Catapult?

[kmcclary]

Originally Posted by KenWittlief

how much 'throw' do you think a catapult will need to launch the nerfball at 25mph?

we are not talking about launching a car 2,000 yards through the air here :^)

Well, let's take a crack at that one...

Furthest case: At the end of the stroke, the center of the ball needs
to be moving at 12 m/s max. [edit] IOW, a point on the circle made by
the ball cradle's sweep that intersects the center of the ball must
be traveling at 12 m/s. That means the final rotational speed will be
related to the Throw Radius, which I'll define as distance between
the pivot center and the ball's center. [/edit]

We've analyzed 48 Poof-Slinky balls. Amazingly, their sample
weights are fairly evenly distributed between 175 and 186 grams,
which places the median at about 180-181g. Therefore, we then
calculated a ball will contain roughly 13.7-13.8 J of energy at 12 m/s.
(Can someone else here, please check our math? Are we right?
Anyone have more weight samples, to improve our data set?
We suspect our sample set is too small, because we didn't
get the expected 'Bell Curve distribution'...)

[edit] To calculate the ENERGY required, you now require: the
arm's parameters (specifically the arc range of motion, the
distance between the pivot and the center of the ball, and
the rotational inertia of the arm). [/edit] From those, it should be
possible to calculate the torque required to accelerate the ball
over that arc to impart the required energy, and guarantee the
system still meets the "12 m/s max muzzle velocity" FIRST spec.

You then check to see if you have a motor still available capable
of imparting the required torque, and design an arm torque system
that'll properly clutch itself to prevent self-destruction from
repeated "stop shocks"...

BTW, a big question for all: Is there an easy way to hand
calculate the rotational inertial of a wheel and/or arm design,
to evaluate them before construction? Weighing it is insufficient,
as you need the radial mass distribution.

Professionally, the only way I know of is to Solid Model it with
mass properties on, and run it through a Mechanical Simulation
System (MSS) software suite like ADAMS. But we don't have
that software here now. It'd be VERY expensive (and take awhile
for approvals) to buy it for the school, and we don't have training
time during the build to learn it, even if we could get ahold of
a seat or two of it... (Darn...)

We also don't have the time to build a bunch for testing. Otherwise,
the other "simple" way would be to "make one, apply a known torque,
and measure its acceleration" with some improvised measurement
widgetry (like the time it takes it to traverse a known arc between
two retroreflectors). Then tweak, and repeat... <sigh>

How do you simply measure (or calculate) the rotational
inertia of an arm system, or of a sample object (like a wheel
you have on hand), before building up a system using it?

Back to catapults...

Now a problem with catapults in general is that (when compared
to continuous feed methods like belts or flywheels) unless you
"complete the arc full circle", you are wasting a LOT of energy
per throw. With a traditional arm catapult, you have to put in
the energy to accelerate the ARM as well as the ball, and the
remainder is all lost when it hits its stop. Since the arm is
normally a lot heavier than the ball, the relative energy cost
is huge to launch a bunch of balls. And, you still have the whole
"recocking cycle time" issue to contend with.

OTOH, if you think a set of "Jai Alai" style shooters (Cestas) arranged
like spokes around a wheel, you may have something there!
You KEEP the energy you spent revving up the wheel, and now
only have to replace the momentum lost by throwing each ball.
You either "drip in" balls, or catch them off a dispenser to throw.

Now getting this all synced up to have the Pelota (Spanish
for a Jai Alai "game ball") properly intersect the Cesta
(Spanish for a "basket", the Jai Alai "shooter") at the right
point in each cycle to make it repeatable would IMO be an
interesting technical challenge.

Controlling exit angle is another problem. A combination of where
it first intersects the Cesta and its rotational speed determine
how long it remains on the Cesta accelerating. So, exit angle
COULD be controlled by adjusting the intersect or radial drip point,
(or by changing the wheel's speed), but all this could require a LOT
of experimentation and tweaking!

Of course, assuming that all worked, how do you then "shield"
the whole assembly to match FIRST's safety rules?

I think other rotary designs may be easier to package,
aim, and be more repeatable, which is your true desire
here. (You need repeatability first, before you can possibly
calibrate your shooter.)

But man oh man, it'd be REALLY COOL to see a two to
four armed "Cesta Wheel" (Cesta Rueda? Basket Wheel?)
in action, whipping out balls!

Comments?

For more info on Jai Alai, some terminology, and to see
a real Cesta (a traditionally made wicker basket shooter),
Google it, or go to: http://www.dania-jai-alai.com/page6.htm

- Keith