

#13 25 Oct 2011 at 7.22pm    

In reply to Post #10 Volume of a sphere
Circumscribed cylinder to a sphere.
In 3 dimensions, the volume inside a sphere (that is, the volume of a ball) is given by the formula
\!V = \frac{4}{3}\pi r^3
where r is the radius of the sphere and π is the constant pi. This formula was first derived by Archimedes, who showed that the volume of a sphere is 2/3 that of a circumscribed cylinder. (This assertion follows from Cavalieri's principle.) In modern mathematics, this formula can be derived using integral calculus, e.g. disk integration to sum the volumes of an infinite number of circular disks of infinitesimal thickness stacked centered side by side along the x axis from x = 0 where the disk has radius r (i.e. y = r) to x = r where the disk has radius 0 (i.e. y = 0).
At any given x, the incremental volume (δV) is given by the product of the crosssectional area of the disk at x and its thickness (δx):
\!\delta V \approx \pi y^2 \cdot \delta x.
The total volume is the summation of all incremental volumes:
\!V \approx \sum \pi y^2 \cdot \delta x.
In the limit as δx approaches zero[1] this becomes:
\!V = \int_{r}^{r} \pi y^2 dx.
At any given x, a rightangled triangle connects x, y and r to the origin, hence it follows from Pythagorean theorem that:
\!r^2 = x^2 + y^2.
Thus, substituting y with a function of x gives:
\!V = \int_{r}^{r} \pi (r^2  x^2)dx.
This can now be evaluated:
\!V = \pi \left[r^2x  \frac{x^3}{3} \right]_{r}^{r} = \pi \left(r^3  \frac{r^3}{3} \right)  \pi \left(r^3 + \frac{r^3}{3} \right) = \frac{4}{3}\pi r^3.
Therefore the volume of a sphere is:
\!V = \frac{4}{3}\pi r^3.
Alternatively this formula is found using spherical coordinates, with volume element
\mathrm{d}V=r^2\sin\theta\,\mathrm{d}r\,\mathrm{d}\theta\,\mathrm{d}\varphi
In higher dimensions, the sphere (or hypersphere) is usually called an nball. General recursive formulas exist for deriving the volume of an nball.
For most practical uses, the volume of a sphere can be approximated as 52.4% of the volume of an inscribing cube, since \pi/6 \approx 0.5236. For example, since a cube with edge length 1 m has a volume of 1 m3
, a sphere with diameter 1 m has a volume of about 0.524 m3
.
Thought you knew all that Brian.



#12 25 Oct 2011 at 6.46pm    

In reply to Post #11 Based on the evidence thus far, i have put the 2 main posts at the top of the thread.If this all turns out to be factual it can be made a sticky .
Can we please have our resident bait makers input on this please .



#11 25 Oct 2011 at 6.32pm    

In reply to Post #10 Hollow as in 'glass bubbles'.
what do they look like...........in the bag.......a very fine light powder, out of the bag........a very fine powder that slowly drops to ground level and floats around if disturbed. A bit like powder snow or wading around in polystyrene balls.
Buoyancy........think of an airball popup as being 20% micro encapsulated air



#10 25 Oct 2011 at 5.58pm    

are these spheres solid glass? or hollow??
how do they make bait so buoyant??
i've never used, nor am i likely to seeing as i hate bait making! these nor have any idea what they look like.



In reply to Post #8 Agreed Keith IF, and thats a very big IF, you do follow the precautions, which is my point exactly.
Matt



#7 25 Oct 2011 at 11.53am    

In reply to Post #6 you might say you would never do it to bait....bet a lot of people think that, and don't realise that half the pop ups they've got are glass!!!
The effect on the fish is secondary in my opinion, how many pop ups get ingested by carp  not many!
Spread the word to anyone you know that's even thinking about making their own.
cheers
Matt



In reply to Post #5 are glass spheres any good for fish ?
I cant say id ever do this to bait



In reply to Post #4 Learn something everyday.....didnt know that ...good info..



#4 24 Oct 2011 at 10.56pm    

In reply to Post #3 silverfish great link which backs up what i am saying. I am reading more and more "how do i make pop ups" replied with "just add 20% glass spheres..."
Be warned. And I ask the Mods again, this really should be a sticky  plenty of stickies about fish safety, this one is even more important, its anglers' safety.
For those that dont read silverfish's link,its the health and safety data sheet from the manufacturer 3M and it recomends proper goggles and PROPER facemask, not just a thin dust mask like you would wear decorating or something.
Be safe guys!
Matt



In reply to Post #1 http://multimedia.3m.com/mws/mediawebserver?mwsId=SSSSSuUn_zu8l00xMx_1M8tUPv70k17zHvu9lxtD7SSSSSS



In reply to Post #1 good warning post

