NEW YORK—“Billionaires' Row” is rising over midtown, a collection of glassy new pinnacles that promise the kind of condo views you can only get in Manhattan by building taller than everything else around.

With its $95 million penthouse, 432 Park Avenue tops out just shy of 1,400 feet. It will remain the tallest residential building in the Western Hemisphere until the Nordstrom Tower — high-end shopping below, lavish apartments above — goes up four blocks away. Between them are a few more audacious developments, all part of a race for ever-taller towers to distinguish luxury living in an increasingly crowded city.

These new buildings — a product of developer ingenuity, architectural advance and international wealth — are changing more than the city’s famous skyline, though. They will also transform New York far below, further darkening city streets and casting long shadows that will sweep across Central Park.

Together, these towers, and new additions in neighborhoods undergoing a building boom from San Francisco to Toronto to even low-rise D.C., have revived a long-simmering urban tension: between light and growth, between the benefits of city living and its cost in shadows.

For cities, shadows present both a technical challenge — one that can be modeled in 3-D and measured in “theoretical annual sunlight hours” lost — and an ethereal one. They change the feel of space and the value of property in ways that are hard to define. They’re a stark reminder that the new growth needed in healthy cities can come at the expense of people already living there. And in some ways, shadows even turn light into another medium of inequality — a resource that can be bought by the wealthy, eclipsed from the poor.

“There are certain things you just can never go back from,” said Renee Cafaro, a longtime resident of the neighborhood just south of Central Park and a member of the local community board that’s been studying the shadows there. “Laws can be changed. Even trees and traffic patterns can be changed. But once you have buildings of that caliber and that height and that massing, there’s nothing we can do to save the park any more. Those shadows are there in perpetuity.”

These tensions are rising with the scale of new development in many cities. As New York's skyscrapers set height records, Mayor Bill de Blasio has also proposed building 80,000 units of affordable housing over the next 10 years, much of which the city would find room for by rezoning land to build higher. Boston wants to find space for an additional 53,000 units. Toronto in the last five years has built more than 67,000. All of which will inevitably mean more shadow — or even shadows cast upon shadow, creating places that are darker still.

“We support development. We think it’s essential to the growth of the city. And I do think spectacular architecture and buildings are always exciting,” says Margaret Newman, the executive director of the Municipal Art Society of New York, an urban design organization that has criticized the shadows creeping over Central Park. “Where does density belong? That’s kind of the key question here that this has really provoked: Where is it OK to build these things?”

In New York, legislation was introduced in the city council this spring that would create a task force scrutinizing shadows on public parks. Lawmakers in Boston in the last few years have repeatedly proposed to ban new shadows on parkland, though they haven't succeeded. In San Francisco, the city has tightened guidance on a long-standing law regulating shadows in an era of increasingly contentious development fights. In Washington, where the conflict arises not from luxury skyscrapers but modest apartments and rowhouse pop-ups, the zoning commission voted in April on rules that would prohibit new shadows cast on neighboring solar panels.

The stakes are highest in Manhattan, a crammed borough with few of the back yards, balconies, or even clear window views that city dwellers count on for light that doesn't come from a fluorescent bulb.

"Parks have become the place where we go for this incredibly important experience of being in the sun," says Mark Levine, the New York councilman who introduced the bill that now awaits public hearings. "And if even parks lose the sunlight, then I think it diminishes the experience of living here."

Shades of inequality

New York City has been regulating shadows, if in an indirect way, for a century. When the 42-story Equitable Building was completed in Lower Manhattan in 1915 — rising from the sidewalk like the sheer face of a cliff for more than 500 feet — it cast a seven-acre shadow over the neighborhood.

The outcry it caused helped prompt the city’s first comprehensive zoning law. Those rules didn’t require buildings to cast shadows of a certain size, but they influenced the shape of skyscrapers in ways that controlled how they loomed over the city below. Tall buildings required "setbacks" at higher floors. This is why the Empire State Building grows narrower as it rises, why New York’s skyline looks like a collection of wedding-cake toppers. This is also what creates space and light between buildings that might otherwise rise shoulder to shoulder.

In Central Park today, the new generation of luxury towers on Billionaires' Row reach higher than many in the city ever envisioned. The developers behind them merged multiple building lots or purchased the “air rights” above adjacent properties to legally build taller than what would historically be allowed.

As a result, multimillion-dollar apartments in the sky will darken parts of the park a mile away. Enjoyment of the park while actually in the park — a notably free activity in a high-cost city — will be dimmed a little to give millionaires and billionaires views of it from above.

That picture is an apt symbol for the city’s widening inequality. But it’s also an example of a much broader conflict: New York, and many cities desperate for new housing, must find space to put it.

“Right now, we’re concentrating on trying to get affordable housing, and we’re going to have to provide more density,” says Mitchell Silver, a longtime planner who is now the parks commissioner in New York. “Do you reduce density in order to reduce shadow impacts on the park? Those are the values that start to bump up against each other.”

San Francisco, long torn between high housing demand and a reluctance to build more of it, faces a similar dilemma.

“We’re in the most extraordinarily gigantic building boom that we’ve seen,” says Rachel Schuett, an environmental planner in San Francisco's planning department. “And a lot of the buildings that are going in are over 40 feet.”

Since 1984, San Francisco has had a “sunlight ordinance” that requires the parks commission to review any proposed building taller than 40 feet that might shadow public parks. Last year, the planning department wrote new guidance on how developers must measure their shadow impacts with tremendous precision to comply with it.

First, they must hire shadow consultants to calculate how much theoretical sunlight, in square-foot-hours, a park would receive over a year if nothing were blocking it. The park is then modeled in 3-D with the buildings around it, taking into account how the sun moves over the course of the day and changes position over the year.

"This software," Schuett says, "is literally like a calculus model."

This animated video models how potential new development could cast shadows in San Francisco over the course of a fall day if the city permitted taller buildings. (Fastcast)

The software recognizes the intricate geometry of sunshine: that the sun isn’t as high at “high noon” in San Francisco as it is in Mexico City, that it casts shorter shadows when it’s overhead and long, gloomy ones when it’s low in the sky in winter.

In a model like this, it's possible then to insert a new building and measure how the shadow load changes, maybe subtracting another few percentage points of theoretical sunlight. This is the number the parks commission in San Francisco then considers, alongside diagrams of where those shadows would fall.

Earlier this year, the commission rejected for the first time a new project: a six-story condo that would have increased shadow in the park nearby by less than 1 percentage point. That small number meant a loss of 42 minutes of sunshine on summer nights, on the basketball court and grassy knoll in the only multipurpose park in the neighborhood.

“I’m glad to live in San Francisco with all the noise and traffic and everything else involved in living in a dense urban environment, but I do want to be able to go the park and have there be sunlight to enjoy,” Schuett says. “It’s a human need to have sunlight. It’s a quality-of-life issue that we’re trying to preserve.”

The analysis has become incredibly technical, Schuett adds, but at the end of the day it’s still accompanied by more human concerns. How do children use public space? Is a park less enjoyable in partial light? Is that patch of public sun worth more than 20 new market-rate apartments in the city? How about 10 affordable ones?

The bright side of shadows

Away from public parks, the issue grows even murkier: What about sidewalks, schoolyards, back yards and private rooftops?

This last area has become increasingly testy in Washington, where costly rooftop solar panels have spread alongside pop-ups in many residential neighborhoods. This spring, the city’s zoning commission voted to approve new rules on additions, including one that would prohibit them from shading nearby solar panels. If the rules are adopted, D.C. will join several cities that now have zoning laws protecting if not sunshine then at least "solar access."

Washington otherwise doesn’t have quite the problems that exist in Manhattan — the city’s height act ensures, for now, that a billionaire's condo won't lord over the Mall. But the height act also limits the ability of architects to sculpt their buildings with shadow in mind, to build up instead of out, creating slender shadows instead of squat ones.

Washington also illustrates that shadows, like buildings themselves, are relative. In a city full of light, where you barely have to crane your neck to glimpse the sky, a third-story pop-up feels like an affront. A new six-story apartment creates the pushback that a 60-story one might in New York.

“I think you have to be careful not to show a bias towards those who came first,” says Washington architect Shalom Baranes. “The whole point of cities is to rejuvenate, to rebuild, to densify. And if you get overly concerned about shadows, then it’s always the latest building that gets handicapped, because the existing building already casts shadows — it’s the status quo.”

In entirely different contexts — Southern cities, the Middle East — shade is an essential resource in its own right, and shadows can add a dimension to open space that can be quite pleasant. It appears in the reflections of trees that cast shivering patterns on the sidewalk, in the stark lines between light and dark that give drama to our photos of cities, in the shadows that turn ornate buildings into two-dimensional cityscapes.

Baranes argues that new buildings also add something to a city that’s greater than what they take away. Central Park is an extraordinary place as much for its vast green space as its uniquely urban setting. The park is an outdoor room, surrounded on four sides by glass and steel, 19th century apartments and Beaux-Arts buildings.

“To me, as an architect, that’s much more important than losing some sun — the contribution of the building to creating that outdoor room,” says Baranes, who makes the same case for a proposed apartment he’s designed across the street in D.C. from Meridian Hill Park. “I don’t think any of our squares and circles downtown would be nearly as wonderful if they didn’t have any buildings around them.”