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Fat folk, airplanes and ignorance of basic physics

Over the last week I kept running across articles and video about a heavy weight couple who lost weight after the embarrassment of being asked to move to a different seat so the airplane could take off safely. On one Fox News show the talking heads went on about the times they were asked to move. None of them were particularly large so they talked overly long about how a jumbo jet could be unsafe to fly because a mere wisp of a talking headess was in the wrong seat.

This riled me a bit and has been roiling about in the back of my mind for some days. The people who write or talk about these things are supposedly educated, but the level of ignorance shown makes me very worried about what schools are actually requiring students to learn, even at the university level.

In hopes some of these ignorant but otherwise intelligent folk happen to drop by Samizdata, I will provide a bit of a remedial lesson in basic physics and a bit on aeroplanes as well.

I am hoping everyone is at least familiar with what a lever is, or at the very least a childhood teeter-totter. If two children sit on a board on opposite ends, they can find a balance point regardless of how fat or skinny the two are. One can move closer to the fulcrum, the thing upon which the board rests, or farther away. A child of a given weight at a given distance from the fulcrum creates what is known as a torque. The two children can balance these torques: Mass of child 1 times distance from fulcrum = Mass of child 2 times distance from fulcrum. In more typical notation: m1 * d1 = m2 * d2.

If you understand a teeter-totter, you can understand everything else I have to say.

An aeroplane has a number of points that are of interest. The most important to this discussion are the ‘center of lift’ and the ‘center of gravity’. If you had a very hefty jack and the underside of your 747 could handle it without a requirement for body work afterwards, a single point at which the aircraft could balance like a toy on a pencil is the center of gravity. This is just like the balance point of the children, but with the entire class and their teddy bears instead.

The fulcrum is the center of lift. This is a balance point created by the airflow over the surfaces of the plane in flight. Ideally, and in the simple case, the center of lift should be near the center of mass and both should be on the center line of the aeroplane. If one wing were longer than the other, the center of lift would shift away from the center line. This would not be a good thing unless you are Burt Rutan and know how to do tricky things which no normal mortal would think of doing.

In practice it is impossible to get the two exactly together. If the center of lift is forward of the cg the airplane will want to pitch up. If it is aft of the cg it will try to pitch down. Similarly if it is to the right or left of the cg. the airplane will want to roll right or left.

You can control the attitude of the aeroplane by neutralizing these forces. If you have a pitch up tendency, you dial in a bit of pitch down on the elevator trim tabs. Likewise for the other directions. In worst case you can use the control column and use deflection of the elevator or ailerons themselves to counteract the problem. It is not wise to fly like this under normal circumstances. If you run out of trim you have either not done your weight and balance papers properly or you are flying a Lancaster to Europe in WWII with a max bomb and fuel load and expect you are going to die anyway.

Airplanes have a bunch of numbers which pilots have to know. Among them are the ‘aft cg limit’ and the ‘forward cg limit’. Basically these mean you are too tail heavy or nose heavy to fly with enough of a safety margin to deal with the unexpected. They are not absolute limits. You are not going to reach the ‘my god we are all going to die!’ limit unless everyone piles into the tail and the pilot can not keep the nose down even with full downward elevator deflection.

Inside the cabin the pilot has readings off the landing gear that tell him what the weight and balance looks like after all the luggage, consumables and passengers are on board. If those indicators show the aeroplane is approaching the aft limit he or she will have a flight attendant pick someone from far aft and move them as far forward as possible.

That is all this whole storm in a teacup story was about. It is standard aviation practice that goes back to the first time Wilbur took Orville along with him.

45 comments to Fat folk, airplanes and ignorance of basic physics

  • Jim A.

    2 notes:
    The center of lift can change due to things like flaps and speed.
    Fuel economy can be affected by shifting the CG. If you have to use the elevators to compensate for CG you can increase drag.

  • Dale Amon

    Yes and a hundred other complexities I could have thrown in as well. I am not trying to teach everyone to be a pilot, just give them a little basic knowledge they should have learned before graduating from secondary school. I left out the center of thrust, the variations of lift and control authority with the effective wind, the ability to control attitude in a multiengine using differential thrust and lord only knows what else.

    I might point out thought, that the only way you can balance things on takeoff using thrust is the same way the bombers did it. Extend your roll and don’t rotate until you have enough control authority to counteract the pitch or roll problem. That does not strike me as a good thing to do on a commercial airliner, but then I have never flown anything outside the GA realm myself.

  • Dale Amon

    To put it more bluntly… I suspect that if Continental took off with a plane full of passengers while outside the aft cg limit and the FAA got wind of it… there might be a ‘former pilot’ looking for work.

  • Ivan Ivanovich

    “you dial in a bit of pitch down ”
    Yes, Jim A. got it right. Any pilot will tell you that the Dials, or trim tabs, are to be used only during special conditions such as take off and landing. Use of trim during cruising flight is like driving a car with one foot on the gas and one on the brake.

  • Dale Amon

    Ivan. I beg to differ. If you are flying a Cessna 172 and the guy in the back seat is a bit on the heavy side, you are going to dial in a bit of trim to neutralize that so that you do not have to keep a steady forward pressure on the control column. That could get quite tiring after awhile.

    You always trim for level flight once you are at cruise setting.

  • Jerome Thomas

    I think the lack of a basic knowledge of physics demonstrated by news readers, is just a symptom of the incentives faced by news media organizations.

    The market consistently rewards those peddling the notion that the world (whether social, financial or physical) is not particularly complex and can be understood with a minimum of thought.

  • andrewdb

    Yes, but…

    If moving a couple of hundred pounds makes the difference in a 737 (or 747!), it seems to me you are cutting things a little too close. More margin of error would seem safer.

  • Dale Amon

    There are several ways to answer your question and all are meaningful.

    First, Read the article a bit more closely. The line at which the pilot starts moving people around is not the point at which the airplane is in dire straights. it is a line which says you are safe under all foreseeable circumstances on this side; and if you step one inch over you start accumulating risk. The aft cg is going to be a line drawn in the sand, but it will not be the true aftmost point the plane could take of at with reasonable safety; it will be even farther from the aft cg at which a pilot in fear for his life if he doesn’t get off the ground before that alien’s ray on the White House takes out all of Washington DC would get off the ground with reasonable luck.

    The reality is the line is an absolute number and is going to be somewhat arbitrary. In aviation you learn to go by the numbers. They are the law and if you ignore them or push them for too long or too hard you will eventually lose the bet. Airplanes are not automobiles, at least not at the state of the art we are at today. if the limit says X, and you have exceeded X by Delta, you will correct it.

    This may be an alien way of thinking to the populace at large. If I run a calculate of a+b and have a limit of 5.00 and the result I get is 5.01, then I am out of limit. Yes, it is not usually quite that simple. I might know that on a day like to day I have a bit of a safe fudge due to temperature and humidity and the altitude of my takeoff and a dozen other factors. The point is, it is not like driving where a speed limit says 60 mph and you figure 65 is okay. When flying, you do not do that if you can help it. Unless the circumstances are dire or you are a test pilot, you stay ‘inside the envelope’ at all times.

  • RAB

    Damn there are a lot of very smart people on this site arnt there (thank God!) ?

    For myself, I weigh so little, 10 stoneish, and 6′ 2″,nobody ever moves me, you can fold me up and shove me in the overhead locker for all I care.

    No worse than the seats I’ve had on some Boeings lately!

  • Ivan Ivanovich

    I’ve flown the 172 and I agree that you have to trim. All I was saying is that a proper weight distribution allows for a neutral trim and best economy.

    For those fat people: You might want to consider booking your next flight on this plane:
    Payload = 175,000 kg and check out the rear door!
    I’ve been in one of these also. Just on the tarmac. Awesome!

  • Dale Amon

    Nearest I have ever been to one was sitting in a commercial jet as it taxied by one. Actually I do not believe there are very many of them around. They fly all over the world and take on the jobs that few other aircraft (if any) can handle.

    I believe there is a crew quarters up in the tail boom isn’t there?

  • manuel II paleologos

    I’ve only flown these on Windows 98 and read lots of books on it (have you read Mikoyan’s autobiography?). Even then, it’s not hard to know enough about these things to howl in horror at pig ignorance on the TV. The Horizon investigation into the Space Shuttle Columbia, for example, seemed to have a major factual error (or at least deliberately misleading exaggeration) in every scene.

    So do drinks trolleys affect trim as they move up the aisle?

  • Dale Amon

    The short answer, in theory, is yes. The longer answer is that since the airplane is at cruise and probably on an autopilot, I doubt anyone notices the difference as it moves down the aisle and very tiny (if any) control adjustments occur. The difference between the cart at one end of the aircraft and at the far end while in cruise might be (wild ass guess) down in the inches per minute change in altitude.

    The primary worry is at takeoff and landing because the airplane is operating at the lower end of its speed range and thus control authority is at a minimum and the airplane as a whole is closer to the knifes edge. The takeoff is the diciest time of course. That is when you have a full load of fuel, and as my instructor taught me: “the runway is behind you”.

  • KenB

    This discussion reminds me that, when I was a college student many years ago, I was once asked by the stewardess to move from coach up to first class. There were few people on the flight, and I think no one else was in first class. I always assumed she took pity on a college student and maybe that is why I was personally picked, but this phenomenon may be why somebody had to move.

  • Fred the Fourth

    Ah yes: What are the three most useless things to a pilot?
    1. Runway behind you
    2. Altitude above you
    3. Gas left in the fuel truck

    Remember kiddies: Always try to fly in the soft middle of the air. Avoid the edges of the air, they tend to be hard and jagged.

    Why are pilots so picky about this stuff? Because the pilot is usually the first to arrive at the scene of the accident.

  • Dale, thanks that was really interesting. I’d never really thought about the physics of planes that much before, although on the smallish (about 20 seats) planes I sometimes fly on as a passenger up to the north of Scotland its not that unusual for the pilot to ask some of the passengers to move seats.

  • Dale, thanks that was really interesting. I’d never really thought about the physics of planes that much before, although on the smallish (about 20 seats) planes I sometimes fly on as a passenger up to the north of Scotland its not that unusual for the pilot to ask some of the passengers to move seats.

  • Bruce Hoult

    Dale writes:
    > The reality is the line is an absolute number and
    > is going to be somewhat arbitrary. In aviation you
    > learn to go by the numbers. They are the law and
    > if you ignore them or push them for too long or
    > too hard you will eventually lose the bet.

    I agree with the “too long or too hard” part, but the attitude that “the book says 5.00 and we’re at 5.01 so we can’t fly” seems to me to be a peculiarly US thing, at least in the part of the aviation fraternity I’m most familiar with, which is gliding.

    I think, as Dale alludes to, it’s purely a result of the legal culture. If you’re a fraction of a percent on the right side of the arbitrary line and something goes wrong *anyway* then you’re blameless, but if you’re a fraction of a percent on the wrong side of it then you’re in big big trouble, even if the thing going wrong is unrelated.

    I have, in the USA, been told “the max all up weight for this glider is 1040 lb, and with the two of us it’s going to be 1045 lb, so we can’t fly”.

    Any where else in the world the result of that calculation would have been: “This glider is rated for 5g aerobatics at a weight of 1040 lb. We’re gonna be 1045 lb, so let’s try to keep the aeros down to 4.97g ::smile::”. The smile being because we all know perfectly well that we’re going on a soaring flight in which we’re not going to exceed 2g for any period of time.

    As an indication of the arbitrariness of the line and the size of the safety factors involved, here in New Zealand agricultural operators are routinely issued with permits to operate their aircraft at take off weights 40% above those specified by the manufacturer. The only requirement for this is that the excess weight be able to be dumped at five seconds notice.

    If you don’t know what you’re doing or don’t want to think too hard about it then stick to the published limits and you’ll probably be fine. For a small plane by far the most important consequence of operating over the weight in the manual is the rapidly increasing takeoff distance (approximately proportional to weight cubed) and the reduced rate of climb. That’s what kills lots of the unthinking.

  • Dale Amon

    I have only ever flown in the US. I could never afford it here in the UK where I have lived the last 20 years… and I most certainly could not afford owning a Cessna like the one I and two friends shared back in the early 1980’s when we flew out of AGC in Pittsburgh. So I can’t really speak to the strictness of the by-the-numbers culture elsewhere. I might add though Bruce, that in ‘our industry’ those numbers can get to be really critical. Rockets will bite you in arse if you don’t respect them sufficiently.

    Also, even in the US you will find that the adherence to a ‘by the numbers’ philosophy starts out at maximum laxness in sport flying and gets stricter and stricter as you move up into higher performance and larger size.

    I also want to note for the sake of non-flyers that most of the prior discussion was about the balance of the aircraft, but Bruce brought up the issue of the total weight. You can be in perfect balance and still be so heavy that your Continental can’t flap hard enough to get you out of ground effect. There are performance tables for defining your takeoff run given all up weight, temperature, humidity and runway altitude. The trick is to have the length of runway needed for take off come out as a number lower than the length of the runway you’re on. It’s rather messy if it doesn’t and if you think body work on your car is expensive….

  • Alsadius

    Andrewdb, they said this was “a heavy couple” – that could easily refer to 500-600 pounds between them, and you’re moving them forward hundreds of feet. We could easily be talking a difference of 100,000 lbf of torque, which even on the heaviest 737 ever made at max takeoff weight, would move the centre of gravity better than six inches. Given how, as mentioned above, a lot of these limits are treated as bright lines you do not cross if at all avoidable, then six inches can easily make them go from illegal to legal for takeoff.

    You’re right that them being in the wrong seat won’t crash the plane, but it’ll break acceptable margins, which is just not cool.

  • Fred the Fourth

    On the subject of numbers and the adherence to them:
    I am intimately acquainted with a lifetime research pilot, who had a significant side-specialty in aviation safety and accident investigation. This guy was Air Transport rated, flew everything from choppers to C-141, test-flew Concorde back in the day, was CO of a Marine A-4 squadron, type-rated in just about everything you can name, flew in hurricanes (but never in a Hurricane :-)), etc. etc. ad nauseum. Of the notorious F-104 “Widowmaker” (or “Ground Nail” (tentpeg) for the Germans in the crowd), he once said “It flies like an airplane.”
    If anybody was qualified to shade the numbers, he was.
    His philosophy was: Inside the envelope you know where you are. Outside the envelope is Research. Not knowing the difference will kill you.

  • Fred the Fourth

    Hell’s bells, I just remembered. When he retired he went right out and got rated in seaplanes / floatplanes. Said it was the one type the government would not pay for him to get rated in. 🙂

    I sense a biography coming on. Too bad I can’t write.

  • Dale Amon

    Fred: I am in complete agreement with your friend. He is obviously an old pilot because, as we all know, there are no old bold pilots..

  • steveH

    Another point, regarding large and high-performance aircraft, is that they often have provision for pumping fuel between tanks during flight as the fuel is burned off to maintain optimum trim for best fuel economy.

    There are limits to how much of an effect it can have on performance, but it’s enough to make the extra complexity (and pilot workload) worth it to the operators.

  • Dale Amon

    Depends on the type of aeroplane. If you are a big lumbering airliner that mostly goes in straight lines and shallow banks, it probably does not make a huge difference, but if there are any ATP’s here I’ll let them speak to it.

    If you are talking about a fighter, you want to burn off the outer tanks first because they will have the greatest moment arm and the greatest impact on your combat performance. That moment will also put the greatest stress on the airframe during high G maneuvers. I am not sure to what extent this is still true… I have studied WWII warbirds much more extensively than fast jets, and as I have said, my own flying is strictly GA… but even there we usually did the tanks from outer to inner.

    Just as an aside, the Spitfire had quite a good size tank right in front of the pilot. Quite a few paid the price for that, even those who managed to bail out before turning to toast.

  • AughtSix

    Eh, someone needs to grow up and get over it, which, I guess they did, to some extent.

    On a college football (american) official visit (where a school can pay for your recruiting trip) there were 6 offensive linemen averaging about 280 pounds and a handful of other recruits on a 15 or 20 seat plane. As it turned out, all of the linemen were assigned to one side of the plane. When the co-pilot a/k/a flight attendant saw the seating arrangement, he said some rather choice words, then rearranged the whole plane. I don’t think any of us were offended that we were told in no uncertain terms that we were too big to sit on the same side of the plane.

  • Doug Sundseth

    For evidence that this is a real problem (not that any pilot would think otherwise), you can take a look at Air Midwest (d.b.a. US Airways Express) Flight 5481, which crashed in Charlotte, North Carolina, on January 8, 2003.

    The breach of the aft cg limit was exacerbated by a misrigged elevator cable that limited elevator travel. The result was the deaths of 19 passengers and 2 crew.


  • Dale Amon

    I had not read the accident report on that one, but that is a classic example of ‘cascading failures’ and is the very reason I noted earlier that busting the aft cg limit was something you would probably get away with if there aren’t any other problems. It is the thing which catches people out… you get away with something for time after time. And then one day a second problem happens and you find you have just had the limb you have stood on so many times in the past sawed off behind you.

    That’s why you don’t bust limits. They are there for a very good reason.

  • nick g.

    All of you are overlooking the obvious point- the people lost weight! This could be the secret side to joining a weight-watchers program- they tell people about your ‘condition’ as part of the program! Maybe the pilot was tipped off by an anonymous telephone call, and decided to embarrass them for their own good!!!
    Or maybe the pilot is a recruiting agent, and saw someone to embarrass as a part of a valuable sideline….
    In any case, it worked- they now have the incentive to lose weight…

  • Ken Mitchell

    Back in the day when I was flying as Navigator in U.S. Navy P-3 Orion patrol aircraft (the P-3 was a converted Lockheed Electra airliner) we used to have a lot of fun at the expense of the newbie pilots. With a crew of 13 people, we’d all run as far aft as we could go, and wait until the pilot would trim the aircraft for level flight. Then we’d all run forward until the airplane would pitch down. The new pilot would adjust the trim again, and we’d all run aft again. The plane would pitch up, and the senior pilot would give the new guy a hard time about not being able to keep the aircraft level.

    It was generally good for three or four iterations before the new pilot would figure it out…..

  • J.M. Heinrichs

    Ah yes, “Aaliyah”:

    Then her 300-lb bodyguard and another man of similar weight boarded the Cessna and finding themselves unable to squeeze up the narrow aisle lowered themselves into the two rear seats by the door. With skinny Aaliyah up the front and the two heavy dudes and all the bags at the rear, the Cessna wobbled up into the air and came down almost immediately

    Death By Entourage


  • Johanthan Pearce

    I am going to forward this article to my dad, who was a navigator on jet fighters and bombers. Surely, this stuff shows why bombs are positioned in certain parts of the aircraft, such as under the wings; when an aircraft drops a bomb, it presumably has to make certain adjustments to avoid the aircraft not being manageable.

  • Dale Amon

    Yes. If you are interested, the Haynes guide for the Avro Lancaster shows the arrangement used for various types of missions as they often carried a variety of ordinance and the placement was important, as well as the order in which things were dropped.

    I have often read about how those old bombers ‘jumped’ as the load left the bomb bay.

  • Midwesterner

    Ken Mitchell’s story reminds of something I heard a couple of decades(?) ago about the Stanford Marching Band. Apparently they did something similar at altitude but moving from side to side on a charter flight. I couldn’t find anything with a quick net search but as I recall the FAA, NTSB etc types got involved and the SMB was sanctioned or grounded or something.

  • This prompts me to reminisce about when my sister used to live in the Shetland Islands and I was flying back after a winter visit.

    Getting from the terminal building to the plane (some kind of twin turboprop thingy) on foot in about a Force 8 was an adventure in its own right. The airfield in Shetland is on a strip of sand with the North Atlantic on one side and the North Sea on the other. Spray from the wavetops was visible over the dunes on the Atlantic side.

    Having made it to the plane, we were firmly advised/instructed not to sit in the rear six rows of seats “because of the weight of ice that is going to build up on the tail”.

    Oh. OK. If the pilot doesn’t sound worried, then I suppose I shouldn’t be either.

    Off we go. Some way out over the North Sea, the plane starts to shudder a bit. The pilot comes on the PA: “do not worry about the vibration. It’s just ice buildng up on the propeller blades”.

    Oh. Ok. If the pilot doesn’t sound worried … etc.

    (He may have been scared out of his wits for all I know. I doubt it though. I assume pilots and controllers in places like Shetland know where the limits are and don’t actually go anywhere near them)

    We made it to Aberdeen and the most spectacular landing I’ve ever experienced, with several inches of fresh wet snow on the runway. This makes a big big splash when a plane lands in it. We were the last flight allowed in or out for several hours.

  • Fred the Fourth

    Re: fuel burnoff and balance
    My acquaintance once arrived in California from Hawaii driving a Convair 990 (roughly like a B-707) with about 10,000 pounds of fuel trapped in one outer wing tank. The transfer valve stuck. Don’t know if they were precisely legal W&B when they landed, but they did not have a lot of options by that time. Not a lot of usable gas left, and (I think) could not dump directly from the stuck tank. Landed without incident. I should ask him about the details, and if he had to buy new pants afterward.

  • Laird

    I was flying out of Salt Lake City once on a hot summer day in a completely full plane. I guess the air (which is thin enough in Salt Lake at the best of times) gets even thinner on very hot days. (Engineers, please correct any error here.) Anyway, the pilot got on the speaker and announced that we were too heavy to take off in the heat. They then removed all of the luggage from the hold and we were OK. Even got to Atlanta on time to make my connection.

    I’m glad I only had carry-ons.

  • Dale Amon

    The number I have from a reference book that was close at hand was the takeoff roll increases .42 to .65 percent per degree F above 59F. So at 85F the takeoff roll is 11% to 18% longer. Altitude has another large factor, about 7% per 1000 feet above sea level. ‘Hot and High’ are bad news for aircraft and have caught more than one pilot out.

    Humidity also affects the density altitude and has some impact.

  • Dale, that’s why I like flying in rocket-powered aircraft- with thrust:weight of at least .5 (and rapidly increasing), the takeoff roll is gratifyingly short.

    [insert smug smirk here]

  • steveH

    Increasing humidity means increasing density altitude, as water vapor is a bit lighter than air.

    I was interested to learn during my last biannual review that at least some business-class turbines aren’t legally able to fly if the altimeter’s kollsman window adjustment exceeds some particular limit.

    (The kollsman window is used to adjust the altimeter for local barometric changes; if your airport is a 1500′ ASL, it’s nice to have the altimeter actually read that value on the ground.)

    Anyway, takeoff tables are run only so far, and once you’re past the published limits, you can’t legally fly the plane. Nothing for it but to wait for the barometric pressure to come back within the limits.

  • Fred the Fourth

    Somewhat counter intuitively, humidity does not make the air “denser” even though it feels that way. Humidity is H2O vapor which is a lot less dense than the basic N2+O2 mix. Also, with minor exceptions, the extra H2O displaces O2 in the fuel-air mix, reducing the effective displacement of the engine (at least on a recip. Never thought about a jet, but it’s probably the same.) The reduced density from heat + altitude + humidity affects not just the engine, but also the wings and prop (if you got one 🙂 (and if you don’t, how can you call yourself a pilot?).
    Departing Denver on a humid summer afternoon is an exercise in precise calculation of accelerate-stop distance. For extra fun, try LaPaz, Bolivia, elevation 11,942 feet.

  • Fred the Fourth

    Side note: So now we know how to get the pilots to come out of the woodwork.

  • Alasdair

    Possibly silly question from a small-boat sailor …

    I understand (and can teach) why, with increased speed, the centre of lift can change with a non-rigid aerofoil like a mainsail …

    With a rigid aerofoil like a plane’s wing, what causes the centre of lift to change with change in speed ?

    (or are we talking about the shift from subsonic to supersonic flight ?)

    (that latter NOT usually being a problem even with a sailboat with a planing hull (grin))

  • Dale Amon

    Hi Doug. You’re just trying to make me jealous. I can tell 🙂

    So hurry up already and get loads of dosh in so you can have me do some more work for you guys!

    I’m dying to see your new engine up close and personal!

    Well, not *too* close…

  • CaptDMo

    Gliders (sailplanes)-
    Gee, it must be nice to account for all that math stuff when the passenger just happens to be at the controls,
    which brings me to point two-
    Beverage trolleys.
    As major airlines tend to frown on me touching all the knobs, wheels, sticks, and stuff, I tend to do my best by assisting in redistribution of the concentration of mass of fore, or aft, fully loaded carts of tranquilizers in tiny little bottles a little further back from the nose where the “first to arrive at the scene” hang out.

    I can only assume that pilots of the larger commercial flights have estimated the amount of time after those delectable meals are served that there will be a steady
    “live” cargo migration about the cabin, with a subsequent gross transfer of mass from the seats to the alleged black ice “holding tanks”, and trim/transfer fuel/reload-redistribute the trolley mass accordingly.

    All in the interest of lowering fuel consumption, ecology,
    and public transportation economics of course. At that point they REALLY won’t let me past the door of the forward head, but I don’t care anywhere NEAR as much.