Massless lightsabre blades?

[Hardy]

It could be that the saber really is spinning on its hilt, but accelerating downwards at the same time, so that it looks like it's spinning on a point foreward of the hilt.

[Dangermouse]

We can get an estimate of likely locations for the lightsaber's center of mass by doing a motion analysis. Consider an object undergoing rotation and translation. The center of mass should follow a roughly quadratic shape that is dependent on the object's starting velocity and the acceleration of gravity. Points not on the center of mass will deviate from a quadratic shape depending on the distance from the center of mass as well as the rotational velocity of the object.

Lets begin.

The saber is first marked with six points that will be tracked through the scene.



Here blue and pink represent the extremes of the hilt, red is a short distance into the blade itself, green is the middle of the hilt, and yellow and light blue are along the hilt.

We can then map these points through the scene:



Using a standard coordinate system in which Y is up and X is to the right, we can make a plot of Y as a function of X. First, the original points:



Next, zooming in on the region between Red and Green and fitting curves between Red and Blue, Yellow and Blue, and Yellow and Green, we can make this plot:



Inspecting the plots, I am tempted to discount the red, pink and light blue plots for the deviation away from a quadratic shape. For example, the red point appears to undergo a slight oscillation around a linear line. The pink and light blue points on the far extreme of the hilt also appear to be highly nonlinear and nonquadratic; I believe the extreme dip is due to those points rotating downward quickly near the end of the shot.

Its hard to pinpoint a likely center of mass based on inspecting the other interior curves. Certainly there is some error in this as the saber is probably moving in and out of the plane as well. Based on the curves alone and not running any numbers, I think that the area between blue-yellow and yellow-green is the most likely area of the center of mass. These curves have a fairly smooth quadratic shape.

So my interpretation is that the center of mass for the lightsaber appears to be in the upper half of the hilt; this shift away from center could be due to heavier top half or as others have pointed, factors such as blade/air interaction. I don't think the center of mass is in the actual blade although this entire anaylsis here is somewhat dodgy and quick.

[Spanky The Dolphin]

Holy crap, we need more shit like that in discussions.

[Dangermouse]

Holy crap, we need more shit like that in discussions.

Thanks. We got blown out tonight in softball so no one was up for doing anything so I did this instead.

[Hardy]

Very impressive, DM.

I suggest that you ignore the motion of the saber through space for the sake of simplicity. It might be easier to find the center of mass if you lay each set of dots directly over each other and then plot your curve.

So my interpretation is that the center of mass for the lightsaber appears to be in the upper half of the hilt

That makes sense, in my opinion. If the swordsman wants to simulate a real blade's momentum, he could add more mass to the top.

[Dooey Jo]

That's fine work, Dangermouse. What program did you use?

But I don't know how good it would be to make the top of the hilt heavier, because that could cause even more balancing problems than just having a massless blade. Also Luke's sabre in RotJ, when he uses the force to get it from the Emperor's chair seems to spin around a center in lower half of the hilt (sorry about being unable to supply pictures of this, though). Though, Luke is using the Force there which could influence things, and it's not even the same model as in the scene in ESB nor do ever see it spin with the blade active for comparison...


BTW, notice how they missed to rotoscope Vader's blade in the second frame of Dangermouse's sequence. You can see a green stick where the red blade is supposed to be

[Dangermouse]

That's fine work, Dangermouse. What program did you use?

Thanks. I used Paint and placed the markers manually. Once the markers are placed, its fairly easy to get the pixel locations. In reality, you would want to have the markers already placed on the object and track using high speed video.

But I don't know how good it would be to make the top of the hilt heavier, because that could cause even more balancing problems than just having a massless blade. Also Luke's sabre in RotJ, when he uses the force to get it from the Emperor's chair seems to spin around a center in lower half of the hilt (sorry about being unable to supply pictures of this, though). Though, Luke is using the Force there which could influence things, and it's not even the same model as in the scene in ESB nor do ever see it spin with the blade active for comparison...

<Shrugs> I don't know much about swords. Maybe you want to shift the center of mass slightly upward to give yourself a feel of how the blade is oriented if the blade is massless?

BTW, notice how they missed to rotoscope Vader's blade in the second frame of Dangermouse's sequence. You can see a green stick where the red blade is supposed to be

That was interesting. The clip is also from the SE so I am a little suprised they missed it.

[Spanky The Dolphin]

Well, either way the points of rotation are still in the hilts, so that's good enough for me.

[McC]

Unless my understanding of swords is totally wrong, the point of rotation is always near the top of the hilt, typically centered at the intersection of the hilt and the crossguard. This is done purposefully, to balance the blade. The fact that the center of mass for a lightsaber is in the same location doesn't do a damn thing to dispute its massive/masslessness That's where you want it to be no matter what to present a balanced weapon.

[Dangermouse]

Unless my understanding of swords is totally wrong, the point of rotation is always near the top of the hilt, typically centered at the intersection of the hilt and the crossguard.

That surprises me a little bit since I would expect the center of mass to be slighlty above the hilt within the blade itself. This is based on my initution looking at the length of a typical sword blade. I would think the center of mass would creep toward and might even be at the hilt/blade interesection for lighter swords such as foils and epees but not for a broadsword. I have never held a sword so hopefully others who know a little about swords and have used them can speak about this.

The fact that the center of mass for a lightsaber is in the same location doesn't do a damn thing to dispute its massive/masslessness

It provides the possibilty for a massless blade. A point of rotation within the blade itself would argue more against a massless blade. Lightsabers do not appear to be tapered. If we did assume that the blade itself had mass, then persumably this mass would be uniformally distributed along the blade; I don't think there are compelling reasons to model it as anything other than a uniformally distributed load if we are considering the blade has mass. Based on the torque alone, a blade with uniformally distributed mass would shift the center of mass more toward the center of the sword away from hilt, assuming the blade's density is comparable to the density of the hilt.

I don't think we will be able to say either way whether the lightsaber has mass within the blade based on this alone. We would have to know the center of mass for the hilt alone and see if it shifts at all when the blade is activated. I think there are a couple of choices though:

a) The blade is massless. The shift of the center of mass away from the true center of the hilt is due to an unbalanced hilt.

b) The blade has mass and its contribution is enough to shift the center of mass away from the true center of the hilt. However, its contribution is not as significant as lets say a broadsword since the center of mass has not shifted over the hilt onto the blade.

c) The blade is not very dense and its contribution is very small compared to lets say an unbalanced hilt.

d) The blade is massless and other factors (air resistance / gyroscopic rotations/ magic/ gnomes/ Vin Diesel) cause the shift away from the center of hilt.

<Shrugs> I wish I knew more about swords. The hilt is the handle right?

Edits: Grammer is my friend, not an enemy. Grammer is my friend, not an enemy.