Within the US: When, and by whom, is the Transition Level determined/published?

The "Lowest Usable Flight Level" ("Transition Level" [TL] - term used outside North America) is FL180 when the (local) altimeter setting within a controller's area of jurisdiction is 29.92 inHG or greater. This is normally, not necessarily always, the province of ARTCC controllers in the U.S.

Your Questions:

  Is the entire US using the same TL at any given point in time?

This is not the case because the local pressure in San Francisco can be (for example) 28.92 and the pressure in Miami could be 30.20.  Therefore, the lowest assignable/usable FL over San Francisco would be FL 190 and the lowest assignable/usable FL over Miami would be FL 180.

From FAA JO 7110.65W, para. 4-5-4: JO 7110.65W

  Or, are individual ARTCCs setting their own TL based on the lowest QNH reading in their geographical area?

Individual areas of jurisdiction within ATC Facilities would be responsible for determining the Lowest Usable Flight Levels based on local QNH/altimeter settings.  Keep in mind that some sectors (areas of jurisdiction a single controller may be responsible for) can be enormous in size (part of Nevada west to near San Francisco, for example).  There can be a significant difference in local QNH settings within that sector that may require adjustments to the Lowest Usable Flight Level.

  Or, are individual sectors within an ARTCC setting their own TL based on the lowest QNH reading in their even-smaller geographical area?

See the answer above.
and 5. In my experience, an individual controller maintains all separation authority and responsibility within his/her assigned sector.  There may be supervisory input or oversight, but the responsibility to separate aircraft in accordance with the JO 7110.65 rests with the assigned controller.  There also may be internal SOP's that dictate how a facility will handle the flow of the information regarding lower than 29.92 local altimeter settings.


In a jet, are Vy and Vx achieved at a constant AOA at all altitudes?

It might help to derive both speeds from first principles. We assume that the drag polar of the aircraft can be described by a parabola, like this:
$$c_D = c_{D0}+\frac{c_L^2}{\pi\cdot AR\cdot\epsilon}$$
 The symbols are:
$\kern{5mm} c_D \:\:\:$  drag coefficient
$\kern{5mm} c_{D0} \:$  zero-lift drag coefficient
$\kern{5mm} c_L \:\:\:$  lift coefficient
$\kern{5mm} \pi \:\:\:\:\:$  3.14159$\dots$
$\kern{5mm} AR \:\:$  aspect ratio of the wing
$\kern{5mm} \epsilon \:\:\:\:\:\:$  the wing's [Oswald factor][4]

Next, we describe thrust $T$ over speed $v$ with $$T = T_0·v^{n_v}$$

Now first to the maximum climb angle. This is reached when the condition $$\frac{\delta \gamma}{\delta c_L} = 0$$
holds true. No change in lift coefficient $c_L$ will improve the climb angle $\gamma$, it is only downhill from here to both sides. In order to get a grip on the climb angle, we look at the force equilibrium in steady flight at full power, assuming small values for $\gamma$:
$$sin\gamma = \gamma = \frac{v_z}{v} = \frac{T - c_D\cdot \frac{\rho}{2}\cdot v^2\cdot S_{ref}}{m\cdot g} = \frac{T_0·\left(\sqrt{\frac{2\cdot m\cdot g}{\rho\cdot c_L\cdot S_{ref}}}\right)^{n_v}}{m\cdot g} - \frac{c_{D0}+\frac{c_L^2}{\pi\cdot AR\cdot\epsilon}}{c_L}$$
 The symbols are:
$\kern{5mm} m\:\:\:\:$ aircraft mass
$\kern{5mm} g\:\:\:\:\;$ gravitational acceleration
$\kern{5mm} \rho\:\:\:\:\:$ air density
$\kern{5mm} v\:\:\:\:\:$ velocity
$\kern{5mm} v_z\:\:\;$ climb speed
$\kern{5mm} S_{ref} \:$  wing area

Ideally, we would also multiply the climb angle with an acceleration factor, but I leave this out here for simplicity.

Now we can derive the expression for the climb angle with respect to the lift coefficient and get
$$\frac{\delta \gamma}{\delta c_L} = -\frac{n_v}{2}·c_L^{-\frac{n_v}{2}-1}·\frac{T_0·(m·g)^{\frac{n_v}{2}-1}}{\left(\frac{\rho}{2}·S_{ref}\right)^{\frac{n_v}{2}}}+\frac{c_{D0}}{c_L^2}-\frac{1}{\pi·AR·\epsilon}$$
The general solution is $$c_{L_{{\gamma_{max}}}} = -\frac{n_v}{4}·\frac{T·\pi·AR·\epsilon}{m·g}+\sqrt{\frac{n_v^2}{16}·\left(\frac{T·\pi·AR·\epsilon}{m·g}\right)^2+c_{D0}·\pi·AR·\epsilon}$$
For jets ($n_v = 0$) the solution is quite simple, because the thrust terms are proportional to the thrust coefficient $n_v$ and disappear: $$c_{L_{{\gamma_{max}}}} = \sqrt{c_{D0}·\pi·AR·\epsilon}$$
For turbofan and propeller aircraft, we have less luck and get a much longer formula. This is the one for propellers ($n_v = -1$):
$$c_{L_{{\,\gamma_{\,max}}}} = \frac{T·\pi·AR·\epsilon}{4·m·g}+\sqrt{\left(\frac{T·\pi·AR·\epsilon}{4·m·g}\right)^2+c_{D0}·\pi·AR·\epsilon}$$
So yes, pure turbojets have an optimum lift coefficient for maximum climb angle that uses only terms which are constant over altitude. They do indeed climb steepest at a constant lift coefficient.

But the thrust-dependent optimum for other engine types hints at an altitude dependency which might affect the other optimum, that for best climb speed.

In order to find the conditions for maximum climb speed, repeat the process above with an expression where both sides are multiplied by speed:
$$v_z = \frac{T\cdot v - c_D\cdot \frac{\rho}{2}\cdot v^3\cdot S_{ref}}{m\cdot g} = \frac{T_0·\left(m\cdot g\right)^{\frac{n_v-1}{2}}}{\left(c_L\cdot\frac{\rho}{2}\cdot v^2\cdot S_{ref}\right)^{\frac{n_v+1}{2}}} - \sqrt{\frac{2\cdot m\cdot g}{\rho\cdot c_L\cdot S_{ref}}}\cdot\frac{c_{D0}+\frac{c_L^2}{\pi\cdot AR\cdot\epsilon}}{c_L}$$

Now the solution for turbojets becomes the more complicated one, but that needs to be the case - how else would those optima converge at altitude?
$$c_{L_{{\,n_{z_{\,max}}}}} = \sqrt{\left(\frac{T·\pi·AR·\epsilon}{2·m·g}\right)^2 + 3\cdot c_{D0}·\pi·AR·\epsilon} - \frac{T·\pi·AR·\epsilon}{2·m·g}$$

While the angle of attack for steepest climb is constant over altitude, the angle of attack for best climb speed increases as excess thrust disappears with rising altitude. Thus, the question can be answered: No.


Why are aircraft tyres not grooved horizontally?

Almost all the aircraft operating from prepared surfaces have circumferential grooves in order to remove water between the tyre and runway surface.
From Dunlop site:

Most Dunlop aircraft tyre designs feature circumferential grooves moulded into the tread to disperse water from beneath the tread in wet runway conditions.
The tread helps to reduce the risk of aqua planing and improves traction and grip between the tread and runway surface.

In 1960s, NASA carried out a number of studies to determine the effect of tread design (among other things) for operating on wet runways and settled on the circumferential groove shape.
In case of aircraft operated from unpaved surfaces, the tyres may have some type of cross-tread pattern.


Could the Boeing 787-9 near vertical takeoff demonstration be performed by Airbus A350 aircraft?

No.

Firstly, as a comment noted, the takeoff was hardly "near vertical", the camera angle makes it look so. The takeoff angle in the video certainly is much steeper than a normal one, but Airbus aircraft are more than capable of doing the same - in fact an A350 did very much the same thing at the Paris Air Show.

The notion that an Airbus doesn't let the pilots have complete control is a little bit misleading. I'm not going to go into too much detail in this question, but what most people are referring to when they say that is the Alpha Protection system. This system kicks in when the aircraft is at extreme angles of attack. For example, if an aircraft is about to stall, it will not let the pilot pull the nose up. In any plausible situation the pilot would not want to raise the nose anyway, yet we have seen accidents such as Colgan 3407 where the pilot did exactly that (and, also AF447, however the system was disabled in that crash).

In summary, the Airbus system pretty much only prevents pilot actions that are dangerous (OK it is more complex than that, and the Boeing design has benefits too, but..). Back to your question, why does the Airbus system also allow such a steep takeoff? Because only the attitude was high, but the angle of attack was still within normal limits. These takeoffs are possible on lightly loaded aircraft with engines near full power.


What are Forward flight, Straight flight, Level flight, and Cruise flight in a helicopter?

Forward flight is how the helicopter flies in most situations. It flies similar to an airplane in this situation, with pitching up and down to increase and decrease airspeed. This is controlled by use of forward and aft cyclic.

Straight flight is where the tail rotor is set so that it opposes the turning tendency of the main rotor. This essentially prevents the helicopter from yawing while in flight. This is controlled by using the anti-torque pedals.

Level flight is simply when the helicopter is flying at a constant altitude. This does not mean, however that its nose is pointed ahead, or that it is flying forward, merely that it is not gaining or losing altitude.

I'm not sure exactly what cruise flight is. When a helicopter is "cruising", it most likely is maintaining altitude and flying straight ahead, but I don't think there is a separate term for it.


What is this propeller on the A330 MRRT refueling pod?

It’s a ram air turbine which drives a fuel pump to provide pressure to transfer gas through the hose and drogue to the receiving aircraft.


Why is there a provision of pressure setting in GPS?

By either manually entering the indicated altitude, total air temperature, barometric pressure, etc., or feeding those variables via sensors connected to the GNSS unit, it is able to know the true airspeed, wind direction/speed and the head/tail wind components.

Very useful for knowing the performance in-flight.

Example interface for the Garmin GTN 650/750 series with software 4.10:


What is the relationship between mountain breeze and air pressure?

There is nothing to reconcile: the higher pressure is where the cool air is. The weather report shows pressure fronts, and the low pressure ones are the ones heated up by the action of the sun.

If the mountainside warms up, the air in contact with it warms up. Warmer air has a lower density and it wants to float upwards, like a hot air balloon on a cold day. Meanwhile, surrounding air not heated up by the mountainside flows into where the heated air was, going from cool to hot. The reverse happens when the mountainside cools down: air gets denser and it wants to sink - when it hits the mountainside it just follows that down.

In a vessel with a constant volume, the higher pressure is at the hotter gas. In the unlimited volume of the atmosphere, the gas can expand as it pleases.


What are the experience requirements and process for becoming an FAA Designated Pilot Examiner?

You can start with the FAA's reference page for Designated Pilot Examiner.

It will point you to the FAA Order 8900.2 General Aviation Airman Designee Handbook.  It's all there.  You'll need to talk to your local Flight Standards District Office (FSDO) as they are responsible for administering the program. The general eligibility requirements are:

  General Eligibility Requirements. The managing office must carefully consider all of the requirements before designating an
  applicant or renewing a designee. The general requirements for
  appointment, which are reviewed by the NEB, are:

  a.    Minimum Age. Minimum age of 23 years for all designees.

  b.    Personality Traits. Must exhibit integrity, professionalism, and
  sound judgment.

  c.    Training Requirement. Must have satisfactorily completed the
  applicable training requirement before appointment/renewal as a
  designee.

  d.    Knowledge of Guidance Materials. Must have access to, and
  adequate knowledge of, the current regulations, policies, directives,
  and related guidance material appropriate to authorized functions.

  e.    Command of English Language. Must be able to fluently read,
  write, speak, and understand the English language.

  f.    Objectivity. Must maintain the highest degree of objectivity
  while performing authorized functions.

  g.    Good Record. Must have a good record in the aviation industry.

  h.    Technology Access. Must have internet access, as well as access
  to a computer and printer with hardware/software sufficient to support
  the required activities.

  Note:  A designee is not required to be a U.S. citizen.

  Note:  Additional eligibility requirements for specific designee types
  are included in the applicable designee type specific chapters
  (Chapters 6 and 7) of this order.

As to what the FAA is looking for (this from a DPE, I used to work with), the FAA is looking for someone they can trust to perform the job to standards. They expect a DPE candidate to be an experienced instructor.  They'll look at the the history of students signed off for check rides by that person. If any significant number of recommended students aren't passing check rides or 'just squeak by', it won't reflect favorably on the applicant.  OTOH, if the recommended students are well prepared and almost always pass, that's a good indication. That shows the instructor's standards are the same as the FAA's.

'Openings' for DPE positions are driven by supply and demand. The purpose of any Designee is to help manage the workload imposed on the FAA's office. If the office can handle the number of applicant's, they won't add a DPE. And if an existing DPE isn't performing a minimum of examinations, they'll lose the Designation. Most of the DPEs I've known worked for flight schools where there was a steady stream of students.


How is the centre of lift and centre of gravity misalignment problem solved in Delta wing aircraft?

The effect of a horizontal tail can be built into a tailless aeroplane in two ways:

By integrating into the wing profile: a horizontal s-shape with the trailing edge turned up.
By combining positive sweep with negative twist.


Why are the cockpit displays swapped between the captain's and first officer's sides?

It's hard to see from the angle that your example photos were taken from, but the main reason is that they want the primary flight instruments (which are on the PFD, or Primary Flight Display) directly in front of the pilot, no matter which seat they are in.
The PFD gives the most critical information which is used to actualy control and fly the aircraft, so is designed to be in the pilot's direct line of sight.
Less critical information is put on the MFD (Multi Function Display).  Since the pilots sit close to each side of the cockpit, this usually means that there isn't room to place the MFD on the outside of the PFD.  Even if there was room, the extra display is used partially for redundancy, so they don't want to put it further away from the other pilot.
Since the PFD is directly in front of each pilot, it doesn't take any effort to switch between seats because of that aspect.
This photo (it's night, so a little dark but I think that you can see what I'm referring to) was taken from my head level while sitting in the right seat, which should make it pretty clear:

own photo


If an airline purchases an aircraft, do they have to/feel compelled to change the livery?

Yes - logos, trading names, liveries etc are all covered by trademark and you would need permission from the trademark owner to use them yourself. Besides, the schemes are good marketing so a commercial operator would want their own livery on it as soon as practical.


Can a passenger realistically replace suddenly incapacitated pilots?

I guess this is a secret dream of many of you here: You sit on a scheduled flight, and hear in the PA system: "Both our pilots just passed out. Any volunteers to take over their duties?"

Won't happen.

Think of what would happen next: Panic! The volunteers won't even make it to the cockpit. All cabin crew are focussed to keep the cabin calm, so this announcement will never be made.

Instead, one of the cabin crew will take over. That is part of their duties, actually, and some airlines even give them basic training so they have a fair chance when they are in contact with someone on the ground who can talk them through all steps.

Edit: Thanks to some commenters for pointing out that the question also includes GA traffic. Yes, I did not cover this. Generally, I think a passenger should have an easier time to take over, when he/she is sitting already in the right seat. He/she could watch the pilot before and has a full set of controls available. GA planes move much more slowly, so things happen at a slower pace and much less kinetic energy is involved if the touchdown is not perfect. Much depends on the constitution of the new pilot: Some people will simply panic and not be able to follow even the best remote help. But if they keep their cool, a good landing (meaning one you can walk away from) should be possible.

I had been in the right seat of a Lancair once and the pilot turned the plane over to me on final. The Lancair was so sensitive in pitch that I porpoised the aircraft - I first had to get adjusted. So even a pilot in a new type might not be able to land it immediately when he gets to fly it first time on short final!


Could a wing be designed to exploit both normal flying and ground effect?

Ground effect is measured using the non-dimensional height parameter 'h/c', i.e. the height above ground divided by the chord length. By increasing the chord length, the height of the maximum efficiency height is raised, as the location of the h/c does not change.
Increasing the span also adds efficient lift due to aspect ratio effects, however creating too much lift is not always better, because it will move the operating altitude above the most efficient height (h/c max).
Ground effect therefore favours larger chord length to get the required ground clearance, however larger aspect ratio wings are better for atmospheric flight. An aircraft could be designed to operate in both modes, but it will always be a trade-off between efficient ground effect flight and efficient atmospheric flight, there is always going to be a compromise of one or the other or both.


What would be logged as the destination for an emergency landing in a field?

I would just write "off fld" in the destination box, if there is one, and describe the location in Remarks.  "Emerg ldng on I-90 2 mi S of Whereverville"  or "Pracaut lndg field 2 mi W of Middleofnowheretown".

You aren't going to get audited over that kind of stuff so don't worry about hyper precision.  If anybody ever looks at your logbook it's just going to be to validate flying times for the purpose of a license or rating.  The other stuff is mostly for your own historical record.


Would a takeoff be aborted if 'rotate' is not called out?

That could end up being a really bad idea if you've accelerated past your V1 speed -- your abort would then put you off the end of the runway, and the consequences from that range from bad to catastrophic.

A much better idea would be to look at the markers on your airspeed indicator, and if you're at/above rotation speed, go ahead and rotate.  Then sort out what's up with your copilot.

The worst case is, he's incapacitated, unconscious, experiencing a stroke or heart attack or something similar, and you'll probably end up returning to land as quickly as possible.  While the idea of staying on the ground to get him EMS help sooner might seem to be appealing, he'll probably NOT get better attention if your aircraft just ran off the runway, through the airport fence, and into whatever terrain/water/civilization lies beyond, because you didn't start your abort until several seconds after you should have been flying.  Better to come back and land with ONE sick person on the airplane, rather than crash, making your copilot now one of potentially MANY injured/scared/incapacitated people on a damaged jet -- and he with the very least ability of any of them to evacuate himself!

Or, maybe he got distracted and he's fine, and after he overcomes his embarrassment for missing the important callouts, the rest of the flight will go fine.

So, no, if the copilot doesn't call "V1, Rotate" I would NOT recommend aborting the takeoff.  If you see him slumped over when he should be making an "80 knots" or "airspeed alive" call, that might be a different decision; at that sort of speed you're in no danger of running off the runway & you could probably taxi back to the gate promptly.  But if he's missed his calls at significantly higher speeds, aborting is a bad plan.


Why do some T-tail aircraft have a protrusion on the top front of the tail?

It's a "bullet fairing".  Sometimes you get the pressure fields of the vertical and horizontal surfaces in alignment so the lowest pressure zone of the vertical fin is merged with the lowest pressure zone of the horizontal tail right at the intersection of the surfaces.  It results in a more extreme pressure recovery aft and can cause flow separation and vibration, and sometimes shock wave effects at high speed.

The bullet effectively moves the pressure field of the vertical surface forward to bring it out of alignment with the one of the horizontal surface.  It's usually an add on resulting from interference issues that are discovered in the wind tunnel, or during flight testing.


Is there a disadvantage to the "fan in fin" design seen for the tailrotor on many Eurocopter helicopters?

The fenestron is a lot heavier than a free tail rotor. This is probably the main disadvantage; helicopters are more sensitive to extra mass than aircraft.

At the time Eurocopter was produced by joining Aerospatiale's and MBB's helicopter divisions in 1992, a follow-on to the successful Bo-105 was under development. That was the Bo-108. Immediately, development was stopped to implement a fenestron into the finished design in order to give all Eurocopter products a common, distinctive feature. This resulted in major structural changes and a heavier helicopter. The result is now known as the EC135.

From this Aerospaceweb article:

  The only significant drawback to ducted fans like the Fenestron is
  that the shroud adds weight that offsets at least some of the
  improvements in performance.

As @Koyovis' answer points out, the low position of the lateral thrust vector is also a clear disadvantage. See here for more.


Glad you asked!

I referenced historical FARs from 2013, 1993, 1988, and 1969.  Here's what I found:


Is the aircraft used by NOAA specially modified?

Except for modifications related to instrumentation, not much. The WP-3D was developed from the Lockheed P-3 Orion, which was  a navalized L-188 Electra.

Orion is a sturdy platform. Used during the Cold War as an antisubmarine patrol aircraft, the plane is built to take punishment.

As the NOAA noted in a Reddit AMA

The WP-3D is built like a tough old pickup truck. It can handle a lot of abuse in the storm environment and come back and fly the next day. This is mainly because of the extremely talented maintenance team at NOAA’s Aircraft Operations Center (AOC)

Simply put, it is a normal aircraft with extensive instrumentation, albeit maintained well. The same applies for the WC-130J used by the 53rd WRS:

The 53rd WRS uses the WC-130J to penetrate tropical storms. These aircraft are not reinforced in any way in fact the only differences between a WC-130J and a C-130J is the addition of two external fuel tanks (giving them longer range), a radiometer pod on the left wing and the two addition crew pallets in the cargo bay...

and of course, the instruments. Actually, the NOAA has replied to your question in their FAQs:

Why aren't NOAA's Hurricane Hunter planes torn apart in storm?
Planes are generally not destroyed by strong winds while in flight. Airliners routinely fly in jet streams with winds exceeding 150 mph over the U.S. during the winter. It's the shear, or sudden change in horizontal or vertical winds, that can destroy an aircraft, or cause its loss of control. That's why NOAA's Hurricane Hunter aircraft don't fly through tornadoes. In a like manner, NOAA pilots and crew routinely (but never casually) fly in the high-wind environment of the hurricane and don't fear it tearing the plane apart. However, they are always monitoring for "hot spots" of severe weather and shear that they can often identify on radar and avoid if it's too severe.


Some energy from the expansion is used to turn the turbine which powers the compressor

And in some engines it turns the turbine which has a large fan attached to the other end. The engine produces more power than needed to run itself.

Inside the engine, everything is a very careful balance of pressures. Basically the job done by valves in a piston engine is done by careful engineering in a turbine, which is one of the reasons they cost so much. The inflow to the combustion chamber balances the outflow to the power turbine to the point where it wants to go that way - get it a little bit out of balance and you have noisy stalls like you see in the referenced video.


Where to find the callsigns of the en route controllers?

You can look in each country's AIP, specifically section ENR 2.1. Below is for the Netherlands:

Note the name/call-sign 'Maastricht Radar' for at or above FL 245. Maastricht UAC is...

  ... an international non-profit air navigation service provider, operated by EUROCONTROL on behalf of four States – Belgium, Germany, Luxembourg and the Netherlands.

Also from the AIP's you can find the division of the FIR's, example:


Why do we have to perform a normal APU shutdown if a fuel spillage occurs?

I would reason that any source of ignition,such as an APU or vehicle could ignite the spill causing a fire.


How does a bearingless rotor work on a helicopter?

There are still bearings for the spinning part of the rotor mast coming out of the transmission, and for blade pitch in the hub itself.  The bearingless part is that the blade flapping and lead/lag functions are accommodated by "elastomeric" hinges, basically, rubber-type compliant bushings.  It's very similar to the control arm attachments on modern cars where the control arm is attached to the frame with a large rubber bushing, bonded into a sleeve that is bolted to the structure, that accommodates the arm's rotation while isolating the control arm from the car.
Some helicopters also achieve this function by making the root section of the blade into a flexible shaft that is free bend in the flapping and lead/lag direction.
Hingeless rotors have been around since at least the late 70s.


Were inclined runways ever under consideration?

Yes, it does work, but cannot really be called practical.

The first reason is wind: It helps to take off and land with a headwind. If the runway slope is on one end, this has to be the end where the take-off run starts and where the landing run ends. Since both are in the same direction, this scheme now needs twice the runway length, the first half for landings and the second half for take-offs.

The next reason is the magnitude of what can be saved. The energy from the height change $∆h$ can be translated into a speed gain $∆v$ by this formula: $$∆v = \sqrt{2\cdot g\cdot ∆h}$$

Let the ten stories be a height of 40 meters, and your speed gain is only 28 m/s. This was significant in the age of propeller aircraft, but jets need much higher speeds to get airborne - 150 knots or more. In sane units this is 77 m/s, and since the energy is proportional to the speed squared, the 40 m slope will save only 13% of the energy needed for take-off. It is simply not worth it.

Now look at the operational consequences: The landing has to be performed such that the aircraft has slowed down to 28 m/s when it reaches the foot of the slope. If it is still too fast, it will overshoot and roll down the other side, and if it is too slow, it needs to run up the engines in order to climb up the slope, expending the energy it hopes to save at take-off.

No, practical is not what I would call this.


Do pilots who have color deficient eyesight see light gun signals differently?

It depends on the type and severity of the color deficiency and on the individual.

When I first applied for a 2nd class medical, I couldn't pass the color test. I took a practical test with an FAA inspector to get a waiver. We walked outside the FSDO office, and he had me identify the color of the lights being directed at me by the tower. Fortunately, I had been warned to have the tower do this for me on a previous day so I wouldn't be surprised. In my case I had to remember that if I saw yellow, that was white. If I saw white, that was green. Red was red.

When I first applied for a 1st class medical, I again had to take a practical test, but this time from an airplane. I noticed that from the airplane, the white of the green signal was more white, and the yellow of the white signal was more yellow.

Whether the difference from the ground test was due to the increased distance or to my individual daily variation I don't know. I have noticed during physicals through the years that my performance on the color test varies greatly.

In my opinion every pilot should have the tower shoot light-gun signals at him during training so that she/he can see how they look.


Why are commercial flights not (publicly) trackable in some locations?

The reason is that there is no member of the general public in those areas with an ADS-B receiver sharing live data with the public tracking sites.

Websites like Flight Radar 24 rely largely on volunteers installing ADS-B receivers and sharing their received data. They have a good coverage, but some areas are still not covered.


Is it possible to have dual contra-rotating rotors on a gyrocopter or gyroplane? Are there disadvantages that would outweigh the extra lift?

You can get additional lift with a larger rotor, without going to the extra complication of having two of them. Present-day autogyros are very light machines that have more than enough with one rotor. Besides, in the case of the coaxial configuration, the centre of mass of the machine will be much higher, a very undesirable thing for landings, as any gyro pilot would attest...


No, there is no limit. Aircraft stay as long in holding patterns as they have fuel on board.


I agree that this can be confusing.

The load factor is indeed inversely proportional to weight, unlike the load factor on an aeroplane, which might be thought of as the lift required divided by the certified MTOW for the category of operation (g limit).  If the aircraft is in a steady 1 g flight at MTOW, the load factor to achieve this is one.  Start turning in a steep bank and the load factor becomes two in relation to the design load factor of the aeroplane's structure. If you then reduce the weight of the aircraft to, say, half the MTOW, the load factor in 1 g flight is a half of the load factor the aircraft was designed for.

The load factor on an aeroplane differs from the abstract concept of load factor as it relates to the load imposed on the aircraft compared to the load imposed on the aircraft when operating at gross weight at 1 g.

I hope this helps.


2 reasons really:

Airplanes need most of their thrust right when their airspeed is low. (to get more airspeed at takeoff and go-around).
The maximum airspeed in cruise is not dictated by how much thrust the engines can throw out. Instead it's dictated by the aerodynamic forces on the airframe. They cruise right below the speed of sound where the rules of aerodynamics change drastically. Going too fast would rip an airplane apart.


How much is the minimum safe distance between two planes in-flight?

The question specifically asks about FAA regulations, so I will try to provide specific citations.

Summary

For a commercial airliner (as the question asked), separation will usually be at least 3 miles laterally, or 1,000 feet vertically. In the enroute environment -- at higher operating speeds above 10,000 feet and based on the type of Radar and distance from the antennae -- a 5 mile rule is applied laterally. This is true in most but not all situations. There are exceptions: see below.

Note also the "or": it is allowed (and in fact rather common) for two jets to cross paths at the same moment, with one 1,000 feet directly above the other. The 3 miles is only required if the jets do not have at least 1,000 feet of vertical separation.

Pilots

The regulations do not set a specific distance that pilots flying under VFR must maintain from each other. There's just the following blanket statement:

§91.111, Operating near other aircraft: (a) No person may operate an aircraft so close to another aircraft as to create a collision hazard. (b) No person may operate an aircraft in formation flight except by arrangement with the pilot in command of each aircraft in the formation.

In addition, there is the catch-all "careless or reckless operation" clause:

§91.13, Careless or reckless operation: No person may operate an aircraft in a careless or reckless manner so as to endanger the life or property of another.

Pilots flying under IFR are subject to the same kinds of rules, and are still responsible for maintaining separation from other traffic when in visual conditions. The rules are the same: the pilot is given the discretion of deciding what a "safe distance" is.

Actual distance limits only come into play for the air traffic controllers, who are responsible for providing minimum separation distances between IFR traffic.

Air Traffic Controllers

The set of FAA regulations for air traffic controllers is FAA order 7110.65. These regulations are quite complicated and there are lots of exceptions and corner cases for various scenario. I'll try to give only the most basic rules here, but note that a full reading of 7110.65 would be necessary to understand all the minutiae.

Vertical separation:

4-5-1 Vertical Separation Minima. In general, 1,000 feet for IFR traffic (with exceptions).
7-7-3 Separation, 7-8-3 Separation, 7-9-4 Separation. 500 feet for VFR aircraft (with exceptions).

Lateral separation:

5-5-4 Minima. In general, 3 miles in the terminal environment and 5 miles in the enroute environment (with exceptions).

Things get more complicated in the following scenarios, and exceptions apply to them:

Oceanic environment (7110.65 Chapter 8).
Approach environment, especially at large/busy airports with parallel runways and special approach monitoring radar. (7110.65 Chapter 3, Sections 9 & 10).
Nonradar environment (anytime the controller is not able to "apply radar separation") (7110.65 Chapter 6).

For these scenarios the regulations are rather lengthy and complicated, so I would simply refer you to Order 7110.65 in general.

Military

When flying in airspace controlled by ATC, military pilots must follow the same rules as civilian aircraft. ATC will keep them separated according to the rules above. However, there are two main exceptions to this.

When flying in formation, such as for training, aerial refueling, or intercepting aircraft, they are much too close for ATC to provide safety. In these cases, ATC will allow the pilots to fly under MARSA (Military Assumes Responsibility for Separation of Aircraft). In the case of interception, if the fighter pilot is not able to see the aircraft they are intercepting before the minimum separation, they must break off. They can only fly under MARSA if they can actually ensure visual separation.

The FAA can also define an MOA (Military Operations Area). Once military aircraft enter this area, ATC is no longer responsible for them and they are under MARSA. When the aircraft leave the MOA, ATC resumes control. They can still be under MARSA for a formation, but ATC will keep that formation separated from other traffic.

In tactical formation flying, there is no limit. The Blue Angels routinely fly with only 18" separation between the wing tip and the cockpit canopy. Combat aircraft fly a variety of different formation patterns at varying distances, and pilots are extensively trained on each pattern and what the appropriate/safe distances are. (For example, a fingertip formation allows for much closer flying than a line-abreast formation.)


Can pilots hear a car horn while on the ground?

Airplane engines are loud, so if they are running I would say no, a pilot is not going to hear a car horn. If you want to get a pilot's attention without a radio you'd use light or hand signals.


What is the process for a TFR based on law enforcement activity?

TFRs around "volatile situations" on the ground aren't a daily occurrence, but they do happen fairly frequently.

The concerns are usually twofold: Events on the ground posing a hazard to aircraft (people shining lasers at aircraft, firing guns at them, etc.), and aircraft posing hazards to each other (News 2, News 4, News 11, and Police helicopters all wanting to cover the same area at the same time and smacking into each other).

There are procedures in effect for agencies to request TFRs, and for the FAA to review them. These are covered in detail in FAA JO 7210.3Y, Chapter 19. Particularly relevant to this situation is 19-2-5 (e): "TFRs issued for law enforcement activities require approval from the ATO Director of System Operations Security (or designee)." - a relatively high level of approval intended to safeguard against the use of TFRs to, for example, keep the media away.

In the case of Ferguson the regulatory basis for the TFR is cited as FAR 91.137(a)(1) (to protect persons and property on the surface or in the air from a hazard associated with an incident on the surface), so presumably their major concern is laser illumination or weapons fire from the ground, and the potential for such incidents to cause a surprised pilot to crash into a building or crowd of people.


Can an airline order a 777 with 787 flight deck avionics?

I'll answer based on the one precedent I'm aware of. Yes. But whether the manufacturer agrees is up to them.
In 1996 Saudia ordered 29 MD-90s with MD-11-style cockpits from Honeywell, including the overhead panel.
Which Honeywell then supplied for the MD-95 (later renamed Boeing 717) as well.
From Honeywell's press release:

Saudi Arabian Airlines (Saudia) has specified Honeywell's 8-by-8-inch flat panel liquid crystal displays for its new McDonnell Douglas MD-90 airliners.
(...)
In a separate development, Douglas has also decided to provide Honeywell's flat panel displays for the recently launched MD-95 aircraft program.

Regarding the specific 777/787 example, the 787 shares a lot already with the 777, which reduces the cost of training a 787 flight crew if they're already type-rated on the 777. Therefore, there's little incentive for both the airline and manufacturer to go that specific way.

For different reasons (not one airline's order) the 767-400ER comes with a 777-style cockpit, including the big displays.

The 767-400ER incorporates a new flight deck similar to that on the 777 (...) The overhead panels are largely unchanged (Boeing).


Engine out over a mountain road. Do you land upwind or up hill?

Admittedly, the 10 degree sloped roadway is an anomaly, and you would never see an actual runway built on this grade.  Don’t try to apply any of this logic to a shallower runway without some careful analysis.
Here's my take on the possible landing approaches.  I think my performance estimates are generally conservative.  I think the flight maneuvers are fairly pedestrian until landing and roll-out.  Your mileage may vary.  These are not optimal, but I think it is possible to land either uphill or downhill with varying degrees of risk and maneuver aggressiveness from nearly any initial heading.  Obviously, some headings significantly reduce the risk of one direction over the other.  In half of all cases you may have to make right turns instead of left.
Here are my assumptions:
Altitudes are all referenced to the roadway midpoint elevation
Aircraft weight is 2000 lbs.
40 KIAS -- stall in landing configuration
45 KIAS -- 1320 ft/min descent - 30 degrees flaps
48 KIAS -- stall in clean configuration
50 KIAS  -- 780 ft/min descent - 10 to 20 degrees flaps
55 KIAS  -- 725 ft/min descent
60 KIAS  -- 800 ft/min descent
65 KIAS  -- 870 ft/min descent - best glide angle through the air  approx. 7.5 to 1 glideslope
70 KIAS  -- 970 ft/min descent
75 KIAS  - 1115 ft/min descent
80 KIAS - 1285 ft/min descent
The wind is blowing from the South at 15 knots
Horizontal wind component up the slope:  ~1500 ft/min
Vertical wind component (upward) up the slope:  ~264 ft/min
Uphill landing

Using your cat-like reflexes and finely-honed piloting skills, track outbound on a heading of 235 for 16 seconds while trading your 100kts of airspeed for a little more altitude.  I calculate you can pop up about another 80 feet from the mid-field starting altitude during that time.
Fly for an indicated airspeed of 70 kts because you must now turn (~1.1G load factor) at 6 degrees per second to a heading of 180.  This takes about 9 seconds; you are 1600 feet south, 2280 ft west, and about 950 ft above mid-field.  26 seconds have elapsed.
Fly on a heading of 180 for nearly 40 seconds.  Think about making a radio call stating position and situation.  Maintain 70 KIAS for better penetration into the wind.  You are in your downwind leg and it has been over 1 minute since your engine failed.  You are 5230 ft south, 2280 ft west, and 495 ft above mid-field.  About 65 seconds have elapsed.
Now turn, maintaining 70 KIAS, at 6 degrees per second to the "runway" heading of 360.  Take a few extra seconds to roll out and line up with the roadway.  You are about 3935 ft south (thanks to that upslope wind), aligned with the centerline of the road, and 108 ft above midfield (about 750 ft AGL because of the slope).  About 97 seconds have elapsed.
Slow to 65 KIAS and fly this heading for about 27 seconds.  Wait until the end to drop maybe 10 degrees flaps to preserve speed for the zoom-climb, flare landing.  Nose-high attitude will be your friend on the upslope landing so don't use too much flap deflection.  About 114 seconds have elapsed.
You cross over the landable portion of the road at 65 KIAS with over 100 ft AGL.  It has been about 118 seconds since your engine failed.  Fly the aircraft through an energy-preserving flare (actually climbing at the last) until a few feet above the rapidly rising road.  You will touch down just past the first third of the landable roadway a little over 2 minutes since your engine failed.  Your speed will bleed off, the airplane will stop flying, and because of the upslope, you will roll to a stop, with or without brakes in 10-20 seconds.  Apply brakes so you don't roll backward down the hill!
Downhill landing

Track outbound from the midfield point on a heading of 90 degrees for 7 seconds while trading airspeed for altitude.  The maneuver takes about 15 seconds to complete, but half-way through, begin a 6-degree-per-second turn, stabilizing at 70 KIAS and rolling out on a heading of 360.
Fly the 360 heading for about 4 seconds.  You are now about 2340 feet north, 2255 ft east, and about 925 ft above the midfield point.  26 seconds have elapsed.
Maintaining 70 KIAS, begin a 30-second, 6 degrees-per-second turn to heading 180.  You are now about 2940 ft north (upslope wind again), aligned with the roadway, and 550 ft above the middle of the roadway.  Your height AGL is only about 65 ft (!), but that’s okay.  You are on final approach and you can fly into and out of ground effect as you like to fly to the threshold of the landable portion of the roadway which is on the steeply descending slope.   It has been about 56 seconds since your engine failed.
Just under 60 seconds have elapsed.  At this point you need to increase your rate of descent to more than the 10 degrees (17% gradient) downslope of the hill and roadway.  You might choose to drop 30 degrees flaps and decrease airspeed to 45 KIAS and plunk down on the roadway at about 30 knots groundspeed, but you have to bleed off 35 knots of airspeed without ballooning too much and end up at only about 5 knots above stall.  Your angle of attack would be so high that you would not be able to see the roadway at all - not even the far end because of the down slope. And you would strike the tail on the ground before the main wheels touched.
Instead, you will need to increase your airspeed to about 80 KIAS and use about 30 degrees of flaps to keep from flying up and away from the ground.  This feels like a fairly steep approach but you are only descending at about 250 ft/min with respect to the ground which is falling away steeply.  You are about 2000 feet from the landable portion of the runway.
In about 20 seconds you are down and on the roadway about 100 yards down from the start of the landable portion.  About 1 minute and 17 seconds have elapsed since your engine failed.
Here's where things start to get a little sketchy.
You are rolling down the roadway with 80 knots indicated (65 kts ground speed) – give yourself 6-8 seconds to get the flaps fully retracted while you try to keep the aircraft “stuck” on the ground.  On a 10 degree downslope your brakes are (cosine 10 degrees) still about 98% as effective, if you weren’t still generating a lot of lift.  Conservatively, you might get 50% of your weight onto the wheels initially.  And don’t forget your mass is effectively pulling you down the slope (sine 10 degrees * 2000 lbs) with about 345 pounds of force.
For reference, this source: (https://aviation.stackexchange.com/questions/67979/is-there-an-actual-rated-thrust-for-a-cessna-172-engine-at-takeoff-power#:~:text=As%20John%20K%20said%2C%20it,be%20aware%20of%20before%20takeof) puts the thrust of the 160hp, fixed pitch 172N at between 500-600 lbs force when at takeoff power.
You will trade lift at higher speeds of the roll-out, which will make your brakes less effective, for the drag at the higher speeds which will counter-act the downhill force.
It’s probably a 30+ second, white-knuckle ride down the roadway managing your energy, trying to keep the plane “stuck” on the ground and to not lock up the lightly loaded mainwheel brakes until you get it stopped just before the end of the useable portion.
I conclude that the uphill/downwind landing is the better choice for the following reasons:

Time.  Compared to the downhill/upwind landing you have about 30 seconds more seconds to collect your thoughts, take calming breaths, and possibly make a radio call reporting your position and situation on one of the straight legs of your “pattern”.  You buy the extra time by landing on the end of the roadway that is almost 350 feet lower than the top end.
Distance.  Right up until touchdown, the proximity of the ground is not a factor at any part of the uphill/downwind approach.  Contrast this with virtually skimming the ground for 15 seconds at the last of the downhill final.
Energy.  Granted, change in energy on the uphill approach happens much more quickly at the landing, but because you are flying up the slope there is some leeway on the timing and aggressiveness of the landing flare.  And once you are down, you will roll to a stop even if you don’t use the brakes.  On the downhill landing both your kinetic energy and your potential energy are working against you getting your aircraft stopped.  The relatively feeble upslope wind does little to help you here, and in fact, hurts you once down by producing more lift and reducing the weight on wheels for braking.  There will likely be an excruciating 30 seconds of managing flaps, brakes, and elevator so you can brake to a stop before the end of the useable roadway.


What effect does wing loading (high and low) have on aircraft performance?

Wing loading is, as a North American industry standard, defined as weight/wing reference area (W/S). But then again, there is nothing wrong to define it as mass/area; so be careful of comparisons against literature.

As you have correctly cited in your OP, a large wing loading inversely affects performance, this includes takeoff performance and turning performance, all due to increased stall speed. Assuming a constant maximum lift coefficient, the larger the wing loading, the higher the stall speed:

$$V_{{s}}=\sqrt{\frac{W}{S}\frac{2}{\rho C_{L_{max}}}}$$

Large wing loading, however, is beneficial from a ride comfort perspective and offers structural benefit (i.e. weight saving) when considering gust loads. Assuming the same level of gust, the faster an airplane flies, the higher vertical acceleration (G) it experiences. A particularly salient and approximate relationship can be found in 14 CFR 23.341 (pre Admt 64), whereby the load factor from gust is given by:

$$n_z=1+\frac{K_gU_{de}Va}{498(W/S)}$$

In the above, $K_g$ is the gust alleviation factor which increases with W/S, $U_{de}$ is the gust speed in ft/s (found in 23.333 and decreases with altitude), $V$ is equivalent airspeed in kt, $a$ is the lift curve slope. As you can see, the load factor decreases with increasing wing loading and increases with increasing airspeed.


Are there any calculations involved for designing pulse jets?

YES

There are calculations involved in the design of a pulse jet. (title question)

YES

There are requirements for calculations... (first body question)

NO

The end of the combustion chamber does not need to be a hemi-sphere. (second body question)


Has this "straight through" airport design ever been contemplated?

Yes. An architect named Miklos Deri seems to have contemplated something similar: Drive Through Airport – Inversion of Procedures. The design is based around smaller aircraft (which reduces some of the height and size problems) and stacks aircraft together in lines to address the space efficiency issues.

Nobody has built such an airport (it's a concept, not created for any particular project), and there are practical problems associated with moving aircraft multiple times during a turnaround.


Can I log simulated instrument time in a complex plane without having a complex endorsement?

Yes. You can, as long as you have the appropriate rating and are the sole manipulator of controls. From a FAA response to a similar question:

  ... a private pilot may log pilot-in-command time, in a complex or high performance airplane, for those portions of the flight when he or she is
  the sole manipulator of the controls because the aircraft being operated is single-engine land and the private pilot holds a single-engine land rating.

  ... 14 CFR section 61.31 requires a person to have an endorsement from an authorized instructor before he or she may act as pilot in command of certain aircraft (a complex airplane, a high performance airplane, a pressurized airplane capable of operating at high altitudes, or a tailwheel airplane). These endorsements are not required to log pilot-in-command time under 14 CFR
  section 61.51(e). (emphasis mine)

Excerpt from §61.51 Pilot logbooks:

  (e) Logging pilot-in-command flight time.

  (1) A sport, recreational, private, commercial, or airline transport pilot may log pilot in command flight time for flights-

  (iv) When the pilot performs the duties of pilot in command while under the supervision of a qualified pilot in command provided—

  (A) The pilot performing the duties of pilot in command holds a commercial or airline transport pilot certificate and aircraft rating that is appropriate to the category and class of aircraft being flown, if a class rating is appropriate


How to calculate bending moments and shear forces on a wing?

I would highly recommend to discretize your problem, for two reasons:

You are using Matlab which is most suitable for a discrete approach anyways
More complex load cases will make analytical continuous modelling difficult. This is why these kind of problems are typically solved numerically

So now the question how can we discretly regard this problem? For the wing bending moment, this is pretty straightforward. First of all, lets make a small sketch.

The process of discretization is now to look at equally spaced points of the wing seperated by the distance Δd. I call them discretization points. I have labeled them in the following sketch as a vertical line numbered as 1, 2, 3 ... until point i.

What you need to do now, is to calculate the force acting on each discrete point. This part in turn is divided into two parts:

Calculating the exact shape of the different forces: Therefore force of motor weight, force of the wing structure and as a function of these two, the bell function of the lift
Integrate the wing lift force and structural weight force from discretization point k-1 to point k.

Now you have the exact weight acting on each point k (simply the integration of the wing lift force and the structural weight force from point k-1 to point k). Calculating the bending moment is now straightforward. For example, the bending moment at point i-1 is just the force acting on point i times the distance from point i-1 to i:
$$ M_{i-1} = i \cdot \Delta d \cdot F_i $$
the bending moment at point i-2 is now therefore:
$$M_{i-2} = 2*\Delta d \cdot F_i + \Delta d \cdot F_{i-1}$$
and so forth and so on.
The shear force at these points is even simpler. It is just the sum of all forces at the different outboard. So for example at point i-2:
$$ F_{i-2} = F_i + F_{i-1} $$
You can see that this type of equations can be easily programmed in Matlab. If you program this a bit cleverly, you can even play around with different values of Δd, which enables you to see the effects of discretization.
Hope this helps. If you need more help with the code, feel free to ask.


Not likely. Pilots wear headphones, so we cannot hear the idle prattle of the pax in the hold. In any case, we don't take orders from passengers. Think about that for a second: would you like it if aircraft pilots followed the instructions of a crazy screaming passenger? What if there were TWO crazy screaming passengers giving contradictory commands? Which one should we obey?

In any case, nowadays cockpit doors are closed during flight anyway.


Is there any flight school that uses jets as part of their training program?

Yes, Lufthansa flight training in Bremen uses the Cessna Citation CJ1+.

D-ILHA
D-ILHB
D-ILHC
D-ILHD
D-ILHE

The KLM flight academy used to have Cessna Citations, but I think they no longer use them as part of the training.


Is it possible to have V1 greater then Vr?

I think the answer is no.

If you think about V1 as primarily based on runway length, it is certainly possible for an aircraft to easily reach Vr long before reaching the "point of no return" as far as stopping distance is concerned.

However, you must also consider the meaning of Vr. This is when the aircraft is going to rotate. After rotation and leaving the ground, the distance required to still stop on that same runway increases significantly.  For this reason, maximum V1 is generally considered to be Vr (see this discussion).

In large aircraft, rejecting a takeoff after leaving the ground is generally discouraged, unless the pilot feels that the plane could be uncontrollable. It's much safer to continue the takeoff and fly for a normal approach. However, it can happen.

In smaller aircraft, it's more reasonable for the aircraft to take off and then land safely (I'm thinking a C172 on one of the low density altitude runways you linked to).


What do jet pilots say during the takeoff as they are speeding down the runway?

What you are hearing is "V-One", written as V1.
It actually is said when they can no longer safely abort the takeoff with the remaining runway, but they still are not quite ready to takeoff.
As they get a little faster, there should then be a second callout of "Rotate" when they have achieved the required takeoff speed, and that is when they actually takeoff.
To answer the "why" part, it is said by the pilot who isn't actually flying the airplane since he has more time to monitor the speed and can say it at exactly the right time.  It alerts the other pilot that it is no longer safe to abort the takeoff and that pretty much no matter what happens now, they should continue and come back to land if needed.
Edit:
In my answer above, I simplified somewhat by only mentioning the available runway.  There are other factors that can come into play even with a runway that is longer than needed.  One example would be the speed after which the brakes can no longer stop the airplane because they would over-heat and become ineffective.  This is known as the brake energy limit, and it is not safe to abort above this speed, even if you have "plenty" of runway.
V1 must be calculated or looked up prior to every takeoff, along with the other performance numbers.  They vary based on the weight of the aircraft, the configuration of the aircraft, the altitude of the runway, and the weather (outside temperature, wind, etc.).  Sometimes this is done via a computer and sometimes manually via lookup tables or even graphs.
For an example of the graphs, and more information about how temperature and altitude affect takeoff performance, see my previous answer here:
Does temperature affect takeoff performance?
There are also times when a pilot may increase or decrease V1 intentionally, even when it is not required.  For instance, if there is wet ice on the runway it may not be safe to abort even at a very low speed, so you would be forced to continue no matter what (note that I'm NOT saying that this is a good idea). Using a lower power setting to extend engine life is another example, and you can read about it in my question here:
Why would an airplane pilot choose to intentionally use more runway than required for a takeoff?
For way more information than you probably care about takeoff performance, see my other answer here:
Minimum Runway Length and V1
In closing, aircraft performance planning is a rather complicated subject and it is only one of many subjects that we must master in order to safely fly an airplane.  This only just scratches the surface of it, and there is a lot more that must be considered (such as "hey, will we be able to out-climb that tree off the end of the runway?").


Why does the B-2 have a smaller payload than other bombers of comparable size?

The simple answer is that it is optimized for being low observable/stealthy, and long range, rather than for maximum payload.

When you design an aircraft, you make a variety of trade offs depending upon which features are most important for that design.  The design of the B-2, which reaches back into the 1980's1, put a premium on the ability to avoid being detected by radar.  This informed the shape.  The USAF's strategic purpose for that aircraft was to enable it to reach globally, so that it could be launched form the continental US or a forward deployed base.  This put a premium on range/fuel capacity.

@Durandal points to another detail/difference: The B52 and B1 both can carry ordnance on external hard points (and this is a must to get up to the cited payloads). The B2 has no such hard points because it would nullify its stealth capability. There is simply no room to put more munitions within the bomb bay.

With the advent of precision weapons, which were in parallel development to the B-2, the raw tonnage wasn't as important as getting to the target area, and getting out "without being seen."

Because aircraft are all constrained somewhat by the cube/square law in terms of size, the trade offs/compromises on that model arrived at a payload that fit in with the rest of the requirements.

Both the B-52 and B-1 were build under a different design paradigm, under different requirements combinations, and were "pre-stealth" bombers: the B-52 was meant to get the most range and raw payload together, while the B-1 combined speed (supersonic, back when speed was perceived to be at a premium) and payload foremost.  While both have since benefitted from the use of precision munitions, the original designs (all nuclear weapons carriage considered) had to account for the problem of non-precision munitions shortcomings with accuracy.  (Experiences in WW II informed this problem, as did experience in Viet Nam).  You need to drop a pattern of "x many bombs" to have a high probability of hitting a given target.

1 Insofar as the "flying wing" idea for the shape of the B-2, the initial attempts in that direction go back to the 1930's and the Ho_229 as so @paracetamol kindly reminds us.  Also, and FWIW, it is related to a DARPA  project that goes back to the 1970's (stealth / radar resistant in general) that was compromised publicly by President Carter during a press conference.  Actually, those paying attention had heard of it from Kelly Johnson: In fact, that existence was far from secret. On July 23, 1976, readers of Aerospace Daily were informed that Clarence L. (Kelly) Johnson, "the nation's premier aircraft designer" and architect of the U-2 and SR-71 spy planes, was bulding "a new 12,000-pound, one-man Stealth aircraft" at the Lockheed plant in Burbank, Calif. The magazine claimed that the $90 million program, sponsored by the Defense Advanced Research Projects Agency, was designed "to reduce aircraft visibility -- optical, acoustic, and radar signatures -- through new technology."


Are you required to fly a full hold when doing a course reversal?

When performing a HILPT, typically the aircraft will pass the hold point outbound and perform the correct entry.  When you are inbound, you will continue with the approach once crossing the hold point again.
The aircraft will only pass the hold point twice unless a request is made to ATC for further hold to get ready to fly the approach.


What is this small black rubber strip protruding out of the flap track fairing of the A320?

It appears to be one of the rubber seals that are on the moveable flap track fairing.

source

Since the fairing moves away from the wing it has probably come loose and is caught between the fairing and the flap.

I can't find a good photo of a fairing from an A320, but here is a photo of the fixed fairing from an A350. It's hard to tell if they are exactly the same, but you can see that they look similar.

source


What's this biplane built by a 16-year old?

I don't know about this being from the 90s, but it sure looks like the Laird Baby Biplane in the Florida Air Museum to me:

On display at Florida Air Museum, Lakeland Linder Regional Airport, Florida (wikimedia.org)

The identifying features that I observe to be common between this picture and other pictures of the aircraft are the shape of the nose, the details along the fuselage, the shape and placement of the struts, the tanks beneath the top wing and the shape of the engine protrusion. I would also note that the Wikipedia page indicates that the specimen in the museum is a replica that was built in the 90s (whereas the original is from 1912).


What is the motivation behind designing a control stick that does not move?

The stick does not need to move in order for the pilots to sense their inputs!
Humans have very accurate force sensors in their fingers, and no direct position sensors. Without looking, we only have a very vague idea where our hand is due to muscle tone sensing, but we don't need to look at our hand to know exactly how hard it is pushing at an object. For the human, force is the imminent control feedback factor.
The F-16 can do 9G in manoeuvres, and the pilot is inclined backwards with their arm on an armrest. If this arm needs to move a stick it shifts position, and during a manoeuvre can get grabbed by the load factor - precise control is much easier if the hand, wrist and arm can stay in one position.
A pilot who has flown both the F-16 and the centre stick F-18 has this to say about it:

Flying a side-stick control takes a while to get used to, but once you do, it's a joy. The conformai stick's shape feels very natural (it fits in the hand like a melted candy bar), and it allows easy access to nine of the 16 hotAS controls. Two fully adjustable forearm rests on the right cockpit bulkhead stabilize and isolate the pilot's arm and wrist, so when rattling around the cockpit during turbulence or going after the bad guy, the pilot's arm won't accidentally move and initiate unwanted control inputs.

Initially the stick was fixed completely and pilots would get comfortable with the novel concept of no stick movement pretty quickly. But there were two issues:

Cross-coupling. The control input must be separated in two axes, pitch and roll, and this is difficult to separate if feedback is from force only. In order to aid this, a small bit of movement was introduced with a breakout force in the centre: upon release, the stick moves back to neutral and requires a bit of force to be deflected from there. From the article linked above:

However, after initial F-16 flight tests, a ¼ inch of stick movement was incorporated to give a small dead band and a nominal breakout force to give better "feel" of a neutral stick because otherwise it was entirely too sensitive. The control harmony is quite good (the pressures required for pitch and roll mix well), but without the capability to physically position the stick, it's easy to contaminate roll inputs with unwanted pitch inputs, and vice versa

F16s kept getting back with bent sticks. During chasing another plane and pulling, pulling on the stick, they pulled excessively hard while the fly-by-wire was already generating the deflection for maximum load factor. With the stick now moving a little bit, the pilot can feel that the limit is reached when hitting the travel stop at 25 lbs. At this force the acceleration is 9G and pulling harder has no additional effect.


How long has the term "situational awareness" been used in aviation?

According to M. Press, in his 1986 unpublished manuscript Situation Awareness, let's get serious about the clue-bird which is cited by many authors, the concept of SA can be traced back to aces of WW1, in particular Oswald Boelcke.

According to M. Press, his success was due to him being aware of the enemy before the enemy sees him.

From Situation Awareness Analysis and Measurement, Mica R. Endsley, Daniel J. Garland, p7:

  The earliest discussions of SA undoubtedly derive from the pilot
  community going back as far as World War I (Press, 1986)


What skills do aviators have uniquely that could cross over to another industry?

I'm just asking but, have you thought about teaching PPL/ATPL? It's obviously not the same income as a pilot (usually), but you still keep in 'our industry' which I'm sure you really like the most.

Sorry about those sensitivities...


How does radar detect turbulence and wind speed?

The answer you are referring to explains how radar is used to fly through a squall line whilst avoiding the most turbulent areas.

Conventional weather radar cannot detect wind speed or turbulence directly, it only detects solid and liquid objects above a threshold size.

The most turbulent areas of thunderstorms are also those areas that contain the most water and ice. This precipitation reflects radar waves very well so the most turbulent areas have the strongest reflections and shows up as red / purple on the scope. The area downwind of the core is usually very turbulent as well.

So the weather radar is merely detecting the presence of water. It is the pilot interpreting the picture who is really detecting the turbulence.

Clear air turbulence  (CAT) does not have condensated water in it and is therefore undetectable by conventional radar. There are systems such as LIDAR that can detect CAT but they generally not installed on aircraft.

As @reirab noted in a comment, a Doppler radar can be used to detect the relative speed of the particles from an aircraft. This is not used to reliably detect wind speed, but when there are large variations in wind speed (a.k.a. turbulence) the Doppler shift in the reflections from the particles causes a spectrum spread. This is an indication for turbulence. The traditional S-band airborne weather radars do not have this capability but the newer X-band radar (e.g. this Honeywell radar (PDF)) can detect wet turbulence to distance of up to 40-60 nautical miles using this technique.

LIDAR (a portmanteau of Light and RADAR) is a technology that uses light instead of radio waves. LIDAR can measure position and relative velocity of aerosols and therefore it can be used to detect turbulence. It has been used successfully to detect wind shears and map wake vortices on final approach from the ground (paperPDF).

Currently investigation (paperPDF, presentationPDF)is going on into airborne use of LIDAR to detect CAT. One of the difficulty is to detect vertical components of the turbulence. This causes very little Doppler shift but at the same time have the most effect on the aircraft (since the vertical component of turbulence causes changes in angle of attack).

As far as I know there are currently no commercial applications of LIDAR for airborne turbulence detection.


Is it possible for a Citation Jet not to have an APU or AIR COND?

It is possible for a Citation jet to not have an APU, two of them that come to mind are the CJ2 and CJ3 aircraft. An aircraft with an APU can have an independent air conditioning system or not, it just depends on the installation and manufacturer. Some airframe manufacturers use engine (or APU) bleed air to condition the cabin air temperature. Something like an APU would have overhaul limits similar to an engine, propeller, or a combustion heater like in smaller aircraft. Anything with a life limit would have to be tracked, so that could be individual components of a larger system, such as the starter/generator of an APU, or a compressor motor of an air conditioning system. I think what you're seeing is a coincidence.


Can a non-A&P fabricate and install his own hydraulic lines?

Generally speaking someone who does not hold a mechanic's certificate may not fabricate their own hardlines or hoses, nor may they replace hardlines. This work must be done by someone holding the appropriate Airframe and/or Powerplant mechanic rating.

An owner/operator with a private pilot certificate may install prefabricated flexible fluid carrying hoses (with the specific exception of hydraulic hoses) as preventive maintenance,as allowed under FAR 43 Appendix A.

There are three notable exceptions to the above general statements:

An owner of a Special Light Sport aircraft may acquire a repairman certificate, enabling them to perform this kind of work on their aircraft.
The builder of an Experimental Amateur-Built aircraft ("homebuilt") may perform this work on aircraft they have built, as FAR 43 does not govern maintenance on aircraft with an Experimental airworthiness certificate.
If working under the supervision of an A&P mechanic you are authorized to perform any work your supervisor is authorized for (per FAR 43.3 (d), and subject to some specific requirements).


What is the initial direction from Sydney to Santiago on a great circle?

Yes, the map is accurate. You can see the same thing on this map from gcmap.com:

On a polar orthographic projection, the great circle looks like this:


How does the efficiency of a piston aircraft change with altitude?

You are right, flying higher will be more efficient. However, the inverse relation between thrust and speed in propeller aircraft means that the available speed range is much smaller, and thus the possible altitudes are more restricted. Simply put, the possible gains are smaller.

If you look at the thermodynamic cycle of a turbo-compound engine, it looks almost like that of a jet. Still, the high bypass ratio translates into a lower optimum flight speed and the lower power-to-weight ratio usual for piston aircraft limits the maximum altitude and makes them more susceptible to adverse winds. Also, turbo-supercharging, which is much more efficient that supercharging, was developed to a practical solution only a few years before gas turbines were introduced, so pre-WW II piston engines relied on the less efficient supercharger for boosting power, reducing the benefit from flying higher yet again.

Why historic flights were performed at lower altitudes has probably more to do with the low ceiling of the initially heavy airplane and the lack of supercharging than with a deliberate choice by the crew. Maybe the lack of cabin heating or de-icing equipment, or even an open cockpit, made lower, warmer altitudes also preferable. Another reason might be the need for terrestrial navigation in the absence of today's infrastructure of radio beacons and GPS satellites. That flying higher translates into better range was known as early as WW I.


Are there modern airplanes with two propellers driven by one single engine?

NASA has proposed to use single gas generator cores to mechanically drive multiple fans in various advanced vehicle concepts, but those are a long way from actually being built.

Airbus and others are also proposing hybrid-electric airlines where a few gas generator cores drive many small fans, although in that case the power is electrically distributed rather than mechanically linked. There are some hybrid-electric vehicles in development that might qualify (Airbus E-Fan-X, UTC 804).  With all the current development in electric aircraft, it is likely some vehicle that meets your description will fly in the near future, with the caveat that the linkage between the engine and multiple propellers is likely to be electrical and not mechanical.

Images from NASA


The "position" and "velocity" include more than what the title would suggest.

Airborne position gives you:

Latitude/longitude
Altitude

Airborne velocity gives you:

Horizontal ground speed vector
Vertical rate
Air speed (when ground speed not available, can be true or indicated)
Heading (when ground speed is not available)

Together these two message types give you all the basic information you need about an aircraft's location and velocity. You are correct that given two lat/lon/altitude points, you can calculate the average horizontal speed, heading, and vertical rate. Keep in mind that ADS-B is already using the Compact Position Reporting format which calculates position with either two sequential messages or a reference position.

In addition to the additional computation cost, the measurement accuracy also needs to be considered. ADS-B broadcasts a "Navigation Integrity Category" or NIC, which expresses the accuracy of the GPS position. In terminal airspace, ADS-B is required to have about +/-300 feet in positional accuracy. While this is sufficient for giving general position and providing separation, it would create a lot of error in computing velocity. In reality the positions are fairly consistent but data errors still happen.


Do "water bomber" aircraft pilots have more relaxed rules?

All aircrews have to comply with laws and regulations, unless they have a waiver that makes them exempt for certain regulations. Aerial Fire Fighting need to fly lower than the minimum safety altitude in order to pick up water, so they will have a written permanent waiver to do so.

This is similar to ATO's conducting training for student pilots. They can be allowed to fly below the minimum safety altitude (in Germany: 500ft) for the purpose of training engine failures and attempted emergency landings in fields.

In all honesty, it does not look like recklessness to me, it looks like the pilot miscalculated his approach and came in too low and with not enough speed, as he bounces off the water surfaces instead of doing a proper flare.


What is the climb-out angle of a twinjet upon one engine failure scenario?

The 737 and A320 are certified under Part 25, and they meet the certification requirement in 14 CFR § 25.121. With the gear retracted and one engine out:

... The steady gradient of climb may not be less than 2.4 percent for two-engine airplanes ...

Aircraft Flight Manuals (AFMs) don't typically include the all-engines gradients of climb as noted in AC 120-91A:

... It is recognized that many AFMs generally contain only the OEI performance for loss of an engine at V$_1$ on takeoff ... [emphasis added]

The OEI (One-Engine Inoperative) scenario is what matters more for obstacle clearance.
MTOW alone isn't useful
The performance tables are typically set up for ease of use. Instead of gradients, they list the maximum weights that would guarantee the regulatory gradient for the different pressure altitudes and temperatures, which are known as climb limit weights.
Consider a 737-800 at MTOW at a hot-and-high airport, it is not given that it can attain the 2.4% with an engine out. The TOW needs to respect the climb limit.
And a 737-800 at MTOW at sea level and cold temperature may exceed the 2.4% with an engine out. In this case, that 737 is not climb limited.

As an example, here's the climb limit graph for a 737-800 with flaps 5, note how when it's hotter and/or higher, the climb limit weight is reduced.

Source: 737-800 FPPM; click to view


How much clearance is provided when taking off over a 50 foot obstacle?

Calculated figures for take-off distance required (TODR) are to only just clear a 50-foot obstacle at that distance (with gear down), and figures provided by aerodromes for take-off distance available (TODA) are the measured distance to the obstacle, with no extra clearance added.

If there's any uncertainty when they measure TODA, they'll give the most pessimistic value. The obstacle may be further away than the given TODA but no closer. Measuring distances is easy with modern equipment so it's likely to be an exact figure. However, it's rare for the first obstacle to be exactly 50 feet high. If the obstacle is (say) only 30 feet high, you get 20 feet of separation for free.

Be sure to apply the standard safety factor (e.g. 1.33) when comparing your calculated TODR with the published TODA, to ensure you get plenty of separation over the obstacle. As StephenS points out, if there are any significant obstacles in your take-off path, it's good practice to go for a best-angle climb until you overfly them.


Why should I not use a "lifting tail" on my ultralight design?

You can use a lifting "tail" for any plane design but it will depend on the design. The only requirement for a naturally stable flying aircraft is that it must have a reasonably good positive static margin. And for that to happen the rear flying surface must have a lower wing loading than the forward flying surface - this does not necessarily mean downforce though that's an easy way to comply with the rule.

In one extreme case you must use a lifting "tail" or the aircraft would not have enough lift to fly. These are canard planes such such as the Rutan Long-EZ. Now, you may make the argument that the thing at the back is not a tail but a wing. Yes, if you were to insist on classifying planes by rigid categories then the rear flying surface of canard planes are normally called "wings" but this mindset will make one blind to what really happens to aircraft stability as you change the planform design.

CG placement, forces on the tail and planform

The correct CG placement for stability depends on several things including the distance between the wings and stabilizers and the airfoil of the wings but the dominant factor is the relationship between the area of the wings and the area of the stabilizer.

Most full-scale aircraft including ultralights tend to have very small stabilizers:

In this configuration the stable range of CG is usually between the leading edge of the wings and the midpoint of the chord. Typically this manifests itself in the rule of thumb of between 25% to 33% of the chord but for actual values you need to calculate the CG based on your desired static margin.

You will notice that most model planes tend to have larger stabilizers. This is especially true for non-scale models and even more so for free-flight models:

In this configuration the CG for the same static margin (stability) appears to be quite far back. In most cases it is 50% of the chord - right near the middle of the wings. It only appears that way compared to full-scale planes or scale models. Aerodynamically the CG placement gives exactly the same level of stability.

This is when some planes can start to be trimmed with a lifting tail. Some real-world planes with large tails such as the Avro Lancaster may in some conditions fly as if the tail is lifting.

As you increase the size of the stabilizer further the CG for stable flight shifts further back:

This is commonly seen in free-flight duration models. Almost all planes with such planform have a lifting "tail". It is rare to see a real plane with this planform however there is one very famous design where you can obviously see the lifting tail - the Pou-de-Ciel:

(Note that the original design of the Pou-de-Ciel has a catastrophic fault where the rear wing interacts with the downwash of the forward wing - later revisions moved the wing back several inches - DO NOT BUILD THIS unless you know all the issues)

If you change the relationship between the forward and rear lifting surfaces further you will end up with a tandem wing. If you've been following the trend at this point I think you can see where this is going: yes, the CG moves even further back:

The typical CG for tandem wings is completely outside the forward wings and sit between the forward and rear wings. Remember, all the planforms so far including this was calculated to have exactly the same static margin - they are all similarly stable.

All tandem planes have both forward and rear flying surfaces configured to be lifting.

Tandems are less rare in manned airplanes than the almost-tandem configuration above. The most well known is probably the beautiful Rutan Quickie:

As we progress with changing the relationship between the forward and rear flying surfaces we will eventually end up with the canard configuration:

Canards obviously have a lifting rear flying surface. So much so that people instinctively refer to them as "wings". And the CG moves further back still (in relation to the forward flying surface, obviously it is in front of the "wings").

TL;DR

As you can see, weather or not your tail is lifting or generates downforce is not simply a choice you make. In some instances you will be forced to make your tail lifting. In some instances it will depend on your current maneuver. It all depends on the design of your plane.

Side note: Why most planes have (relatively) tiny stabilizers?

There are two main reasons why most designers chose to make the tail small:

First is to reduce weight in the tail. The larger the tail the harder it is to get the weight distribution right for the correct CG. Note however that this is mostly due to most designers using conventional wisdom because as we see above if you make the tail large enough you can shift your CG further back for exactly the same stability.

But this leads us to the second reason: to reduce drag. The larger the tail the more drag it generates. Tandems are the worst-case scenario where both the wings and "tail" generate the same amount of induced drag. However several designers such as Burt Rutan have taken advantage of the characteristics of tandem wing planes to produce very efficient designs.


Why do aircraft cockpit displays use uppercase fonts?

The specific reason all-uppercase was adopted is just historical. Traditional steam gauge faces use capital lettering exclusively. The reason for that is that capital letters are easier to produce with limited tooling. When they were installed in aircraft, this cost-efficient convention was followed.

This pattern is not exclusive to gauges: historically, in Indo-European languages, uppercase letters came first. Bicameral script is a later invention, present only in a few (albeit very popular) language scripts.

Early typewriters were all-uppercase. Upper case persisted in teletype communications and early computers. Mixed case always added complexity, so its adoption in tech took time throughout the 20th century. This made all-uppercase text very familiar to the technically-minded people involved in aviation, right at the time when its conventions were being established.

The reason uppercase hasn't been replaced, even in glass cockpits, is a simple case of getting the best size:readability ratio. Capitals are fixed height and allow for twice larger letters (thus more readable) within the same amount of space.

For the same reason, exit signs in buildings spell "EXIT", not "Exit", most book covers feature all capital letters, and "NO STEP" won't be replaced with "Please avoid stepping here" anytime soon.

Mixed case has superior readability for natural English, but the language used in aviation is a specific lingo with heavy use of abbreviations. The word-recognition advantage you use reading this post would not initially work in reading "ALT" or "HDG". These are new symbols to learn. Once learned, they become more familiar than the original non-abbreviated terms they stand for.

Aviation documentation is written in mixed case, but the use of uppercase in cockpits continues to be beneficial, as uppercase helps automatically emphasize the exact terms as seen in the cockpit and elsewhere.

Will aviation displays ever switch to mixed-case? The process is ongoing, but rather than changing the old function, it's just the use of mixed-case for some new functions. These involve incorporating paperwork into the glass, which uses more natural language, for which mixed case is suitable (and, as Gerry correctly adds, officially recommended).

Aviation-specific, abbreviation-rich jargon is an artificial language, not a natural one, so there's no case for it to switch.


From the point of view of a private pilot, the answer is that mayday calls are not terrifically common. I've certainly never heard one made in anger in a couple of hundred flying hours.

However your assumptions are correct in parts and wrong in others. First lets define what an emergency requiring a possible mayday call is, which answers your question about when it makes sense.

  Mayday - A condition of being threatened by serious and/or imminent
  danger and of requiring immediate assistance.

That said, some of your assumption is correct:

  I assume when confronted with an emergency on board, they will first deal with it

Absolutely! Pilots are taught to "Aviate, Navigate, Communicate" in that order. Any emergency while airborne requires you to keep the aircraft flying as a first priority. You'll notice Communicate is last after "knowing where you are and where you're going" (Navigate).

  not waste time contacting any one who would not be able to help anyway

As pointed out in comments, this is an incorrect assumption. Once the pilot has some bandwidth to communicate there are numerable ways ATC could help in an emergency, such as (but not limited to):

Clearing surrounding airspace
Aiding with navigation, such as giving vectors to the nearest runway
Prioritizing landings
Helping you once you're (hopefully) safely on the ground - see below.

  And when they have time for such a call, there's no emergency anymore.

Again, an incorrect assumption. Take the example of an engine failure. The aviate part calls for you to set up for maximum glide ratio, and do some checks to see if you can restart your engine. The navigate part could require you to find a suitable field to make an emergency landing. At this point (depending on your altitude) you might have a number of minutes before touchdown. Here's where you tell ATC the problem ("Mayday mayday mayday. G-ABCD, engine failure, 2 miles east of [city], 2,000 ft heading 180 degrees. emergency landing on field beside [big road]"). This has the benefit that they can communicate with emergency services - or at very least send someone out in a car to help you.

As you can see from the above example. The emergency still persists once the pilot has time to tell ATC about it.


How to choose between BasicMed an a Class III Medical?

I guess it depends on whether you intend to fly a larger aircraft at higher altitudes at faster speeds or one with a limited number of passengers at lower altitiudes and airspeeds.  If the latter is going to be the only flying you do, then a basic medical will be a good choice.  If you intende to undergo additional training and obtain additional certificates, ratings, or type ratings, I believe you will be required to hold at least a third class medical to do so.


Why does gas turbine engine have pressure oil supply tube and the scavenge oil tube?

Oil Pressure lines typically sends oil to the Bearings and Gearboxes of the Engine, from the oil pump.

The Scavange lines typically collects the oil from those areas and send it back to the Oil tank, getting cooled and filtered along the way.


Is the quickest way to reverse direction by turning horizontally or vertically?

The formulae appear correct, as far as they go. But there are some problems with the underlying assumption of the question; specifically, that you can achieve either condition in a steady-state fashion.
Firstly, and most importantly, you can see looking at both formulae, the most significant thing you can do to improve your turn rate (angular velocity) is to slow down. This also has a significant effect on the turn radius as well. Since the scenarios where one cares about maximum performance turn rate often also involve a need to avoid an obstacle (cumulonimbus, cumulogranite, etc.), minimizing the turn radius can be just as important as maximizing turn rate, and both can be accomplished by drastically reducing speed.
Conveniently, one of the things that makes it difficult to compare the two scenarios is the fact that the moment you begin the turn, the increased load factor will cause an increase in drag, which will help reduce the speed. The speed reduction (which may be aided by judicious reduction of power) can dramatically improve turn performance, but this reduction will depend on exactly how that turn is made. It may even involve an increase in speed, if attempting the looping turn by performing a split-S.
Importantly, you are trying to compare apples-to-apples by keeping the load factor identical in both scenarios, but I don't find that a plausible assumption. It's not too hard to maintain a constant load factor during a level turn, but a looping turn is likely going to involve either increasing-then-decreasing, or decreasing-then-increasing load factor, making the assumption of load factor being the same in both scenarios unreasonable. And in either case, the speed will be changing by a large amount, eliminating the possibility of using those formulae in an apples-to-apples manner.
Finally, there is the issue that many planes cannot be safely looped, and even among those that can, you may not be able to initiate a loop (Immelmann or split-S) from cruise speed. You have set the assumption that you are cruising at Mach 2, which seems to be an attempt to address this concern. But it raises new ones: even an airplane capable of traveling at Mach 2, may only be able to fly that speed when at altitude, and at an angle-of-attack close to its critical angle of attack, making an Immelmann loop impractical, if not impossible. Similarly, it does not seem likely that one could safely accomplish a split-S that is initiated at Mach 2. The altitude loss incurred could easily exceed the altitude the airplane is starting the turn at, and even if not, the increased airspeed from Mach 2, as well as the G load required at the bottom of the loop, could easily exceed the airplane's structural limits (or the pilot's!).
The conclusion of your question is particularly confusing:

my LIFT FORCE (no matter where it acts on my aircraft) is the limiting factor, nothing else. Is that correct?

and

lift should not be responsible for a quick turn but the lever arm?

Indeed, during a level turn, with a large enough bank angle, one can improve turn performance at the expense of added drag and reduced speed by pulling on the elevator, i.e. adding nose-up elevator input.
But I'm not sure that's what you're asking. It sounds like maybe you're wondering about using lift to modify the attitude of the airplane. If so, that's not how it works. While it's true (for a conventional airplane configuration) that whether in level flight or not, the pitch of the airplane, controlled by the elevator input, changes around the center of gravity, it's important to keep in mind that the center of gravity in unaccelerated flight is directly below the center of lift, since the elevator has effectively added weight, shifting the CG rearward.
I.e. there's no "lever arm" related to any distance between center of gravity and center of lift.
But more to the point, changing the attitude of the airplane isn't the same as changing the flight direction of the airplane. Taking this to its extreme, you can imagine an airplane that could somehow yaw 180 degrees instantaneously. Such an airplane would not effect a 180 degree turn instantaneously; instead, it would just wind up flying the same direction it had already been going, just backwards.
The bottom line: the formulae you're using do not appear to be amenable to an apples-to-apples comparison, so the academic line of reason doesn't seem resolvable. And in the practical sense, if you're going Mach 2 and actually need a maximum performance turn, one of the first things you need to do is slow down. It is most likely safest and most practical to accomplish this in a level turn, or possibly some combination of bank and climb (e.g. like a chandelle). Either way, it's likely the main limiting factor will be the maximum load factor that the airplane and pilot are capable of sustaining.
I don't think it's possible, given only and based solely on the formulae and conditions stated in your post, to determine whether it's always true that a level turn or either type of looping turn is going to produce the maximum rate of turn, first and foremost because you're never going to keep the velocity term in the formulae constant, but for other reasons as well.


During an engine restart procedure, what are the purposes of a.) throttle back to idle and b.) primer "in and locked"?

Source

Idling, or closing the throttle, might help break up any ice that may have formed and caused the engine to quit. That's why it's followed by Carb Heat On.

Also, a failed engine (of any type) is best restarted at idle power. Otherwise the extra fuel will either flood or overheat the restart. But nevertheless, always stick to whatever the checklist says.

  Throttle ice forms when your throttle is partially closed, typically between cruise power and idle. As air moves through the the Venturi in your carburetor, it decreases in temperature, condensing water vapor from the air. The water then starts freezing to the carburetor parts, restricting airflow. Eventually, you'll start losing RPM or manifold pressure, your engine may start running rough, and if the ice gets bad enough, your engine will quit.

If a primer is inadvertently left in the pulled / unlocked position, it may flood the engine with fuel.


How fuselage creates lifting force when plane flying on a side?

The photo that you posted already gives quite a few hints on how this can be possible:

The aircraft is flying at a sideslip angle (the nose pointed slightly up), so a part of the thrust vector is counteracting the weight.
It seems like the aircraft is not exactly perpendicular to the surface, so a part of the lift vector is still counteracting the weight.
The vertical stabilizers produce some "lift" in this situation due to the sideslip angle mentioned in 1. Note that these typically have symmetrical airfoils, so without the sideslip angle, these would not create any force.
The aircraft might be descending in a controlled way. In that case, not all of the weight must be carried.

As an example, look at the high sideslip angle here:

            . There you can also see the rudder being deflected for trimming.


Is it possible to balance a tail heavy plane with a vertical prop on its tail?

Tryin' to cheat the laws of stability, aren't we?

In both videos it is evident that the plane is unstable in pitch. Adding a lifting prop will not change this, because changes in the angle of attack will not affect this prop's lift force much. Stability is achieved by shifting the center of gravity forward, so that changes in the angle of attack will produce additional forces which create a counteracting pitch moment.

In fact, adding the motor will shift the center of gravity even further back. In some cases this helped because the increased pitch inertia made it easier for the pilot to keep the aircraft under control.

If you need to keep the center of gravity so far backward, add artificial stability with a pitch rate sensor and a microcontroller which deflects the elevator appropriately. There are many pages with Arduino-controlled artificial stability solutions - take your pick!


Does the first portion of a trip that was < 50nm count as XC on a long trip?

The relevant regulation is in 14 CFR 61.1(b)(3):

  Cross-country time means—

  (i) Except as provided in paragraphs (ii) through (vi) of this
  definition, time acquired during flight—

  (A) Conducted by a person who holds a pilot certificate;

  (B) Conducted in an aircraft;

  (C) That includes a landing at a point other than the point of
  departure; and

  (D) That involves the use of dead reckoning, pilotage, electronic
  navigation aids, radio aids, or other navigation systems to navigate
  to the landing point.

  (ii) For the purpose of meeting the aeronautical experience
  requirements (except for a rotorcraft category rating), for a private
  pilot certificate (except for a powered parachute category rating), a
  commercial pilot certificate, or an instrument rating, or for the
  purpose of exercising recreational pilot privileges (except in a
  rotorcraft) under §61.101 (c), time acquired during a flight—

  (A) Conducted in an appropriate aircraft;

  (B) That includes a point of landing that was at least a straight-line
  distance of more than 50 nautical miles from the original point of
  departure; and

  (C) That involves the use of dead reckoning, pilotage, electronic
  navigation aids, radio aids, or other navigation systems to navigate
  to the landing point.

Note that the rule under paragraph (ii)(B) is "a flight" that includes "a" point of landing more than 50nm from the point of departure.  It does not specify that all points of landing must be further than 50nm from the departure point, or even that the first point of landing must be further than 50nm.

Since the overall trip was over 50nm, does the FAA allow you to consider that 24nm leg to be part a single overall flight?  Unfortunately, the FAA doesn't provide a definition of "flight" in this context.  However, it is generally accepted that short stops (to pick up a passenger, refuel, eat lunch, etc.) can be logged as part of a single flight.

Edit to add:  Please also this this previous question, and especially the AOPA article it links to.