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Federal Highway Administration > Publications > Public Roads > Vol. 65 · No. 2 > Iron and Asphalt: The Evolution of the Spiral Curve in Railroads and Parkways

Sept/Oct 2001
Vol. 65 · No. 2

Iron and Asphalt: The Evolution of the Spiral Curve in Railroads and Parkways

by Mary E. Myers

The spiral curve was first used in railroads in the late 1800s, and its use peaked in the design of the parkways of the 1930s. The spiral curve continues to be used today in roads of all types. However, it has ceased to be part of the professional education of many landscape architects.

Although the United States has the most efficient system of highways in the world, aesthetics is not a primary goal or requirement in the design of the "modern highway." This article, which was inspired by a desire to better understand the aesthetics of roads, presents a general overview of the spiral curve and its evolution from railroads to parkways. The specifics of mathematical properties are not discussed as these are documented far more completely in the tables and charts of civil engineering texts. Historic development and aesthetic application are emphasized.

American parkways are considered to be some of the most beautiful roads in the world. Better understanding of the design approach used for parkways can benefit future road design. This article, reflecting the perspective of a landscape architect, explores the background, evolution, and aesthetic application of a single, but important, parkway characteristic — the spiral curve, and finally suggests that it be reintroduced into educational programs for landscape architects. The Blue Ridge Parkway, a collaborative effort of landscape architects and civil engineers, is presented as an example of the artistic application of spiral curves in road design.

Background

It has sometimes been assumed that modern highways evolved from roads designed for horse-drawn vehicles. After all, the automobile replaced the horse and wagon as the primary mode of transportation, so wouldn't their road requirements be similar?

But, of course, one significant way in which automobiles differ from horse-powered transportation is that the automobile can travel at much higher speeds, and the auto's capacity for speed grew with technological innovation. By the 1930s, autos matched trains as the fastest mode of land transportation.

For this reason and others, designers looked to the "iron roads" for inspiration in designing asphalt roads. One of the most important characteristics of railroad development was the spiral curve — a feature allowing a safe transition from straight to curved sections of track. American parkways, whose peak era was from about 1920 to 1941, were the first motorways to consistently feature the use of the railroad spiral in their design.

Definition and Background of Spiral Curves

Spirals are curves used to transition between a circular curve with a specific radius and degree of curvature and a straight tangent (whose radius is infinity). The term spiral is interchangeable with easement or transition curve. The radius and sharpness of a spiral curve increase uniformly along its length. The length and degree of curvature of a spiral curve are based on the anticipated speed of traffic and the sharpness of the circular curve that the spiral must meet.

"For example, for 70 [miles per hour] [113 kilometers per hour], a spiral of 400 [feet] [122 meters] is needed to connect a 4 degree circular curve with a tangent. The sharpness of the spiral will increase 1 degree for each 100 [feet]. At 100 [feet] along the spiral, it will have the same radius as a 1 degree curve; at 200 [feet], its radius is that of a 2 degree curve; at 400 [feet], both spiral and circular curve have the same radius and 4 degrees of sharpness."1 If one were designing to meet a four-degree circular curve for a slower speed, the length of the spiral would be less, and its degree of sharpness greater. The authors of railroad engineering manuals and later engineers in highway departments developed tables of design standards to facilitate the application of spiral curves.

The use of spirals was first documented in the late 1600s in "Sino Loria," a treatise by James Bernouilli. Spirals were rediscovered in 1874 by Cornu and used in optics. Shortly afterward (sometime in the 1880s), spirals began to replace parabolic curves in easing transitions for railroads.2

Spiral curves allow railroad cars to proceed into a simple curve without derailing. Combined with superelevation, or raising, of the outer rail, spiral curves help to counteract centrifugal force. Both spirals and superelevation were calculated carefully for specific situations.

Few, if any, railroads today are without spiral curves, so it is not possible to experience the jolts and jars and changes in speed associated with abrupt tangent-curve connections. However, you may have had the opportunity to experience such connections while driving. If you have driven on a road with straight or tangent sections connected to sharp curves, you have noticed a threat to your equilibrium and the stability of the car as you round the curve. Centrifugal force is strongest at the center of a curve where the vehicle can veer out of the lane, creating a driving hazard. Spiral curves ease the transition into the curve and help to limit the duration of the full impact of centrifugal force.

Another safety hazard occurs when the wheels work at different angles to the axis of the railroad car. "On a curve, the bogie trucks (a group of four wheels) of a car make an angle with the axis of the car."3 A change from straight track to full curvature had to be accomplished in a short time — the time required to run the length of the wheelbase of the truck. "For a high-speed train, this would be only a fraction of a second. On a transition curve, this change of position is accomplished gradually and without jar."3 The higher the speed of the train, the greater the danger of overturning at the juncture of the tangent and simple curve.

Concern for costs prompted the adoption of the spiral curve and the accompanying adjustment of the outer rail. Railroad developers and operators (mainly private entrepreneurs) wished to minimize construction and operating costs. They were concerned about the expense and delay caused by the wear and tear of the car wheels rubbing on the rail and by derailment.

Railroad location engineers did extensive field reconnaissance to select routes that provided the best balance of construction and operating costs. The increased expense of constructing a longer but more level route was justified as an investment that would soon pay off. Train wheels would last longer, and cars would avoid the bumps and potential derailments. Another very important advantage was that trains could travel at a more constant speed. As "time is money," this became an important argument for employing the spiral curve.

The spiral curve made the train ride more comfortable for passengers and reduced freight damage from jostling and bumps. Engineer Arthur Wellington described the pre-spiral condition of travel in a book published in 1887. Wellington wrote, "The worst effect usually comes from entering and leaving a curve … as [rail] roads are ordinarily located, the line instantly changes from a tangent to a sharp curve. The consequence is, inevitably, a disagreeable lurch and thud."4

Although comfort was secondary to economy as a reason for using spiral curves, improved comfort led to increased passenger travel and greater profitability.

Use of Spiral Curves on Parkways

Spiral curves were used on parkways for safety reasons. The automobile, like the railroad car, is a massive object that travels at a high velocity and must contend with the same laws of physics. Thus, superelevation, or banking, of the outside edge of the curve was also incorporated into the design of highways and parkways.

Spiral curves allowed parkway designers flexibility on the issues of location and alignment. Because the great parkways were designed for leisurely driving for pleasure, much attention was paid to developing the road in a multidimensional way. The parkway had to be safe. Furthermore, it had to be aesthetically pleasing, making the most of its environmental setting. As in railroad location, spirals with their subtle adjustment to the terrain simultaneously permitted the avoidance of obstacles and the maintenance of a constant speed.

Combined with other parkway characteristics — such as grassy, rather than paved, shoulders and the absence of a painted line between the pavement and the shoulder — spirals helped to make travelers feel connected with the landscape. Designers could plot courses that made the most of landscape features, such as promontories, without destroying them. For example, the Blue Ridge Parkway skirts rugged outcrops, and coming sometimes as close as five feet (1.5 meters) to the side of a mountain, it gives the driver and passengers a sense of Appalachian geology. The sweep of the curve and the banking of the pavement are subtly adjusted to highlight the height and character of the stone.

Landscape architect Wilbur Simonson, designer of the Mount Vernon Memorial Parkway and the George Washington Memorial Parkway along the Potomac River across from Washington, D.C., was one of the first to exploit and advance the use of the spiral curve. In an article in Landscape Architecture in April 1932, Gilmore Clarke described Simonson's approach for the Mount Vernon Memorial Highway. "The alignment, except through the city of Alexandria, consists almost entirely of continuous, easy curvature established so as to create the effect of following the topography of the country. … All curves were spiraled to give easy flow lines for traffic and to add to the appearance of the road."5

Simonson and other designers understood the comfort associated with spiral curves. There is a relaxing effect because abrupt connections are absent. The spirals provide a natural rhythm, allowing the driver to enjoy the landscape outside the car, and the scenery itself has an additional stress-reducing effect.

Expanded Use of the Spiral Curve in Parkway Design

Reverse spirals were introduced by Simonson and others to produce an easy rhythmic flow to the driving. This requires a certain amount of concentration — but no tension unless one goes appreciably over the speed limit.6

The reverse spirals and accompanying superelevation regulate speed on a parkway to a greater degree than on standard highways. Parkways are designed and engineered very precisely for a set speed. On the Blue Ridge Parkway, that speed is 50 miles per hour (80 kilometers per hour), and the official speed limit is 45 miles per hour (72 kilometers per hour). On a parkway — unlike on a standard highway — if one drives 10 or 15 miles per hour (16 to 25 kilometers per hour) above the speed limit, he or she will distinctly sense danger and lack of control. This sense of danger may be due to centripetal and centrifugal forces occurring too rapidly to permit a safe driving response. Therefore, on the Blue Ridge Parkway and other parkways that have not been straightened or "modernized," there is little need for repetitive speed-related signage. Drivers can sense that they are going too fast to take the curve properly and will adjust to a more comfortable speed.

In the design of the Blue Ridge Parkway, tangents are not altogether avoided, but spiral curves are preferred. Spiral curves are used to ease transitions from one curve direction to another. Blue Ridge Parkway landscape architect H.E. van Gelder understood and agreed with the standard for alignment used for the Mount Vernon Memorial Parkway.

photo of curve in road
This shows an enclosed view with rhododendron and pine. Notice that the curve directs visual attention ahead to an anticipated, not entirely revealed, view. (Photo credit: Mary E. Myers)

"In designing alignment, it was noted that the engineers have a tendency to regard the line as a series of tangents, connected by curves no longer than necessary. This tends to result in a hard line with abrupt curves. The landscape architect would rather consider a parkway alignment as one continuous flowing curve," said Van Gelder.7

Engineers seemed to want to break apart the problem into pieces and then connect the parts. The landscape architectural approach was more unified, perceiving the connectedness of the road sections with each other and with the landscape.

Landscape Aesthetics of the Spiral Curve

My research indicates that landscape scenes may "work" in conjunction with the spiral curve. Reverse spirals accommodate a rhythmic sequencing of views, and that stimulates driving interest and also serves to keep drivers alert and awake. Each spiral directs the driver's attention and cone of vision to a different view.

On a 10-mile (16-kilometer) section of the Blue Ridge Parkway, for example, the following views are revealed as the driver passes from one spiral into another: open, distant mountain vistas; close-up views of enclosing walls of rhododendron and laurel, which seem to brush the sides of the car; geometric patterns of rows of corn in contoured fields; distant views of mountains seen beneath a canopy of pine branches; and middle views of farm buildings and grazing animals in pastures.

The variety of distant, middle, and close views is stimulating. There is little or no line of demarcation between road and adjacent landscape. The spiral curves allow landscape views to be synchronized similarly to Japanese stroll gardens. Everything is not revealed at once. There is a sense of anticipation of what is to come. The effect of the changing views is interesting and, at the same time, soothing. The parkway is a ribbon of reverse curves — a ribbon that threads through and connects with the surrounding landscape.

Parkways have varied scenery, but there is no visual "litter." Regulations restrict views of billboards, gas stations, and strip malls. This reduces the number of visual elements competing for the driver's attention.

Conclusion

The understanding and application of spiral curves by landscape architects has waned in the last 40 years. Spiral curves are no longer discussed in landscape architecture courses and textbooks.

"The major disadvantage against the use of spiral transition curves is that their calculation is tedious and complicated," according to Robert W. Zolomij in Vehicular Circulation: Handbook of Landscape Architectural Construction, one in a series of handbooks published by the American Society of Landscape Architects in the 1970s. "At the site scale where landscape architects are primarily delegated with road layouts and their calculations, such as parks and residential projects, the use of transitional curves for low design speeds are not essential if properly designed circular curves with superelevation and adequate lane widths are employed."8

In later texts, such as Site Engineering for Landscape Architects published in 1985, a discussion of spiral curves is omitted again because of the perceived difficulty in calculation and layout.9 Thus, these curves, which were considered essential components of road design in the 1920s and 30s, were considered inconsequential to landscape architectural education in the 70s, 80s, and 90s.

The disappearance of the spiral curve from popular textbooks is symptomatic of the technological split between civil engineers and landscape architects. This breach occurred during the major building period of the Interstate Highway System. At that time, civil engineers took the lead in issues of road location and alignment, and landscape architects were relegated to cosmetic landscape improvements.

The aesthetic results have been dismal: a stultifying sameness to highways, roads that are objects in — but not part of — the landscape, boring views, and visual clutter of signs and roadside developments. Although the purpose of modern highways is different from parkways, there is much to be learned from the parkway design approach. It was multidisciplinary and valued aesthetics and environmental impact as much as speed and safety.

photo of vista from the Blue Ridge Parkway
The vista from the Blue Ridge Parkway reveals parallel, distant ridges. (Photo credit: Mary E. Myers)

In an earlier Public Roads article, Elizabeth Fischer, a landscape architect with the Federal Highway Administration, and her co-authors stated, "This situation calls for landscape architects to play a greater role, even take the lead, on multidisciplinary teams challenged with redesigning roadways."10

True, and if landscape architects are to be taken seriously as leaders in the design process, they must "rediscover" and understand the creative application of engineering techniques such as the spiral curve.

References

1. Clarkson H. Oglesby and Laurence I. Hewes. Highway Engineering, John Wiley and Sons, New York, 1963.

2. Arthur Lovat Higgins. The Transition Spiral, Van Nostrand Co., New York, 1922, p. v.

3. Walter Webb. Railroad Engineering, American School of Correspondence, 1908.

4. Arthur M. Wellington. The Economic Theory of the Location of Railroads, The Scientific Press, Brooklyn, N.Y., 1887.

5. Gilmore Clarke. "The Mount Vernon Memorial Highway," Landscape Architecture, Vol. XXII, No. 3, April 1932, p. 184.

6. Robert Hope. "Interview With Mary Myers," Blue Ridge Parkway Archives, National Park Service, Asheville, N.C., Nov. 4, 2000.

7. H.E. van Gelder. "Notes on Alignment and Grading on Skyline Drive," Blue Ridge Parkway Archives, National Park Service, Asheville, N.C., April 27, 1934.

8. Robert W. Zolomij. Vehicular Circulation: Handbook of Landscape Architectural Construction, American Society of Landscape Architects, McLean, Va., 1975.

9. Steven Strom and Kurt Nathan. Site Engineering for Landscape Architects, AVI Publishing Co. Inc., Westport, Conn., 1985.

10. Elizabeth E. Fischer, Heidi Hohmann, and P. Daniel Marriott. "Roadways and the Land: The Landscape Architect's Role," Public Roads, Vol. 63, No. 5, March/April 2000, p. 30-34.


Mary E. Myers is an assistant professor of landscape architecture at the College of Design at North Carolina State University, where she teaches a course called "American Parks and Parkways." She has developed interdisciplinary design studios with colleagues from architecture, civil engineering, forestry, and water quality. Myers, a registered landscape architect, was in private practice for many years. She has a bachelor's degree in landscape architecture from the University of Wisconsin and a master's degree in landscape architecture from Harvard University.

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