By Catherline Carlock

In exchange for allowing a tower at Winthrop Square that would result in a big windfall for the city, Boston Mayor Martin J. Walsh on Monday expects to file a home rule petition that would limit height and density for future buildings proposed in the city’s Midtown Cultural District.

Walsh will call for amendments to state legislation governing shadows on the Boston Common and Public Garden, the first in a series of steps that would ultimately allow for a skyscraper at the site of the Winthrop Square garage downtown.

Brian Golden, the director of the Boston Planning & Development Agency, said the expected $153 million payout expected from Winthrop Square developerMillennium Partners is an “outrageously compelling” enough reason to alter state shadow laws that have been on the books since the 1990s. The city expects to allocate that funding toward Boston Common, Franklin Park, the Emerald Necklace and refurbishing public housing in South Boston and East Boston.

“The benefits to the people of Boston will be profound,” Golden said. “This is a once in a multi-generational thing.”

The Midtown Cultural District, which runs south and east of the Common and Public Garden, has an existing “shadow bank” developers tap into when proposing new buildings that would cast shadow on the two parks. The home rule petition calls for the 1.15-acre parcel at 115 Winthrop Square to be treated as part of the Midtown district, using up all the remaining “shadow bank,” which would restrict both height and density at future buildings proposed in the district.

The home rule petition also calls for a downtown planning study, which would likely guide new zoning standards for the downtown neighborhood and allow the city to get an advance read on future development sites that could generate shadows. Millennium Partners would partially fund that study, Golden said.

Millennium has proposed a 775-foot tower at 115 Winthrop Square, currently the site of a dilapidated city-owned parking garage. As part of the deal, Millennium is expected to pay the city $102 million ­for the acquisition of the garage, while another $51 million to the city is dependent on revenue generated by the tower.

“In that public ownership there is a really magnificent return to the people of Boston, and the people of Boston would not get such a return on the development of a private parcel,” Golden said.

The home rule petition does not outline a specific height for a tower at Winthrop Square.

At its longest duration, the proposed tower at Winthrop Square would cast shadow on the Boston Common for more than an hour and a half during certain periods of the year; the average shadow duration is between 35 and 37 minutes, according to two shadow studies done on the proposed tower.

The topic of the shadows cast on the Common and Public Garden by a Winthrop Square tower has been a hot-button issue in recent months, with critics arguing that altering state legislation to allow for a single development sets an inauspicious precedent where well-capitalized developers can seek one-off exemptions for projects. Indeed, 13 representatives of neighborhood parks associations wrote as much in a letter dated March 21 to the Boston City Council.

“The development proposed for Winthrop Square threatens the historic greenspace heart of the city – Boston Common and the Public Garden – not just with shadows from this one building, but the precedent it sets for other developers to seek exemptions for their projects,” the 13 representatives wrote. “As parks advocates we are all concerned, because a threat to one greenspace is a threat to all, and what happens to one can happen to others.”

Elizabeth Vizza, executive director of the Friends of the Public Garden, said last week that her organization looked forward to reviewing the legislation.

“We are continuing to work with Mayor Walsh and the BPDA to ensure that a final resolution provides broad, permanent protections for the city’s landmark parks and minimizes the impact of shadows from the proposed Winthrop Square project,” Vizza said.

The home rule petition will be read at the Boston City Council meeting this Wednesday and then referred to a hearing at the government operations committee, the BPDA said. Following its time in committee, the petition would be voted on by the City Council; if it passes, Walsh would sign the petition and send it to the state Legislature. Golden said the BPDA felt confident in the petition’s successful passage at city council.

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