When trying to communicate some information, it's nice to be able to use
words that mean the same thing to all parties. For those of you who might
be a bit befuddled about a "CW" or what a "30 degree pin angle" is, perhaps this
page will help. A lot of images, so be patient and let them load.
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Here is a model Trebuchet in the cocked position. Note the relative position of the CW to the vertical support pole. (Most of the frame work has been stripped away for clarity.) | ![]() |
As the beam rotates, the horizontal distance from the end of the short arm to the pivot is getting longer. This causes the CW to start moving towards the right. | ![]() |
As the beam goes through horizontal, the CW is still moving to the right, but it's still gaining some speed in that direction as well as moving downward with the end of the short arm. The horizontal distance between the end of the short arm and the pivot is now at maximum. | ![]() |
Now things start getting more interesting. The horizontal distance between the end of the short arm and the pivot is now getting shorter, but the CW still has velocity towards the right. It will start slowing in that direction (right) but it's still headed that way. | ![]() |
In the meantime, the sling has been whipping around, gaining some nice velocity and is approaching the release point. But now things gets critical in their timing. The CW has reached its maximum horizontal movement to the right at the same time that the CW, hanger, beam and sling all line up (or close to it.) Despite the poor angle for it to be turning the beam from, there is enough energy applied by the CW to give the beam a real nice 'jerk' when it's needed most. In a properly tuned machine, the CW will actually stop at this point (for a split second) before starting to swing back to the left and completing its downward motion. But as the payload is already gone, this is wasted motion/energy. | ![]() |
Here is a picture from a newspaper that happened to catch the Trebuchet of Rob Kohler, just at the stall point. Notice the wonderful alignment of the CW, Beam and Sling. The projectile hasn't quite left the pouch although the slip ring has come off the release pin. An excellant example of release at stall. (Thanks Rob!)
Variables
A lot of analysis has been done on
Trebuchets. Over time the various angles, masses and linear components
have come to have labels that are commonly used.
mb = Mass of Beam
m1 = Mass of Counter Weight
m2 = Mass of Payload
(0,0) = Origin for X,Y plots
(X1,Y1) = Position of end of short arm.
(X2,Y2) = Position of end of long arm.
(X3,Y3) = Position of center of
mass of payload.
(X4,Y4) = Position of center of mass of counter weight
Psi = Included angle between Beam long axis and from Beam end to center of
mass of Payload.
Phi = Included angle between long axis of hanger and long
axis of Beam.
Theta = Included angle between short arm and a vertical line
from the Beam pivot point downward.
(Myself, I don't care for the angular labels and would prefer references of
Theta 1, Theta 2 and Theta 3. It's more consistent with the other labels
and doesn't confuse the Psi and Phi labels with other Engineering labels. But
hey, that's just me...)
Pin Angle
The angle
that is subtended by the Release Pin in reference to the long axis of the
Throwing Arm. An important feature that, along with other factors, helps
determine what angle the payload is released at. In this view the Throwing Arm
is at horizontal, but it's important to understand that the Pin Angle is
relative to the Throwing Arm, not the ground or the frame of the Trebuchet, so
no matter where the Throwing Arm is, the Pin Angle will remain the same.
Cocking Angle
With the Trebuchet cocked, ready to fire, the
Cocking Angle is referenced to the frame base and is subtended by the long axis
of the Throwing Arm.
Hanger Angle
This is a simple one, but is referenced
differently. It is that angle between the long axis of the Throwing Arm
and the long axis of the Hanger. I haven't included a graphic for it but will if
pressed into it.
Prop Angle
This is the same as the Hanger Angle, but since there
would be a device (the Prop, not shown here) that holds the Counter Weight in a
new position it's called something else. The long axis' of the Hanger and
the Throwing Arm are still the reference lines. Propping is not often used
but is spoken of often enough to include it here. Refer to my Theory page for
more about Propping.