bell and the skewed tower of the old church in Delft
The first parish church of Delft, the old church, was built around
1200. In front of the church a 75 meters high tower, with brickwork
spire and four turrets, was built in 1350. Even during its
construction, the tower was plagued by subsidence. This could be
because the water in the Oude Delft had to be redirected to make way
for the existing church. The tower therefore was probably built on a
filled-in canal. Throughout the ages, the leaning tower has been the
cause of considerable alarm to many an inhabitant. The tower leans 1.20
meters to the west and 1 meter to the north.
Two unique bells hang from a heavy oak bell cage in the fourth loft in
the tower of the Oude Kerk (Old Church). These are the Trinitas bell
dating from 1570 and the Laudate bell dating from 1719. The Trinitas
bell, or Bourdon bell, is the most exceptional of the two, weighing
almost nine tonnes (!). The Bourdon can still be heard each day,
although somewhat modestly, when a hammer chimes the hour and
half-hour. The Bourdon is only rung on very special occasions such
as, for example, the funeral of a member of the Dutch royal
family. The powerful chime of the Bourdon causes such heavy vibrations
that regular use could damage the monument.
In this problem for the studygroup, we try to model the effect of
ringing the extremely heavy bells inside the leaning tower with
mathematical methods. Is it possible to analyze the effect of ringing
on the stability of the tower and on the occurance of damages in the
tower ? Is there resonance ?
Modeling a skew beam with a heavy pendulum can be mathematically
interesting, because of the possibility of a chaotic behavior. But is
this model too simple ? Should one include damping ? How does one model
ancient stone constructions ?
To be able to work on this problem, it is necessary to collect detailed
information about the old church (height, width, weight of bells,
position of bells, other relevant issues). It is known, for example,
from scaled drawings of the construction, that the backside of the
tower is heavier than the leaning fore side (more stones are used in
the backside part). Also the heaviest bell is placed on the backside.
The body of the tower has four floors and a thirty meters high spire,
in which again four floors. The lowest tower room can be reached via a
short porch, built after 1500, the now closed passages left and right
to the aisles are still recognizable. It is obvious that these were
made when the tower was already leaning over.
In the northern aisle is a spiral staircase. The first floor
accommodates the large wrought-iron clockwork (1605); it is out of
order now. The much smaller clockwork that took over in 1885 is also
out of order and is now placed inside the old one. The present
clockwork is placed at its appropriate place near the clockfaces. In
the northwestern corner of the tower, at second floor level, is a
charter chamber with an old iron door. It is said that here Balthasar
Gerards, the assassin of Prince William of Orange, was locked
away. The third floor only heightens the tower. After all, it was
important to be able to place the bells as high as possible. The fourth
floor is the ´klokkenzolder´ (bell attic). Here stands a robust oak
frame from the 16th or 17th century, in which the bells rest.
To see a photo of the skewed tower please click photo 1.
A close up of the skewed tower, click photo 2.
At this image you will find some (repaired) cracks on
For drawings of the achitectures of the old church please click drawing 1,