Latest Squirt Equations
Ron Shepard
I was complaining last week about why some of my equations didn't work in
the limit of large stick mass, and Mike Page pointed out in email my
mistake.
It has to do with what happens when the tip doesn't slip on the ball. I
said that this meant that the sideways tip velocity had to be the same as
the sideways velocity of the contact point of the cue ball. This is
correct, sort of, but the equations that I gave regarding velocities were
correct only in the ball's frame of reference, not in the general case,
and in particular not in the lab (table, shooter, etc.) frame of
reference. Mike's correct equation describing this is
V_sy = V_cpy + V_by
V_sy is the sideways stick velocity, V_cpy is the sideways velocity of the
contact point of the tip and ball, and V_by is the sideways ball
velocity. This should be compared to my *incorrect* working equation:
V_sy=V_cpy.
So, if this is substituted into the conservation of sideways momentum equation
M_s * V_sy + M * V_by = 0
the result is
V_by = (M_s/(M+M_s)) * V_cpy
And if the contact point velocity expression from the previous posts is
substituted, then the final equation for the tangent of the squirt angle
is
V_by / V_x = (5/2) * (M_s/(M+M_s)) * (b/R) * sqrt(1 - (b/R)^2)
This equation seems reasonable in the limit that M_s-->infinity.
Say, what's this black feather doing in this funny tasting chicken sandwich? :-)
Just to plug in something and get a number, suppose M_s/M=0.1, and
b/R=0.25. The predicted squirt angle for this combination would be 3.1
degrees, or about 4 inches of squirt on a 72 inch shot.
Anyway, thanks to Mike for pointing out this error. I still don't know
how well this theory will agree with experiment, but I think it is an
improvement. There are still the details of what exactly is the effective
stick mass, M_s. I think this accounts correctly for all of the squirt
that corresponds to an ideal zero contact time collision. It is still an
open question what effect a finite contact time has, but I would hope that
this equation provides a reasonable point of reference.
$.02 -Ron Shepard
Phil Freedenberg
static? Where are the effects of stick dynamics, wave propagation, etc? Or
is squirt simpler than we had all believed?
--
O
/\
-\--\---o Phil Freedenberg
Ron Shepard <she...@tcg.anl.gov> wrote in article
<shepard-1412...@sabb.tcg.anl.gov>...
Dog8it
variables have far too wide a range for the math to have any
reasonable application.
The nap of the cloth, the deflection ("springiness") of the cue, the
force of the contact or stroke, the point of impact on the cue ball
(i.e. how far off center), the angle of impact (level stroke or
elevated stroke).....
The math is fine if all things are equal, but all things are never
equal.
The masse shot, in all it's applications, requires FEEL...that
subconscious calculation which accounts for all variables.
On Mon, 14 Dec 1998 13:21:53 -0600, she...@tcg.anl.gov (Ron Shepard)
wrote:
Ron Shepard
<pfre...@fedeng.com> wrote:
>I haven't followed this thread from startup, but aren't these equations
>static? Where are the effects of stick dynamics, wave propagation, etc? Or
>is squirt simpler than we had all believed?
This has to do with how well these equations agree with real data, which
is sparse at this time. You are correct that there is still lots of room
for improvement. These equations are an attempt to get at the simplest
explanation possible for squirt, and then see how accurate it is. The
things neglected (ignored) in these equations include the shaft stiffness,
finite tip-ball contact time, the deformations of the tip and shaft during
the contact time, etc.
The effective stick mass M_s might depend on dynamical effects, speed of
sound, and so on, so these things might have an effect on squirt even in
this simple theory in this indirect way.
These equations do predict how squirt depends on such things as the
effective stick mass, the ball mass, the ball radius, and the tip offset.
That's a start. Now we just need some data to prove or disprove these
hypotheses.
$.02 -Ron Shepard
WCrimi
thread, but are they at all useful in a practical sense. Every table, every
cloth, every day (weather), every set of balls and every combination of the
above changes all sorts of things. On a day to day basis, it seems to me that
it comes down to a general understanding of the priciples at work and FEEL!
Leonardx3
a true straight follow thru.
Phil Freedenberg
These equations are a true breakthrough in our understanding of the squirt
phenomenon.
For example they tell us that the effective stick mass is critical in
determining squirt. They also tell us that, for a given stick, squirt
increases as the amount of english increases, so to avoid squirt, use less
english.
They may even hold the key to radically reducing squirt -- by using a cue
ball whose moment of inertia is maximized, i.e., a hollow ball of the same
mass as customary. (Unfortunately, you also give up the ability to spin the
cue ball in this extreme case.)
IMO, we RSBers should undertake serious experiments to attempt to verify
the validity of these equations. For example, try balls of different
materials to see what happens as the ratio of effective stick mass to ball
mass changes, e.g., a foam ball, a steel ball, etc. (This seems to me to
make more sense at this stage than to try different sticks, since we still
don't have a sure way to characterize the effective mass of a stick.)
For a styrofoam ball, hit with a brass cue at a maximum english of 0.4
radius from center, the equations predict a squirt angle of 42 degrees.
Measurements anyone?
BTW there seems to be a minus sign missing from the squirt equations. This
is needed to show that the squirt is opposite in direction from the
english.
--
O
/\
-\--\---o Phil Freedenberg
WCrimi <wcr...@aol.com> wrote in article
<19981214221614...@ng33.aol.com>...
Ron Shepard
<pfre...@fedeng.com> wrote:
[...]
>IMO, we RSBers should undertake serious experiments to attempt to verify
>the validity of these equations. For example, try balls of different
>materials to see what happens as the ratio of effective stick mass to ball
>mass changes, e.g., a foam ball, a steel ball, etc. (This seems to me to
>make more sense at this stage than to try different sticks, since we still
>don't have a sure way to characterize the effective mass of a stick.)
Here's an experiment that I'm going to try in the next few weeks. I agree
that the effective stick mass definition is unknown at this time. I
suspect that it is the actual stick mass of a small segment of the shaft
multiplied by some decreasing function as the distance increases from the
tip (due to speed-of-sound and elastic medium effects, for example), and
summed (integrated) over the entire stick length. With this in mind, I
think that mass concentrated at the very end, on the ferrule for example,
has an effective mass the same as the actual mass. So if mass could be
added (artificially) to the ferrule, and squirt measured, then this might
verify the (M_s/(M+M_s)) dependence on the stick mass. Bob Jewett has
suggested in the past that lead tape might be a good way to weight the
stick in this manner. Squirt could be measured for a few different added
weights, compared to the above expression, and both the general trend
could be verified and the residual M_s of the stick could be backed out.
>For a styrofoam ball, hit with a brass cue at a maximum english of 0.4
>radius from center, the equations predict a squirt angle of 42 degrees.
>Measurements anyone?
Yep, I agree with the arithmetic. It's Christmas time, maybe I'll steal a
styrofoam ball from our tree. ;-) BTW, it should be a solid ball with
uniform density, not a hollow ball (which would require a factor different
than (5/2) in front).
In general, I think that the (b/R)*sqrt(1-(b/R)^2) dependence of squirt on
the tip offset might be a bit harder to measure without special
equipment. I think that the two cue companies with jigs (Clawson and
Meucci) might be able to verify this, but it would be difficult for
someone using just their normal pool stroke. Maybe this would be easier
to verify with that styrofoam ball than with a pool ball?
>BTW there seems to be a minus sign missing from the squirt equations. This
>is needed to show that the squirt is opposite in direction from the
>english.
Yes, the signs are pesky, especially if you can't draw ascii pictures well
enough to keep things straight. This *is* the predicted trend, however.
:-)
$.02 -Ron Shepard
Phil Freedenberg
brass headed rake (bridge) which already has lots of mass at the end. Just
paste on a tip and make some measurements. I have already done this and
found mucho mucho squirt. Try it.
--
O
/\
-\--\---o Phil Freedenberg
Ron Shepard <she...@tcg.anl.gov> wrote in article
<shepard-1512...@sabb.tcg.anl.gov>...
John Ahlstrom
Phil Freedenberg wrote in message <01be285a$f72de3a0$855120cf@Phil>...
>Here's a suggestion for concentrating mass at the end of a stick. Use a
>brass headed rake (bridge) which already has lots of mass at the end. Just
>paste on a tip and make some measurements. I have already done this and
>found mucho mucho squirt. Try it.
>--
> O
> /\
> -\--\---o Phil Freedenberg
>
I tried using a piece of .062 inch diameter lead solder wound around the cue
shaft as close to the tip as I could get it (about 1/4 inch). Held in place
with a piece of masking tape. The length of the coiled solder was about 1.5
inches and weighed about one half ounce. I'm using a McD cue with 13 mm
shaft.
The increase in squirt is enough to make a believer out of anyone. A 3/4
table length shot at a full tip of english and the cue ball squirted a full
ball more with the solder.
JohnA (Kent, WA)
Zozzl
this has been an old trick for many years; insert a brass rod four or five
inches long in the end of the shaft (using the rod as the ferrule tenon) and
challenge someone to make a spot shot with the cue. In most cases they will
completely miss the spot ball the first few shots. A variation of this foolery
has been used more than once to convince someone they had a bum cue and to sell
it, cheap...
Ron Kilby, Kilby Kues (zo...@aol.com)
Mike Page
<joh...@foxinternet.net> wrote:
> Phil Freedenberg wrote in message <01be285a$f72de3a0$855120cf@Phil>...
> >Here's a suggestion for concentrating mass at the end of a stick. Use a
> >brass headed rake (bridge) which already has lots of mass at the end. Just
> >paste on a tip and make some measurements. I have already done this and
> >found mucho mucho squirt. Try it.
> >--
> I tried using a piece of .062 inch diameter lead solder wound around the cue
> shaft as close to the tip as I could get it (about 1/4 inch). Held in place
> with a piece of masking tape. -snip-
Oh yeah!, well I duct taped a crow bar to a shaft --thick part over the
ferrule..
> The increase in squirt is enough to make a believer out of anyone.
amen.
--
mike page
fargo
Ron Shepard
pa...@plains.nodak.edu (Mike Page) wrote:
This past summer I dug up some old fence posts that were sunk in
concrete. That blob of concrete stuck on the end should make for some
substantial endmass. Maybe I'll glue a tip onto the end of one of those.
:-)
$.02 -Ron Shepard (still looking over the Christmass tree at those
styrofoam balls)
John Ahlstrom
didn't believe the effect end mass has on squirt.
My point was, it doesn't take a huge increase in end mass to change squirt.
It doesn't take a crowbar, concrete block or brass rake to change squirt
significantly. That is why I added only 1/2 ounce to the end mass.
JohnA (Kent, WA)
Mike Page
<joh...@foxinternet.net> wrote:
> Sorry for being redundant. I thought there were still some people who
> didn't believe the effect end mass has on squirt.
Well maybe, but I don't know any.
>
> My point was, it doesn't take a huge increase in end mass to change squirt.
> It doesn't take a crowbar, concrete block or brass rake to change squirt
> significantly. That is why I added only 1/2 ounce to the end mass.
>
Your point was --and is-- well taken, John.
But I do feel a need to point out that while the lead tape, the brass
rake, and the crow bar were actual experiments, the dug-up fence posts
with blobs of concrete on the end were mere speculation. So as it stands
*I* hold the record for endmass overkill. And *I'll* be the one to decide
whether that's something to be proud of! ;-)
--
mike page
fargo
Ron Shepard
>Sorry for being redundant. I thought there were still some people who
>didn't believe the effect end mass has on squirt.
>
>My point was, it doesn't take a huge increase in end mass to change squirt.
>It doesn't take a crowbar, concrete block or brass rake to change squirt
>significantly. That is why I added only 1/2 ounce to the end mass.
Don't worry, we were just poking a little fun at ourselves.
Happy Holidays.
$.02 -Ron Shepard