The VOR Visualised (as a lighthouse)

Last night, I watched the recorded video session of TWiT.tv network podcast, "Maxwell's House" (which is currently undergoing a slow redevelopment along strictly aviation lines).

The topic for the episode (74) was aviation navigation. Ray Maxwell tried to explain how a VOR beacon worked using a visual metaphor. I found his explanation a bit confusing in the moment, but after re-listening today, I now have his visual idea burned into my head, and it's so elegant that I now just have to write it out!

Ray kept expanding the acronym as visual omnirange, but VOR actually stands for VHF Omnirange. However, a search of the interwebs revealed quite a few aviation authorities who use the word, visual, as the first word encoded by the acronym, strangely, as the signal is entirely radio.

I suppose they're meaning "visual" in the sense that interpreting the signal in the cockpit for navigation is normally done by visual reference to an instrument (In the way way back, there were aural navaids that depended on your listening to a certain formatted sound for changes to determine your location in relation to the signal).

A VOR is an improved radio beacon which, by the way of it's construction, permits the user receiving its signals to determine with great precision their exact bearing from the beacon's perspective (called a radial in the parlance).

Before VORs, most radio navaids were NDBs (non-directional beacons). So called because they provide no directional cues. They are simple AM stations. An ADF (automatic direction finder) receiver in your aircraft (or boat/ship, they were also commonly used for coastal navigation at sea) used a directional antenna to localize the NDB, causing a pointer on your aircraft instrument to literally point to the direction from which its signal was strongest (presumably co-incident with the station's transmitting antenna...but this is radio).

Because an NDB's signal can tell you nothing about what direction you happen to be from the station, it's use for fixing your position is less accurate. Its direction from your perspective must be estimated with respect to a compass reading and the ability of your ADF equipment to precisely pinpoint the azimuth of the strongest signal.

To get a sense of how this might not be the most accurate thing, take a handheld AM radio (its internal bar antenna is directional) and swivel it around while listening to a station. Notice how the signal fades? Notice how the strongest signal occurs over a rather wide span of arc?

With a compass, you can compute a compass bearing to the NDB. And with such a reading from two NDBs, you can plot a position fix, and thereby know where you are!

Unfortunately, accuracy is limited by your compass and ADF equipment. Magnetic variation is also a factor, possibly a major one, because it varies with location. When you measure your compass bearing to two NDBs, it's with respect to the magnetic variation at your location, which cannot be known precisely because you don't yet know your location.

This is its own interesting problem to think about, but suffice it to say that if you're following a constant compass track toward or away from an NDB, the varying magnetic variation along your route will cause this line of constant bearing to be curvy, perhaps significantly so in areas on sectional charts called out with special warnings about magnetic disturbances.

With VORs, the variation programmed into the station will be the same or often similar to the actual variation at the station's location. It actually doesn't matter because the programmed variation is depicted on your chart, evidenced by the differing cant of the north-arrow for different VOR stations. Since the unique signal of a VOR lets you determine in what direction you lie with respect to that station, you can use those values to much more precisely plot your location when you take readings from two or more stations. You don't need to take magnetic variation into account (in fact you don't even need a compass) because the bearing being determined is referenced from the station, where the variation is known, to you. Not the reverse, where the variation is not known.

The way a VOR does this is where the novelty of Ray Maxwell's description comes in, re-imagined now by me into hopefully clearer terms. This is so cool, and so simple, it blew my mind!

Imagine a VOR station, not as a radio beacon, but as a lighthouse. It has a bright white rotating beacon, which emits a powerful beam in a single direction and rotates at a constant speed, say one RPM, sweeping clockwise when viewed from above. Now, imagine that as the beam rotates through north, a red beacon on top of the lighthouse flashes at the instant the rotating beam hit 360 degrees.

If you were standing due north from this lighthouse, staring south back at it, you would see the white beam rotate past you giving you a flash of white as it hit 360 degrees. You would also see the red beacon above flash at the same instant. Now, the steady white beacon is still rotating, one RPM, or in other words, six degrees per second.

If you were now at some random location nearby the lighthouse, knowing its configuration as we do, once you sighted the beacon on the horizon, you would be able to quickly determine your location relative to the beacon by timing the appearance of the red and white flashes. Start your stopwatch when you see the red beacon flash. Stop timing when you see the steady white rotating beacon sweep past you. Then, your location relative to the lighthouse is:

time	from the lighthouse
simultaneous red+white flash	due north
white 15 seconds later	due east
white 30 seconds later	due south
white 37.5 seconds later	due southwest

For each additional second between the red and white flashes, you are located someplace along a bearing from the lighthouse, 6 additional degrees from the north reference. These bearings radiating away from the station are then known as radials. If you know the timing between the red and white pulses, you know which radial you are on.

This can be plotted accurately on your chart because the depiction includes the station's north reference. You can draw a line away from the station corresponding to the radial you observed. Repeat this with a second station and you have an accurate position that's immune to the effects of compass accuracy and magnetic variation!

As you travel along, by keeping the radial indicated by a given station constant, you are assured to be travelling along that radial, either toward or away from the station.

For the real VORs, the signals are radio, not light. The signal analogous to our flashing red timing beacon is broadcast omnidirectionally, while the signal analogous to our rotating white beacon is a tight directional radio beam, rotating through a full circle, just as our light beacon was. On old VORs, there is a directional antenna inside the VOR housing that physically rotates. Newer VOR stations have a circular array of antennas that are electrically modulated to create a tight, directionally focused radio beam which rotates without moving parts.

Simplifying slightly, these two VOR radio signals are modulated differently so the VOR receiver in your airplane can tell them apart. The receiver handles comparing the two signals to determine their timing with respect to each other, as we did by looking at the lighthouse in our example. And in this way the receiver knows which radial it is located on from the VOR it is receiving. Because of this fact, no special directionally tunable reception antenna is required for a VOR receiver, unlike ADF. This makes VOR navaids more accurate, and the airborne equipment is simpler and cheaper.

A technical discussion is available on Wikipedia, but this simple and intuitive visual analogy just made so much sense to me that I decided I had to share it here.

On doppler VORs, or D-VORs, I think both radio signals are omnidirectional, but the phase of the modulation of the "rotating" signal varies around the circle of antenna elements, creating a unique phase relationship between the two signals as one travels around the circumference of the station. There is no directional beam, but the VOR receiver computes the radial you're on by referring to this unique phase relationship between the signals that couldn't be received along any other radial from the station. I think... The Wikipedia article started to get math heavy at that point.

To my knowledge, our visual lighthouse analogy for VOR operation has never actually been used for real navigation by nighttime visual reference, but it could be. An additional light signal would be required to flash out an identifier signal, so you could determine which lighthouse-VOR you were looking at on your chart.

An audio morse-code identifier is part of a radio VOR's signal, to which you listen after tuning the station to confirm the signals you are receiving are from the station you wanted (and these days, more advanced avionics monitor this morse ID code for you and present the three or four letter code on your navigation display, saving you the trouble).

The lighthouse example did remind me of my coastal navigation days, where different signal lights and lighthouses do indeed flash various ID codes at you, to which you can reference on your nautical charts to determine which light you're looking at. But in this case, the signal lights are the visual equivalents of NDBs. The flash pattern contains no embedded directional signals. Taking a bearing to the light from the pelorus, and along with the ship's heading you can draw lines of position on your chart radiating from lights sighted, a process essentially the same as using an ADF with NDBs in the air, with the same accuracy pitfalls from compass and magnetic variation variances.

Later in life I observed that the visual airport beacons for different airports in my local area tended to rotate at significantly different speeds. From my earlier nautical light knowledge, I assumed that aeronautical charts might have timing data for each airport's beacons so that one might confirm the identity of the field they have in sight at night. Alas, it's just a coincidence. The timing is crudely specified, a slower range of flash rates for airports, a faster range for heliports. There are also color codes in the flashes which serve to differentiate civil, military, land, water, and emergency services aerodromes, but specific aerodromes are not positively identified by this signal.

I should note that terrestrial radionavigation aids are effectively obsolete now by the extremely accurate, increasingly cheap, and highly available satellite navigation systems. It's expected that these satellite constellations will become more numerous and feature rich, increasing the likelihood of guaranteed signal access for civil navigation uses. It's practically this way already for lower accuracy positioning, but for the most precise uses (i.e. for instrument landing systems and automated landing) there are periods of unsuitability due to the configuration of the orbits of the satellites, or maintenance of the error correction mechanisms (check RAIM and WAAS). Most of the time though, you can get accuracies of a few feet, anywhere with a decent view of the sky. That's better than any terrestrial system.

The FAA desires to shut down most VOR stations as soon as the GPS system is deemed available and precise enough, as they are expensive to maintain. But if the decommissioning of LORAN is any guide, we'll probably have access to VOR signals for some years to come.

In the event of a major space storm disabling a good deal of orbiting satellites (plausible, but not very likely), access to such terrestrial systems would become highly desired again.

Most VORs and NDBs are used for navigating from one station to another, or along specific VOR radials. The better GPS based systems allow one to specify any GPS waypoint for use as a "virtual VOR", whereby traditional VOR-style course-deviation-indication (CDI) and omnibearing-selector (OBS) controls allow you to precisely fly a given course to or from the waypoint. Such functions can be helpful when given random holding fixes to fly, for example. Today, however, much of the emphasis is on database navigation. Where any and all possible waypoints and procedures for flying between them are encoded in a database stored inside the GPS navigator, and you fly by querying the database for the route between desired waypoints and procedures for instrument approach. The navigator, if coupled to an autopilot, can then navigate the aircraft all the way through the approach with little for you to do but monitor and assure yourself it's going where you expected and intended.

With the newest "highway in the sky" features available as part of the synthetic vision systems of avionics like Garmin's G1000, flying complex procedures with curving approach and departure paths and tight glidepath and obstacle restrictions is as easy and ubiquitous as using the flight controls to guide the little computer airplane through the series of hoops on the video display. It's becoming literally as easy as a video game. Remember Pilotwings for the SuperNES? Or Independence War on the PC? Or the dropship sequence from Aliens on the C64? Like that.

You just have to be sure you programmed your navigator correctly before you start out!

This is one area where general aviation has advanced (temporarily) ahead of the airlines. Most airliners do not have avionics as advanced as a G1000 system with synthetic vision. A rare instance were the smaller guys were able to be more nimble, thanks to ever cheapening computer technology. The airlines are catching up, however, and G1000-type systems with synthetic vision are going now into business jets, with similarly featured systems planned for the latest iterations out of Boeing and Airbus.

That's all, thanks for reading! Hope you had fun!

The mystery of N10TM

So, I'm out driving to get groceries here in the south-end of Grand Forks, ND, and down the avenue comes this heavy pickup truck with a kingpin thingy to haul this semi-sized flatbed trailer. What's on the trailer immediately gets my attention, I mean, you don't just see stuff like this every day. It's a wrecked airplane! And by the looks, it had been a really nice medium GA airplane.

I see the trailer turn into the parking lot of the Super One strip mall area. It appears the driver's going for a break or pizza at the Pizza Hut or something. I cross over the lanes and follow him into the parking lot and then come to a standoff distance alongside, gawking over the awesomeness of the man's cargo.

He jumps out of the heavy pickup, and heads for the Hut. I want a picture, but I don't have a camera on me, but it appears I'll have some time, so I complete my grocery shopping and return 30 minutes later with a camera.

I arrive just in time to meet the driver as he's emerging from the Hut. He proceeds to check the straps securing the load of wrecked airplane: mangled engine pods forward, mostly intact fuselage in the middle, and wings, bit of gear, and empennage at the back of the trailer.


I quickly go for my camera and approach, snapping a few shots on what's about the end of my memory card (still nearly full after a wedding shoot).

The driver notes my interest and I engage him with questions. He's hauling salvage. This airplane wrecked in 2007. Ran out of fuel and crashed into a truck in a parking lot almost exactly like the one we were in now. I didn't recognize the model immediately. The driver tells me it's a King Air, and I mentally note from the three rows of cabin windows that it must be a C90 King Air. I note the tail number. Since it wrecked in 2007, the NTSB probably has an accident report up on it by now.

The driver shows me pictures of the accident scene. I note to him how the cabin is squished a bit under the nose, but is otherwise fully intact and ask if there were serious injuries. "Yes," he replied, "pilot and three passengers got thrown around pretty bad."


"He ran 'er out of fuel," the driver explained.

"Wow, do you know how high he was when he ran out, I mean, was he on approach to an airport?", I asked.

"Oh God no."

I gave a grimace in acknowledgment. The driver offered all he knew, which was that he appeared to run out of fuel at a bad moment, and didn't seem to have the height necessary to execute any better a forced landing, like on an airport or away from people and cars and buildings. Considering this, some unoccupied wrecked cars and no fatalities seemed to be a decent outcome to a bad situation.

He explains that the stalling speed of this airplane is something like 90 mph, so coming into the parking lot would be like wrecking your car at full interstate speed.

He's preparing to depart, so I quickly walk around a shoot a couple more pictures, filling the memory card and hoping for the best, and then thank him and allow him to be on his way. This was a privilege. The airplane crashed in Chattanooga, TN and sat around there, and now was sold for scrap and though I didn't catch the final destination, I got a little insight into the life cycle of downed airplanes.

So, curious to know more about the circumstances, once home again I plug the tail number into the NTSB's database and get the accident report.

If you're reading this, skim the report and come back. Okay? Now it felt to me that the NTSB didn't care all that much about this incident, doing a phone interview of the pilot. It doesn't appear anyone else was too much involved. An FAA inspector confirmed the absence of fuel in the wings, but the pilot's story begs some questions in my mind:

He reported gauge readings between FULL and 3/4 and estimated by this he had fuel for 3 hours at least, more than enough for the 1h20m flight. Now...I don't know the preflight procedures for this type of airplane, but I do know that aviators generally regard fuel quantity gauges in GA airplanes to be liars. I guess certification standards are such that they must read accurately when the fuel tanks are full, and when they are empty, but the middle indications that come during operation may mean only that the tanks are neither full, nor empty, but by how much...? Are you timing your flight? Do you have any sort of totalizer measuring fuel burned?

Well, I was almost right on my guess as to aircraft model. It was a B90, the late 1960s forerunner of the C90 which I had guessed. The changes amounted mainly to perhaps a slightly buffed engine model and longer wingspan, so I mostly nailed it.

Pulling some B90 performance specs off the internet, I see that in cruise the airplane ought to burn about 64 gallons/hour. Now if the gauge indications are anything like my car's, when the gauge reads 3/4, the actual level is more like 1/2. And having half-full tanks in this airplane at that cruise burn rate would yield something close to 3 hours cruising time. So the pilot's estimate of flying time available seems to check here.

To my total surprise, Flightaware.com still had the accident flight's history in its database! Humorously, it listed the destination as Chattanooga (it was really Georgetown, KY), and that the airplane had "arrived." Yeah, I'll say that's true. One way or another, they always arrive. This data features prominently later.

According to the report, the airplane had reached its cruise altitude of FL210 when the pilot noticed that two of the four gauges suddenly read practically empty. Reassessing his situation, he reported to the NTSB he estimated having about 50 gallons of fuel aboard at this point, and opted to make a diversion to Chattanooga.

Okay...no emergency. It's quite strange that the left side gauges went from nearly FULL to empty in just 22 minutes, but...maybe there's some sort of electrical fault with the gauges. Who knows?

Do I dare to call shenanigans on the pilot, and on the NTSB for not making this clear in its report? Not being a real-world pilot myself, just an enthusiast (for now?), I'm about to get pretty presumptuous. But, this is the internet after all.

Again, according to the data on the B90 from the internet, in cruise power the airplane will burn approximately 64 gallons per hour. So that means with 50 gallons estimated remaining he ought to be able to continue up there in cruise for another 45 minutes at about 200 knots.

According to the report, it's with this estimate in mind that our dear pilot elects to prudently divert to Chattanooga, about 45 nautical miles away. If he stays at altitude and cruise power, he'll get there inside of 14 minutes, leaving 30 minutes to descend and execute an approach (at cruise power, which he wouldn't use of course, so he may have even more absolute reserve).


But instead, he's out of gas and crash-landing on some guy's pickup in the middle of a strip mall parking lot! How could this be?

Well now I turn to the Flightaware data for N10TM on the 19SEP07 incident flight. Flightaware gets its data on aircraft position from the same data network air traffic controllers use to monitor the skies. Radar sites get controllers the raw data. Their terminals process it for their needs. After that it goes into a network to which other entities may acquire special access for fleet monitoring, ground service planning, traveller updating, etc.

From this data, I noted that the airplane never reached its cruising altitude, and entered a turn toward Chattanooga near the apex of its flight, around 19600 feet. From this point the flight proceeded more or less direct to the field in a continuous descent. The descent rate and airspeed appeared to be not always stabilized, but averaged 1300 feet/minute at 180 knots groundspeed. That's enough height and speed to go 45 nm, and the straight line distance between reported radar points was in fact 45.6 nm. The field was about .6 miles further along.

It appears from internet sources that a best glide speed isn't published in the POH for the B90, but one source inferred one from data published for a C90 and listed it as about 125 knots. I don't know what sort of descent rate that would translate into, but 1300 fpm doesn't seem out of the ballpark to me.

Now in his report to investigators, he'd estimated having 50 gallons aboard about the time he noticed the two empty gauges and elected to divert. In descent, the power is normally pulled back somewhat, in some cases (certainly for jets, but maybe less so for turboprops like this) all the way to idle. This allows essentially a gliding descent and initial approach, making up for the excess fuel used on the climb to altitude by now using very little on the descent back down, certainly much less than that used on cruise. So the picture should still be okay.

Somewhere in this descent he reported he ran out, and too late to do anything but strap down tight and pancake on the nice pickup truck, like it was a last minute happenstance. I don't buy it. If his estimate had been right, he ought to have ample fuel to make a normal approach and landing. Maybe even enough to afford one go-around if he messed up flying his approach path. How could this be?

In my view, simple: he's shading the truth to investigators. He doesn't appear to have made it to cruising altitude at all (about 1400 feet under it). At the time he decided to divert he was probably already out of gas or very close to it. He didn't methodically consider and then execute a diversion while still carrying at least some reserve of fuel. He hastily and with OK, but somewhat less than perfect form beat a hasty retreat to the nearest suitable airport that came to his mind.

He turned direct from his climb heading, to the airport at Chattanooga, and didn't even try to line up for an approach to the closest runway end. He appeared to be trying to make a B-line for the field and I think he hoped to kick the airplane 'round at the last second to line up and touchdown on the runway there.

Only, he didn't even make it that far. His groundspeed and descent rate suggest a path that might not be unreasonable to expect from a gliding aircraft of this type. Surely if he were still powered, as he suggests when he elected to divert, I would expect he'd want to keep his altitude until he was certain of making his diversion airport. This would mean a delayed descent by some amount.

Even in normal circumstances, one wouldn't choose to make a continuous descent from the point he had, as obviously it's still too far out, and the data doesn't suggest any level flying segment. I think under normal circumstances one might plan to be in the airport vicinity at around 3000 feet, so as to have some flexibility to set up a normal approach.

In my armchair cockpit, I think I'd keep at cruise altitude to benefit from the fact that my fuel burn would be more efficient up there. I'd start down only if an approach and landing was assured, and for utmost margin, I might even fly until overhead the field at cruise altitude, and then enter a descending holding pattern above the field and inbound to a holding fix lined up with the landing runway. You can be certain of gliding in, in that situation.

None of this happened, and I believe that's because he'd already lost power. And while the outcome was a fair one for he and his passengers, he got lucky that no one was injured or killed on the ground. The track data had him near a golf course just before the parking lot. That might have been a safer forced landing site. I think he was fixated on just trying desperately to make it to that field.

The NTSB might have been wise to this pilot though. They didn't seem to care about the obvious possibility that there might have been a gauge problem when the gauges seem to be showing close to FULL, or maybe some sort of fuel leak. A conservative assumption of 1/2 full tanks at this stage would, as the pilot mentions, rightly given him at least 3 hours of cruise flight. Yet only 22 minutes after takeoff, he's noticed two gauges reading about zero (it's not reported what the other gauges read). And fifteen minutes and 45.6 nm later, he's glided that bird to the deck. I'd say his gauges were all probably reading closer to empty all along.