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Ok, so I'm a student pilot, and I'm going over the Vx, Vy, Vne, ... etc., and I see that "maneuvering speed" (the speed at which you can safely apply full flight controls) "changes with weight".

Which airspeeds don't change with weight? I can pretty much guarantee the the takeoff speed changes with weight, as would flap operating speeds, never exceed speed, and cautionary zone, because that is just the basic application of physics (inertia).

Why do we treat maneuvering speed as the only variable airspeed?

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Your instinct is correct; almost all of the key airspeeds — those at which something special happens aerodynamically — vary with weight.

There's a distinction, though, between "speeds at which something special happens aerodynamically" and "regulatory limiting speeds that prevent you from doing something bad."

For example, VNE is a regulatory value; it is prohibited to exceed this speed at any weight. This value includes a safety margin and is determined from flight test data. Nothing special happens aerodynamically at the published VNE speed. (Thank goodness!) The special stuff, like aeroelastic flutter or structural failure, happens at some speed well above VNE, regardless of your weight (as long as it's within the allowable CG envelope of course).

Another example, VFE, is similar. Nothing special happens at this speed. It's just a safety value: as long as you're below this speed, you won't tear the flaps off the plane if you extend them, regardless of your weight.

Almost all speeds that aren't "regulatory limits" do indeed change with weight. Some examples:

  • VA design maneuvering speed
  • VX best angle of climb speed
  • VY best rate of climb speed
  • VR rotation speed
  • VS0 landing configuration stall speed
  • VS1 "specific" configuration stall speed

For larger multi-engine airplanes that you'll encounter later in your flying career:

  • V1 engine failure recognition speed (or takeoff decision speed)
  • V2 takeoff safety speed
  • VMC minimum control speed

(Note that a lot more factors besides just weight can go into these latter speeds, such as atmospheric conditions and reduced-thrust takeoffs.)

For small airplanes, it is common to publish these speeds as single values, measured at gross weight. For many of them there are also graphs in the performance section that show you how the actual speed varies with weight.

For larger aircraft, the performance graphs (or calculations) are always used. For example, you won't use a single "stall speed" value from a handy table in the "POH" of a 747. In these types of aircraft, key numbers are calculated as needed on each flight for current weight.

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To explain why these speeds change with weight:

VA design maneuvering speed: this is because it takes a lot more force to move a heavy plane than it does a lighter plane. On a lighter plane, the surfaces deflect, apply a force, and the plane moves. Once the plane is moving, the surfaces move too, which lessens the force on them. A heavier plane will move less, which means the surfaces are applying more force and for longer to move the plane the same amount.

VX best angle of climb speed
VY best rate of climb speed:
A heavier plane will need to produce more lift, and therefore have more drag, which affects climb performance.

VR rotation speed
VS0 landing configuration stall speed
VS1 "specific" configuration stall speed:
A heavier plane needs more airspeed to produce enough lift to take off or not stall. Here is why:

Among other things, lift is dependent on speed and angle of attack. So at a given speed, angle of attack can increase to generate more lift. The plane will have a maximum angle of attack above which it will stall. Since these are minimum speeds, they are at the maximum angle of attack, so speed must increase to provide the lift.

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Well, top of my head: Vtyre and MMO are two speeds which are totally independent of aircraft mass. The first is simply a tyre speed limitation and the second is aerodynamically determined by the wing. The rest should all change one way or another with mass.

Why then use single values for most of these speeds? Well, for one thing, in smaller aircraft, those changes will ammount to 1,2 maybe 5 knots from Basic Empty Mass to Maximum Take Off Mass, so memorizing your stall speed as variable between 39 to 41.2 knots (when you have about +/- 5 kts accuracy on the airspeed indicator anyway) is pointless. Round it up to 45 and stay above that. Remember that most of these "fixed" speeds are CAS while some are EAS (and remember how that influences things), then remember those speeds will change from flight to flight depending on weight, but not too much.

As you get into slightly bigger airplanes you will start seeing the AFM giving 2 or 3 sets of speeds for different weights (850 kg, 1000kg, 1150kg) and it is your job to know them and interpolate them for today's weight.

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