The aeroplanes are the twice and sometimes three times weekly flights Bryan and his colleagues have been taking to and from their company HQ in Calgary, Canada, to London to do battle by fax, telephone and personal appearance in the campaign to gain control of a piece of the British oil exploration and production sector.
But it is numbers - about the value of oil still in the ground, of debt levels and of exploration prospects - which have provided the ammunition in the long-running and frequently confusing bid battle between the two companies. And frankly JP is sick of them. "I will be so glad when I can get back to talking about what we're going to do as a company in the future," he says.
Despite the acrimony of the bid, and the distinct possibility until a few days ago that his company could walk away clutching only a sheaf of advisers' bills, JP seems relaxed and confident. The silver hair is in place, the tie verges on the loud (but, interestingly, not the arresting car-motif model he wore when Gulf opened hostilities on 18 December last year), and the thick braces are in place.
"We will still be happy to walk away from this bid with nothing, because we don't want to overpay for Clyde," he says. "If we offered the kind of price they were demanding, it would be a hollow victory." He believes there are plenty of other fish in the sea.
Until Gulf finally raised its bid to 120p a share last Tuesday, Clyde had had the better of the often bitter exchanges between the two camps. Clyde's advisers painted their opponents, with some degree of success, as shark-like foreign opportunists who were using the different valuation methods that are applied to oil exploration stocks on each side of the Atlantic (the North American model, which works on a cash-flow multiple, is more generous to a company's market value) to pull off a nice bit of transatlantic arbitrage which significantly undervalued the company.
The argument developed some holes over time, particularly in light of the aggressive valuations attached by Clyde to its Australian and Dutch North Sea assets and the fact that a number of Clyde directors sold shares at 80p just days before the Gulf bid.
Perhaps because of the volume of mudslinging, the outcome of the bid remains on a knife edge as both companies enter the final nine days of the offer period under the timetable set down by the Takeover Panel. Neither side will have much time for seeing families, and both chairmen and their cohorts will be getting to know the insides of meeting rooms throughout the City as they do the rounds of the institutions which hold around 70 per cent of Clyde's equity.
In light of the raised bid, these institutions face the dilemma of whether to take the money and run or hold out for the promises of value generation and share price growth offered by Malcolm Gourlay and Roy Franklin, chairman and chief executive respectively of Clyde. The fund managers will have plenty of opportunity to take the measure of both sets of managers over the next few days.
Iain Reid, the influential NatWest Securities oil analyst, thinks it will be a squeaker, "but we believe 120p will be just enough to win the day." He also warned, in a research note published just before the bid was increased, that Clyde's share price would inevitably fall away if the bid failed. Most analysts now discount the prospect of a "white knight" emerging to sweep shareholders off their feet with a much higher offer.
There is a part of JP Bryan that really enjoys the cut and thrust of deal-making, the lifeblood of the oil exploration business. He was born in Freeport, a deeply Texan seaside town on the Gulf of Mexico coast about 40 minutes south of Houston, the undisputed capital of Texas oil country. Nowadays the town is a faded beauty, like most seaside towns, and with his two children grown up and him spending much of his time in Calgary, he says he does not get back there much.
JP's 30-odd years in the oil industry, first as an engineer in Houston, then as a manager, and finally as an entrepreneur-financier who set up companies to buy and manage oil assets on behalf of managed fund clients, have given him a taste for the deal. At one point, two years ago, he thought he would quit, having put two companies, Nuevo and Bellwether, on the New York Stock Exchange and made a good pile in stock options.
"But then Gulf Canada came along. It was not in very good shape. It had been part of Chevron after they took over Gulf [the US oil giant] and they spun off the Canadian arm. Then it was bought by the Reichmann brothers, and ended up in the hands of the banks when the Reichmanns' Canary Wharf development went bust. Between them they collectively proved that 26 banks could not run an oil and gas outfit."
Bryan and some investors raised $300m (pounds 185m) in January 1995 and bought 25 per cent of the company, gaining control of the board. Since then, he claims, the culture has changed, the staff has shrunk and the business has been rebuilt. And he has grown used to living in Canada. "It's been a little tough on the old lifestyle. But I meet my wife at her place in Colorado Springs when I get time off."
Lest this become too fluffy a picture of the Texas oilman exiled in Canada, it ought to be noted that JP's company has a fairly aggressive profile: debt levels of over C$2bn (pounds 900m), and a track record of walking away from as many hostile bids as it has won. His opponents in this bid, Gourlay and Franklin, have called the Gulf bid "transparently opportunistic", and contend that the only reason it is being made is because there is a chance to pick up oil assets relatively cheaply and then sell them. They also argue that Gulf's high leverage does not give it the leeway to pay a fair price.
"Yes, this is opportunism, I agree," says Bryan. "But it's the kind of opportunism that says in this case we will not overpay for this company."
So what happens if JP and his international operations director, Dick Auchinleck, gain control of Clyde? The assets will be reviewed, and they will probably end up keeping Clyde's interests in the Dutch North Sea, Australia and Indonesia. The rest of the assets, including Clyde's share of the Wytch Farm onshore production site in Dorset, might be for sale, to pay down some of the debt incurred with the bid. They also promise to relocate the headquarters from Ledbury in Herefordshire, "which is too damn far away from anywhere if you ask me", says Bryan.
Inevitably, there would be staff cuts. In the current climate of acrimony it would be hard to imagine Gourlay and Franklin working for Gulf. But having said that, both Bryan and Auchinleck say they are interested in Franklin's services. For his part, Franklin is equivocal: "I would never say never," he says. "In many respects our two companies have a lot in common."
What Gulf plans for Clyde if it succeeds will be of purely academic interest to the institutional shareholders, as the bid is a cash offer and no one will be left holding Gulf stock afterwards. It may be of more interest to Clyde employees as they contemplate their job prospects. But it will also be an interesting case study for students of bid strategy. Neither side has done anything drastically wrong, and if nothing else the flurry of statistics has caused an epidemic of migraines to break out among financial journalists covering the story.
The outcome, however, may set a precedent for bids: will the gamble of not paying the City's asking price (135p at the last count) work? Or will Clyde's robust defence of its record, and equal gamble of not seeking a white knight, prove wise? JP has everything to play for.