More Hold Timing

I figured out my hold timing puzzle in the shower. I had made it far more complicated than I had to.

See, while I need calculus to determine the travel of the aircraft at an arbitrary time t, I don't need it at all to determine the total travel during a 180 degree turn. I am considering only the distance the aircraft moves in the direction parallel to the inbound radial; the distance along the curved track and the distance the airplane moves perpendicular to the inbound radial are not relevant for this calculation. Performing a 180 degree turn in still air, the aircraft covers zero distance in the direction parallel to the inbound radial, so I can consider that the airplane is standing still for one minute, under the influence of the wind w. Speed times time equals distance. During the one minute turn, the aircraft travels a distance in nautical miles of w/60. (The 60 is the result of multiplying by 60 and dividing by 3600, because t is in seconds and w is in knots).

With this amazing escape from the need for definite integrals, I'll consider the case where we have a headwind on the outbound leg:

If there is a headwind on the outbound leg, the aircraft finishes its turn before passing abeam the fix, so the pilot travels that distance w/60, in order to draw abeam the fix, and then starts the timer. Thus the time taken to make up that distance is irrelevant. The pilot then flies outbound for one minute, covering a ground distance of (v - w) / 60 nautical miles, where v is the true airspeed and w is the wind speed. At the other end, of the hold, the turn to inbound ends up closer to the fix than it started, so the inbound track is w/60 shorter than the outbound track. Therefore the length of the inbound straightaway on the first turn is (v - 2w) / 60, and the time required to fly it will be speed divided by distance: 60 * (w + v) / (v - 2w).

Now the case where there is a tailwind on the outbound leg:

If there is a tailwind on the outbound track, the aircraft passes abeam the fix w/60 nautical miles before wings level, so the outbound distance (v + w) / 60 is increased by w/60. The outer turn drifts the aircraft a further w/60 nautical miles from the fix, so the inbound distance is (3w + v) / 60, and the time recorded for the first inbound leg will be 60 * (v - w) / (3w + v).

Initially I thought I could consider only one wind direction, without loss of generality, because the wind velocity could be positive or negative, but that doesn't work because the procedure changes.

Honestly, while I'm in a hold I think normal thoughts like "ack, the timer didn't start," "What was my EFC time again?" and "damn, I really have to pee." I only think about this stuff on the ground.

Next time I'm on the ground, I'm going to crunch some numbers through Excel and find out which is the best procedure to determine how long to fly outbound.

Inspiration

So I'm driving home after a long day at work. I've had two strong disappointments in the last twenty-four hours. I'm tired. I've had a headache since two pm. My headset doesn't usually hurt my head, but it was bothering me today. It didn't seem to matter how I adjusted the radio, it was either too loud and gave me a headache from the noise, or too quiet and gave me a headache from straining to hear. This isn't whining, I promise. This is context.

I'm driving home, and I'm thinking about my career, wondering if I have, in Peter Principle fashion, reached the pinacle of my career. I'm considering concentrating all my energies at excelling at my current job, instead of beating my head against the next level. They are tired, headachey end-of-the-day thoughts, because deep down I know I'm good at what I do. And then a song comes on the radio.

It's a country song, one so generic that I can't even Google it, because all the lyrics are cliches. Like many country songs, the verses are a series of vignettes, in this case about various people who had every reason to give up, but didn't: the couple who had been told by the nth doctor that they couldn't conceive, the lonely single mom waitress who can't make ends meet, you get the idea. And in each case the verse ends with the revelation that the couple is already pregnant, or the regular customer she's so fond of has already bought an engagement ring in order to make his proposal. They "just don't know it yet." The song urges the listener not to give up on hopeless causes, nor to underestimate the power of the heart. Standard country fare. But the coincidence of timing gets me, and it chokes me up.

I wouldn't blog about my fatigue-induced hallucinations that a song on the radio was speaking to me, except that when the song ended, the DJ announced, "This song brought to you by Badger Airlines." Really. Except he used their real name.

Update: one of my readers found the song online. It's by Canadian artist J.R. Vautour.

Hold Timing

Sometimes IFR aircraft (aircraft on flight plans that allow them to fly through clouds) have to stay in one place and wait, while they are flying. Typically they'd be waiting for their turn to land at the airport, and the way air traffic controllers say "take a number" is by issuing a hold clearance.

A "hold" is an oblong path: two parallel straightaways connected at the ends by semicircles. It is defined by a point called a "fix," a direction to that fix, an altitude, and whether the turns are to be made to the left or the right. The pilot identifies the fix using radionavigation equipment. The oblong is flown so as to put the fix at the end of one of the straightaways, just before a turn. Sometimes the length of the straightaway is defined in miles, but usually the length is defined in terms of time: the inbound leg is supposed to take one minute, or, if the hold is flown at an altitude above fourteen thousand feet, a minute and a half. With no wind, the opposite straightaway would require the same time. In wind, the timing of the outbound leg must be adjusted so as to satisfy the timing of the inbound leg.

Pilots' web has a great picture.

Imagine the wind is such that the aircraft experiences a tailwind during the outbound leg. That will make it cover distance faster, so that when one minute has elapsed and it turns inbound, it is further from the fix than it would be in still air. But if there is a tailwind outbound, there is a headwind inbound, so the airplane not only has further to go, but covers the distance at a lower speed. Reaching the fix, the pilot will discover that the inbound leg took more than one minute. On the next leg, she flies outbound for a shorter time, to compensate. But how much shorter?

There are many rules of thumb. During my initial training, I learned that if the inbound leg took more than a minute, to take two thirds of the excess inbound time off of the outbound time on the next leg. If the inbound leg takes less than a minute, add one and a third the excess to the next outbound leg. A pilot I respect, who can talk mathematical rings around me, subtracts half the excess or adds all the shortfall. As long as you're correcting in the right direction at each turn in the hold, you'll eventually converge on an outbound time that gives you a one minute inbound. It's a cockpit not a calculus class.

This being the internet, not the cockpit, I have filled a few sheets of paper with calculations, and determined that the distance travelled in the direction of the inbound track during a ninety degree rate one turn away from the inbound track is equal to the definite integral from t=0 to t=30 of (v cos (3t) + wt) dt, where v is the speed of the airplane and w is the wind speed. That ground to a stunning halt when I realized that whatever part of my brain had once known how to integrate trigonometric functions has found a new life, possibly storing and cross referencing the details of Friends episodes.

If someone has a more cooperative calculus-related brain segment, and wants to help out here, here are a couple more things to know about the path in the hold.

According to AIP-RAC 10.2, we "are expected to make all turns to achieve an average bank angle of at least 25 degrees or a rate of turn of three degrees per second, whichever requires the lesser bank." That "three degrees per second" turn is a common requirement, known as a rate one turn. We even have a rule of thumb to determine the bank angle in degrees that will produce it: ten percent of airspeed (in knots) plus seven. So for an aircraft flying at an indicated airspeed of 175 knots (the maximum permitted in a hold for any propeller-driven aircraft), the bank angle for a rate one turn is 175/10 + 7, or 24.5 degrees. Therefore, for all propeller-driven aircraft the 180 degree turns at the hold ends will each take one minute.

Timing of the outbound leg starts abeam the fix or when the wings are level after the turn, whichever comes later. Timing of the inbound leg starts with wings level. I have deliberately neglected the effects of wind not parallel to the inbound track.

Sweet Wine or Sour Grapes?

I should find out by tonight if I'm going to be typed on the Z92. That means the next post to this blog will be either an incoherent jumble of keystrokes made by me bouncing off the walls in ecstatic delerium, or a highly technical treatise on timing holds, as I focus on something else to avoid lobbing my sour grapes around the internet.

Jetsgo Gone

I've been trying to post this since my first cup of coffee this morning, but Blogger refuses to accept it.

Discount carrier Jetsgo announced early this morning that it is suspending operations, and will be seeking bankruptcy protection. I was wondering what their business motivation was for advertising one dollar fares to a number of destinations. Now I know. It was desperation.

Transport Canada was looking at the company for a few problems, but nothing that would have shut them down. They just weren't able to compete. All jokes, snide remarks, and competition-bashing aside, it's not the employees' fault. If your last paycheque said Jetsgo and you've just found out that there won't be a next one, I'm sorry to hear about you losing your job, and wish you the best of luck at finding the next one. Anyone advertising an MD-80 job this month is going to have a lot of applicants.

Playing With Fire

From AIP-AIR Annex 1-4, Survival Advisory Information

In the hands of a trained person, pyrotechnics can be very good. In hands of a novice they can reduce chances of survival.

Maybe I have an odd sense of humour, but it makes me laugh. I imagine the various ways in which a novice could use a flare pack to reduce his life expectancy.

That entire survival section in the A.I.P (Aeronautical Information Publication) seems to have been written somewhat tongue in cheek. The attitude seems to be, "If they aren't smart enough to realize the essential minimum equipment, they won't be smart enough to realize that they are being openly mocked." How else do you get advice like this?

Training is also needed in how to melt snow in a container over a fire.

Hint: don't use pyrotechnics. Here are some tips and some more.

Progress Report

It's been a good couple of days on the new job hunting front. It's emotionally draining making phone calls to people you don't know, telling them that you're a fantastically wonderful pilot and they would be missing out if they didn't hire you forthwith, so I intersperse those calls with calls to mentors, friends, and generally nice folks who I know will tell me to keep it up, and perhaps drop a few juicy rumours.

I had promising conversations with folks at Groundhog and Badger, and then the chief pilot at Aardvark picked up his own phone and let me in on some recent changes to the company that may mean Aviatrix has a fighting chance at flying airplanes featuring the silhouette of an extensile-tongued mammal on the vertical stabilizer.

It all made it easier to smile nicely and be happy for the pilot whose interview with Badger went very well. I still haven't got one, so it's unlikely I'm being looked at for this round of hiring.

See and Avoid

The Globe and Mail ran an article yesterday on corporate policies regarding employees' blogs. It's a shame they just ran an American AP story, complete with references to the First Amendment. I would have been interested in research for an equivalent Canadian story.

Quite a few people have been fired for blogging. A flight attendant, a librarian, a congressional intern, and I'm not sure what this last one did, but her name, dooce, has become a verb meaning, "to be fired for your blog." I think technically most of these people have been fired for being rude to their customers or supervisors, for publically criticizing their employers, or for blogging when they are paid to be working.

These people, and many more who continue to hold down jobs, blog as if their customers, co-workers, and employers inhabit a world that does not have access to the internet. Yes, some customers are amusing in their ineptitude or arrogance. Some co-workers rival the characters on television dramas when it comes to back-stabbing guile. There are airlines managed worse than the fictional Wings. (How was that airline supposed to stay solvent with one single-pilot airplane and at least five employees? They must have done a few extra night flights bringing agricultural products from Cuba). I admit to sharing a few tales through gritted teeth in the crewroom, but in public I've got to be sober, sane and respectful of the people who pay my salary. The internet is a public place.

I can be fired for wearing my uniform into an establishment that serves alcohol. A pilot is legally allowed to go into the grocery store in uniform and yell, "These frozen turkeys are smarter than my management, and these grocery carts are better maintained than our airplanes!" But if there's a company VP checking out maynonnaise specials in the next aisle, advancement might be in question. Besides, you'd would have to be mad to do that, wouldn't you? If you did it regularly, sooner or later you'd be found out. The internet is a public place, packed with far more people than the grocery store.

And that's why I don't blog about my company.

Coffee: Part Two

Fatigue-related aviation accidents are extensively studied, but what about coffee-related accidents? I've never seen a report that commented on the availability of coffee to the pilots at various stages of flights, or a toxicology analysis that remarked on the absence of caffeine. Searching for "coffee" in the NTSB Accident Database finds mostly reports from witnesses who were drinking coffee when they observed an airplane crash in their back yard, or accounts like, "The pilot stated that he and his passenger had some coffee, and he then called the Flight Service Station."

There are a few like this one:

"The flight encountered moderate turbulence, while in cruise flight. During the encounter, a coffee pot fell from a serving cart into the lap of a passenger. The top came off the pot, and hot coffee spilled on the passenger, causing injury."

The passenger was a seven-year-old kid, too, so that's a definite vote against coffee.

I remember hearing an anguished cry on the company frequency, followed by a rueful voice informing us that the captain had spilled his coffee all over himself. A bit like the joke everyone knows ...

The pilot is making a routine cabin announcement, "Ladies and Gentlemen we have reached our cruising altitude of thirty--AAAAAAGHHHHHH!"

After a moment of silence the pilot sheepishly reactivates the intercom, "I uh apologize for that folks. As I was speaking, one of our fine flight attendants was handing me a cup of coffee and it spilled all over me. You should ... uh ... see the front of my pants."

A passenger hollers back, "You should see the back of mine."

I'm not going to tell the one with the punchline, "Miss, don't forget the coffee." You all know it, and Cockpit Conversation has to draw a line in the sky somewhere.

Suspicious Female?

I'm hoping that this story is leaving something out that would explain why the authorities consider a helicopter crash suspicious. According to the article, a helicopter crashed near Abbotsford, British Columbia and the only occupant was a woman, who died at the scene.

There is a "suspicious element" to the accident, said Kirk because police are not sure who was the pilot of the copter or if the [sic] left the scene.

If an aircraft crashes and there is one person on board, doesn't one start by assuming that that person was flying it? It isn't uncommon for men to assume that a woman on board an aircraft is a passenger or a flight attendant, instead of a pilot, but when she's the only occupant? Possibly she was belted in a seat without access to the flight controls, but the story implies that the police arrived on scene after the woman had been removed from the aircraft. Or the "copter" as the article puts it.

[Edit 8 March 2005: It turns out that the suspicious part was one of the two men assisting at the scene had been on board the helicopter and the police suspect that yet another who left the scene had been piloting.]

Not Air Transat's Week

A couple of days ago a $7.65 million compensation settlement was finalized for passengers traumatized by Air Transat's A330 no-engine landing in the Azores in August 2001. The company takes the official stance that the matter is over and will not affect finances.

Today an Air Transat A310 taking off out of Cuba experienced a mechanical problem with its rudder. The exact nature of the problem is unclear, but the CBC story quotes a spokesperson for the airline saying the plane's rudder "partially fell off." I spent a while looking for details on that story, but this National Post story is equally vague.

Half Mast

Every airport flag I saw today was flying at half mast. I know that it's a gesture, just a piece of protocol, but it accurately reflects the public mourning for RCMP Constables Peter Schiemann, Anthony Gordon, Leo Johnston, Brock Myrol, all killed Thursday, doing their job. This is not a grow-op story, an automobile repossession story, a pedophile story or a gun registry story. It's a story about one completely unhinged individual operating outside the bounds of society and law.

In the months ahead this shocking event will be spun to support or oppose a number of political agendas. I hope that one of them is to improve whatever training, resources, or policies could have been in place to protect those four young men from a shooter whose own father termed "evil."

Hydrocarbon Fuel

All aviation fuel, whether avgas or turbine fuel, is a mixture of hydrocarbons: substances made of chains of carbon atoms, with hydrogen atoms attached. Different hydrocarbons have different freezing points, boiling points, densities and energy content. In general, the longer the chain, the higher the boiling point, but some chains are branched, and the three dimensional shape of the molecule affects its properties, too. Crude oil is a mixture of many different hydrocarbons, as well as compounds containing other atoms.

Crude oil is refined by distilling it in a column, and separating out fractions with different boiling points. Light hydrocarbons like butane and propane come out the top of the distilling column, with gasoline lower down, followed by kerosene and diesel. The products may be again refined by removing undesirable components such as sulphur compounds through further chemical reactions. The big molecules left over at the bottom of the column may be broken up to produce more gasoline, kerosene and diesel.

Avgas, for piston engines, is refined to increase its octane number, a comparison of the amount of a particular eight-carbon chain molecule versus n-heptane, a straight chain seven-carbon molecule. Additives such as tetraethyl lead can improve the smooth running qualities of the fuel in an engine and increase the octane above 100, where it is called a performance number. Avgas has a higher ratio of energy per unit weight than turbine fuel, but a lower ratio of energy per volume.

Turbine engines orginally used kerosene, not for its properties, but because turbine engines could burn anything, and development took place in wartime, when gasoline was in short supply. After the war, the US Air Force started using "wide cut" fuel, spanning the range from gasoline to kerosene. The logic was that you can make more of it from the same amount of crude oil. Unfortunately, it also evaporates at a lower temperature, leading to loss of fuel at high altitudes and increasing the risk of fire during ground handling or crashes.

Americans standardized on kerosene-type Jet A fuel, which freezes at -40 degrees, for domestic flights. Much of the rest of the world uses Jet A-1 (almost the same as US military JP-8 fuel), which freezes at -47 degrees Celsius.

Wide cut fuel, known as Jet-B, is still used in northern Canada, because it doesn't freeze until -51 degrees Celsius. The Russians use something similar, called TS-1. Because jet fuel is a mixture of so many different fractions, it remains pumpable for about ten degrees below the temperature where it starts to freeze. I wonder at what temperature human testicles freeze. I'm glad I haven't got any, in a country where the difference between -47 and -51 is significant enough to warrant a grade of fuel.

Engine Recipes

Old Lady 1: I've been shopping!
Old Lady 2: What d'you buy?
Old Lady 1: A piston engine!
Old Lady 2: How d'you cook it?
Old Lady 1: You don't cook it.
Old Lady 2: You can't eat that raw!

    --- Monty Python's Flying Circus, Episode 43

Actually, you can cook a piston engine. One stellar way is to lean out the mixture at high power and run it for several hours. You still can't eat it, but the company has to eat the substantial cost of replacing the cylinders. What a company pays a pilot in a year is a fraction of what the pilot can cost the company through poor engine handling.

In a piston machine, the pilot controls the ratio of vapourized fuel to air that is burned in the cylinders, using the mixture knob. It's usually red, an attention-getting colour that should underscore its importance. By sliding, twisting or pulling (aircraft manufacturers didn't get together on these things) the mixture control, the pilot decreases the flow of fuel to the engine. Pull it all the way out and there is no longer enough fuel flow to sustain combustion. That's the normal way to shut down a piston engine. The fuel actually has two purposes. One is to participate in the combustion reaction and the other is to provide cooling.

I could, and will later, write a whole post on combustion but essentially it's a recipe. Like a screwdriver: two ounces of vodka, six ounces of orange juice. You can slide that ratio a fair way in either direction. Excess orange juice serves to quench your thirst without getting you drunk, while excess vodka gets you drunk without filling your belly. An exceptional excess of vodka leaves you passed out on someone else's floor with one of your eyebrows shaved off.

The pilot's job is to adjust the mixture such that fuel is not wasted, but the engine does not overheat. At high power, that usually means full rich. The engine will burn a lot of fuel, producing a lot of heat, and the extra provides cooling through evaporation. That cooling is especially needed in the climb, when the forward speed and thus cooling (most piston engines are air cooled) is reduced. In cruise, the mixture can be reduced ("leaned out") so that the fuel flow more closely matches the available air, according to the altitude. This saves fuel and produces a smoother running engine. Before increasing the power, the pilot should increase the mixture. Lean the mixture too much or leave it lean while applying full power and you have a recipe for a cooked piston engine.

Turbine engines are even easier to cook, if the internal turbine temperature limits are not adhered to, but Monty Python doesn't have a sketch about them.

Cute But Useless Mnemonics

In continuation of my checklist rant, I present my complaints about checklist mnemonics, the little acronyms people stuff into their heads and recite at crucial moments in aviation. They have their place. Sometimes they are great. Sometimes they are misapplied, and sometimes they were poorly devised in the first place.

The most common is probably GUMPS:
Gas - correct fuel tanks selected
Undercarriage - landing gear up or down as appropriate
Mixture - full rich for sea level take-offs and landings, leaned in cruise
Propellers - full fine for landing, lower rpm for cruise
Switches - fuel pumps, magnetos, landing lights, heater, whatever

Likely half a dozen people are looking at this saying things like, "No, no, Aviatrix. The P is for pumps." However you say it probably attaches to the airplane you were flying at the time you learned it, and whatever that was had its own unique set of prelanding and after takeoff tasks. That in itself is not a problem, and if you have mapped the letters to tasks that are required for your aircraft, and those tasks properly associate with the letters in your mind, well GUMPS away and I won't even give you a dirty look.

But the trouble begins when the words don't properly associate. For North American pilots half the time the GUMPS recitation stands for Gear, Um ... The only time many pilots here would refer to the landing gear as "undercarriage" is during a GUMPS check. It's more of a British word. Which is odd, because gas for fuel is more of an American thing. Most pilots say fuel. Look at Kristopher, the student pilot who inspired this posting, saying "I had to ask the instructor to remind me what 'P' and 'S' stood for." So here's the poor guy, smart enough to program computers for a living, and instead of just memorizing a sequence of prelanding checks, he has to memorize it in association with a nonsense word. If you can't remember something, sure, use a mnemonic. But if the mnemonic is harder to get right than the task?

And then there's the fact that Kristopher is flying a fixed gear aircraft with a fixed pitch propeller. That means that (a) the gear is welded permanently in the down position and cannot be raised or lowered in flight and (b) the propeller is one solid piece of metal and the angle of the blades cannot be adjusted. So what is he using GUMPS for? If he has been advised to say, "Gas: fullest tank, Undercarriage: already down, Mixture: full rich, Propeller: still going around, Switches: fuel pumps on, landing light on," then no wonder the sequence was difficult to learn. If his instructor has twisted GUMPS to align with the tasks that actually have to be completed before landing, then good, but will those associations stick in a complex airplane, causing him to neglect gear and propeller levers? Probably not, because the appropriate lights and levers will be in plain sight. I'm not sure what the use of the mnemonic is when being in the airplane tell you what to do.

Mnemoniccs get worse, though. I've seen CCCC recommended for an overshoot checklist.
Cram - the mixtures, propellers and throttles
Cowl flaps (and/or carb heat)
Climb
Call and advise ATC
Presumably at some point in here you remember to get the flaps and gear up, too. CCCC is useless, because there's nothing in the mnemonic to put the tasks in the very essential right order. Raise the nose before adding power and you may not be doing much climbing.

Dreaming of Airplanes

Last night I literally dreamed about a conversation with a member of the Badger management team, where he was setting up an appointment for me to check out in one of their airplanes. The difficulty (don't dreams always have difficulties?) was that he seemed to have mistaken me for someone else, so I didn't know which aircraft I needed to learn about (they operate several types), in advance of the checkout.

I like the suggestion below from David. I need to get my mentors on the phone.

The Only Thing Worse ...

I've been suffering from a ridiculously harsh schedule the last couple of weeks, which hasn't given me a chance to do much lobbying for a job at Badger, nor to prepare for the job interview I really thought I had a good chance of getting. Today I found out that someone I know has an interview with Badger scheduled already this month. It hit me in the gut. Here I had been worrying about getting an interview and not being as prepared as I wanted to be. I will be very disappointed if I don't get an interview at all.

I'm not a very good nagger. When you invite people to a party, want someone to change a routine, or expect someong to hire you, you have to keep reminding them. You keep checking in on them to make sure they don't forget. I tend to assume people got it the first time, and that they will call me when they want me. I'd make a lousy politician. Which reminds me:

"To fly a plane with even two passengers a man must pass a test to prove himself intelligent, sane and well balanced. But there are no such tests for politicians, although an unbalanced politician can be much more dangerous than any pilot."

    ---Dr. Brock Chisholm

Update Update

lost av8r has reconsidered detailing his employer's woes in a public forum, so the links to his blog below no longer lead to salacious details. The original post is still in my browser cache, but I won't tell if he won't.

Skyward Aviation Update

Skyward Aviation, grounded a few weeks ago for maintenance problems, isn't telling customers much, but my referrer logs revealed that new pilot blogger, lost av8r, is less shy than me about revealing corporate information. The first entry of his blog up in the air includes the inside scoop on recent events at Skyward.

I'm less blasé than Shawn about the discovery of another Canadian commercial pilot blogger. I'd been looking and thought I was the only one.

U/S, eh?

When I was a beginning student pilot I spotted a set of three coloured lights on the communications panel of the training plane and asked my instructor what they were.

He said, "Those are marker beacons, but they don't work: they're American."

Later I encountered a logbook notation that the landing light was "U/S." I asked what that meant.

"It means it's broken."

U/S, U.S., U.S.A., American, broken. Okay, they all mean the same thing. Aviation slang is strange sometimes, I could deal with it. It was a while before I discovered that marker beacons really are an American system, that U/S means "unserviceable," and that "American" isn't really pilot slang for broken.

I still giggle inside every time I see an airplane with US Airways stenciled on the fuselage. I believe the Americans prefer the term INOP for their broken equipment, so it isn't so funny for them.