There’s no shortage of analysts at the banks and brokerage houses who claim expertise on Apple (AAPL) and publish earnings estimates in advance of the company’s quarterly reports.

But for the past year and a half, the most accurate predictions — by far — were the ones made by Financial Alchemist‘s Turley Muller, an occasional blogger and amateur analyst who has beaten the pros at their own game for six quarters in a row. (See here for Q2’s comparisons.)

So when Muller talks, we listen.

What kind of numbers is he expecting to hear when Apple reports its Q3 earnings on July 20? For the most part, he’s more bullish than the Street, although not as much this quarter as he usually is. The big payoff, he says, will come in Q4.

His bottom line for Q3:

• Gross revenue: $15.15 billion ($590 million higher than consensus*)
• Earnings per share: $3.35 ($0.29 higher)
• iPhone unit sales: 7.8 million (nearly 550,000 lower)
• iPod unit sales: 9.9 million (94,000 higher)
• Macintosh unit sales: 3.23 million (23,300 higher)
• iPad unit sales: 3.38 million (nearly 320,000 higher)
• Gross margin: 38.9% (nearly .3 points higher)

*Consensus for revenue and EPS are from Thomson Financial’s polling; unit sales and gross margin come from our own poll of Wall Street analysts.

Pressed for an explanation, Muller is terse:

“Revenue increases considerably from Mac strength and iPad introduction,” he writes. “Earnings growth is slightly tempered by lower gross margin. Quarter numbers might not appear to be as solid as reality given constraints in iPhone & iPad supply, plus temporary GM headwinds.”

Among the factors he sees as pushing back Apple’s gross margins, which were 41.7% in Q2, to below 39% in Q3:

• Unfavorable foreign exchange due to the dollar’s strength
• Unusually low (for Apple) margins on the iPad, perhaps as low as 30%
• Launch costs for the new iPhones and close-out costs for the older models
• Softer gross margins on the Mac due to educational discounts and transition costs for the new MacBooks

As for unit sales, Muller believes the shipments Apple reports for the iPhone and iPad will be considerably lower than actual sell-through. “Apple entered the quarter with 2.7 million units of channel inventory, and exited with only 3 days of iPhone 4 and new 3GS sales,” he writes. “Unit sales going forward should be massive to meet demand and fill channel. iPad production capacity has been ramping to meet lingering demand as well as to fulfill large corporate orders (I hear are out there).”

“It will be hard to read a whole lot from this quarter due to all the moving parts (drawdowns, launches, supply shortages etc.),” he concludes. “However, it sets Q4 to be a MASSIVE quarter.”

See also:

• Apple’s blow-out quarter: The bloggers called it. The Street blew it.
• Apple’s Q1 2010 earnings: The Street’s big miss
• Apple earnings: How the analysts got it so wrong

[Follow Philip Elmer-DeWitt on Twitter @philiped]