Ed Rybak wrote:Your work at http://www.myarmoury.com/talk/viewtopic.php?t=14063 , using right triangles with the right angle "hung" on the point O in your graph, really makes this clear. Rotate the triangle a bit, and it's easy to see how H and F change without changing k; all that's needed is a little mathwork to reapportion mass between Hmass and Fmass, and M and G remain unsullied. Very nice!
That graphical representation is actually quite handy, it gives a good feeling of how the points depend on each other. I'm glad you liked it
So, for a given weapon, which of many sets of H, F, Hmass, and Fmass are "right"? I would think the answer is "all". That is, looking at my odd model weapon above, if Fmass can be taken to represent impact mass, then 0.5kg is the right impact mass when looking at the point F=0.6m, and 0.2kg is right when looking at a point further toward the tip, F=0.7m. At least, that sounds reasonable...
You mention more work along those lines, deriving a better "theoretical" H and F for modeling weapon feel. Would be great to see that whenever it's ready.
All sets are indeed right, my personal belief is that one of these sets carries more meaning. But I'm not currently completely sure of which yet
Perhaps dynamic length, etc. should vary with the point where the weapon is gripped! If so, then the fact that dynamic length, etc. vary with the "arbitrary" selection of H (based on point of grip) is actually a feature, not a bug?
I do think that handling properties depend in part on the point you grip. As you understood using the cross gives a fairly accurate idea of where the hand actually lies.
If you consider a plain old stick, for example, and grip it near the end, you will feel less weight in your hand and more weight towards the tip than if you grip it nearer the middle. Yet it's the same stick... So the handling perception is a combination of the intrisic properties of the object and of your grip. That's one complicated point.
The other complicated point is that if you have the same k and the exact same position of the center of gravity relative to your hand, but different overall lengths, your perception of the objects is different, because you expect some mass distribution properties based on the objects' lengths. Two objects might have the same balance with eyes closed, but feel very different once you know their actual length.
As I see it, there are three ways to get k:
k = l * sqrt( (Fmass * Hmass) / (Fmass + Hmass)²)
k = sqrt(HG * GF)
k = sqrt (MOI/Mass) if MOI is known (as with a rod).
At least three ways, yes
It all depends on what data you start from...I think it's obvious that only a single rod, or only a single point, isn't enough to model swords, etc. As models that do work, you've suggested the following:
a) A single rod plus a single-point mass, per http://www.myarmoury.com/talk/viewtopic.php?t=15288
b) A two-mass model, per this thread
Just curious, when and if you have time: Have you abandoned a) in favor of b) as the better model? Or do you see them as equally valid models?
I consider them as complimentary and equally valid.
The mass on a stick is really nice, because it takes into account the physical extent of the object as well, and as I said before I think this is an important part of our perception (it's taken me some time to fully realize that). It is also fully objective, you can compute it without singling out a particular reference point, though you'd obviously need one if you want to compare weapons.
Its first shortcoming is that it cannot be directly measured as I describe in the article for the two-mass system. You have to measure the weapon, then feed the results to some computer that will give you the position of the point mass, the stick mass, etc. The equations are really a notch up from what I've put in my article; I actually don't know them by heart, as I do for some others. So it's something more advanced that non-scientific users might find a bit mysterious.
Its second shortcoming is that it's not actually that easy to interpret. Specifically, the relative magnitudes of the point mass and stick mass, and the position of the point mass, have an impact on handling perception for sure, but it's hard to say exactly what kind.
The two-mass system that I proposed settles the first shortcoming, and almost solves the second. Almost, because by itself it does not include any influence of the physical extent of the weapon, so fails to represent fully what we perceive. That's why I'm still mulling over some sophistication...
A final shortcoming is the variability of the point mass and its location. I cannot measure k to an absolute precision; for objects that are close to sticks, it gives a big uncertainty on the point mass position (though the point mass is also quite small, so intuitively we understand that the effect is not really big).
As far as I can tell, they both seem good models. In terms of actually visualizing things, though, the two-mass model b) can be a little difficult. For example, to model a staff, you have to find k based on length (easy enough) but then place two equal masses on opposite sides of G, each located the distance k away from G. Which may be perfect as a model, but it's hard to "see" the actual staff in there.
Quite true, and even worse you don't have just one two-mass system but many, and you have to pick one. That's one advantage of the mass + stick equivalent object, it gives a unique reasonnable representation, that gives a pretty good indication of how the object was made.
I wonder, too, if the rod + single-mass model a) has a shortcoming. It's perhaps able to model any weapon with a k equal to or lower to that of a rod – but wouldn't it be unable to model a weapon with k greater than that of a rod? (Example: Very tip-heavy weapon, counterbalanced by heavy pommel. Extreme example: barbell.) Maybe that's of zero practical concern for real weapons; just pointing it out.
That's absolutely true!
Indeed a mass on the stick cannot represent all possible objects. The case is not as simple as "k must be less than for a rod" but that's the idea. In my original code I made a special case for objects like that that built an equivalent out of a stick and two point masses, one at each end. That said, I have never measured an actual weapon that had such mass distribution. Basically it seems that a barbel-like distribution is not selected for good weapons, that rather have a concentrated mass somewhere.
The original idea of the stick + mass was this: What is the equivalent object that is closest to a stick?
I was not originally planning to restrict myself to one point mass. It's just that when you can use just one point mass, it is also less big. Also, if you add more point masses when you need just one, you find the same problems as with the two-mass problem: you have to choose some appropriate location for some of the point masses, and you'll find different results depending on the location(s) chosen. I have also considered using combinations of several rods (that's more realistic than point masses after all), but that raises the same problems. As you make the equivalent model more complex, the computations become more complex as well, and more and more assumptions have to be made. Assumptions that I do not want to make...
Anyway, I'm glad you like these equivalent objects. I've learned a great deal while considering them. Thinking about it, perhaps a more detailed article about equivalent objects and graphical representations could be useful too (the triangles you've seen are only the most simple, you can actually figure the effects of any mass modification by drawing circles through the right points on these diagrams)...
Regards,