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Heliotrope Takes Manhattan(henge)!

July 7, 2014

Today I’m presenting the technology behind Heliotrope at the American Solar Energy Society (ASES) Solar 2014 Conference in San Francisco.

I developed Heliotrope as a plugin for Rhino and Grasshopper that performs solar analysis using geometric projections. Algorithmically, its most complex components are the spherical shadow projections, or what I like to call “shadow bubbles.” A shadow bubble shows the annual exposure of a single point location to the sun. It is the mathematical “dual” of a typical computer shadow study which shows shading at a single point in time over an area.

Since this week also marks a Manhattanhenge occurrence on July 12th, I thought it would be fun to use a Heliotrope shadow bubble to analyze the coming event.

An overview of the 3d model of Manhattan used for the analysis.

Overview of the 3D model of Manhattan used for the analysis

Manhattanhenge, a term coined by astrophysicist Neil deGrasse Tyson, occurs twice yearly when the setting sun aligns with the east-west streets of the main street grid in the borough of Manhattan in New York City. The biggest challenge for my quick analysis, was finding a model of Manhattan in short order. The top Google result shows Harvard GSD has huge online GIS models of Manhattan and Boston, but they are only available for those online at Harvard. Not so useful for a non-Harvard person living in Portland. After some searching, however, I was able to find a nice block model at TurboSquid for only $6. The model came in an Autodesk fbx exchange format, which I easily converted into a dwg using a free Autodesk fbx converter and from there, loaded into Rhino.

Overview of model with 34th Street and the shadow bubble in place in front of the Empire State Building.

Overview of model with 34th Street and the shadow bubble in place in front of the Empire State Building

For simplicity, I narrowed the model down to just the buildings along 34th Street, which is one of the most dramatic locations from which to observe the event. Next I created a shadow bubble – a projection of the urban geometry surrounding a single viewpoint onto a sphere centered at that point – in the street in front of the Empire State Building.

The shadows of overlapping buildings may be combined into single geometric elements that, when combined with solar arcs mapped onto the same sphere, result in a bubble that shows when that point of view will be exposed to or shaded from the sun over the entire year. Heliotrope does this projection particularly well because it uses a spherical geometry model. In spherical geometry, points on the sphere may be treated as two dimensional locations because the 3rd dimension of the sphere’s radius is arbitrarily set to 1.0 for analysis and then scaled as needed afterwards. Line segments on the building models project as great circle arcs on the sphere. Intersecting these arcs is easier than intersecting general 3D curves in space. Such simplifications make Heliotrope’s spherical geometry approach faster and more accurate than attempting to do the same analysis in Cartesian coordinate space.

View looking down 34th Street from the west with solar arcs for May 29th and July 12th dropping into view just at sunset.

View down 34th Street from the west with solar arcs for May 29th and July 12th dropping into view just at sunset

Looking straight down 34th Street from the west, the shadow bubble shows dark grey where the sky will be occluded from view and blue in the narrow slot where it can be seen. When we add the solar arcs for the dates of this year’s two events – May 29th and July 12th – we see that they drop right into the projected shadow canyon at sunset on those dates. Beautiful.

The analysis made me wonder, however, why only sunsets are of interest in Manhattan. What about the sunrise dates? Turning the model around and looking from the east, I used Heliotrope’s “When” component to determine the dates on which the sun would align with the street grid at sunrise. I found that it does in fact align on January 10th and December 2nd, 2014.

From the east, on January 10th and December 2nd the arcs also line up with the street grid for a brief moment at sunrise.

From the east, on January 10th and December 2nd the arcs also line up with the street grid for a brief moment at sunrise.

Which leads me to further ask, why don’t New Yorkers ever mention these Manhattanhenge sunrise events? Is it possible that the weather is always bad on these wintery dates? Or is 7am too early for our modern day druids to hit the streets? One does wonder!

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2 Comments leave one →
  1. July 9, 2014 12:04 pm

    Very cool, Brian!

  2. July 9, 2014 12:07 pm

    Thanks Rob, wish I was going to be in NYC this Saturday to enjoy it!

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