The Norwegian University of Science and Technology (NTNU)
celebrated its centennial in September 2010. The posted coordinates
point to the Dragvoll campus, where Open Days started the festive
month. The main festivity took place at the Gløshaugen campus. To
advertise the forthcoming event, a big blue balloon made of nylon
had been attached to the old main building with a 40-meter-long
string at the coordinates N 63° 25.167 E 010° 24.119. The balloon
had a diameter of 3 meters, and it was daily refilled with helium
to overcome its own mass of 2 kilograms.
The other day, as I (Nestori) was watching the balloon, a
staggering idea popped into my mind: a traditional cache attached
to the balloon. That would be an extreme cache with at least four
stars for terrain! Eagerly I prepared a small container (total mass
0.5 kilograms), and in the darkness of a late evening I climbed on
top of the main building. After having pulled down the balloon, I
attached the container to the string, just below the balloon. A few
days later I was about to publish my cache, but I found that
something most unexpected had happened. On September 10th 2010,
just a few days before the official birthday,the
balloon was taken away by strong wind. In the hope of getting
the balloon back by the big day, a reward to the finder was
announced.
Alas, the balloon was not found before the party, thus I decided
to trace back my lost cache container. With some loose pieces of
information, I managed to reproduce the path taken by the balloon,
and as I walked along that path, I luckily found my box (but not
the balloon). This was such a good exercise that I decided to leave
the container where I found it, but I had to do some cunning
camouflaging. The cache is rather visible, and there certainly is
no need to dig, or to turn over
stones/moss. Depending on the snow condition, the cache may
be available during winter. In what follows, I give you information
that you can use to find the cache.
The balloon was taken by strong wind blowing from the northwest.
The drag force due to wind had tilted the balloon by 37 horizontal
meters, until the high tension induced in the string snapped it
off. The balloon together with the attached cache travelled at the
air speed for 108 seconds, and then the wind changed its direction
to blow from the west. After additional 125 seconds of flying, the
box was detached from the balloon. From this point, the box still
continued to fly 800 meters (measured horizontally), till it landed
at the point where I found it.
You may find the cache in the following way:
- Calculate the total vertical force: buoyancy - weight
- Using the tilt angle of the string, calculate the horizontal
drag force (see the
force diagram below)
- Using the drag force,
calculate the air speed
- Follow the path! Use the local UTM coordinate grid (32V), and
assume that the grid north aligns with the true north.
- If you keep three decimals in your calculations, you should
land within 5 meters from the right spot.
Lastly, here are some constants that you may need:
- Air density: 1.2 kilograms per cubic meter
- Density of helium in the balloon: 0.18 kilograms per cubic
meter
- Free acceleration g = 9.81 m/(s*s)
- Drag
coefficient for sphere: 0.47
Original contents: FTF certificate with a small present, log
book, pencil.