Archibald Logan was born on 28 November 1865 at Greenock, Renfrewshire, Scotland, the third of eight children of Margaret McLay and her husband, Robert Logan, a boat builder. In the early 1870s Robert, who was foreman of a boat-building firm on the River Clyde, received a commission from his brother James in Auckland, New Zealand. He was to build a small steamer, named the Eclipse, for the Auckland to Riverhead service on Waitemata Harbour and have it shipped there. Robert Logan and his family subsequently emigrated to New Zealand, arriving in Auckland on the Zealandia on 15 October 1874. In 1878 he set up in business as a boat builder in Devonport. He rapidly became successful and produced a number of significant yachts. Based on his experiences in building lifeboats on the Clyde, he pioneered the use of diagonally planked two- and three-skinned boats made of kauri.
After attending school at Devonport Archibald Logan, together with four of his five brothers, was employed in his father's business. The Logan brothers became skilled boat builders and designers in their own right and were prominent in yachting and rowing sports. About 1890 Archibald and his brother Robert set up in business as R. & A. Logan on land reclaimed for the freezing works on the city side of Waitemata Harbour. They were joined in 1892 by a third brother, John, and the firm became known as Logan Brothers. Their business became very successful, and from 1898 they began exporting yachts to Australia, South Africa and the Pacific region. Their keel yachts were especially sought after but they built a large number of centreboard craft, pleasure launches and commercial craft as well.
By 1900 Archibald (known as Arch) Logan had become the principal designer for Logan Brothers and the pre-eminent yacht designer in the southern hemisphere. He was spare of frame, quietly and well spoken, reserved by nature, and held strong religious beliefs. On 24 May 1905 he married Emma Sarah Shortt at Mangere; they were to have four children. Emma and Arch Logan later became members of the Open Brethren community.
In 1910 Logan Brothers closed their business after accepting compensation from the Auckland Harbour Board for the surrender of their long lease on the Auckland waterfront so that construction of the King's Wharf complex could proceed. Arch Logan, who was then living in Stanley Point Road, Devonport, with a boatshed on Ngataringa Bay, continued to build boats at a modest pace but increasingly provided designs for other builders. He designed and built the champion shallow-drafted mullet boats Ngaira (1911), Valeria (1913) and Omatere (1913), and after the First World War designed many keel yachts, centreboard craft (in particular the 18-foot patiki M class) and power craft. By 1930 Logan was doing little building but much yacht designing. Some of his later designs were the Silver Fern 12-foot class and Little Jim (1934), Tawera and Waiomo (1935), Aramoana and Spray II (1938), and Gypsy (1939).
Archibald Logan died in Auckland on 27 March 1940 survived by his wife and four children. As a result of his early training and study of overseas trends in design, Logan was the outstanding figure in New Zealand yachting from about 1895 until his death. His yachts were long-lasting. The Arch Logan Memorial Trophy is the premier trophy of the M class. After 1945 his son Jack became a prominent designer, builder and helmsman of 18-foot yachts in New Zealand.