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ON THE BEST ARRANGEMENT OF CITY STREETS.'
LEWIS M. HAUPT, C. E.
It may be safely assumed that facility of communication is
one of the most potent elements of human progression and development, hence any obstacle to mobility, however small, becomes a
bar to progress, and should, if possible, be removed.
It becomes immediately evident, therefore, that the rectangular system of streets is, by itself, defective in consequence of
the angles which it opposes to diagonal communications.
Great merit has been awarded Wm. Penn for his prescience
in planning this city of Philadelphia, but whilst that plan might
answer admirably the requirements of a village, it is very inappropriate to a city of this magnitude. As a matter of history,
Penn's letter of instructions to his three commissioners,
appointed to execute his designs, will be read with interest.
They were "to seek out a spot on the Delaware River,
where it is most navigable, high, dry and healthy, where ships
may best unload without lightering, and where there is good
soyle for provisions.
"Having found such a place, lay out ten thousand acres
contiguous to it in the best manner you can, as the bounds of
said towne; that no more land be laid out until this is taken up;
which is the best both for comfort, safety and traffic.
"Be sure to settle the figure of the towne so as the streets
may be uniform down the river.
"Let the place for the store house be on the middle of the
key, which will yet serve for market and state house too, only
let the house built be as much upon a line as may be.
"The distance of each house from the creek or harbor
should be in my judgement a measured quarter of a mile, at least
two hundred paces, because of building hereafter streets downward to the harbor.
IReprint from Franklin Institute Journal. April, i877.
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"Let every house be placed, if the person pleases, in the
middle of its platt, as to the breadth way of it so that there may
be ground on each side for gardens, orchards or fields, that it
may be a greene country towne which will never be burnt, and
always be wholesome.
"Given at London, Sept. I15, I68I."
Such was the inception of this, the largest city in area of
the western world. Its growth has far surpassed the most sanguine expectations of its founders, because it combines in its
site so many natural advantages.  It is readily reached by land
or water, its topography is sufficiently undulating to furnish a
most perfect system of drainage, with cheap and good water
supply, and it has in general a firm and dry soil. Had the original idea of disconnected buildings been adhered to, however, it
would always have remained a "greene country towne" of such
magnificent distances that but few people could have afforded
to live in it. Where would our present population extend to if
so domiciled? As concentration and proximity were found to
be important elements of defense, intercourse and social and
intellectual development, the colonizers soon abandoned the plan
and congregated along the river front in both directions until
communication became inconvenient, when they began moving
along High (now Market) Street toward the Schuylkill.
The rectangular arrangement of streets as proposed being
found objectionable, it becomes necessary to examine what other
systems, if any, may be used, and determine their relative
merits. They may be, I st, regular, or 2d, irregular, and the first
class may be subdivided into rectangular, diagonal and circular;
the second into every possible kind of distortion more or less
intricate, according to the circumstances attending the growth of
a city. All the latter class are discarded as being unscientific,
expensive, inconvenient and poorly adapted to the requirements
of a growing community.
As people move through a city in every conceivable direction, it will be impossible to provide the shortest lines for all,
but the case may be met by supposing a greater or less number
of centres orpoints d'appui, to and from which the currents of
daily life flow and ebb.
With reference to the subdivisions of the first class, it is
evident that the straight line being the shortest distance between 
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two points, the chord will be shorter than its arc, and hence the
circular system is defective.   The rectangular compels a waste
of distance and time and the diagonal by itself becomes the rectangular, so that no single system fulfils all possible requirements.
A combination must therefore be resorted to, and that composed
of right line elements is both the simplest and most direct. A
judicious arrangement of diagonal streets with the rectangular
system will doubtless be found to meet more fully than any
other the requirements of the case, but it is evident that if the
streets be too wide or too numerous, the building areas will be
correspondingly decreased and a certain proportion of people
forced beyond given limits, thus increasing their distances. On
the other hand, the diagonals will in general open new building
lines, with more than residences enough to provide for all the
displaced inhabitants.
To illustrate the utility of such a combination, suppose a
portion of a town or city to be laid out in the form of a square
whose side is L feet long, and in which the blocks are I feet square
and the streets w feet wide..
Let the diagonals of the large square be opened as thoroughfares, and note their effect. The blocks or small squares
extend from the middle of one street to that of its parallel, or
from the building line of one block to that of the next, hence
the length of a side of such square must be l+ w (Fig. I).
The area of the small square, including the streets, multiplied
by the number of such squares will give the area L2 of that portion of the city, and the ratio of street to property area is the
same for the small as for the large squares, but the area of the
small squares is (1  t w)2   = 12 + 2 iw +  w2 in which /2 is the
property or building area and 2 tw + W2 is the street area; the
ratio being 2 I  12w2 and the percentage of street to property
12a                                           ey
area,
2 Iw+w'
12
For any rectangle with streets, of unequal widths, the general formula would be:
bc- + a d +  bd..                       (A1)
a    oo..
in which a and c are the sides of the rectangle, and b and d the
*'"  * *.
I,    
~   (A)
IOO
a c 
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IL   ) 7 z D   D     [      ]     F     i     \     Z     ];'     D     L     ]      D     L     \~~~~~~~.
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widths of the streets. If these quantities are equal, each to
each, A1 becomes A.  The number (n2) of blocks in a given
square, whose area is L2, will be:
L2
~2    -
(IAW)2    fi.              *    *..(B)
If now two diagonals,'./ffv  and P Q, be introduced, it is
evident that where they cross the rectangular streets no additional area is taken from the private property of the city, but
they will cut out of each of the small squares which they cross
an area whose length is 1/-22 -   breadth w, and whose area
for one block, 12, is (/12-_ W-) w (see Fig 3).  For n blocks,
the total building area consumed from L~2 by both diagonals
when n is even, will be 2 n w (I/212 — 2)-, and the percentage
of the building area will be 2     (22   -) X   0oo, which
12 2         2o
reduces to  2 (2'828 1 - w) Ioo.... (C)
the formnula for diagonals when n is even.  If n be odd, G becomes:
w 12(-88)  O-22846w
1 (2'828 1) I00 —- 282'8426'n —1
If diagonals be opened, benefits will accrue both from the
shortening of distance and the additional frontage which will be
furnished, while but a small proportion of the inhabitants will
be displaced. The greatest economy in distance will be in passing from N to 0 (Fig. 2), which by the square system is equal
to L, and by the diagonal ~ v/, the ratio being
_I/       I'4142    70  the numeratorindicating the dis             L   2 — IOO'
tance (in feet) by the diagonals, the denominator by the squares.
This gives a gain of 30 per cent., which is the greatest amount
possible, and from which it diminishes to zero at P.
The total length of frontage on the streets in the square
system is 4 ln2. The diagonals give an additional length of
4 n (I/2 12- w), and the percentage of increase is, therefore:
1/ i2- w
-00 Z   - IO.  i,..   (D)
I n- o....
(cl) 
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The ratio of people displaced is the same as that of the
area consumed by diagonals to the entire area L2.
To determine these values for any particular case, and so
discover whether or not the diagonals will be beneficial, let
= 500 ft., w = 50 ft., and n = Io.
Formula (A) gives 2I as the percentage of large or small
squares consumed by streets in the rectangular system.
Formula (C) gives only 2'82 per cent. of additional building
area consumed by diagonals.
Formula (D) gives I3 per cent. as the increase in frontage
due to diagonals, and it has been shown that the saving of distance varies from 30 per cent. to nothing.
The number of people displaced, which is but 2'82 per cent.,
will be abundantly provided for by the additional frontage on
the diagonals, revenues will be augmented by assessments on
the new buildings erected, and a large saving will be effected in
time and distance for a majority of the inhabitants by this combination of systems, which is therefore found to fulfil the
requirements of practice more fully than any other.
Similar applications of the above formulae will show to
what extent the plans of cities already established or to be built
may be improved by the opening of diagonals, the most economical relation of street to building area, the proper distribution of
the street area, and, by extending the analysis, the ratio of pavement to carriage way may also be readily determined. All of
these questions have a direct bearing on the convenience, health,
and extension of our cities.