Why do military transport aircraft usually have top-mounted wings?

Yup. Airplanes rotate in all three axes about the center of gravity. An airplane with high mounted wings experiences what is known as pendulum effect. Much like a pendulum hanging below a pivot, the center of gravity of the airplane hangs below the center of lift of the wings. This increases stability in both roll and, to a far lesser extent, pitch.

As you correctly stated, stability is a tradeoff for maneuverability. You’ll notice that high-winged airplanes have the wings canted downward (the tip is closer to the ground than the root). This is called anhedral, and it lowers the center of lift, reducing roll stability and increasing maneuverability. Conversely, you’ll notice that most low wing aircraft have the tips of their wings higher than the root. This dihedral raises the center of lift closer to the height of the center of gravity, increasing stability.

Oops, sorry for the double post.

Also, I think I may have explained dihedral poorly. For a much better explanation, try here.

I don’t think that is a valid cite apart from it being an anecdote. The KC-135 was derived from the 707, a design that had to be cost effective for the airlines to operate. The C5A design was plagued with engineering flaws such as cracked wings which prompted the military to replace the wings on the earliest version.

Aerospace design engineer checking in : Dihedral is for roll stability, but the vertical position of the CG has nothing to do with it. When a low-wing plane with dihedral rolls to one side, the low wing has a higher projected area (when seen vertically) and the high wing has a smaller projected area. The low wing produced more lift and counteracts the roll.

The low wing position also provides lateral stability (holds the plane’s nose pointing forward) - if it sideslips, one side of the fuselage faces a little forward, air piles up along it, and on top of that wing at its root. That pushes the wing down a little, acting to counteract the slip as well.

In a high-wing plane, things are a little more complex - like it says here.

Airliners stick with low wings due to greater aerodynamic efficiency, and because it puts some structure between the engines and the passengers for cabin noise reduction. They don’t go right through the cabin because that would take up a lot of passenger space.

High-winged military transport
Advantages:

  • keeps the wings and engines farther away from the ground (important when not landing at a nice paved civil airport), so you don’t get damage from rocks, etc.
  • clearance for cargo loading (mentioned by someone else previously.)

Disadvantages:

  • more expensive for engine & wing maintenance, since they’re so high ie. need lifts for access

Low-winged civil assenger transport
Advantages:

  • easy access to wings & engines
  • load-bearing structure can be shared between wing & landing gear
  • wing structure goes through or under the cargo area = no valuable space in passenger cabin taken up
  • wings block some noise from engines
    Cheers,
    NB

I’ve been suspicious of this explanation since I was in fifth grade. Yes, the low wing will have a higher projection of area, but why should vertical projection matter one whit? What we want to know about is torque on the plane, and the torque from the wings will be the same no matter what the plane’s orientation.

Well, grande picture, vertical position of CG in relation to aerodynamic center (or lift center) can have an effect on roll stability - in part because practically it is related to the position of roll control surfaces (generally ailerons and/or spoilers) and a craft’s associated inertial moment about the roll axis.

Does this necessarily matter? The high wing is not lifting exclusively in the “vertical” axis. Assuming a coordinated constant-bank turn, the high wing (of a craft with positive dihedral) necessarily has an element of horizontal lift component into the direction of turn. I think Chronos is right here; See Wikipedia’s explanation of dihedral.

Nitpick: although Boeing’s “Dash-80” prototype bears 707 tail markings, I believe the KC-135 predates the 707 and was the earlier mass production of the design.

Maybe it would help to think of force vectors. On a plane with dihedral, the total lift of wing has a vertical and horizontal component. The vertical component works against the force of gravity. When the vertical component of lift on both wings is the same, the plane flies level. Now imagine an impulse upsets the plane in roll. The wing that rolls towards the vertical has its horizontal force vector shrink, and the vertical force vector to grow. The opposite happens on the other wing. Now we have a net force on the lower wing pushing it back up again. The plane begins to roll back the other way, until the force vectors balance again. After an oscillation or two.

Or, although it’s not an exact analogy, think of a canoe in water. If you tip it to the side, a strong force builds to tip it the other way.

With anhedral, the opposite happens, which is why anhedral by itself is unstable.

This page mAkes it sounds like, yes the KC-135 was first, but not by much

I don’t have the date of the first flight, but the roll out was on May 14, 1954. There was only a 5 month gap between rollout and the first civilan sale. I doubt if any KC-135s were finished before the 707 was sold.

Actually, the reason for the inverted gull wing on the Corsair was to make the landing gear stronger. The Corsair had a huge radial engine swinging a big prop, and the result was very long landing gear struts. Because the Corsair had to be designed to land on carriers, it needed stronger gear than the standard struts could provide. The inverted gull wing was the solution to that problem.

Well, to correctly re-pick this nit, the KC-135 and 707 were both derived from the 367-80 prototype but it is not accurate to say the 135 was derived from the 707 since the 135 bears the original narrower fuselage and simpler wing (two significant changes for the 707). Aside, it would be accurate to say that the E-3 and E-8 were derived from the 707, because they in fact were. Wikipedia’s explanation is consistent with the accounts I’ve read before:

Elsewhere, they cite Pan Am’s first commercial 707 flight in October 1958, and the first KC-135 delivery to the USAF in June 1957, at least 15 months earlier. The way I read it, both Pan Am and USAF ordered their planes in 1954 and though I don’t know when Pan Am took their first 707 delivery, I don’t imagine Pan Am would have sat on a new plane for 15 months without generating revenue. I might be wrong though.

14 May 1954 was the roll out of the 367-80 prototype. It may not be obvious, but big airplanes are generally sold before they are built, so it would not be at all surprising for the first 707 to be sold before the first KC-135 was finished - apples and oranges.

I have some problems with this, Sam. First, the wing that becomes more vertical would increase the horizontal component of lift, not decrease it. Where does this net force come from? It doesn’t follow from what you previously stated. Gravity acts at the CG irregardless of the roll angle.

I feel you are look at the problem too one dimensionally and should could consider a more two dimensional approach. Assuming that the plane is at a roll angle, but has not yet begun correcting itself (no roll rate and therefore no forces due to roll rate) the moment due to lift about the CG is just the same as when the plane is in level flight. Thus, there should be no restoring moment just due to lift. There is now a component of lift pointing sideways though. This causes sideways motion of the aircraft (sideslip). The wing that was raised is exposed more heavily to a downwash over the wing from the sideslip which results in a lower angle of attack and therefore lower lift. It is this reduction in lift in the raised wing that cause the plane to right itself.

Lots of people get this wrong, heck even ElvisL1ves who is an aerospace design engineer gets it wrong. I his defense though, he talks about “efective anhedral”. These terms tend to take more complex phenomena and reduce them to terms designers are more familiar with and can utilize better. Thus he may be taking the actual physics and reducing it to more commonly used tool.