers, the farthest person to see 
Tribute in Light would be about 710 kilometers away. intervening 
topography and overwhelmingly obscuring air never allow this sight. 
Numbers 
 -----
    From these observations the height of the beams and hotspot come 
from the right triangle of (my house), (the beams or hotspot), (the 
base of the beams). 
    For the hotspot I got 
    (height) = (11 km) * tan(34 deg) 
             = (11 km) * (0.6745) 
             = 7.4 km
This sounds reasonable for a layer of haze above the ground.
    The top of the beam is
 
    (height) = (11 km) * tan(72 deg)  
             = (11 km) * (3.0777)
             = 33.9 km
This is an incredible height! 
Other factors
 -----------
    Remote observers look thru a longer air path to the beams than 
those close to them. Intervening weather can reduce the observed 
altitude. The also see the beams attenuate as light is absorbed along 
their length. The density of photons at higher elevation is less, the 
more so in hazy or moist air.
    A remote observer sees the beams almost faceon over their whole 
height, which may be only a few degrees. He does not benefit from a 
densification of photons like a close observer. The latter looks more 
and more along the beams at high altitude, and gets photons from a 
longer column, partly compensating for the aerial attenuation. 
    One the other hand, all observers should get about the same height 
for beads in the beams because they are bright and at moderate 
elevation above the ground. The quality of the observation form a 
remote observer can be evaluated by the heights for these beads 
compared to those of a close observer.
    It would be curious to learn the function of beam height against 
remoteness from the lamps. If I get enough reports I'll present the 
correlation. 
Optical aid
 ---------
    It may be possible to extend the altitude of the beam top thru 
binoculars but any magnification of a diffuse source tends to further 
dilute the brightness of the source. It's like applying too high a 
power for a misty nebula in a telescope. It's best to stay with bare 
eye assessments.
    Near sighted observers, surprisingly, fair quite well in studying 
diffuse sources! Since most of what they see, without full ocular 
correction, is blurred anyway, the beams may simply be just as 
visible for them as for a well-sighted person. They also don't have 
reading problems with any scales or dials when they use the fist & 
finger method of taking altitudes.
Test nights 
 ---------
    If you chance to catch the beams when they are under test in the 
days before September 11th, take altitude measurements! The night will 
surely be of different quality than on the 11th and you may be in a 
different location. SInce the lamps are turned on and off as tests 
call for, there's no telling when they'll shine. It's a matter of 
luck. 
Photography
 ---------
    You can take pictures of the Tribute in Light beams with ordinary 
nighttime techniques. Expose for the surrounding landscape to darken 
the sky and give the beams a stronger contrast. The shafts may extend 
so high that they can not fit within the picture. You have to use your 
camera smarts to compose the best scene of the instant.
    You may try taking altitudes off of the picture, if you have a 
calibrated scale for the image. You may take by bare eye the altitude 
of several landscape points next to the beams as samples . Then 
proportion the beams against them. I didn't try this but I suppose the 
beams are higher in photos because of the generally better image in 
them than seen by eye at night.
    By chance you could have a celestial background like a bright 
asterism or a planet. Tr moving to get a pleasing arrangement, maybe 
with the Moon sitting between the beams. 
Airplane view
 -----------
    If you're lucky to view from an airplane as it departs or arrives 
at one of the City's airports, try taking altitudes. It may be tough 
from a cramped seat, bright interior o the cabin, small window, to day 
nothing of the plane's maneuvering.
    You'll have to fins out, like from an airport tower, what the 
elevation of your plane was at such & such time on September 11-12. Be 
ready to withstand some interrogation! 
    Same considerations apply to views form other aircraft, like 
helicopters, zeppelins, balloons. In such small craft you may 
restrained against squirming around by straps, harnesses, helmets. You 
can't easily face the beams and extend arms to capture their 
altitudes. 
Atmosphere content
 ---------------- 
    We see the beams because dust, aerosols, water vapor, other 
substances, reflect and scatter the beam's light back to us. In 
vacuum. like in outer space, we can not see the beam with nothing to 
show them off of. 
    The actual height of the beams is infinite. The photons do not 
stop nor dilute at a definite elevation. The beams are pretty tightly 
collimated so there is no deviation or spread. 
    We are seeing the presence of some material over 30 kilometers up 
that's dense enough to bring out the beams! 
    Some astronomers suggested that the top of the beam is merely when 
the brightness falls below the trigger for the eye cells to register a 
response. This could be true but the photons have to be there to enter 
the eye. The 33 km is my own observation. A person with more sensitive 
eyes, 
    I'll see is there are any observations from ISS that show the beam 
really terminating some where in the stratosphere as the air gets too 
thin to disperse and scatter photons. 
Conclusion
 --------
    There was some fascinating astronomy in this viscerally emotional 
a display. What just about every one else sees as a pretty pair of 
light shafts, we astronomers can glimpse at the contents of the upper 
atmosphere.
    In this specific instance in 2012 the beams were visible to almost 
34 kilometers up, about three times the elevation of commercial 
airliners! From pictures taken from balloons the sky up there s 
awfully dark, with just about no blue scatter left. 
    Yet something is up that high to reflect back some photons of the 
beams to our eyes. What will Tribute in Light for future years reveal?