Why is there a relationship between maneuvering speed and weight? [duplicate]

Could you explain the relationship between maneuvering speed and weight? Why are they linked?

• aopa.org/news-and-media/all-news/1999/march/… Somebody could turn that article into a good answer with a little selective copy/paste work. – Ralph J Mar 23 '18 at 3:16
• bottom line - considering the same airplane/ critical AOA: the heavier the mass (airplane) the more force (airspeed) it takes to accelerate that mass thus creating a specific load factor (normal category airplane is max 3.8 g load factor). This means if the airplane is heavier it can fly faster (than when it is not so heavy) before reaching the max load factor (3.8 g in this example). As long as you stay at the Va (or less) for the weight, any increase of critical AOA due to turbulence will result in a stall before you exceed the 3.8 Gs (and may break the airplane). – 757toga Mar 23 '18 at 3:51

stall speed goes up as weight increases. Since maneuvering speed is set a certain margin above stall speed, it goes up too as weight increases.

Maneuvering speed is called corner velocity on the military. It is the lowest airspeed at which you can generate Lift equal to the aircraft weight times the maximum allowable load factor or "G". Obviously, a given specific aircraft configuration determines a specific Lift Coefficient function (specifying the lift coefficient for each angle of attack.) This function has a peak (the maximum value of the lift coefficient) which occurs at what is defined as stall Angle of attack (AOA). This stall AOA is the AOA that will generate the maximum lift available at any airspeed. But as Lift is a function of the lift coefficient times the airspeed squared, the higher the airspeed the more lift is generated at that maximum lift AOA. Below Corner velocity or maneuvering speed, as you increase AOA, the lift (and the Load factor or G-load) increases until you reach maximum Lift OA, then if you increase AOA beyond that point, lift decreases as the wing stalls.
Above Corner velocity or maneuvering speed, however, as you increase AOA, the lift,(and the Load factor or G-load) increases beyond the aircraft Maximum load factor or G-Load before you reach maximum Lift AOA, and you can overstress the aircraft.

The higher the gross weight of the aircraft, the lower the Load factor as a result of any specific amount of lift being generated by the wing (Load factor is of course Lift divided by gross weight). But it is the actual Lift (the forces), that produce stress on the structure of the airframe (wing spars, etc.) not the load factor. The airframe is designed to withstand a specific amount of stress (or lift force). SO, at higher gross weight, the allowable load factor (or aircraft G) will be lower, because the maximum allowable lift (which will cause the maximum allowable stress on the airframe) will generate a lower amount of aircraft G.

In the military we used a diagram called a Vn diagram. This is a graph of airspeed versus Aircraft G-Load at a specific gross weight.

The upper left curve represents flight at maximum Lift Angle of Attack (AOA). the upper horizontal boundary represents the maximum allowable load factor or G-loading. The upper left corner, (labeled Maneuvering speed) is the intersection of upper left curved (maximum AOA) boundary of the flight envelope, and the upper horizontal (Load factor) boundary .

Because gross weight decreased the load factor at which maximum lift would be attained, there was a different chart for each gross weight. The higher the gross weight, the smaller the flight envelope became. The upper (maximum AOA) boundary moved down and to the right (since the same AOA at higher gross weight would produce less Load factor or aircraft G), and the upper horizontal boundary would also move down (for the same reason).

Maneuvering and turbulence create loads on the air frame. In the case of maneuvering, any time you change your direction you are accelerating, in that direction. Newton's second law says any time you have acceleration, you must have a force and the force is that mass of the object multiplied by the acceleration. In aviation, this acceleration is generally talked about in "g-forces," which is the ratio of the rate acceleration vs the acceleration rate of gravity.

Further, if you think as maneuvers as simple turns (or pitch) around a given radius, you can calculate the acceleration by a = v^2/r, where v is velocity (speed) and r is radius. Therefore, high speed drives higher acceleration, which drives higher forces.

Since the force acting on the aircraft is the acceleration multiplied by the mass, the larger than mass the higher the force. This force must be reacted out through the aircraft structure. For example, if an aircraft pulls a positive 3g, the wings must carry 3 times the aircraft weight, engine mounts must carry 3 times the engine weight, the cargo floor has to carry 3 times the cargo weight, etc.

Therefore, it is a design trade off. If the same maneuvering speed is allowed throughout the weight envelope the structure must be stronger, which also makes it heavier. If a lighter air frame is desired, maneuvering speed can be reduced at higher gross weights.

Section 2.14.2 Maneuvering Speed of See How It Flies by John S. Denker explains the relationship between mass (not weight) and maneuvering speed.

Unlike $$V_{NO}$$, the maneuvering speed varies in proportion to the square root of the mass of the airplane. The reason for this is a bit tricky. The trick is that $$V_A$$ is not a force limit but rather an acceleration limit. When the manufacturers determine a value for $$V_A$$, they are not worried about breaking the wing, but are worried about breaking other important parts of the airplane, such as the engine mounts. These items don’t directly care how much force the wing is producing; they just care about the acceleration they are undergoing.

By increasing the mass of the airplane, you decrease the overall acceleration that results from any overall force. (Of course, if you increase the mass of cargo, it increases the stress on the cargo-compartment floor — but it decreases the stress on unrelated components such as engine mounts, because the acceleration is less.)

This means you should put $$V_A$$ along with $$V_S$$ and $$V_Y$$ etc. on your list of critical airspeeds that vary in proportion to the square root of the mass of the airplane. However, $$V_A$$ depends on real mass not on weight, so unlike the others it does not increase with load factor.

Later in the same section, the author clarifies.

Finally, we should note that there are two different concepts that, loosely speaking, are called maneuvering speeds.

• The design maneuvering speed, which we can denote $$V_{A(D)}$$, is primarily of interest to aircraft designers, not pilots. The designer must choose a value for $$V_{A(D)}$$ and then build an aircraft strong enough to withstand certain stressful maneuvers at that speed. Higher values of $$V_{A(D)}$$ promote safety, by forcing the design to be stronger.
• The maneuvering speed limitation, which we can denote $$V_{A(L)}$$, is of interest to pilots. It is an operating limitation. It appears on a placard in the cockpit. Lower values of $$V_{A(L)}$$ promote safety, by restricting certain operations to lower, less-stressful airspeeds.
• wrong. It is the actual force, NOT the acceleration, that engineers are concerned about. Acceleration does not break anything. Stress, from forces, breaks critical; airframe and/or engine components. The higher the gross weight of the aircraft, (and the mass) the lower the acceleration that will be produced by whatever critical amount of lift (force) is sufficient to break something. That is why the acceleration or load factor limits decrease as gross weight increases. – Charles Bretana Mar 23 '18 at 19:42
• Also, although I cannot be sure, it sounds like the author might believe that the it is the airspeed itself that can effect damage. If so, this is also wrong, Maneuvering speed is simply the minimum airspeed at which it is possible, (by establishing the angle of attack that produces the maximum possible coefficient of Lift - Clmax), to generate sufficient stress on critical airframe components to damage them. – Charles Bretana Mar 23 '18 at 19:48