Operation Catherine Wheel has been set up in order to test the War Office's latest weapon: a large, radio-controlled, high explosive-carrying wheel. The Walmington-on-Sea platoon is chosen for fatigues. When Pike and Walker sneak off to listen to the wireless, they cause interference for the wheel, which promptly rolls out of control.
The episode opens with a General briefing two others in the War Office building in 1941: the General briefs the others about a weapon called the High Explosive Attack Device Propelled by Ultra High Frequency (HEADPUHF) and the test called "Operation Catherine Wheel". Several local Home Guard units will be roped in to help during the test and the smarmy Captain Stewart tells them he will get the Walmington-On-Sea brigade to do the dirty work.
When Captain Stewart arrives in Walmington-on-Sea to recruit the platoon, Captain Mainwaring misinterprets his hesitancy in describing what exactly they are required for to mean 'special duties' - Stewart allows him to believe this to get his co-operation. Mainwaring debriefs the platoon down in the church crypt to maintain secrecy, but ARP Warden Hodges barges in. Deciding they cannot trust him to keep quiet, they take him with them to the base where the test is taking place - Hodges is highly amused when it turns out that their 'special duties' include peeling potatoes.
Private Pike gets bored and sneaks out back to Jones' van with Private Walker. It's revealed that Pike has built a kit radio and brought it along, so they try to tune in to the popular programme Hi Gang! Unknown to them, the signals from the radio interfere with the control signals for the secret weapon - a giant rocket-propelled wheel - and make it go berserk. It rolls out of the base and the Walmington-on-Sea platoon find themselves having to pursue it - if they don't stop it, it will explode and the town will be destroyed.
The chase is a shambles, with the wheel repeatedly chasing the platoon's van and even appearing to ambush them - then they run out of petrol. When Walker suggests they could use Pike's radio to lure the wheel, Mainwaring is infuriated about Pike's secret radio, but they follow Walker's plan, with Mainwaring, Hodges and Pike taking off on a commandeered motorcycle. Knowing the only way to stop the wheel is to knock out its antennae, Lance-Corporal Jones suggests they head to a nearby railway bridge. As Pike and Mainwaring lure the wheel under the bridge, Jones is lowered down and manages to cut the antennae off with a pair of shears. The platoon gather around the fallen weapon as Jones reports "Mr. Mainwaring... I've killed it" and hang their heads in respect.