SaLIS Vol. 65, No. 4
December 2005
Letters to the Editor
RE:
SALIS vol. 65, no. 3, 2005
Dear Editor:
In the
above issue of Surveying and Land Information Science (SaLIS)
you asked for our views as readers on the important topic of surveying
education. First, let me commend you on the excellent decision to publish the
proceedings of the 20th Surveying Educators Conference held in Texas in June
2005. One can only wish and hope that most of our “professional” surveyor
members read the thought-provoking papers and that at least some of them read
them very carefully. For all of us practitioners there is much food for thought
in them.
Professor
N.W.J. Hazelton, who among surveyors in Ohio may also be known as “The Great
Satan,” has stirred up a hornet’s nest. In his two papers he strongly advocates
exporting or “off-shoring” sophisticated high-tech surveying/geomatics services to foreign countries that have a proven
reputation for advanced education and a ready supply of highly skilled young
professionals. Hazelton’s radical idea would leave data collection by low-cost
American crews in local hands and shipping field note data and documents via
the Internet overseas, thus improving quality, turn-around and even profits for
the American surveying firm.
There are a
couple of flaws in his revolutionary thinking. As an example, he uses the IT
industry which is moving jobs overseas. Unlike certain products, surveying
requires local knowledge and judgment, not only of cadastral boundary history
but also for topographic surveys and construction control. Even automobile
manufacturers have partially replaced their exports with new overseas factories
located where their customers are; for instance, Ford has been building cars
for the German market in Cologne for decades. Mercedes luxury vehicles are
built in Alabama and several Japanese cars are manufactured in the U.S. too.
He likens
sending data to surveyors overseas to the unfortunate practice of some
irresponsible American surveyors who sign and seal plans of land which they
have never visited even once. I disagree with him on that; U.S. surveyors have
a duty to go out and look at the land before signing a plat. After all, our
clients—whether lawyers, owners or architects—have a right to expect from the
professional surveyors, whom they have engaged, that they at least be familiar
with the real world out there, and not just the one on paper. It will reduce risk and liability.
Even
Hazelton recognized that off-shoring would make the U.S. surveying profession
less capable in the long run and would lead to a weakening of the U.S.
cadastral infrastructure—not to mention national security.
EDITOR’S NOTE: In the paper mentioned above, Dr.
Hazelton did write (page 145):”Readers should note that simply because a topic
or scenario is presented and discussed in a paper such as this, it does not
follow that the author supports, advocates, or holds to the inevitability of
the scenario. Critics who make that presumption will be very publicly directed
to this paragraph and addressed as the comprehensive fools they are. It simpler
to shoot the messenger than heed the message, of course, but the long-term
focus is an important part of this discussion”.]
In his
second paper, Professor Hazelton is equally unkind to our profession, although
some of his critical remarks are on target. He is convinced that we, as a
collective entity, have a “collective mental illness” exacerbated by
“collective paranoia.” “The U.S. surveying profession, as a whole, does not
understand why it exists,” he wrote, “and most of us put pressure on
educational institutions to produce ‘field crew fodder’ instead of aspiring
professional surveyors who are educated, thinking, and forward-looking.
He
questions the need of calling ourselves “professional” surveyors, something surveyors
in countries, where surveying is considered a profession, would never do. There
it would be “tautology.” He forgets that America’s unique history of openness
and great personal freedom has both a positive and a negative side. Here,
surveying technicians who have learned to hold a leveling rod, to pull a
measuring tape, or to push a few buttons on a total station instrument will
proudly tell their family and friends that they are now “surveyors.” Even American engineers have found it
necessary to add “professional” to their title of engineer in order to
distinguish themselves from “maintenance engineers,” radio “sound engineers,”
or locomotive “railroad engineers,” as Dr. James A. Elithorp
observed in his paper.
Professor
Hazelton is concerned that the recent weakening of ACSM and its structure as a
central body may have led to a “balkanization” of our larger surveying/geomatics field. (By the way, I have noticed the absence of
our traditional and honorable ACSM logo from the cover of SALIS.)
Balkanization
“suits a reductionist view of knowledge,” and it
certainly suits the mentality of those who fear intruders, he warned. He
contrasts the breakup of ACSM with the AMA and ABA who, respectively, cover all
medial specialists and all lawyers, regardless of specialty. Neither will, however, cover nurses,
paramedics, or paralegals.
We need
mindsets who can rise above structure and process and who can see the big
picture. Hopefully Hazelton was wrong when he concluded with a pessimistic
prediction that our internal divisions will ossify the structure and prevent
any long-term solutions to the erosion of our profession.
With regard
to the other papers, I notice that Professor Earl F. Burkholder’s teaching
premise is to help students “learn how to learn,” while Professor Robert Burch
cited another quote “that the purpose of education is not to fill the minds of
students with facts….it is to teach them to think.” Burch analyzed training vs.
education and warns of “nuts and bolts” surveyors who demean the need for
education to become licensed. Problem solving without the theoretical
underpinning is dangerous, and a disservice to the profession, he warned.
Surveying education must strive for the proper balance between practicality and
theory. And he is right.
Burkholder
discussed the enormous overlap between surveying and engineering and urges us
to promote collaboration and interaction between individuals at all levels. He
asked if members of the ASCE Geomatics Division
should be invited to participate in discussions about surveying program
criteria. My answer is yes, absolutely.
We can not be narrow minded and risk ossification!
Professor
Gary Jeffress traced the professional lineage of
surveying to the educated elite of history.
Many surveying education programs in the United States “were born at
civil engineering schools,” he wrote (or vice versa, I might add. It’s the old
chicken and egg question.) He points out that real estate is the largest
category of tangible assets within the economy and that risk management is one
of the functions of surveyors. He used the term “error budget” repeatedly
without giving us a precise definition of that term.
We
practitioners know or should know that surveying and platting of real property
is, in fact, a value- added activity. While Jeffress
decries the well known low enrollment and very low esteem, he is quick to
distinguish between the surveying and the GIS professions, thus stoking the
fire of “balkanization” even more.
Dr. James
A. Elithorp makes a similar distinction. He correctly
warns of the need to cover potential liability in our litigious society.
Besides technical fundamentals, a professional education must allow students to
acquire the professional perspective necessary for successful practice. A few
years ago, the NHLSA Newsletter of New Hampshire reprinted a letter by Michael
Hoffman, PLS (The California Surveyor, spring 2001). He reported that the
Oregon State Board had received complaints against surveying professionals at a
surprising imbalanced 5 to 95 ratio, i.e. 5 percent on technical ability and 95
percent on professionalism and ethics. As Elithorp
concluded, critical thinking skills and other intangibles are as important as
technical know-how (if not more so) to most employers. Most private
practitioners will agree with him on that.
When it
comes to surveyor education, a European model could serve as a beacon to
American surveyors of the future—not to imitate but to emulate, and adapt as
time goes on and knowledge becomes paramount. The GIS organization “Geometer Europas” has drafted a Multilateral Agreement with high
educational standards. It was approved by a EU
Commission in Brussels, last year (read “The Global Land Information
Explosion,” SALIS Vol. 64, No. 4, 2004, pp. 253-257).
The new
bachelor degree curriculum at East Tennessee State University is heavily
concentrating on technological advances. It prides itself in producing current
surveying graduates that will be able to operate sophisticated data collectors.
Their claim that “a graduate from the program can work as a professional
surveyor,” may be a little too optimistic, if not unrealistic. Time will tell.
The
Surveying Educators Conference 2005 has once again highlighted the ongoing
struggle against the prevailing ignorance and short-sightedness of both
employers and students. To expect instant gratification and success is a sign
of our times and a symptom of our impatience. Fortunately, unrealistic
expectations by those who want to have the proverbial cake and eat it too are
tempered by the real world. Dedication,
perseverance, and cooperation between far-sighted employers and educators will
succeed— slowly but surely.
Very truly yours,
Gunther Greulich, PLS, PE
Fellow and Life Member
Former president ACSM
Response from Dr. Gary Jeffress, RPLS
Mr. Greulich requests a definition of “error budget.” I am
happy to supply one. An error budget is a logical and orderly method of tabulating
errors. In surveying, it basically boils down to the accuracy and precision
required to meet various positioning standards (e.g., regulatory standards,
ACSM/ALTA standard, etc.) The concept is
also tied to the cost the client is willing to pay for the desired accuracy and
precision, that is, the more accurately the position is to be known, the more
the client needs to pay.
My paper
was not designed to stoke the fire of balkanization between the surveying and
the GIS professions. I am trying to point out that the GIS profession can take
advantage of the surveying profession’s unique skills in positioning and
providing risk avoidance for those who seek out our services, such as property
owners. Also, the surveying profession needs to communicate to the GIS
profession the pitfalls involved in getting positions wrong. Unfortunately, the
number of surveyors is declining and they are getting older. Surveying services
continue to be in high demand, so there is very little incentive for these
older surveyors to move into the GIS realm. Maybe, the GIS profession could be
attracted to take on the surveying mantle (go through the surveying license
process) and assist in these endeavors.
Response from James A. Elithorp, Ph.D., P.L.S.
Thank you
for the invitation to respond to the letter dated 25 October 2005 by Mr. Gunther Greulich, profiling the
20th Surveying and Educator’s Conference papers published in the September 2005
issue of the Journal of Surveying and Land Information Science.
A good part
of Mr. Greulich’s letter deals with the myriad of
issues presented by Dr. N.W.J. Hazelton in his two papers on potential
“off-shoring” of geomatics services and the
definition and structure of the geomatics profession
in the United States. I appreciate the fact that Dr. Hazelton was able to frame
these issues for our consideration in his two papers. The term “balkanization”
caught my eye, and the more I thought about the term, the more the term began
to resonate with me. To my thinking, balkanization is a good term to describe
the splintering of a profession into small groups of well defined practice at
the expense of the greater profession. If the behavior of the organizations
formed to represent the interests of the members of the geomatics
profession is any guide—we are currently suffering balkanization. First, ACSM
and ASPRS ceased having joint annual conferences; then ACSM reorganized into a
support structure for several member organizations. To the extent that
balkanization creates structures that hinder the profession’s response to the
changing needs of our greater society, it is undesirable.
It is the
relentless technological change facing our greater society that should be our
primary concern. It is the American
experience that laws are changed to allow for the provision of services by
those who can meet societal needs faster and/or at a lower price, or expensive
services are bypassed in favor of another way of accomplishing the same result
using a new technology. We should be concerned about our place in society and
our competitiveness in the greater economy.
The
four-year degree requirement for licensure is inevitable because its graduates
are provided a foundation upon which to handle the relentless press of
technological change. Change is occurring at a rate where individuals, in the
larger society, find it necessary to reinvent their place in the economy on a
periodic basis. Education is of great assistance in this process of adapting to
change. To further complicate matters, significant changes are now occurring in
the field of higher education as well.
Students
are demanding courses provided by distance learning technology for the delivery
of coursework. It is a technology that has been made possible by the Internet,
and it will continue to grow and dominate in the future. One of the problems
with distance education is the separation of the student from the central
energy of the classroom where interactions between professors, other
like-minded students, and working representatives of the geomatics
professions provide a synergy. This deficiency will have to be mitigated with
the active mentorship of these students by working geomatics
professionals. The implications of the
distance learning model on the future of the geomatics
profession may be significant and yet unrealized. With distance learning, the
working surveyor is in college.
My
practical experience in geomatics education finds
that those working professionals willing to be mentors and become heavily
involved in undergraduate geomatics education are
those owners and managers of companies wishing to hire these individuals. These
owners and managers can claim a disproportionate influence on the future of
this profession because they are directly molding the new members to the geomatics profession.
The graying
and imminent retirement of much of the geomatics
profession is well documented. The remaining leaders and managers of the geomatics profession will be heavily influenced by the
graduates of geomatics educational programs. Perhaps,
this is a typical American experience—the future of the profession will be
sketched by those willing to invest in the future. If you wish to shape the
future, become involved in your four-year geomatics
program. Your involvement will become more influential and necessary as higher
education moves toward distance learning for the provision of educational
services.
James A. Elithorp,
Ph.D., P.L.S.
Land Surveying/Geomatics
Coordinator
Great Basin College
1500 College Parkway
Elko, NV 89801
RE:
SALIS vol. 64, no. 3, 2004
Dear
Editor:
Recently
Dr. Muneendra Kumar’s paper, “A Geodetic Approach:
Universal NoProjection Seamless Mapping” (SALIS
September, 2004), crossed my desk. Given the spectacular claims tendered in the
paper, and given the fact that it achieved print, I feel compelled to present
an analysis of the method.
The paper presents a simple principle by which
to obtain maps: the cartographer decides upon a latitudinal and longitudinal
extent to be mapped. The northern and southern parallels of that extent are to
be mapped as straight lines in proportion to their geodetic length, as are the
eastern and western meridians. The first question left unanswered by the paper
is how those four line segments are to be arranged with respect to each other.
Figure 1 leads the reader to believe it must be a trapezoid, but the paper uses
the term “trapezium” sometimes, which leaves open the question of whether the
latitudinal boundaries are intended to be parallel and whether the longitudinal
boundaries are intended to subtend equivalent angles with respect to the
parallel boundaries.
Without
resolving this question the paper shows some calculations apparently intended
to convince the reader that the distortion in the trapez(ium?
oid?) must be negligible insofar as extents typical
of a largescale map are chosen. Assuming a
trapezoidal configuration, I agree the distortion must be negligible.
Deviations from the trapezoidal can lead to enormous distortions, however, so
one would think the paper would be clearer on this point. It is not.
What
happens within the trapezium? I do not intend the question rhetorically. The
paper says nothing about it. Instead it insists the method is a “noprojection” technique, and the author apparently believes
specific instructions for transferring spherical coordinates to planar
coordinates are not needed. Now, if the mapped extents are a trapezoid, one
could make reasonable guesses about what is supposed to happen within the
trapezoid; for example, the meridians should be spaced evenly along the
parallels, and parallels should be spaced proportionally to their spacing on
the ellipsoid. However, that is not the only system one could devise. Many
systems could introduce massive distortions. Ludicrous schemes aside, there are
other “reasonable” systems one might pursue (to, for example, prevent kinks
along the borders), but if one keeps the extent to the recommended 15-minute
section of the ellipsoid, the differences between “reasonable” systems are
slight enough to ignore for practical purposes. They can not be ignored for
theoretical purposes, however, since without a rigorous procedure we are left
unable to compare the “new” projection with existing projections.
Since the
paper refuses to tell us how to configure the outer boundary of the map, we are
obliged to follow a chain of logic, eliminating those paths that lead to
absurdities. Hopefully such a procedure will lead us to the author’s intent in
the absence of any coherent statement of that intent. Let us assume then, for a
moment, that the author intends for us to use a trapezoid, rather than a freerform trapezium.
Further on
in the paper, the author claims, “Seamless topographical maps and charts
compiled and drawn using the UNSM system with true North and scale will extend
from pole to pole and from East to West around the globe. They will be with
practically negligible or no distortion.” A remarkable claim, to be sure, as it
has been known since antiquity that a map projection can achieve no such thing,
a principle that has been proven countless times over the centuries both
empirically and rigorously. Perhaps it is for this reason that the author has
chosen to claim his method is not a projection. We shall see that the syntax
one chooses cannot hide the inexorable semantics of mathematics. The method IS
a projection (as is any procedure that transfers spherical coordinates to plane
coordinates), and it abides by the rules.
Since we
have chosen to untangle the author’s intent by first assuming perfect
trapezoids, let us see where the assumption leads us. We are assured the method
can create a map from pole to pole and from east to west by conjoining
trapeziums, so let us start by building one up from the North Pole. The method
states we are to use triangles at the pole, and the meridional
and latitudinal segments must still retain their correct proportions. At the
pole the triangles adjoin around the common center to form a polygon. The
principle is the same regardless of the extent of the sections. The trapezoidal
sections just south of each of the triangular sections share a common segment
of a parallel and thus must be the same length if they are mapped according to
their true proportions, as directed by the method. Therefore, they fit
perfectly north to south. We can extend this as far south as we like until we
reach the South Pole. Now, each southerly increment proceeds in a straight line
from the North Pole, of course, because the trapezoids are regular and their
latitudinal extent are parallel to each other. That does not allow for any
deviation from straight. The trapezoids march outward from the center in a
radial pattern.
What, then,
happens as we go south? If we construct the trapezoids according to the
instructions of the method, we can calculate very quickly that the east–west
trapezoids must separate from each other as a function of how far south they
are, violating the seamless claim. One can see immediately that this must be so
because the widths of the trapezoids begin to contract as we pass the equator,
making it impossible for them to fill up the spaces created by the everwidening concentric circles formed by the parallels.
Lest the reader imagines the problem only starts at the equator:
• Length of
equator on GRS 80 ellipsoid:
2 * pi * semi major axis = 40075017m
• Length of
meridian from pole to equator:
10,001,966m
• Perimeter
of circle with radius 10,001,966m:
2 * pi * 10,001,966m = 62844206m
In other
words, by the time we reach the equator, the trapezoidal bases (which you will
recall are required to have the geodetically correct length) only have 64
percent of the length required to eliminate seams. In other words, the gaps are
over a third the width of the trapezoids.
Clearly trapezoids will not work. What about
trapeziums? If we are not constrained to parallel parallels and equivalent
angles for meridians there should be some way to fill in the gaps that
otherwise would develop. What is that way? In a pattern that should start to
feel familiar by now, the paper says nothing about the problem. Figure 3 of the
article provides some hint that the author does intend to abandon trapezoids,
but remains silent on methodology. If we attempt to start with some arbitrary
section anywhere on Earth, we will find ourselves stymied: there are not enough
constraints on the angles.
For example, imagine laying out a perfect
trapezoid at latitude 45 and straddling the prime meridian, with a
latitudinal extent of 5’ and a longitudinal extent of 5’. At that latitude, the
meridians will angle inward by about 0.03 on such a small section.
Imagine we wish to construct surrounding trapeziums outward to create a smallscale map, as promised by the method. We know we
cannot go with trapezoids because we will be left with seams; we must employ
trapeziums. We know the west edge of the center section angles inward from
south to north by 0.03. That is ALL we know. The west edge of the
center section must be the east edge of the section to the west of it, but what
about the other three legs of the trapezium? How are we to lay them out? We
cannot look to the paper for help. It is not there.
With some thought, however, we can salvage an
answer. By the description of the method, we can imagine the prime meridian as
a straight line from the North Pole to the South Pole, and correctly scaled.
Further, the North Pole is circumscribed by triangular sections, two of which
share the upper segment of the prime meridian. This means that two sides of a
trapezium are defined by (1) the prime meridional
segment one section south of the North Pole, and (2) the southern parallel of
the triangle immediately above (either the triangle to the east or west of the
prime meridian will do). With two sides laid out, and the lengths of the other
two sides known, we are able to plot the entire trapezium. Once so plotted, we
may proceed southward by the same process, developing trapeziums as we go.
The whole thing must come to a screeching halt
eventually, however. Why? Recall that the meridional
segments composing the trapeziums’ east and west edges are obliged to maintain
proper scale. This means that all meridians are scaled correctly from North
Pole to South Pole. We are also constrained to have no seams. Those two
constraints set up an absurdity. Recall that the prime meridian is a straight
line from North Pole to South Pole. Recall that the shortest path between two
points on a plane is a straight line. If all the meridians are the correct
length, then they are all the same length as the prime meridian. If there are
no seams, they must all run uninterrupted between the North Pole and the South
Pole. In other words, they are all the same line. That is no fun at all.
At this point the method has failed
completely. It cannot maintain all the constraints it specifies because they
amount to a geometric absurdity.
In the interest of science, let us relax the
constraint of no seams by allowing one interruption. While we are no longer
strictly talking about the method presented, it might be of some interest to
see what results by applying the tatters. If we consider the point of
interruption, and given there is only one, the equator seems a reasonable
choice by affording symmetry. The resulting map is shown in Figure 1, based on
5 sections. We can choose smaller and smaller section sizes without
appreciably changing the appearance of the graticule,
and certainly without changing the behavior. As the section size approaches
infinitesimal, the kinks go away and the projection becomes a true, analytic
map projection rather than an amalgam of trapeziums.
What can we
say about this new projection? Is it original? Is it useful? Is it anything
that Dr. Kumar imagined? I cannot answer the latter. The projection is cordiform in nature, a class of projections dating from the
16th century. A similar projection was employed in Oronce
Fine’s influential map of 1531, but Fine’s projection preserved areas, a virtue
this new projection lacks. Other cordiforms by Staub and Werner also preserved areas. I think this
projection has never been described; I have not seen anything that matches the
mathematics, though there are cordiform projections
discussed in literature I do not have on hand.
The notion
of using trapezoids to bound regions of interest is ancient. Trapezoidal
projections were employed very commonly throughout the 16th, 17th, and even
18th centuries in large-scale and, occasionally, even smallscale
maps. They are easy to construct yet maintain good accuracy in large- and mediumscale maps. Typically, the mapmaker chose two
parallels along which to keep correct scale, but scaled the central meridian
correctly rather than the two outer meridians. There are strengths and
weaknesses both ways, and indeed, of the thousands of trapezoidal maps created
in those early centuries, variations in construction abound, and it seems
evident that some were attempting to keep the outer meridians correctly scaled.
It is an obvious principle, and it seems very likely the author’s projection
has been conceived of and explored independently many times for smallscale use but rejected because of the limitations I
discuss next.
What are
the properties of this new projection? A casual inspection of the graticule convinces one that the projection is neither equalarea nor conformal. Does it live up to the paper’s
claims of having “true north and true meters” and “everything will be mapped as
it really exists on the ellipsoidal Earth”? Absolutely not.
The projection shows horrible angular distortions away from the poles and the
central meridian. It would be impossible to casually determine true North in
any of the trapeziums that deviate significantly from the trapezoidal. A closer
inspection of the graticule shows critically high
compression in the outer meridians. Nothing in those regions can be usefully
distinguished on a worldscale map. In fact, at the
180th meridian and the equator, the trapezium has been squashed so badly that
it no longer has any area.
What if we restrict the use of the projection
to largescale applications, ignoring the claim of
seamless mapping and a single, worldwide system? How does the method hold up?
Because the paper is silent on how to transfer any coordinates except the outer
boundary, it is difficult to say. We can make some general observations,
however: because the outer boundary all around is scaled correctly, and because
a convex body such as an ellipsoid always has more surface area than a planar
object bounded by a path of identical length, everything inside the trapezium
has less area than reality, regardless of the details of projection. That
immediately compares unfavorably with any of the common cadastral projections,
because they are usually configured to balance compression in the center with
inflation at the periphery. Certainly, for maps of such a tiny extent as the
15’ x 7.5’ sections mentioned in the paper, the point is moot; any “reasonable”
projection will do equally as well because any discrepancies will be
microscopic. But expanding the territory to several degrees in extent will push
the author’s method into trouble faster than UTM.
Is there any
merit to the implication that highly local applications of projections would do
better to use a projection centered on the locale, rather than a standardized
system such as UTM or State Plane where the location of interest may, after
all, be several degrees away from the projection’s center? Of course; there is
nothing novel in that thought. But people use the standardized systems because
they provide context and reference points and readymade maps. If they need none
of those benefits then they certainly could choose the author’s system, but
then again they could choose UTM or something else with better—and
known—properties.
The paper’s
lack of citations disturbs me. It makes no reference to existing literature on
trapezoidal projections, cadastral projections, topographical projections, map
tiling, map projections in general, or anything else it discusses. One wonders
if the many failings of the paper could have been prevented by perusing the
relevant literature, as is customary in academia.
In summary,
Dr. Kumar seems to be describing a projection novel to the literature (if we
take the constraints he has specified at face value), but the projection does
not behave as he claims. It is not a dismal projection, as projections go, but
it is not a particularly good projection, either. If we take the liberty of
interrupting the projection at the equator—we must interrupt it somewhere—then
we achieve a cordiform projection whose utility is
sorely limited by its severe compression of the outer meridians. In any case,
the method as described is useless for cadastral mapping and surveying due to
the angular distortion that accrues inevitably as we broaden the territory we
map, without resetting the origin of the projection. Yet the method falsely
promises we can do just that. It should be no surprise that the paper is hazy
on procedures; it promises an impossible thing.
Daniel “Daan”
Strebe.
Chair the ICA Commission on Map
Projections.
Response from Dr. Muneendra Kumar
When
Galileo said, “The Sun does not go round the Earth,” the Pope of The Vatican
City forced him to withdraw his research. Luckily, Dr. Strebe,
Chair, ICA Commission on Map Projections, cannot do the same to the new
conceptual approach of UNSM System (since renamed as “Kumar Mapping System (KMaps)).
It seems
that Dr. Strebe has not surveyed, plotted, and
compiled a topographic large-scale map and does not know the differences
between (1) an ellipsoid and a geoid; and (2)
ellipsoidal and spherical coordinates. As to him the only way to map is to
“force” through a projection the round Earth to a plane, cone, or cylinder, I
am not surprised that he has not grasped the new conceptual approach. His
letter provides me with an opportunity to re-clarify a few salient features of KMaps, and also show its merits over projected maps.
In KMaps, 99.999999 percent flat ellipsoidal trapezoids are
approximated to flat trapeziums or triangles of the same dimensions. It is NOT
projected. (Here, a trapezium is taken as truncated isosceles triangle with its
top cut off).
Just like
the 7.5’ quad, 1:24 k-scale individual maps produced by the U.S. Geological
Survey cover the whole country, KMaps
will cover the whole Earth. There is no one single KMap
to cover any large country or the Earth, as being conceived by Dr. Strebe.
In the UPS
projection, a 10-km N-S length at the pole is mapped with a distortion of 60 m
and sometimes shown in E–W direction on a topographic map/chart. As a contrast,
in the new approach, poles will remain as points and N–S lengths will retain
their direction.
In the UTM
projection, a 2-km length along the 80o latitude is distorted by about 500
percent; in a KMap, it will retain its length.
What
happens inside a trapezium is the same, as happens inside a projected
rectangle. The main difference is that there will be NO grid lines and the
topographic features will be mapped in the geodetic or ellipsoidal coordinates
and not by spherical or grid coordinates.
The
proposed KMaps are for large-scale national map
series, and seamless mosaic will be achieved sequentially between neighboring
maps. There will not be “breaks” every six degrees as they occur in UTM, which
is used for military mapping from 80o South to 84o North latitudes.
Presently,
in 1:250000 maps or 1: 250000 or 1: 500000 aeronautical charts, bigger
distortions are accepted. But, in the new approach, they will be produced with
practically negligible distortions and thus will be thousands times better. I
can refer to a chart for the Polar area, which is compiled in stereographic
projection, superimposed by the UTM grid. It would be interesting to hear
whether Dr. Strebe would consider this better than a
“KChart.”
The paper’s
objective was to describe the new conceptual approach and not to teach any
Production Division of a map-making agency how to make maps. At his level, Dr. Strebe should be open to the concept of making a 1:24000
quad map from a flat trapezium, approximated from a 99.999999 percent flat
ellipsoidal trapezoid, rather than being locked to “flattening” the USA through
a conical projection. If he still wants to learn “how to” plot and/or compile a
KMap, he is welcome. I can show him in person, as
this will not be possible by e-mails. If he prefers, he can invite me to give a
workshop at the next ICA Conference.
When he
mentioned (in an earlier e-mail to me) the geoid,
instead of an ellipsoid, for projection mapping and commented adversely on the
review process, reviewers, and editor, who are eminent experts in their fields,
I did not feel like continuing any further our scientific exchange.
Muneendra Kumar