[TheForge] Rule of thumb (was Guesstamating)

Fri Mar 29 03:11:06 2002

Speaking of rule of thumb, anybody know where that saying came from?

Donn

----- Original Message -----
From: Larry <[email protected]>
To: <[email protected]>
Sent: Friday, March 29, 2002 12:36 AM
Subject: Re: [TheForge] Guesstamating

> After trying to write this rule on my thumb,  I decided I needed a finer
point pen, then I went to the very fine line pen, but found I could not read
the fine print without a magnifying glass.  Though this is by far the most
interesting of replies, I am afraid for my purpose, I will try the make one
and see pattern till I can get the proportions I am trying to achieve.  But
thanks for the
> excellent information.  I plan to study it till I actually can make work
in practice what you have explained here in text.  I now have a new life
long goal.  Thank you Bruce, I will forever be in your debt.
>
> Larry
>
> Bruce Freeman wrote:
>
> > 1) A one-way taper (to a wedge or chisel edge) draws out the
(rectangular) stock to two times its length.
> > E.g., tapering 6" of a 1" square bar to an edge will result in a wedge
12" long.  Conversely, if you want a 6" taper from 1" square to an edge, you
need a 3" length of 1" square stock.
> >
> > 2) A two-way taper (to a point) draws out the (round or rectangular)
stock to three times its length.
> > E.g., drawing the last 2" of a 1" square bar to a point will stretch
that 2" to 6".  The same is true for 1" round stock.  This is true providing
you don't change shape, such as a round point on a square bar.
> >
> > That's the easy part.  It's more complicated if you're drawing down from
one diameter to another or from one shape to another.  First you have to
consider the drawing from one uniform thickness to another uniform
thickness:
> >
> > 3) Drawing square to round draws out the metal to 4/pi, or about 1.25
times its length.  E.g., start with 12" of half-inch square stock and draw
the entire length down to half-inch round stock and you'll end up with about
15" of round stock.
> >
> > 4) Drawing rectangular stock from one thickness to another (without
changing the width) increases the length of the stock by the ratio of the
thicknesses.  E.g., If we start with 1 foot of 1" square and draw the entire
piece down to 1" x 1/3" strip, we'll have three feet of stock.
> >
> > 5) Drawing round stock from one diameter to another increases the length
of the stock by the square of the ratios of the diameters.  E.g., starting
with 1" diameter, 1 foot long, if we draw the entire piece to half-inch
diameter, we'll have a 4-foot piece.
> >
> > 6) Drawing square stock from one (square) size to another increases the
length by the square, just as in (5).
> >
> > 7) Drawing rectangular stock from one thickness and width to a different
thickness AND width is best approached as a double application of rule (4).
> >
> > Hence to calculate the specific example you give, using these rules,
you'd break the problem up into parts:  (Don't you love word problems?)
> >
> > a) Suppose you drew out round from 1" to a point, such that the portion
of that bar from the 1" diameter to the  half-inch diameter measured 6"
long.  How long would the taper be?  (This is easier than it sounds.)
> > Answer:  6" x (1" / 1/2") or 12".
> >
> > b) How much of the 1" round stock would be consumed in (a)?
> > Answer:  12" / 3  = 4"
> >
> > c) What length of half-inch round is represented by the section end of
this taper (with diameter of 1/2" or less?).  I.e., how much half-inch round
stock does it take to draw a point, 6" long?
> > Answer:  6" / 3 = 2" (of half-inch round, not 1" round).
> >
> > d) How much 1" round has to be drawn out to make 2" of half-inch round.
> > Answer:  2" / (1" / 1/2")^2 = 1/2"  [where "^2" means "squared"]
> >
> > e) So if it would take 4" of 1" round to draw the 12"-long point in (a)
and the last 6" represents only 1/2" of the 1" stock, how much is required
to draw a 1" rod to 1/2" over a length of 6"?
> > Answer:  4" - 1/2" = 3.5".
> >
> > Next question:  Are there other ways to do this?
> > Answer:  Yeah, about as many as there are folks who want to do it!
> >
> > My preference would be integral calculus.  Consider the final taper you
want.  Slice it infinately thin.  (While you're off doing that, I'll just
hypothesize about it.)  Each slice is of area pi*r^2  [where * means
multiply] and of thickness dx (meaning infinitesimal, but not zero).  Now
radius r varies linearly from 0.5" to 1" as the position, x, along the point
runs from 0" to 6", hence
> > r(x) = 0.5" + x/12
> > E.g., r(0")= 0.5"; r(6")=1"
> > So all we have to do is integrate from 0" to 6" the function
pi*r(x)^2*dx.
> > Got that?  [It's easier than it sounds.]
> >
> > Bruce
> > NJ
>
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