Virtual Mass revisited

[DC]

I've looked at those until I'm cross eyed. To me it looks like a low spined arrow has a slower "wave" and if it is low enough the fletching hits the bow. I really can't see what goes wrong with a too stiff arrow. Anyone help me?

[Badger]

 Too stiff will often hit the bow and kick left

[avcase]

Alan, would you be willing to speculate or comment about any limb designs features that may affect these harmonics? or how one could "tune" their design to a particular weight arrow?  This goes a bit beyond making tips lighter  or stiffer I presume.

I like to try to find ways to minimize the interaction of various harmonics on the shot. The best ways to do this is to push secondary vibration modes to as high a frequency as possible. This is done by following the familiar advice of focusing the bending area over as small an area as possible and using a string with maximum tensile stiffness.  Otherwise, it is a matter of being aware that these interactions exist.  A long thin flexible limb design should be more troublesome. A full working recurve with very flexible tips is probably going to be the most susceptible to bad behavior over a very wide range of arrows.

Alan

[willie]

Thanks  Alan. I was playing around with some take down limbs in the riser fixture recently and was reminded of just how much limb vibration occurs when the tips do not come home at the same time.

 

[avcase]

The out of sync vibration does feel bad at the handle. There can be very high lost energy even if the limbs are perfectly in sync.  It is dominated by a little different mode shape, which is the mid limb popping forward and back.

Alan

[avcase]

What do you think of this one?  This is a plot of virtual mass for a wide range of arrow mass.  This is a pretty heavy draw weight modern composite longbow design. I was trying to do everything I could to get it to throw light arrows as efficiently as possible to equal a static recurve that I had built earlier, but it was not cooperating. The plot for the static recurve was almost the opposite of this, with the lowest virtual mass for the lightest arrow, and higher virtual mass for a heavier arrow.

[Badger]

  Odd but still a low virtual mass.

[avcase]

I was trying to get the virtual mass extremely low. I was throwing every trick I knew of to maximize efficiency with a 3ggp arrow, but fell short of my goal. This particular design has stiffened lever-like limbs with a smaller bending area centered near the handle fades.

It makes sense why this happens. There are a couple natural frequencies in the bow limb and combination of the bow limb and properties of the string which either fall in or out of phase with the launch of the arrow. The big dip is driven by the natural frequency of the middle of the bow limb between the fades and string.  This frequency is lower for a long-limbed longbow than it is for a shorter limbed static recurve, and this shifts the bigger dip in the plot so that the lowest virtual mass coincides with heavier arrows. It isn’t easy to change this very much without compromising other desirable properties of the bow such as smoothness of the bow or energy storage versus draw.

Alan

[willie]

The plot for the static recurve was almost the opposite of this, with the lowest virtual mass for the lightest arrow, and higher virtual mass for a heavier arrow.

Alan,

would you be kind enough to post the plot of the static recurve? or at least post a typical curve?

the curve above is non typical? or the static recurve is non typical?

[avcase]

would you be kind enough to post the plot of the static recurve? or at least post a typical curve?

the curve above is non typical? or the static recurve is non typical?

Each bow design will behave a little different.  This is typical for this particular bow, but at 114#@31”, this bow is not representative of what a typical archer would shoot!  What I find very interesting is that I find it more challenging to design a light 35#@28” longbow with lower virtual mass numbers.

I need to disclose that this bow is made using modern composites and modern string material. It just happens to be one that I am currently working on so I have the performance data readily available.  The main point I am illustrating here is that virtual mass can be a useful method to predict arrow speeds for over a narrow range of arrow masses, but it has its limits. I still find virtual mass useful in other ways because it provides a little more insight into bow behavior than pure bow efficiency.  The plot of efficiency versus arrow weight for the same bow is quite different. See below. I have observed many instances where I was testing a flight bow and I would find a particular light arrow mass where the bow seemed to quiet down with less post shot vibration.  In the meantime, I have been trying to figure out ways to find ways to tie design characteristics for targeting a minimal virtual mass at a specific range of arrow mass.

Alan