Haiti: "forklift drivers without borders" doesn't sound so good on TV

So, are the Americans really "prioritising foreign soldiers over aid" in Haiti? Thankfully, the national press tried to answer this question with facts. Well, not really. Spencer Ackerman and Laura Rozen actually asked intelligent questions rather than the usual "Two days after the giant earthquake destroyed all port facilities, critics asked why UN aid was still taking so long to arrive in the stricken region. After all, this 70kg journalist and his 88g sat phone got through just fine...anyone been raped and speak English?" stuff.

Apparently there are about 140 air movements through Port-au-Prince daily on average, of which 50% are allocated to NGOs and the rest to US and other government aircraft. The rate reached 200 on the Sunday following the earthquake; this is despite there being no radar or radio navigation aids since the earthquake.

A logistics system is a linear production process. Computer people would prefer to think of it as a loop construct. Therefore, the total capacity is determined by throughput - by the rate at which it loops. That, in turn, is set by the slowest element of the process.

In this one, goods are being loaded on aircraft, that then take off, fly to Haiti, land, unload, take off, and return. Now, the aircraft can leave from many, many different airports, so I think we can rule out that step as being the limiting factor. For landing, the minimum separation between planes is the limiting factor; the standard 3 miles horizontal separation is a minute's flying time at 180 mph (156 knots - the approach to Heathrow is flown to 4 miles out at 160kts), and the wake-turbulence separation for a heavy aircraft like a 747 is three minutes. So the maximum separation will be four minutes or thereabouts; a lot of the aircraft being used are able to slow down much faster on final approach and some are less heavy, so it's probably somewhat less.

One aircraft every three minutes on one runway gives us 20 movements an hour. If they aren't going to pile up there, they've got to leave at the same rate, so that's 10 in, 10 out, and we'd reach 140 movements in 7 hours. Considering that the landing lights don't work and the control is visual, they can't be far off operating at capacity. But that's still not the last word.

You may be able to land a plane every three minutes, but you probably can't unload it in three minutes. And you've got to return the empties, as well; you can temporarily up the rate by using more of the movements budget for landings, but eventually this will mean you have to stop to send aircraft back. The best performance is achieved by operating at the highest average capacity. So, the slowest part of the process is probably unloading and turn-around more generally.

This brings up another issue. If we start the day with 10 aircraft arriving an hour, that then spend 3 hours on the ground, 30 aircraft will be there before the first one leaves; we'll need at least 30 parking spots.

In fact, because unloading is the most restrictive step in the process, it's optimal to always have a queue. Otherwise, there will be moments when the most scarce resource in the whole thing - a forklift truck and its driver - will be waiting for cargo to move, at which point we're operating below capacity and wasting time.

In practice, this will be the operational limiting factor; it doesn't matter if a plane has to wait to unload, but it does if the next one can't leave the runway and the next one has to go-around and divert. So, we've arrived. Our limiting factors are forklifts and parking.

The USAF air traffic controllers announced a maximum two-hour turnaround on the night after the earthquake, and further insisted that all aircraft arriving in the airfield circuit have enough fuel to go to their destinations without refuelling, there being (obviously) none to spare in Haiti.

You get 11 hours of daylight there at this time of year, and presuming that it's still visual-only, that's 12 movements an hour, six in, six out. That's about 0.25 Heathrows. With a maximum turnaround of two hours, this implies that there are 12 parking spaces available on the ramp. That should also explain what happened to that MSF flight; apparently another aircraft went technical on the ground, blew its two-hour slot, MSF had to go-around, and David Aaronovitch and Noam Chomsky were at once united in blowhardry, not for the first time.

Actually, come to think of it, you can get the NOTAMs for Port-au-Prince by going here and searching for MTPP. It turns out that an instrument flight plan is mandatory...just like at Heathrow, and they want to know how much weight, how many items of rolling stock (!), and how many passengers you have. Oh, and:

M0004/10 - QXXXX PALLETS DOWNLOAD AT MTPP WILL NOT BE RETURN TO USERS. 17 JAN 02:15 2010 UNTIL UFN. CREATED: 17 JAN 02:14 2010

In return for putting up with that, here's some logistics porn.

Major offshore petroleum discharge systems (OPDS) components are: the OPDS tanker with booster pumps and spread mooring winches; a recoverable single anchor leg mooring (SALM) to accommodate tankers of up to 70,000 deadweight tons; ship to SALM hose lines; up to 4 miles of 6-inch (internal diameter) conduit for pumping to the beach; and two BTUs to interface with the shoreside systems.

Deploying the anchor element requires counterflooding the ship onto one beam so far over that the decks are awash. Relatedly, you know a navy is serious when it calls out ugly ships manned by civilians. The French amphibious command ship Siroco is on her way; RFA Largs Bay is too, replacing this entry on the RN Blog as the UK's lead response.