He was born in 1889 (registered A/M/J), and baptised on 21 April 1889 (Bromsgrove), the son of Joseph Arrowsmith and Fanny Arrowsmith nee Goddard.
Joseph was born in Radnor, Radnorshire, and Fanny in Clay Gate, Surrey. They were married in Claygate Holy Trinity, Surrey, on 6 May 1871. According to the 1911 Census they had nine children all of whom were still living at the time of the census. Nine children were named on the census between 1881 and 1911; William Alfred (b. 1868 Long Ditton, Surrey), Alfred (b. abt 1872, Bromsgrove), Edwin Joseph (b. 1873, bap. 5 September 1880, Bromsgrove,), Jessie Anne (b. 1875, Bromsgrove), Robert Philip(birth registered 1878 J/F/M Bromsgrove), Fanny Lucy/Lucy Fanny (bap. 5 September 1880, Bromsgrove), Edith Victoria (birth registered 1887 J/F/M Bromsgrove), Frank Sydney (b. 1889, bap. 21 April 1889, Bromsgrove) and Constance (b. 1895, Sutton Bonington, Notts). The first child, William, was born before his parent's marriage; he was christened at Long Ditton St Mary on 11 November 1868 and his mother was named as Fanny Goddard. The other children, with the exception of the youngest, Constance, who was born in Nottinghamshire, were probably born in Stoke Prior (births registered Bromsgrove).
Joseph was a railway porter with the Midland Railway and in 1881 he and Fanny were living in Stoke Prior, Bromsgrove, Worcestershire, with their five children, William(12), Alfred (9), Edwin Joseph (7), Jessie (5), Robert (3) and Fanny Lucy (8m.).
They were still living in Stoke Prior at Aston Fields in 1891. Five children were in the home on the night of the census: Edwin (18) a blacksmith, Robert (13), Fanny (10), Edith (4) and Frank (2). There were two boarders in the household, Thomas Williamson (16) and William Adams (16), a telegraph clerk.
By 1901 Joseph and Fanny were living at Marl Pit Hill in Sutton Bonington, Nottinghamshire; only their three youngest children were in the home on the night of the census, Edith (13), Frank (12) and Constance (5).
In 1911 only Frank (22) and Constance (15), who worked in the lace trade, were still at home with their parents who now lived at 1 Church Terrace, St Saviour's Street, Nottingham. Joseph was still employed on the railway but was now a lift man. Also in the household wa a boarder, Albert Holborn (25), who was a railway employee with the Great Northern Railway.
Frank married Lilian Crawley in 1917 (marriage registered J/A/S Nottingham) and they lived at 4 Dunkirk Road Old Lenton Nottingham.
Frank's father died on 20 February 1927. Probate was awarded to his widow, Fanny (Effects £116 16s.) They were still living at 1 Church Terrace.