Right now, the world is learning that two dozen ships, nine aircraft and even a few repurposed satellites are not enough to find an airplane – or possibly pieces of an airplane – in a vast swath of ocean. While it may seem obvious, based on what we read in the Twitterverse it probably bears repeating: finding missing aircraft is hard, even when circumstances are ideal. And in the case of Malaysian Airlines flight MH370, there are lot of factors that make the search conditions less than ideal.
Apart from technology and math, no matter how good your sensors are, looking for visual, physical evidence can be very tricky, even for skilled searchers in good weather at close range. Take a look at this picture below: there’s snow, a garbage dump and an aircraft wreck. Would you pick it out bouncing up and down and moving at 90 knots? The answer is at the bottom…
Search planners and air-branch directors (and in my other, non-Aviation Week life I happen to be one) rely on mathematical innovations developed during World War II and refined in recent decades to tailor their search efforts. Applying modern Search Theory principles prevents making bad intuitive choices, minimizes the “Helter Skelter” or “Frantic Effort” phase and generally helps the search planner make the absolute best use of the resources available.
The idea is simple: maximize the statistical likelihood of finding what you’re looking for in the minimum amount of time and with limited resources.
Using math to find things isn’t new. In the past, searchers also calculated a few metrics to understand to what degree their target was contained (“Do you know where your target is?”) and whether if their target was there would they find it (“How well is the area being searched and how good are your sensors?”). These correspond to Probability of Containment (POC) and Probability of Detection (POD).
These are good metrics, but in 1980 researcher B.O. Koopman showed that what is needed is an optimization function. Searching where you have a high POD alone is like searching in your living room for the mobile phone you dropped outside because the light is better. And a high POC is generally useless unless you have unlimited search resources and 100% perfect sensors. Enter Koopman’s insight to apply mathematics to yield a high POS – Probability of Success. If you were to graph the ideal POS, it would be at the intersection of the inversely correlating curves of POD and POC. In fact, the deceptively simple formula is POD X POC = POS.
Now let’s throw in some real-world factors to degrade your calculations.
A 2009 NASA study showed that about half of missing aircraft with radar data available were found within a space less than a mile of the last radar return. What’s the last radar return for MH370?
In the absence of a radar return, about 50% of aircraft were found within a 4.5 naut. mi. offset of the planned route and within the first 63% of the aircraft’s intended route length. Was MH370 flying on its planned route?
How about pilot intentions? Weather? How about the drift of the current and what search planners refer to as “leeway divergence,” the observation that leeway for objects on the water can be up to 40 degrees off the downwind direction? In recent days we’ve discovered LOTS of things floating in the ocean that had nothing to do with MH370.
And those are just the factors involved in assessing POC. To work POD, you need to account for the size of the area to be searched (which is why using radar returns to narrow the search contours is so important), the search speed of your searching tool (airplane, helicopter, ship), the distance between the search tracks of the ship or airplane doing the search, how much time the searchers spend getting on-scene and how much time they can spend actually searching, and the number of resources (airplanes, helicopters, ships) you have to work with.
All of these factors interrelate, and can further diminish your chances of success. The basic formula is Area = Search Speed X Spacing X Time X Number of Resources. Algebra lets you solve for any one of those variables if you know the others.
Another formula we use is Coverage, which measures search quality by comparing search capability (or sweep width) to track spacing, where C = Width/spacing, or, to keep it conceptual, effective coverage is equal to your effort divided by the area over which you’re expending it.
These formulas all get calculated and rolled up to create better POD and POC values, which then yield POS. And after each search sortie, actual results are plugged in to the formula to see how well or poorly the search went. Those figures help make the sorties in the next operational period a little better. And by better we typically mean by a few percentage points; the needle only moves a little.
And that’s why finding an airplane, or potentially many pieces of it, in a vast ocean is hard. Helicopters have limited range, sensors don’t have perfect detection, ships move slowly, radar tracks in this case have been all over the map, the actual flight path was unknown, the search box is vast and includes at least eight political jurisdictions, oceans already contain a lot of junk and debris can move around in the current.
As for the eye test at the top of the post? If you looked at the picture before skipping down to the bottom for the answer, good for you! The wreck is the bigger white blob in the foreground. The blob at the top is the garbage dump. If you had flown over it 24 hours earlier, you would have seen nothing but snow. Welcome to my world.