Question: Which country was Pilot Officer Sydney "Timberoes" Carlin fighting against while serving as air gunner?

Context paragraphs:
Battle of Britain: The Battle of Britain (German: "Luftschlacht um England" , literally "the air battle for England") was a military campaign of the Second World War, in which the Royal Air Force (RAF) defended the United Kingdom (UK) against large-scale attacks by the German Air Force (Luftwaffe).  It has been described as the first major military campaign fought entirely by air forces.

Frank Bell (RAF airman): Sergeant Frank William Bell {'1': ", '2': ", '3': ", '4': "} (23 August 1897 – February 1960) was an observer and air gunner in the Royal Air Force during World War I.  He was a flying ace credited, together with his pilot, with six aerial victories.

Norman Williams (RAAF officer): Norman Francis Williams, (3 November 1914 – 30 June 2007) served as an air gunner in Royal Australian Air Force (RAAF) bombers in the Second World War, becoming its most highly decorated non-commissioned officer.  A rear gunner in a Halifax bomber, he was credited with shooting down 8 German aircraft and damaging several others, making him the RAAF's only "ace" who was not a fighter pilot.

RCAF Western Air Command: Western Air Command was the part of the Royal Canadian Air Force's Home War Establishment responsible for air operations on the Pacific coast of Canada during the Second World War.  When Canada declared war against Germany in September 1939 the command consisted of only five squadrons.  Four of them equipped with obsolete aircraft including a bomber squadron with aircraft from the Great War and there were no fighter aircraft at all for its only fighter squadron (113 Fighter Squadron was thus disbanded).  With the Japanese threat after Pearl Harbor it grew rapidly and played a critical role in fighter and anti-submarine operations in Canadian and American waters during the Aleutian Islands Campaign.  It was there that Squadron Leader K.A. Boomer of No. 111 Squadron shot down a Rufe fighter, the RCAF's only kill in the Pacific Theatre.  On 7 July 1942 a Bristol Bolingbroke pressed home an attack on the Japanese Submarine Ro 32 the pilot F/Sgt.  P.M.G. Thomas of No. 115 Squadron RCAF then led American Destroyers to sink the damaged submarine.  By January 1943 Western Air Command had expanded to include many bomber, fighter and operational units under its control.  By the end of the war the command would involve some twenty squadrons when the last units to join were added in 1943.  These were the 163 Army Cooperation Squadron in March flying Bristol Bolingbrokes and Hawker Hurricanes, in May the 160 Bomber-Reconnaissance Squadron was added flying Cansos from Sea Island BC (before moving to Yarmouth NS in July) and the 166 Communication Squadron formed in September flying various types.  In addition to the new squadrons, new aircraft types came on line replacing the command's remaining Supermarine Stranraers and Blackburn Sharks with Canso's and the Bolingbrokes and Beauforts with the Lockheed Ventura.  Countless training missions and operational patrols bolstered the air activity over the coastal areas but there was not much action until RCAF Western Command was on the look out for General Kusaba's Fire Balloons that the Japanese called the Fūsen Bakudan Campaign.  In February and March 1945, P-40 fighter pilots from 133 Squadron, Royal Canadian Air Force operating out of RCAF Patricia Bay (Victoria, British Columbia), intercepted and destroyed two fire balloons, On 21 February, Pilot Officer E. E. Maxwell While shot down a balloon, which landed on Sumas Mountain, in Washington State.  On 10 March, Pilot Officer J. O. Patten destroyed a balloon near Saltspring Island, British Columbia.  During another interception a Canso forced down a fire balloon which was examined at the army headquarters.  Patrol activity was joined by the Operational Training Schools (OTS) operated by Number 4 Training Command of the BCATP.  They were the No. 3 OTS flying the Canso and Catalina and No. 32 OTS with Ansons, Beauforts and Swordfish at Patricia Bay.  In April, 1944 the No. 5 OTS Heavy Conversion unit stood up at Boundary Bay when 16 B-24 Liberators arrived fresh from American factories.  By the end of September 1944 RCAF 5 O.T.U. had grown to sizeable force of some 87 aircraft including 38 B-24 Liberators, 35 B-25 Mitchells, 5 Bolingbrokes, 8 P-40 Kittyhawks and a single Norseman.  With the end of the war in Europe these aircraft were joined by a number of Victory Aircraft Lancaster X bombers which were to be used to train the British Commonwealth's Very Long Range Bomber Tiger Force that would soon be sent to bomb the Japanese mainland from Okinawa.  With the unconditional surrender of Japan the RCAF's Tiger Force bomber squadrons were disbanded before they flew overseas and the total draw down of the Western Air Command was suddenly undertaken.  Within several months almost all the flying squadrons would be completely stood down.

Sydney Carlin (RAF officer): Pilot Officer Sydney "Timbertoes" Carlin, {'1': ", '2': ", '3': ", '4': "} (1889–1941) was a British World War I flying ace, despite having previously lost a leg during the Battle of the Somme.  He returned to the Royal Air Force in World War II, serving as an air gunner during the Battle of Britain.

Wallace McIntosh: Flight Lieutenant Wallace McIntosh DFC & Bar, DFM (27 March 1920 – 4 June 2007) flew 55 bombing missions with the RAF during the Second World War as an air gunner in Lancaster bombers.  He was recognised as the most successful air gunner in Bomber Command, having shot down eight enemy aircraft (7 were shared with M/U Gunner Larry Sutherland) two "probables" and one "damaged" (also shared with Sutherland).  In one operation on the day after D-Day, they shot down three German night fighters.

Václav Robert Bozděch: Colonel Václav Robert Bozděch (15 July 1912 – 27 February 1980) was a Czech air gunner of World War II.  He was a British Royal Air Force (RAF) squadron gunner and commander of training centers.

Acting pilot officer: Acting pilot officer (APO) is the lowest commissioned grade in the Royal Air Force, being immediately junior to pilot officer.  Unlike other RAF ranks which officers may hold in an acting capacity, acting pilot officer is maintained as a separate grade.  It normally denotes an officer who has recently been commissioned and joined as a non-graduate direct entrant.  Acting pilot officer is not an actual rank, and APOs are later regraded to pilot officer, not promoted.

Radio Operator Badge: The Radio Operator & Air Gunner's Badge (German: "Fliegerschützenabzeichen für Bordfunker" ) is a commonly accepted title for the "Luftwaffen-Fliegerschützen-Bordfunker-und Bordmechanikerabzeichen" (Combined Air Gunner, Radio Operator and Flight Engineer Badge).  It was a German military decoration awarded to radio operators, air gunners and mechanics (flight engineers) who were members of the German Air Force (Luftwaffe) after they completed two months training or had taken part in at least five operational flights.  If wounded during an operational flight, the badge could be awarded and worn earlier.  Later in June 1942, a separate badge was introduced for Air Gunners and Flight Engineers.  That badge had the same qualifications.

Air gunner: An air gunner (AG) also known as "aerial gunner" is a member of an air force aircrew who operates flexible-mount or turret-mounted machine guns or autocannons in an aircraft.  Modern aircraft weapons are usually operated automatically without the need for a dedicated air gunner, but older (World War II and earlier) generation bombers used to carry up to eight air gunners.

Supporting paragraphs: Sydney Carlin (RAF officer) Battle of Britain
Answer: German Air Force