Tell me straight
Question: It occurred to me that without an implement such as a ruler, I
would not be able to draw a straight line. But in order to produce a ruler, I
would need a straight line to compare it with. How were the first completely
straight tools produced?
Answer: The easiest way to create a straight line is by using a tightly
stretched piece of string. The method is still used at construction sites for
longer distances than a ruler can cover.
Daniel Soomer
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Tallinn, Estonia
Answer: My father was a signwriter and he never used a ruler to draw a
straight line. He carried a piece of string with a loop tied in the middle. He
would rub the string with chalk, hold the string between his outstretched arms
and use his thumbs to press the ends of the string against the surface where he
needed to draw the line. He would then pick up the loop with his tongue,
manoeuvre the loop until it sat between his teeth, bite, draw his head back and
let go of the loop. The string would spring back to the surface and leave a
straight chalk mark.
Peter Harris
Swavesey, Cambridgeshire
Answer: A piece of wood can be hand-planed perfectly straight using a simple
reversal procedure. First, plane the edge of a board until it is straight to the
eye. Then use the planed edge as a guide to draw a pencil line on a flat
surface. Flip the board over and match the planed edge to the line just drawn. A
departure from straightness will be revealed where the edge fails to meet the
line. The board can then be re-planed to remove high spots, a new line drawn,
and the procedure repeated until the board fits the line in both orientations.
At this point, the edge is straight. The principle behind this procedure is
called straight-edge reversal, and it is commonly used to measure straightness
errors in the motion of precision machines.
W. Tyler Esther
Precision Engineering Division
National Institute of Standards and Technology
Gaithersburg, Maryland
Answer: Sir Joseph Whitworth is credited with inventing a method of producing
truly flat surfaces in 1830, during Britain鈥檚 Industrial Revolution. Whitworth
started by making three metal plates, probably from cast iron, as flat as he
could. Having ensured that all three surfaces were scrupulously clean, he
smeared one surface with a thin layer of engineer鈥檚 blue, a blue paste like thin
oil paint. This blue plate was brought into contact with the flat face of
another plate and moved in a circular motion relative to the other. The high
points on the blue plate are revealed because their colour is rubbed away, and
are subsequently reduced with a sharp metal scraper. In the early stages you may
scrape away several thousandths of an inch at a time, but eventually you scrape
just a fraction of that.
If you used just the two plates you would almost certainly produce one that
was convex and one that was concave. Although these mate perfectly and may give
the illusion of flatness, they are not actually flat. However, by using three
plates and regularly comparing each with the other two, it is possible to
produce three flat surfaces.
Paul Goodwin
Poole, Dorset
One of our readers has direct personal experience of using the method
invented by Whitworth鈥擡d
Answer: In the 1940s, I was required to make straight edges and flat surfaces
using only the simplest of hand tools and without the use of measuring
instruments. The method was shown to me by craftsmen who learned it in the 19th
century.
A flat surface was required to test the straight edge, and the surface we
used was the top of a cast iron structure known as a surface table. This was
employed as a datum for many precision instruments. Surface tables had to be
made three at a time.
To minimise work by hand, the surfaces of the iron castings were first
machined as flat as possible. The surface of one table was coated with a thin
film of engineer鈥檚 blue and placed face-to-face with either of the other two and
the surfaces rubbed together. Any point of contact between the two surfaces
rubbed off the engineer鈥檚 blue, revealing high spots. These were reduced with a
hand scraper made from an old file. Each stroke of the scraper removed a minute
amount of metal from a high spot.
Three men worked together, one on each surface, until all high points had
been reduced. Then the surfaces were re-blued and the process repeated again and
again. Each surface was worked against the other two in rotation. If two
surfaces are in perfect contact, one may be concave and one convex. But if every
combination of two surfaces makes perfect contact, all three must be flat.
After some weeks of the hardest work I ever did, a state was reached when
every square inch on the surfaces showed more than one hundred points of
contact. An inspector verified this by counting them and certified the tables to
be 鈥渙ne-hundred point鈥� surfaces. These surfaces would, in metric measurements,
be flat within about 1/100th of a millimetre over an area of 1 square metre.
After making a flat surface, producing a straight edge was light relief. The
edge to be made straight was placed in contact with a flat surface and the
points of contact noted. These areas were filed down and the edge repeatedly
tested against the flat surface until it was visibly in contact at every point
along its length. The edge was then refined by defining the points of contact
with engineer鈥檚 blue and reducing them until every point of the edge made
contact with the flat surface. Then you had a straight edge.
L. Williams
Birmingham
Answer: Victorian mathematicians such as Alfred Bray Kempe
(1849-1922), were fascinated by this problem.
Their challenge was to design a mechanism consisting of a number of rigid
links joined by simple hinges which would constrain one point to move along a
perfect straight line.
Although, in 1784, James Watt was very proud of his approximate
solution鈥攁 mechanism using just four links鈥攊t wasn鈥檛 until
Charles-Nicolas Peaucellier, a French army engineer, came up with a
mathematically accurate solution using eight links in 1864 that the problem was
solved. Kempe describes these and later solutions in his excellent book How
to draw a straight line: a lecture on linkages, Nature Series, Macmillan,
1877.
John Downie
School of Engineering
University of Brighton
This week鈥檚 question
Heavy or light?: What causes different types of rain? Sometimes it comes
down in 鈥渟tair rods鈥濃�攍engthened droplets that fall at great speed and bounce
high after hitting the ground. Other times there鈥檚 just a misty drizzle that
blows aimlessly in the breeze. How can rain fall so heavily that it can cause
physical pain, or so lightly that it is just a soaking mist. And how do you get
the types in between?
Martin Reeves
Leicester