New York City Housing Authority’s sheer physical problems — lead paint, leaks, heat and hot-water failures — seem insurmountable.

But fixing a more basic design flaw in NYCHA’s 326 developments could be a major new answer to their problems.

Currently cursed with a “towers in the park” layout, NYCHA developments are cut off from the surrounding city. They are distant from supermarkets. Their isolated, interior green spaces have turned into danger zones.

As the great New Yorker Jane Jacobs said nearly 60 years ago in her landmark book “The Death and Life of Great American Cities:” “Public housing must tie with streets beyond the project borders … the aim should be to bring in uses different from residence, because lack of mixed uses is precisely one of the causes of deadness, danger and plain inconvenience.”

NYCHA’s current crisis has sparked a need to act on her vision. The architecture firm Curtis+Ginsberg LLP and I have worked together on a plan called “Re-Streeting” NYCHA, and our solution is easy: Simply extend neighborhood streets through the projects and they will become far better places to live.

New streets make new buildings possible. These new buildings would include not just new homes but — in a major departure for public housing — new stores and restaurants, which would generate funds to repair existing, dilapidated structures. And it can all be done without displacing current tenants or demolishing any old buildings.

Here’s how “re-streeting” would work at one typical NYCHA development: the Pelham Parkway Houses in the east Bronx, which comprises 23 six-story brick buildings and 1,266 apartments.

Before it was built, surrounding streets cut through the site, and walk-up apartments and small stores abounded. Barnes and Matthews avenues once connected Astor Avenue and the Pelham Parkway. No longer.

Reinstating these avenues will help life in the project flow once again, as you can see by the sliding graphic and five key benefits below.

New streets, new housing

Extending Barnes and Matthews avenues through the development once again would end its isolation. Pedestrians and cyclists would have a route straight through these well-lit avenues, which would also offer new and different types of private housing. Some 270 new units would include four-family walk-up apartment buildings on the east side of a restored Matthews Avenue between Astor and Pelham Parkway; two-family townhouses on the west side of Matthews at the Pelham Parkway corner, and eight-story elevator buildings on the west side of the new Barnes Avenue.

The income segregation of NYCHA would be mitigated by new, privately housed tenants and homeowners — in a neighborhood where small homeowners are already common.

New stores and restaurants

New commercial buildings would spring up to fill in the jagged edges of the development — creating the sort of continuous streetscapes most New Yorkers take for granted. A large new lot at the corner of Barnes and Astor could be the site of a supermarket, restaurants could open on the other side of the same corner. New residents with a range of incomes will help support the stores and restaurants. The elderly would no longer face a long walk to the supermarket on Boston Post Road. New stores also mean employment — including for young people in the project. And new business means activity, which helps discourage crime.

Community facilities

The new streetscapes, perhaps along the Pelham Parkway border, could offer services that residents need but don’t currently have including a child-care center, a dry cleaner or a bodega.

These changes would go beyond repairing the projects and reintegrate them into the vitality of urban life. They would buzz with bicyclists, sizzle with shoppers and attract diners.

Private courtyards

Currently — typically for NYCHA — anyone can walk into the green interior “campus” of Pelham Parkway Houses. A street through the middle would divide the green space into back yards for each building — for both existing public housing and new private homes. And just like with upscale areas such as Gramercy Park, those new back yards would require a key fob, issued only to residents, to enter.

New parking

Diverging from NYCHA’s plan to build new housing on parking lots owned by the authority, our re-streeting scheme would create 116 new, curbside parking spots — for both visitors and shoppers.

Yes, NYCHA itself would benefit. It would still own the land and could generate additional revenues, whether through a ground lease with new property owners or a percentage of profit from retailers. Ideally, all of this extra money would go toward the upkeep of the Pelham Parkway Houses, where emergency mobile heating systems are needed and front-door buzzers don’t work.

Based on market rents in the surrounding area, the housing authority could make some $2 million annually from the new development.

What’s more, the Pelham Parkway Houses is a typical NYCHA project — buildings set at an angle in a campus. If the re-streeting approach were applied to 200 of the city’s 326 NYCHA developments, the result would be 46,000 additional housing units — along with a revenue windfall. The fact that NYCHA already owns the land it would lease to developers would help keep rents low. And developers could even support the cost of “re-streeting” the projects.

Public-housing residents today not only live in dangerous physical conditions, they live with the legacy of bad design, conceived by utopian modernists in the 1930s, with little feel for how city dwellers really like to live. The French-Swiss architect Le Corbusier led the movement. “There ought not to be such things as streets,” he wrote. “We have to create something that will replace them.”

That something was the superblock, which led to the massive demolition of small apartments and stores. It’s time to repair that damage — and welcome public-housing projects into the beating heart of the city’s urban life.

Adapted from City Journal. Howard Husock is vice president for research and publications at the Manhattan Institute and the author of the forthcoming book, “Who Killed Civil Society? The Rise of Big Government and Decline of Bourgeois Norms.”