LDZ trebuchet - quite sure a trebuchet with the highest range efficiency!
Hello! This is my first post on this blog. I would like to present the LDZ trebuchet - a mechanical device which I was working on as a part of my master degree thesis in mechanical engineering supervised by professor Przemysław Perlikowski at Lodz University of Technology.
Trebuchets are medieval siege engines which feature high range efficiency. That quantity tells us how well the input energy is transferred to output range of the projectile. I computed that an optimized variant of such a machine from the Middle Ages gets 73% of range efficiency (friction excluded). Nowadays we have many modern concepts of trebuchet which perform better in this field - e.g.: Floating Arm Trebuchet, Multiple Rotation Trebuchet, Trebuchet On Wheels - but we cannot expect from them a score close to 100% (which is upper limit for the range efficiency not breaking the laws of physics). Given this situation, I designed a new machine which I called "LDZ" and made a mathematical model for it in Mathematica software with the numerical solution. For second version of it I got a score of 95,5% of range efficiency (friction excluded) !! Chances are that further development of this design could reach the upper range efficiency available for all trebuchets (even those not invented yet)!
As I am short of time for now I will only introduce the basic description and the working principle of this LDZ trebuchet device. The following is the quotation from my thesis titled "Dynamics Analysis of Trebuchet":
LDZ trebuchet overview
LDZ trebuchet (Fig. 11) has many more parts than standard one : It consists of counterweight (16)
which upper side is connected with main rope (11) and spring (15). Lower side of CW has a rack
(18) which cooperates with unidirectional clutch (22) when it will fall below platform (20). That
platform is part of the supporting structure (17) which is equipped with a trigger mechanism “1”
shown in Fig. 12 which moving part (24) is joined at the bottom with rope “2” (14) and rope “3” (10)
at the top. This mechanism is engaged by a trigger beam (25). Rope “3” is part of pulley system
which transfers the spring energy directly to the sling (3) and projectile (21) right before launching
it. In this above-mentioned system we can list in addition: pulley “4” (13), set of pulleys “5” and “6”
(7), which consecutively transfer the power via rope “4” to pulley “7” and next to an arm (1) which
can propel the sling. The last mentioned part must be attached to a such an arm that is directed
out of the plane of the presented Figure 11, hence the projectile is not able to hit the beam during
its motion. The main rope is wound first on the arc (9) of a beam (4) and secondly on a pulley “2”
(8). Apart from all these parts, there are also a few clutches and another trigger mechanism in this
LDZ design that will be discussed later on.
Figure 11: View of LDZ trebuchet at the start of the machine.
It is clear to see that LDZ version is far more complex than before-mentioned machines. This is for better movement control, as it aims at the highest possible range efficiency. It should be put that it makes use of spring as a partial storage of energy and not as its source, so it still satisfies the definition of a trebuchet. If someone would like to build it, he might expect higher energy loss due to more significant friction phenomena in preliminary designs/prototypes. But on the other hand, this concept does not require per se any frictional force to be working. Hence, provided that fine tuning is proceeded, we can expect frictional forces to be converging to zero. What is more, we can surely assume that we will never design a trebuchet that features the simplicity of a standard one, but with much better performance - medieval or ancient engineers would have already built it if that was possible. It also should be reminded that for this thesis machine construction engineering issues were skipped, unless it was necessary to prove that this machine may work in reality and satisfies the laws of physics. So an effort was put on mathematical modelling and correct application of physics apparatus.
General motion description of LDZ trebuchet
Movement of LDZ trebuchet starts from position presented in Fig. 11. Falling counterweight unwinds
the main rope off the beam arc. At this time, kinematic relationship between the velocities of CW
and a beam is named gear “1”. Power flows to the projectile, sliding on a trough and afterwards
being hurled in the air. If the missile gains enough speed (e.g. such that the sling can be still tense
when it rotates upside down in the later part of the motion), we can engage a spring to start storing
the kinetic and potential energy of the CW. This process begins with rope “2” gets tense (Fig. 13).
Apart from recovery of all the energy of CW being stopped, we also want to allow the beam to lose
all its speed afterwards. Thanks to this, the whole kinetic energy can be transferred to the projectile.
Efficient slowing down of the beam requires rapid reduction of tension force in the main rope. That
is why spring engagement goes along with switching to gear “2”. Such a transmission means that the
beam is being pulled by the edge of the arc. We may expect the main rope to become loose before
the CW stops at all. Upward movement of CW forced by spring pull is blocked as the rack is already
in contact with pinion of one-way clutch. CW is stopped just above the platform.
Figure 13: Motion of LDZ trebuchet beam on gear “2” with spring being stretched - rope “2” is fully
straightened.
After CW velocity value will reach zero, we anticipate the same for the beam at possibly not high
position - Fig. 14 - we do not want it to gain all its potential energy. After the beam loses all the
speed, it would surely move in the reverse direction, but this is prevented by another unidirectional
clutch (6) that allows only clockwise motion for the beam (Fig. 15). This event leads to releasing a
second trigger mechanism, that blocks also this clockwise movement of the beam, so it is at full stop
from now on.
Figure 14: LDZ trebuchet with beam already stopped and spring being discharged.
Figure 15: The second trigger mechanism is launched when a momentary push of the beam on
the lever (28) takes place. The latter part was pulled up to this particular time by a short rope
(29) attached to the beam. Lever is mounted on a one-way clutch (6) that prevents it and a beam
from a larger reverse movement. Before it happens this clutch is in the dead zone and a little
counterclockwise lever displacement is possible. That causes sliding out the toothing of the ratchet
mechanism (not presented in Figures) that blocks the clockwise movement of the beam. Hereinafter,
the beam is in the state of no-motion. In this picture we can also see pulley “5” (27) and “6” (26).
In fact, both trigger mechanisms may release almost at the same time - it is a good moment to
release the moving part (24) right after the beam stops. It means that the spring begins discharging,
as it can be seen in Fig.14, whereas the pulley system starts flowing the power to the projectile till
the sling reaches optimum launching angle (30). In this place it is vital to say that the mentioned
short arm of the pulley is mounted on another one-directional clutch, hence, it cannot propel the
pulley “7” in clockwise direction. The same relation is between pulley “6” and “5” (Fig. 15). These
two couplings ensure that ropes “3” and “4” remain tense before the mentioned system starts its
action.
That's all for now. Enjoy the world of trebuchets!
Paweł Oleśko
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