Great Links Tor, Bunker Hill, Ben Tee…

EVERY HILLWALKING GOLFER will have mused on what could be done with a driver from the prominences one encounters on the ridges and tops. Potential tees and greens get noticed, even the odd bunker or water hazard. It is not just whimsy: I have considered the practicalities of carting a club uphill. Usually the fact that my driver cost £100 wins out; also — it doesn’t really stow in the old rucksack. The walking boots, by contrast, are not much of an impediment. On my stag day in May 2003 I battered a ball into Loch Lomond using an antiquated four-wood and nary a yard was lost due to the full hillwalking gear I was wearing.

Actually, the main impediment is that a well-struck golf shot can only be appreciated by a well-versed golfer. My long-suffering wife Sheila has been dragged to four British Opens and sundry games of mine and has yet to pick up a ball in flight. Imagine knocking one for 300 yards off Lord Berkeley’s Seat only for your cagouled companion to ask “Did you hit it?”

Thus we come to the Ed’s latest commission. Golf at altitude. The world’s (or at least the USA’s) golfers were about to descend upon the Gallery Golf Club at Dove Mountain Arizona for the World Golf Championships-Accenture Match Play Championship. What had caught the Ed’s eye was that Gallery stands 836 metres above sea level and thus all sorts of freakish effects would be invoked. The same club might be travelling an extra ten or 20 metres due to the 10% reduction in air density. (As an aside, anyone who can be arsed Google-Earthing Dove Mountain Arizona will be shocked at the amount of water wasted to make this desert bloom like the rose.)

Let’s start by stating that sport aficionados are not known for their scientific rigour. Only the other night I heard football pundit Craig Paterson wittering on about the ball picking up speed off the wet turf, and we know without him telling us that he believes in the centre-forward’s “ability to hover”. Sporting pundits love extremes: home advantage has to be crucial, managers have to be inspirational and missed penalties in a European final have to accompany you to your dying day. So when a golf hack starts on about altitude effects, my instinct is to cynicism. However, it should be easily checked — it’s only Newtonian physics after all.

A student of mine — no stranger to Newton’s work — once asked why golfers didn’t hit off a one-metre-high tee and use something like a baseball bat to loft the ball at 45°. Laughable you may think, but Scott Hanvey, like me, had spent inordinate amounts of time solving the equations of motion in a vacuum. In that world, a nine-degree driver would only go 100 metres even if struck by Bubba Watson himself. Give Bubba some spin and some real air and we are soon up to 230 metres on the fly — the distance until first bounce.

So, will a golf ball go further at altitude? Well, spin is a big deal in golf because it produces lift — a non-spinning golf ball hardly travels — and the spin effect is dependent on air density. Air is less dense at altitude, therefore less lift, therefore less distance. But then there is drag. There is less drag at altitude, so the ball goes further. We have two competing effects — less drag lengthening flight, less lift shortening it. It seems that less drag wins out at modest altitudes and the ball does indeed go further overall with a flatter trajectory and more run.

How do I know all this? Once I managed to find a web page with all the necessary equations of motion and lift and drag coefficients, it took only a matter of a few hours to embed them all in Excel and to churn out the data you are about to see.

The highest golf course in the UK is West Monmouthshire, which clocks in at 457m. Apparently it boasts “spectacular views over the Gwent, Powys and Monmouthshire countryside”, although they make the mistake of showing said views on their website. Sweeping flat horizons, really. Would 457m produce any measurable effect on the golf? Air pressure is pretty linear with altitude and would drop from 1.225kg per cubic metre at sea level to about 1.15. Plug that into the lift and drag factors and we find that whereas at sea level Bubba is flying the ball 234 metres, should he ever drag his trolley round West Monmouthshire he’d be flying it 237 metres.

The highest golf course in Scotland claims to be Braemar at 346m. Air pressure would be 1.17kg per cubic metre. Needless to say the views here — Ben Avon etc — are considerably better than the rather tame Welsh-Albion ones. At Braemar, Bubba would fly the ball 236 metres. Not much difference you may think, but the flatter trajectory would give him some extra roll — even I can’t be bothered trying to calculate that. (Can I just say at this point that I have played Ballater, height 201m. Maybe all this explains my having overhit every green that day.)

So finally we come to Dove Mountain Arizona. We know that the Yanks like to exaggerate. I remember being told before skiing in Colorado that I would virtually fall over from the altitude, despite having been higher many times in the Alps. It turns out that Bubba flies it 239 metres in Arizona. So we have a maximum difference of five metres from sea level, with a bit of extra roll. I may for my own amusement go and find out if the more lofted clubs with their extra height show bigger discrepancies, but at the moment it is looking as if some of the differences are hype.

This being TAC, we need to add a couple of outliers. Everest, should they ever build a golf course there (it’s coming, surely — Ed.), will show a massive difference in trajectory with the driven ball only reaching 11m at apogee compared with 20m or so at sea level. But again the lift/drag opposition brings the ball home at about the same range: 235 metres. Amazing. It is as if the golfing gods are creating a level playing-field all over the world. (This assumes the summit of Everest to be a Ben Avon-style plateau rather than falling away somewhat steeply on all sides.)

Go to the moon however and it is a different story. Al Shepard has of course done this, in 1971 in the Fra Mauro Highlands. He hit an adapted Wilson six-iron one-handed while wearing a spacesuit and it went “miles and miles and miles”. At least that’s that he says on the clip: it was later revised to a couple of hundred metres. Stick Bubba Watson on the moon, however, with its vacuum and low gravity, and we finally see a difference. A whopping 1127 metres is the carry.

Perkin Warbeck (currently playing off 9, and with 124 Munros sitting snugly alongside the 14 clubs in his bag)

Next issue: Would Murali’s doosra turn more sharply on Kangchenjunga?