A Superior Court judge upheld a decision of the board of appeals of Rockport denying Chiancola a variance to construct a single-family house. Chiancola needs a variance because access to his long, narrow lot, fronting on Pigeon Hill Street, was entirely precluded by a quarry pit extending across the entire width of his lot and into the abutting properties on both sides, thus effectively cutting off his frontage from the buildable portion of his lot. Chiancola concedes that the Pigeon *637Hill Street lot line does not qualify as “frontage” under the Rockport zoning by-law. Thus Chiancola’s lot is, in effect, a landlocked parcel. To effect access, Chiancola has obtained two rights of way, one forty feet in width, extending from Munroe Drive, a cul-de-sac off Curtis Street, to a thirty-foot wide strip of land (which he owns in fee) that extends to a rear comer of the Chiancola lot. The two strips of land intersect at roughly a ninety-degree angle, and the thirty-foot strip abuts Chiancola’s rear lot line for a width of ten feet and the lot line of town land for the remaining twenty feet of width. Chiancola proposes constructing a fifteen-foot wide driveway extending from Mun-roe Drive over the forty-foot right of way and the thirty-foot strip for a distance of 261 feet to his rear lot line. There the driveway will necessarily shrink in width to ten feet but thereafter become fifteen feet in width again and extend another 320 feet to the spot overlooking the quarry where he proposes to build a house.

The board of appeals conceded that Chiancola met the first three requirements for a variance set out in G. L. c. 40A, § 10: that enforcement of the by-law would involve substantial hardship because Chiancola could not build his house; that the hardship was due to the soil conditions, shape, or topography of the lot, namely, the quarry; and that those conditions are unique to his lot. Chiancola, however, could not meet the last three requirements set out in G. L. c. 40A, § 10: that desirable relief could be granted; that the relief would not result in substantial detriment to the public good; and that the relief would not nullify or substantially derogate from the intent or purpose of the zoning by-law. The reason, the board found, was that the lengthy driveway, with its right angle, its constriction to ten feet at one point, and the uphill-downhill terrain for the last 320 feet, made access by emergency vehicles too precarious.

The board’s findings were upheld by the judge. The evidence was that the town’s fire engines varied from eight and three-quarters feet in width to nine and two-thirds feet; that replacement tracks would reach ten feet (narrower tracks would have to be custom-built and would be more expensive); and that the ambulance serving the town was approximately nine feet wide. Passing another vehicle would be impossible. Thus, the last *638three requirements for a variance were simply not met; and, beyond that, Chiancola would still run into the substantially unbreached wall of cases holding that, even where a board legally could grant a variance, they would not be required by a court to do so. See Damaskos v. Board of Appeal of Boston, 359 Mass. 55, 61 (1971); Broderick v. Board of Appeal of Boston, 361 Mass. 472, 479 (1972); Hunt v. Milton Savings Bank, 2 Mass. App. Ct. 133, 140-141 (1974); Gamache v. Acushnet, 14 Mass. App. Ct. 215, 220-221 (1982); Davis v. Zoning Bd. of Chatham, 52 Mass. App. Ct. 349, 355-356 (2001). On the facts of this case, the best that can be said in Chiancola’s favor is that the problem of emergency vehicle access is a judgment call; and, as in the special permit context, “[i]t is the board’s evaluation of the seriousness of the problem, not the judge’s, which is controlling.” Copley v. Board of Appeals of Canton, 1 Mass. App. Ct. 821 (1973). The judge here correctly deferred to the board’s judgment.

To avoid this result, Chiancola argues that prohibiting construction of single-family homes on lots without frontage is tantamount to a regulatory taking under Lucas v. South Carolina Coastal Council, 505 U.S. 1003, 1027-1030 (1992), and Palazzolo v. Rhode Island, 533 U.S. 606, 626-630 (2001). The argument is without merit. It is untenable that a frontage requirement by which a municipality seeks to ensure emergency access to residences “bears no ‘reasonable relation to the State’s legitimate purpose.’ ” Gove v. Zoning Bd. of Appeals of Chatham, 444 Mass. 754, 760 (2005), quoting from Exxon Corp. v. Governor of Md., 437 U.S. 117, 125 (1978). Nor has Chiancola proved that he has been denied “ ‘all economically beneficial us[e]’ of [the] property.” Lingle v. Chevron, U.S.A., Inc., 125 S. Ct. 2074, 2081 (2005), quoting from Lucas v. South Carolina Coastal Council, supra at 1019. One “cannot prove a total taking by proving only that one potential use of [his] property — i.e., as the site of a house — is prohibited.” Gove v. Zoning Bd. of Appeals of Chatham, supra at 763. Chiancola had the burden of proving the unconstitutionality of the zoning bylaw, Chaume v. Zoning Bd. of Appeals of Fitchburg, 27 Mass. App. Ct. 1135, 1135 (1989), but has adduced no evidence as to the value of his property for other purposes. As to the character *639of the governmental action, the authority exercised by the town here represents a most basic concept of land use planning, to restrict the residential development of backland not capable of being reached adequately by roads, power, and municipal services.

Judgment affirmed.