Padraig Harrington acknowledges the crowd after his closing eagle.Vijay Singh has Tiger Woods and Rory McIlroy breathing down his neck but Padraig Harrington has even more pressing problems despite shooting a seven under par 65 in the second round of the BMW Championship at Crooked Stick.

Ranked 58th in the FedEx Cup standings and desperate for a win that would move him back into the world’s top 50, the Dubliner closed with a magnificent eagle three at the ninth yet is still projected to miss out on the Tour Championship finale for the third year in a row.

Depending on what others do, Harrington will need at least a top five finish on Sunday night to have any chance of making the top 30 in the standings who will compete for the $10m FedEx Cup bonus at East Lake in two weeks’ time.

And while he has flattered to deceive many times over the past four winless years on the world’s big tours, Harrington fans have every reason to believe that he can enter the winner’s circle again soon after watching him move up to a projected 40th in the standings on Friday.

Doing it in Indiana is going to require something extra special from the 41-year old Dubliner, who is four shots behind leader Singh (65-66) and tied for ninth on nine under par with Graeme McDowell, who bounced back from his two-stroke penalty in the first round with a fine 67.

Like McDowell, Harrington doesn’t have to win to make it to the Tour Championship, but a first PGA Tour victory for more than four years would be the perfect riposte to European Ryder Cup skipper José María Olázabal, who opted not to give him a wildcard for the matches in Chicago later this month.

Singh leads by a shot from Ryan Moore (66), Woods (67) and McIlroy (68), with the “Big Two” forced to dig deep and “grind” to remain on course for what could be a fourth win for either of them this season.

Harrington’s putting inside five feet has been his Achilles’ heel this year but he holed a few bombs on Friday and missed just one short effort to rekindle his hopes of a Tour Championship appearance.

Starting on the back nine on a soft course where placing was in operation, he holed a 25 footer for birdie at the 12th and a 10 footer at the next to move quickly to four under par.

After chipping in from 20 feet from the fringe of the 17th, he hit a 160-yard approach to just four feet at the 18th to turn in 32, then made it four birdies in a row and six in eight holes when he picked up further shots at the first and second with putts of 13 and 16 feet respectively.

A bunkered tee shot at the fourth, where he missed from 10 feet for par, cost him his first dropped shot of the day. And while he followed a birdie from 11 feet at the 621 yard fifth by missing from less than five feet for par at the 201-yard sixth, he made amends with that eagle at the last.

Ranked ninth for putts per round after taking just 25 on Friday, he is still 26th in the strokes gained putting category and will need to putt the lights out to keep that top five finish in his sights.

Yet it was ominous to that he picked up just two shots on a struggling Woods and only three on McIlroy, who had an eagle, six birdies and four bogeys in his 68 (his 14th sub-70 effort in his last 18 rounds).

“It wasn’t as good a day as yesterday,” McIlroy said.  “I didn’t hit the ball quite as well, but scored well and did enough to go out there and shoot another good number and set myself up in a good position going into the weekend.  

“You know, as I said, I could have hit the ball a little better from tee to green, but still got it around in four‑under, so pretty happy.

“You shoot a couple of decent rounds, you’re just going to get lapped.  You know you’ve got to go out there and make birdies, and I suppose that’s just your mindset from the start.  That’s just the way it is, and you have to go out there and try to do that.”

Woods birdied three of the four par-fives before picking up shots at the 17th and 18th for a bogey free 67 and again insisted the was playing with his B game.

“I fought hard,” Woods said. “I didn’t have much today.  Swing wasn’t quite there, and I was just grinding along here and just trying to get to double digits under par.  

“That was the goal, the way I was hitting it.  I was just slapping it everywhere, and somehow just grind away and find a way to shoot something where I was in double digits by the end of the day, and I just happened to get a couple more.”

As for McDowell, the Ulsterman missed just one green and made just one bogey in a 67 that gives him a fighting chance of making it to Atlanta.

Three birdies in his first five holes went a long way towards making up for the two-stroke penalty he incurred on Thursday for touching a loose impediment in a bunker on his final hole of the day.

He said: “Of course I would love the two shots back, but they’re gone now, and I managed to come out and make a couple early birdies this morning to quickly negate the two that I had to hand back in the scorer’s hut last night.  

“It’s a pretty fast way to drop two shots.  But I moved on nicely from that last night and hit the ball really, really well again today.  I think I hit 17 greens.  It was good ball‑striking today, gave myself some chances.  Let’s be honest, you’ve got to keep going low this weekend.  If the storm comes in and wets these fairways again, the ball is going to be in our hand all weekend.”

McDowell admitted that the two-stroke penalty was entirely his own fault for not knowing the rule and wondered aloud if the microscopic examination of every shot was not taking things too far.

“I’ve got to admit I didn’t know that rule.  I wouldn’t say I was trying to avoid brushing that twig.  I wasn’t purposely trying to avoid it because I honestly didn’t think there was a problem with touching it.  

“I’ve never been in that position before in a trap where I’ve had something obscuring my address position.  It’s a very unusual scenario, and I didn’t know the rule, and it’s a very costly lesson unfortunately.

“You know, I don’t see why you shouldn’t be allowed to move loose impediments in a prepared hazard.  The surface is supposed to be prepared for everyone, and I guess that was probably my thought process was loose impediment in a bunker, yeah, it’s natural, I know I can’t touch it, as in remove it, but now I know I can’t touch it with my club.  So tough one.  Tough rule.

“We’ve seen this happen a few times now this year, Carl Pettersson getting stung at Kiawah a few weeks ago.  With all those slo‑mo high def cameras, we’re seeing every molecule, every small, tiny movement of stuff, and guys are getting stung now.

“Obviously I called that one on myself yesterday because I knew as soon as I touched it that perhaps there was a problem, even though, like I say, I wasn’t giving it the respect I needed to give it.  I didn’t know the rule, and I know it now.”

McDowell was undone by TV evidence in the BMW PGA at Wentworth in May, though he again had an inkling that he might have a problem.

“The one at Wentworth was very unusual in that I hadn’t even got within eight feet of my golf ball and I managed to move it.  The one at Wentworth was very, very unusual.  This one was worse in that you should know these things.  Like I say, my caddie told me not to touch it, and I thought he meant don’t remove it, but he meant don’t touch it with your club, either, you doughnut.”

He went on to explain why most golfers call shots on themselves. In his case, it’s about integrity and, hopefully, some good karma further down the road.

“Golf is a very self‑policing game.  We’re dropping the ball, we’re marking the ball, we’re doing things where if you were that way inclined, you could gain an advantage, if that’s the way you want to play this game.  

“You know, I guess I’m a believer in sort of what goes around comes around in this game, and you’ve got to self‑police it.  You’ve got to just play a bit of honesty because if you don’t, this game will get you in the end.  There’s no doubt, I mean, guys call stuff on themselves, and it says a lot about what this game is all about.  

“It’s hard, it’s painful at times, but there’s no doubt that the featured pairings every week are under a little bit more scrutiny.  Like I say, with these slo‑mo high def cameras, you can see every blade of grass moving.

“It just hurts when a guy is not in any shape or form trying to gain an advantage, and like me yesterday, I brushed that leaf, and I get a two‑shotter.  I haven’t gained an advantage, I haven’t improved my lie, my ball is still in exactly the same scenario, I believe, has not moved, but yet I’ve got to add two to my scorecard.  

“It’s the rules, and most of them are there for our protection.  Some of them are a little fiddly and a little interesting, and I’m sure as these things keep happening, the referee said to me yesterday, we need to change that rule.  

“No good to me right now, but I get it.  I get it.  It’s one of those things, and thankfully, like I say, I shrugged it off and played as well as I did this morning.”