##

## The Dimensions of Landscape Arch:

### Removing the Uncertainty

by Jay H. Wilbur

June, 2004

Synopsis

Using laser technology and the NABS standard definitions for natural
arch dimensions, a team led by the author re-measured Landscape Arch in June 2004, with a very high degree of accuracy and precision. Our
results are that Landscape Arch has a span of 290.1 ± .8 feet,
a height of 77.5 ± .5 feet, a width of 18.0 ± .5 feet,
a thickness of 6 feet, and an opening breadth of 295 feet. These results
indicate it is likely that, of the known contenders for the title
of "largest" natural arch in the world, Kolob Arch has the greatest
span. However, this can only be confirmed by measurements of Kolob Arch
that equal the precision and accuracy of those now available for Landscape
Arch.

[**2006 update**: Accurate measurements of Kolob Arch made after this paper were published indicate that Landscape Arch has a greater span than Kolob Arch. See The Dimensions of Kolob Arch.]

**Introduction**

Controversy has swirled around the dimensions of Landscape Arch, located
in Arches National Park, for at least the past 20 years. In part, this
controversy is driven by a desire to definitively determine the natural
arch with the world's greatest span. For many, the natural arch with
the greatest span should be given the title of the world's "largest"
or "longest" natural arch. The span, a very precisely defined dimension,
is preferred because terms like "largest" and "longest" are rather ambiguous
when applied to natural arches and can't be quantitatively measured.
Since it's discovery, Landscape Arch has been a leading candidate for
this title. The other contender is Kolob Arch in Zion National Park.

For many natural arches, the span is fairly easy to measure. For others,
it can be very difficult. Unfortunately, for different reasons, both
Landscape Arch and Kolob Arch fall into the difficult category. In the
mid-1980s, two independent attempts were made to measure Landscape Arch.
The results were inconsistent. At about the same time, two other independent
attempts to measure Kolob Arch were made. Again, these results were
inconsistent. Depending on whom you believed, a case could be made for
either arch having the greater span. The published measurements were
anything but clear-cut and certain. Questions were raised about the
methodologies used on all four efforts. Hence, the controversy.

Until this year, there has been no further progress toward a definitive
answer. Two recent developments, however, make new measurements desirable.
The first of these is the ready availability of highly accurate laser
ranging devices. The second is the publication of a standard, precise
definition of the span of a natural arch. Although this definition is
technical, its careful application ensures that span measurements are
repeatable for a given arch and comparable for different arches. This
eliminates many of the problems that plagued the earlier attempts. The
definition, developed by the Natural Arch and Bridge Society (NABS),
is available on their website, along with technical definitions
for other natural arch dimensions.

In February 2004, Arches National Park granted the author permission
to measure Landscape Arch. On June 7 and 8, 2004, he, along with sons
Glen and Bryce and wife Judy, and with the assistance of park rangers
Diane Allen, Sharon Brussell, and Murray Shoemaker, took new measurements
of the arch using modern laser technology and the published dimension
definitions. This effort was successful in obtaining very accurate measurements
of Landscape Arch, including the span. Because these measurements are
of standardized dimensions, they are both repeatable and comparable,
e.g., to Kolob Arch should accurate, standardized measurements be obtained
of that arch in the future. The cooperation and assistance of the Park
in obtaining these results was essential and is gratefully acknowledged.

The following sections of this paper describe the methods used to measure
Landscape Arch, summarize the measurements with analysis of their accuracy
and precision, and discuss these results in the context of previous
measurements and how they influence a determination of whether or not
Landscape Arch has the greatest span of any natural arch in the world.

**Methodology**

Two obstacles must be overcome to measure Landscape Arch. The first
of these is access. As a result of rockfalls in 1991 and 1995, the Park
has closed the loop trail that once provided access to the area underneath
the lintel. These rockfalls also obliterated most of the northern leg
of the loop trail. In addition to safety concerns, the Park wishes to
promote restoration of the fragile desert environment immediately under
and around the arch. Thus, visitors are not allowed to access the arch
beyond viewpoints on the main Devils Garden Trail.

Although we were granted special permission to access the area under
the lintel, we were extremely anxious to minimize our disturbance of
the grounds under restoration. We therefore limited our activities to
two traverses directly under and in line with the lintel. Fortunately,
most of this line lies along the old trail so disturbance was indeed
slight. The first traverse, made on June 7, was used to reconnoiter
the details of the arch's geometry, plan the span measurement, take
height and width measurements at several points along the lintel, and
place reference stakes. The second traverse, made on June 8, was used
to obtain the span measurement and to remove the stakes and other signs
of our activities. Photographs were taken from the main trail both for
documentation and to obtain two other measurements, the thickness and
opening breadth.

A second obstacle to taking measurements of Landscape Arch is the hill
of soil-covered talus under the arch. By definition, the span is a horizontal
dimension. The hill bulges up from a slanted line connecting the abutments
of the arch and makes it difficult to keep a horizontal reference. Furthermore,
there is an undulation in the hill that has a subtle synchronicity with
the undersurface of the lintel. This makes it difficult to determine
by inspection the point at which the height measurement should be taken.

The span measurement was kept horizontal by splitting it into three
horizontal segments laid end-to-end, except that each segment was allowed
to shift up or down along a vertical axis demarked by a laser plumb
bob. Each segment was kept horizontal with a level built into the laser
range finder, which was mounted on a tripod for stability. As it turned
out, it was only necessary for one of the segments to be adjusted vertically
by this method. The other two joined at a common point, the mount axis
of the tripod.

To counteract the hill's undulations, height measurements were taken
at several points along the lintel. The greatest of these then is the
actual height of the arch.

Span and height measurements were taken using a Leica DISTO-classic
laser range finder. Vertical reference was established using a LaserMark
laser plumb bob. The Leica range finder has an advertised accuracy of
a tenth of an inch over a range of 650 feet. Test ranging done prior
to and during the measurements confirmed that the unit used was performing
to this specification. The LaserMark plumb bob has an advertised accuracy
of a tenth of a degree.

Although the lintel of Landscape Arch runs parallel with a field of
sandstone fins that are aligned about 30 to 35 degrees off a true north
axis, for simplicity's sake we refer to the arch and its parts with
the four compass points, i.e., the north abutment, the east entrance,
the west edge of the lintel, etc.

The south abutment of the arch presents an irregular profile. Figure
1 is a photograph of this profile taken looking east. Examination of
the profile reveals a southward pointing indentation or notch in the
abutment that extends the opening beyond where the abutment joins the
base. The western edge of the back of this notch is the correct southern
endpoint of the arch's span. This point is labeled "S" in Figure 2.
Figure 2 depicts how the span was split into three segments to facilitate
measurement.

*Figure 1. A photograph looking east of the notch in the south abutment
that extends the span southward from where the abutment joins the base.*

*Figure 2. This figure is schematic and not drawn to scale. The span
measurement was divided into three segments, A, B, and C. Segment A
measures the horizontal distance from the correct point on the south
abutment, point S, to a reference point, stake 3. Segment B measures
the horizontal distance from stake 3 to a point R on the north abutment.
Segment C measures the horizontal distance from stake 0, directly under
R, to the correct point on the north abutment, point N. See text for
the offset method used to find segment C. Stake 1 shows the approximate
point where the width was measured. Stake 2 shows the approximate point
where the height was determined.*

The elevated notch in the southern abutment presents problems for other
measurement methods but is advantageous for the laser ranging method
used here. A point on the trail under the lintel was found such that
the laser range finder could be placed on a tripod at the same elevation
as S, i.e., the back of the notch. This point is labeled "stake 3" in
Figure 2. Ranging in continuous mode from east to west across the back
of the notch from stake 3 confirmed that the western edge was the correct
point for the span measurement. Several direct ranges to point S were
made to ensure an accurate measurement of the span segment A. Segment
A (see Figure 2) is the horizontal, straight-line distance between point
S, the western edge of the back of the notch, and stake 3.

Next, the laser range finder was swiveled on the tripod 180° in
the horizontal plane and beamed to a point near the western edge of
the north abutment. This point is labeled "R" in Figure 2. Several direct
ranges to this point were made to ensure an accurate measurement of
the span segment B (see Figure 2). The laser plumb bob was then used
to find the point on the ground directly under point R. This point is
labeled "stake 0" in Figure 2. Thus, segment B is the horizontal distance
between stake 3 and R, and also between stake 3 and stake 0.

The correct northern endpoint of the arch's span is shown as point
"N" in Figure 2. This point is not directly under the lintel, but is
a few feet west of it. Figure 3 is a photograph documenting the location
of this point. Because of this, as well as an interfering boulder, the
final segment of the span, segment C, had to be measured as an offset.

*Figure 3. The author uses a stick to point out the northern endpoint
of the span. This is point N in figures 2 and 4.*

To make this offset measurement, a target was placed at the vertex
of a right angle. This vertex is labeled N' in Figure 4. One leg of
the right angle connects points N and N'. The other leg is in the vertical
plane defined by points R, stake 0, and stake 3. Thus, point N', as
well as point S, are in this plane. The correct placement of the target
at N' was accomplished using a sighting protractor with one leg pointing
at N and the other pointing at both stake 0 and stake 3.

*Figure 4. The offset viewed from above (the top of this figure is
to the west, and the bottom is to the east). A target is placed at N'
to measure segment C. Not drawn to scale. *

The target was set at point N' and the laser range finder was used
to directly measure the horizontal distance between stake 0 and N',
i.e., segment C. Addition of the measurements for the three segments,
A, B, and C, then is the first estimate of the span. Error analysis
(see *Results* below) was then used to refine this estimate.

Height measurements were taken at several points along the underside
of the lintel. At each selected point the laser range finder was used
in continuous mode to find the vertical distance from the ground to
the lintel. The largest of such height measurements was found at the
point marked "stake 2" in Figure 2. This measurement is reported below
as the height of the arch.

Since the sun was very near the zenith, measuring the width of the
lintel's shadow was used as a very close approximation of the actual
width. A single measurement was taken using a steel tape at the point
where a minimum value was determined by inspection. Care was taken to
keep the tape horizontal. The width measurement was taken at the point
marked "stake 1" in Figure 2.

The thickness and opening breadth were determined by photographic analysis.
An image of the arch was taken with a calibrated lens with a 35mm focal
length from a point on the main trail that is at a measured distance
from the arch. This image was used to measure the ratios of the thickness
to the height and the opening breadth to the span. These ratios were
then used to estimate the thickness and opening breadth. The thickness
and opening breadth were also estimated using the geometry of the photograph,
i.e., known distance to the arch and the focal length of the lens. The
results were compared for a final estimate of these two dimensions.

**Results**

The span of Landscape Arch was determined by adding the measured span
segments A, B, and C (see Figure 2), and then refining this estimate
using error analysis. Segment A was measured as 113 feet, 5 inches.
Segment B was measured as 170 feet, 11 inches. Segment C was measured
as 5 feet, 7 inches. Thus, our first estimate of the span is 289 feet,
11 inches. However, this result needs to be refined as a result of both
random error and some systematic biases.

First we look at the random errors involved in this estimate. The precision
of the laser range measurements, less than an inch in all cases, is
a negligible factor in the error budget. Because segments A and B share
a common endpoint at the swivel point of the tripod mount, and because
the laser was setup to measure from this point, any translation error
resulting from this join is also less than an inch and is not a factor
in the error budget. The error associated with shifting segment C vertically
is a little larger. The vertical height between stake 0 and R was measured
as 45 feet. The precision of the LaserMark plumb bob is 0.1 degree.
Over 45 feet, this translates to a random error of about 1 inch. However,
to account for any slight misplacement of the bob and stake, we estimate
the random error here to be about 3 inches.

By far the largest random error was associated with placing the offset
target at N'. We estimate it by assuming a 2-degree error in determining
the right angle and sighting it along the line connecting N and N',
a distance of 14 feet. This leads to an error estimate of about 6 inches.
The root-mean-square of 6 inches and 3 inches yields the total expected
random error of about 7 inches.

Some biases must be considered in refining the span measurement. It
is unlikely that segments A, B, and C were exactly aligned with each
other or with the horizontal. At the two junctures, slight deviations
almost certainly occurred. These deviations from exact linearity bias
the result, making it larger than a true result. However, we can estimate
this bias and subtract it from our measurement to get a better estimate
of the true span.

An upper bound on the deviation from the horizontal or from linearity
is 3 degrees. This would translate into a range bias of about 2 inches
at each of the two joins between the three segments. Thus, a worst-case
bias would be 4 inches. To account for this, we reduce our estimated
span value by half that amount, and increase the error bars by the other
half. This puts the span at 289 feet, 9 inches, plus or minus 9 inches.

Another bias results from measuring S to N' instead of S to N. Computing
the hypotenuse of the right triangle S-N'-N adds 4 inches to our result.
Thus, the final, best estimate of the span is 290 feet, 1 inch, plus
or minus 9 inches. Alternatively, this is 290.1 ± .8 feet. 290.1
feet is 88.4 meters.

As stated earlier, several height measurements were taken along the
lintel. Since each of these was a direct range using the laser range
finder, the precision of each is a fraction of an inch. The largest
value obtained was 77 feet, 2 inches. The values obtained on either
side of this value were about 75 feet. Nevertheless, because not every
single point along the lintel was ranged, even our largest value must
be considered a lower bound on the true height. Since it is unlikely
that the true value would be more than a foot greater than the largest
value obtained, we estimate the true height of the arch as 77.5 ±.5
feet. 77.5 feet is 23.6 meters.

As discussed above, the width measurement was obtained using a steel
tape. The error associated with this measurement is estimated to be
less than 3 inches. However, to be conservative, we report a width of
18.0 ± .5 feet.

Using photographic analysis, we report a thickness of 6 feet. This
extraordinary result must be considered an upper bound. The thickness
is probably a few inches *less* than 6 feet, but photographic analysis
does not permit a more precise estimate. Our photographic analysis also
led to an estimate for the opening breadth of 295 feet.

**Discussion**

In 1986, Robert Vreeland measured the span of Landscape Arch using
a tape, gravity plumb bob, level, and other hand-assembled tools. His
result was published in the January 2000 issue of *SPAN* (Vol.
12, No. 1). He reported a span of 290.4 ± .15 feet. An examination
of Vreeland's methodology leads this author to the conclusion that Vreeland's
reported error bars (± .15 feet) are overly optimistic. Given
the complexity and number of segments measured, along with the dependency
on several right angles and calculations, a more reasonable estimate
of his error bars is 3 feet. It does appear that he made a reasonable
effort to ensure a horizontal measurement and also selected the correct
points to measure on both the north and south abutments. However, given
the complexity of his method, it was certainly possible that an undetected
bias or mistake might have crept into his result. Nevertheless, the
close agreement between his result and the span reported here strongly
supports a conclusion that he performed the measurement correctly and
with as much accuracy as his method and equipment permitted.

In 1984, Dale Stevens measured several dimensions of Landscape Arch
using a tape, transit, level, and other hand-assembled tools. His results
were copied in the November 1990 issue of *SPAN* (Vol. 3, No. 1).
He reported a height of 87 feet, a width (labeled "horizontal thickness"
in the paper) of 15.5 feet, a thickness of 16 feet, and an opening breadth
(labeled "light at widest place") of 306 feet, along with a number of
other non-standard dimensions. He did not report a span measurement.
Unfortunately, much confusion has resulted from some readers incorrectly
assuming that his "horizontal line width," calculated to be 301 feet,
was an estimate of the span. However, that dimension, the horizontal
projection of the opening breadth, does not correspond with the standard
definition for the span in the case of Landscape Arch. Stevens did not
include any discussion of the accuracy or precision of his measurements.

It is interesting to compare Stevens' results for width, thickness,
height, and opening breadth to those obtained in this investigation.
His measurements were taken before the 1991 rockfall. This rockfall
unquestionably decreased the width of the arch by several feet. It is,
therefore, hard to explain why his width is significantly *less*
than that found here. A pre-rockfall width of 15.5 feet must be viewed
as incorrect. Using the current width of 18 feet and photographs, we
estimate a pre-rockfall width of about 26 feet.

Another surprise is Stevens' reported thickness, 16 feet, which is
significantly greater than the 6 feet reported here. Although photographic
analysis is certainly less precise than some other methods, it cannot
be that far off. Could the Stevens' number be a typographic error, i.e.,
6 feet with a leading "1" incorrectly attached? In any case, it is very
obvious from even a cursory examination of the lintel that the thickness
is significantly less than the width. Stevens' results would indicate
that they are about the same. This is an obvious error.

Stevens' reported height of 87 feet is also greater than the height
reported here. In his paper, he indicated obtaining height measurements
that varied from 79 to 92 feet. This suggests that Stevens may have
been measuring total height, i.e., from the ground to the top of the
lintel, rather than the standard height. In any case, although the 77.5
feet reported here might not be the absolute maximum height of the arch,
it cannot be off by more than about a foot.

Finally, the opening breadth of 295 feet reported here is less than
Stevens' 306 feet. Again, while photographic analysis of this dimension
is not precise, it is doubtful that our estimate is off by 11 feet.
It is not difficult to conclude that Stevens' results overall must be
viewed as suspect.

Our last point of discussion is to examine how the current measurements
affect a comparison of Landscape Arch with Kolob Arch for the title
of "largest" or "longest" natural arch in the world. We now have a very
accurate measurement of the span of Landscape Arch. Unfortunately, we
do not have a reliable measurement of the span of Kolob Arch. Nevertheless,
certain conclusions can be drawn from the measurements that have been
reported.

[**2006 update**: Accurate measurements of Kolob Arch made after this paper were published indicate that Landscape Arch has a greater span than Kolob Arch. See The Dimensions of Kolob Arch.]

Reed Blake reported a span for Kolob Arch of 310 feet based on triangulation
from a distance. These measurements were done in 1983. It is not clear
from his report that his team measured the correct points of the span
in accordance with the standard definition. Nor is it likely that they
obtained the one-foot accuracy Blake claims. In 1984, Stevens measured
Kolob Arch using photographic analysis. Stevens did not measure the
span of the arch, but rather measured the opening breadth, which he
called "widest light opening." However, in the case of Kolob Arch, the
span and opening breadth should be fairly close. He obtained a value
of 292 feet and did not report an expected error. The author also measured
Kolob Arch using photographic analysis in 1992. The rather imprecise
result of 294 ± 12 feet was obtained. However, in this case it
is at least certain that the correct definition of the span was used
and that the correct points were measured. The author believes it is
impossible to get a more accurate measurement using photographic analysis,
and that therefore Stevens' result should be viewed with a similar expected
error.

Until more accurate measurements of Kolob Arch are obtained, it cannot
be determined with certainty which arch has the greater span. Nevertheless,
the author believes that the new, accurate measurement of Landscape
Arch reported here, i.e., a span that is less than 291 feet, coupled
with three independent results for Kolob Arch that are larger than 291
feet, make it probable that Kolob Arch has the greater span.

[**2006 update**: Accurate measurements of Kolob Arch made after this paper were published indicate that Landscape Arch has a greater span than Kolob Arch. See The Dimensions
of Kolob Arch.]