A D103 Aeroplane crash-lands at an airport and explodes. Fortunately, this is a film shown as a demonstration to a group of people. This should become a thing of the past due to the invention of one Mr. Hiram J Hackenbacker, alias Brains. The Skythrust is to become the safest plane in the air, and is currently being tested at London Airport.

Lady Penelope is in Paris in order to model for a designer friend, François Lemaire. She discovers that there is a bug in his studio, no doubt planted by a rival intent on stealing his new invention. He's developed a new fibre, dubbed 'Pennylon', that can fold up into a tiny space. This is what he wants Penelope to model for him, but the discovery of another transmitter in the room forces them to change their plans.

They are now holding the fashion show on the new Skythrust, and TinTin and Brains will be waiting for them in London.

On board, one of the models, Madeline, disappears. She reappears on the flight deck and hijacks the plane. They are now heading towards the Sahara desert, where the Pennylon collection will be stolen by her partners in crime, Ross and Collins. Lady Penelope manages to contact International Rescue using a ring that she is wearing.

The Skythrust is intercepted by Thunderbird 2, and a non-explosive missile is fired at the Skythrust at Brains' suggestion. The undercarriage fails, and Mason, Madeline's accomplice, realises that they must return to London, as he doesn't want to be in the plane when it explodes.

Back in London, Skythrust demonstrates its special feature, and ejects its fuel pod before landing harmlessly. The fuel is detonated at 40,000 feet, rather than causing an explosion on the ground.

In the Sahara, Virgil and Alan locate the rendezvous point and destroy the makeshift airport that has been built there.