Trivia Testers : Private Pilot Question From the Twenty-Second Century

Question: Two pairs of aircraft are in formation flight. One pair is 10,000 feet, and the other pair is quite a bit higher; at one million feet. (In other words, outside the earth’s atmosphere about 190 miles up, in orbit.) In each case, one aircraft is in front of the other. If the second aircraft in each formation wants to overtake the first, what must it do, in each case?

  1. Both trailing aircraft need to add power (whether that means manifold pressure, jet power, or rocket power).
  2. The aircraft in trail at 10,000 feet needs to speed up, just slightly. The aircraft in trail at ‘FL 10,000’ actually needs to slow down in order to speed up.
  3. Huh?
  4. Formation flight in orbit is not allowed unless all vehicles involved have three-axis orbital maneuvering systems (FAR 91.1415).

Answer number 2 is correct. Figuring out what to do in the case of the two aircraft at 10,000 feet isn’t rocket science but for the two waltzing around in orbit, well, um, it kind of is. Outside the atmosphere, the two ‘aircraft’ are really following ballistic trajectories, either in some sub-orbital parabola or in elliptical orbit. As such, Kepler’s second law of conservation of angular momentum applies. The radii of each vehicle’s orbit must sweep out equal areas in equal times. What this means is that, if the second craft were to add power at its six o’clock, it would move to a new (or higher) apogee (half an orbit later), and actually be at a greater altitude. Hence, it’s ground track would then actually slow down as the earth rotated relatively faster beneath it. So unless you do a ‘re-or’ first, you would actually move above and behind the vehicle in front of you (being furthest away about 45 minutes later). Nope, in orbit, the fact is that you must ‘fire in the direction that you want to go’. The aircraft in trail must turn around, fire just a tinch in its direction of motion, after which it will attain a lower orbit (or ‘perigee’) half an orbit later, and be travelling just a bit faster. Communication satellites in geosynchronous orbit which are periodically adjusted in longitude to stay ‘in the FCC box’ don’t need to reorient themselves first, as they have both East and West-facing thrusters, but they do just that very thing, in fact.

Subject: Follow the Sun

Question: If you took off due West at a given time, and tried to follow the sun so that you ‘stayed with it’—whether that was noon, sunset, whatever— below what latitude would you no longer be able to do so without exceeding the speed of sound?

  1. Unless you could afford to charter the Concorde, or are one of the select few who owns a war surplus fighter that can exceed the speed of sound (or your commanding officer were to let you get real creative next time you took up one of Uncle Sam’s F-16s on a ferry flight), it wouldn’t be possible. The nadir point of the sun crosses longitude lines at about Mach 1.37.
  2. Nice try, Maverick Weenie. I said ‘at what latitude’, so the question does not assume that you’re trying to keep the sun always overhead. Assuming you were to feel free to hug the 49th parallel, if you wanted to, and you just wanted to keep the sun somewhere above the horizon, you’d have to go to about 35 degrees of latitude, where the tangential rotation speed of the earth goes below 762 miles an hour.
  3. Closer, but not quite right. The approximate tangential rotation speed of the earth is its equatorial radius times the cosine of your latitude, in turn multiplied by the earth’s angular velocity. You would have to be at about the latitude of Buffalo, NY (actually 42.9 degrees North) in order for that to be below the speed of sound. And of course, if it were winter, and you wanted some reasonable elevation angle to keep the sun in your sights, you might want to try it at 42.9 degrees South…
  4. Still not quite right. The speed of sound also varies with air temperature. At sea level, at standard temperature and pressure, that’s about 762 mph, yes. But if you’re flying something that fast, you might be up at 36,000 feet, above which point the air temperature stays a relatively constant -56 deg C, and where the speed of sound drops to about 660 mph (or about 573 knots). Limited at that speed, you would need to go even further North… to a latitude just a bit above Moose Jaw, Saskatchewan, would do nicely: 50.6 degrees N.

The answer of course is number 4.

Subject: Bending the Rules

Question: There is actually a Federal Aviation Regulation (FAR 91.905) that specifies which rules can be waived, in order to operate aircraft in ways not normally permitted under Part 91. These waivers involve many different rules including airspeed and altitude restrictions, and are processed by the local FSDO. Aside from helicopters, which are already allowed much less restrictive limits, particularly with regard to minimum safe altitudes and visibility, what other aircraft category (or categories) may fall under this special rule, and under what circumstances?

  1. There are no such permissive changes.
  2. Any category may be authorized, under proper circumstances
  3. Balloon flights at authorized ‘aviation events’
  4. Only experimental NASA flights

The answer is number 2.