A war of words between tech billionaire Elon Musk and the boss of Europe’s biggest airline is spilling into social media, with the airline milking it for all it’s worth.

Ryanair boss Michael O’Leary is relishing his feud with Musk, who has called him a “chimp”, an “idiot” and a “retarded twat” in online sprays after a spat that began over whether the budget airline would buy Musk’s Starlink system so it could offer on-board Wi-Fi.

It began two weeks ago when Ryanair, which is infamous for its no-frills flights and cutting costs, ruled out Starlink.

“You need to put antenna on fuselage, it comes with a 2 per cent fuel penalty because of the weight and drag. We don’t think our passengers are willing to pay for Wi-Fi for an average one-hour flight,” O’Leary told Reuters.

That ignited a flame under Musk, who took to his social media platform X the following day to say O’Leary was “misinformed”.

“I doubt they can even measure the difference in fuel use accurately, especially for a one-hour flight, where the incremental drag is basically zero during the ascent phase due to high angle of attack,” he wrote, adding an explainer from his Grok artificial intelligence platform.

O’Leary said it came down to cost – and that installing Starlink across Ryanair’s fleet would cost up to €250 million ($A434 million) a year.

“Tiny little improvements in fuel drag result in very significant fuel savings. But tiny impediments, like aerials hanging off aircraft, would add to cost,” he said.

“Mr Musk thinks that aerials don’t add to drag.”

Since then, it’s been on — and in increasingly lower levels of mature.

Musk hit back, again on X, with personal insults, prompting O’Leary to accuse him of overreacting.

“I thought that was a reasonably measured response,” he said.

“Elon Musk apparently took great umbrage and resorted to insulting me on X over the weekend, calling me an idiot… [and a] retarded twat.”

In an Irish news podcast, O’Leary was less measured.

“I would pay no attention whatsoever to Elon Musk, he’s an idiot. Very wealthy, but he’s still an idiot,” he said.

The budget airline – which is also known for its cheeky online presence – has also leaned into the controversy.

“Perhaps you need Wi-Fi, Elon Musk,” Ryanair’s social media team posted when X suffered an outage late last week.

Musk responded by floating a mock takeover, asking whether he should “buy Ryan Air and put someone whose actual name is Ryan in charge?”

“How much would it cost to buy you?” he wrote. “I really want to put a Ryan in charge of Ryan Air. It is your destiny.”

In another post he wrote: “Ryanair CEO is an utter idiot. Fire him.”

The airline responded by tagging Musk in a post suggesting O’Leary had called a press conference to address the tech boss’s “Twitter tantrum”.

“Musk knows even less about airline ownership rules than he does about aircraft aerodynamics,” O’Leary said.

Under European Union rules, non-European citizens cannot hold a majority stake in European airlines – although O’Leary said Musk would be welcome as an investor.

“We’re a publicly owned company, he’s free to do so anytime,” he said.

“If he wants to invest in Ryanair, we will certainly think it’s a great investment.”

The official Ryanair account also said it was launching a “Big Idiots” seat sale for Musk and “any other idiots on X”.

The promotion offers 100,000 seats for €16.99, which O’Leary said underlined Europe’s dominance in low-cost travel.

“We do want to thank him (Musk),” O’Leary said. “We have had over 3-4 million hits on the seat sale launch yesterday, which is the Big Idiot seat sale.”

Musk hasn’t spoken about the row outside of his social media sprays. But O’Leary said he was unfazed by days of personal to and fro.

“I do believe social media, X in particular, is a cesspit,” he said.

“There is nothing Elon Musk can say to me that my teenage kids haven’t said to me … I’m well able to take my own medicine.”