Maneuvering speed Va

[fly_sd]

Can anyone explain why for a given aircraft the lighter the passenger load the lower the maneuvering speed becomes.

[Rivet gun]

I'm sure this has been discussed elsewhere on pprune, and I seem to remember various subelties and debates to the issue.

However in simple terms Va can be considered as the speed at which, if you abruptly pull the elevator, the accelerated stalling speed coincides with the limit load factor. i.e at speeds below Va you will stall before overstressing, above Va you will overstress before stalling.

Consider a normal cat aeroplane with limit load factor 3.8g. The square root of 3.8 is 1.95, so Va is 1.95 x Vs (where Vs is the 1 g stall speed).

Since Vs varies with weight, so does Va

[fly_sd]

Yes, I did do a search before posting but did not find much on the subject. Also, in general agree with what you say. To be more specific though - my original question was - why does Va go down with reduction in weight rather than up.

[Rivet gun]

my original question was - why does Va go down with reduction in weight rather than up.

Because Va is a function of Vs

Vs decreases with decreased weight. Therefore Va also decreases with decreased weight.

[fly_sd]

Yes, agree with that also. My question is - why should the aircraft be required to stall earlier when it is lighter. When it is lighter by the definition of load factor you should be able to provide greater lift before overstressing the wings or the airframe and so you should be able to go faster - not slower. Or maybe at the same Va as if it were heavier. So why the reduction.

[Rivet gun]

It is true that, for a given load factor, there will be less bending moment at the wing root when the weight (in the fuselage) is less. However it is not just the wing root that must be considered. Other important bits are also designed to the limit load factor, for example the engine mounting. You should not therefore exceed the limit load factor however lightly the aeroplane is loaded.

At speeds below Va, you will not (in theory) exceed the limit load factor because you will stall first.

For example, suppose that Va at maximum weight is 100 kts and Vs is 51 knots. If you make the aeroplane do an accelerated stall at 100 knots at maximum weight you will pull 3.8 g just before the aircraft stalls.

Now consider that we reduce the weight so that Vs is 45 knots. If you fly at 100 knots and pull hard you could now exceed 3.8 g before reaching the accelerated stall.

In this case Va is now 88 knots.

[IO540]

The idea behind Va isn't so much to do with max elevator deflection as with the capability to withstand vertical (upward moving) gusts.

The idea is that if flying at or below Va, the wing stalls, thus disposing of the load, before reaching the standard +3.8g (or whatever) design limit.

The stall speed, Vs, varies with aircraft weight. An aircraft loaded to MTOW might stall at 60kt; the same one loaded say 20% below MTOW might stall at 70kt (I don't recall the formula).

Therefore, the same aircraft, if lighter loaded, will need to fly slower (i.e. closer to its actual Vs) to be at Va.

[fly_sd]

It is true that, for a given load factor, there will be less bending moment at the wing root when the weight (in the fuselage) is less. However it is not just the wing root that must be considered. Other important bits are also designed to the limit load factor, for example the engine mounting. You should not therefore exceed the limit load factor however lightly the aeroplane is loaded.
At speeds below Va, you should (in theory) not exceed the limit load factor because you will stall first.
For example, suppose that Va at maximum weight is 100 kts and Vs is 51 knots. If you make the aeroplane do an accelerated stall at 100 knots at maximum weight you will pull 3.8 g just as the aircraft stalls.
Now consider that we reduce the weight so that Vs is 45 knots. If you fly at 100 knots and pull hard you could now exceed 3.8 g before reaching the accelerated stall.
In this case Va is now 88 knots.

OK that explanation makes sense. I presume the vn plots we see takes iinto account all of the aircraft sections rather than just the wings.

[fly_sd]

The idea behind Va isn't so much to do with max elevator deflection as with the capability to withstand vertical (upward moving) gusts.
The idea is that if flying at or below Va, the wing stalls, thus disposing of the load, before reaching the standard +3.8g (or whatever) design limit.
The stall speed, Vs, varies with aircraft weight. An aircraft loaded to MTOW might stall at 60kt; the same one loaded say 20% below MTOW might stall at 70kt (I don't recall the formula).
Therefore, the same aircraft, if lighter loaded, will need to fly slower (i.e. closer to its actual Vs) to be at Va.

I thought it was to do with both situations. My initial question was if a lighter plane flew faster before it stalled that should be fine since it was lighter - for the same load factor the wings can be stressed more since the weight is less. However, Rivet Gun has kindly pointed out that there are other load bearing parts that indiviually may exceed their ratings in this situation.

[Rivet gun]

The idea behind Va isn't so much to do with max elevator deflection as with the capability to withstand vertical (upward moving) gusts.


I think you may be confusing your manoeuver envelope with your gust envelope. Va is defined by reference to the limit manoeuvring load factor (CS23.335).

Design speeds Vb ,Vc and Vd are associated with gusts (Vb not usually applicable to light aircraft)

[Tinstaafl]

The 'g' limit is another way of specifying a limiting acceleration. Accelerating the airframe applies loads to it. One 'g' is an acceleration of 9.8 m/s/s. If the limit is 3 'g the the aircraft mustn't exceed 3 x 9.8 m/s^2.

At a given weight & speed elevators can apply a certain maximum force to pitch the a/c. This, in turn, causes an increased AoA leading to increased L (ie a force) and a resulting acceleration to the airframe. If speed is increased then the sequence will result in an increased acceleration ie a greater load. If speed is reduced then the sequence leads to a lower load. Starting at low speed - ie below Va -the wing will reach its critical AoA before the limiting acceleration is reached. As speed increases then the airframe experiences more & more load prior to the wing stalling. Increase speed enough & the airframe eventually reaches its limiting load just as the wing stalls. Any faster & the limit will be exceeded prior to the wing stalling.

Since this is all about accelerations & the forces that cause the acceleration then mass also is a factor. A given force will cause a greater acceleration the lower the mass. The L force goes up by 'X', accelerating the mass of the whole aircraft. The lighter the aircraft then the more it will be accelerated for the same increase in L. Max Va is at max weight because the heavier aircraft can't be accelerated as much by the increased Lift as when it is lighter.

[tmmorris]

You may be right, Rivet_gun - it's certainly not my field of expertise - but I have seen (placarded) Va described as 'turbulent air penetration speed'...

Tim

[Tinstaafl]

Va is not the same as Turbulence Penetration. V turb is based on a certain velocity gust impinging on the aircraft (25 fps? 50 fps? Instantaneous? Over a defined period? Can't remember the details.) One is about externally caused forces & accelerations, the other about what the aircraft can do to itself.

Provided no limits are exceeded then it's entirely possible for a manufacturer to specify a single speed for both conditions.

[fly_sd]

The 'g' limit is another way of specifying a limiting acceleration. Accelerating the airframe applies loads to it. One 'g' is an acceleration of 9.8 m/s/s. If the limit is 3 'g the the aircraft mustn't exceed 3 x 9.8 m/s^2.
At a given weight & speed elevators can apply a certain maximum force to pitch the a/c. This, in turn, causes an increased AoA leading to increased L (ie a force) and a resulting acceleration to the airframe. If speed is increased then the sequence will result in an increased acceleration ie a greater load. If speed is reduced then the sequence leads to a lower load. Starting at low speed - ie below Va -the wing will reach its critical AoA before the limiting acceleration is reached. As speed increases then the airframe experiences more & more load prior to the wing stalling. Increase speed enough & the airframe eventually reaches its limiting load just as the wing stalls. Any faster & the limit will be exceeded prior to the wing stalling.
Since this is all about accelerations & the forces that cause the acceleration then mass also is a factor. A given force will cause a greater acceleration the lower the mass. The L force goes up by 'X', accelerating the mass of the whole aircraft. The lighter the aircraft then the more it will be accelerated for the same increase in L. Max Va is at max weight because the heavier aircraft can't be accelerated as much by the increased Lift as when it is lighter.


Not sure I follow this. Surely the stress on the aircraft is to do with the total force it encounters. By Newton's second law F = Ma and therefore it follows that for a given F if M drops then a can go up. It is not the acceleration that defines the total force - it is the prduct of mass and acceleration. Putting it another way if the max 'g' force allowed on the aircraft is 3.8g then the most upward force will be required at the wings at max weight. At this point the total force will be 3.8 times the force on the aircraft due to gravity. If the plane then becomes lighter if you want to exert the same force you can actually pull more than the 3.8g so the wings should be capable of this at lighter weights. However, as Rivet Gun pointed out there are parts of the aircraft (such an egine mounts) that always support a fixed load and these could be overstressed. So as I see it the reason to slow down a lighter plane in the presence of turbulence is for this reason - to avoid pulling more than the rated 'g's on these parts - not the wings.

I did find this useful document on the web - http://www.flightlab.net/pdf/8_Maneuvering.pdf. Page 8.3 section 5 pretty much confirms that (unless anyone else has another theory in which case please post!).

[Rivet gun]

You may be right, Rivet_gun - it's certainly not my field of expertise - but I have seen (placarded) Va described as 'turbulent air penetration speed'...
Tim

Aircraft must be designed to meet both manouver envelope requriments and gust envelope requirements. For light aircraft, the manouver requirements tend to be the more limiting, at least at lower speeds.

Va is defined with reference to the manouver envelope. Where the manouver envelope is limiting it is generally the "top left corner" of the the v - n diagram.

Theoretically in that case Va would indeed be the speed at which the aircraft could sustain the maximum vertical gust without either stalling or being over stressed. We may not know how big that gust would be but it would be greater than the design gust requirements (since the manouver envelope is more limiting).

We do know that the aircraft will sustain at least the 50 fps "design gust" at Vc. In turbulent air speed control is not going to be accurate, so aiming for a speed somewhere between Va and Vc would seem a good compromise between the risks of stalling and overstressing.

Hope this makes sense?

[englishal]

In simple terms...

Say that during a high speed cruise, the angle of attack of the wing is 3 degrees (hypothetical figures of course) and that the wing stalls at 18 degrees. In order to reach the 18 degree stall AoA will require 6 x the force of gravity (18/3 = 6)....i.e. you will need to multiply AoA x 6 to get 18 degrees.

Now assume you're cruising slowly, and your AoA is 9 degrees. In order to stall the wing will require 2g (18/9 = 2) and so the wing will stall before exceeding the design limitations.....i.e you need to multiply AoA by 2 to reach 18 degrees.

Now assume you're cruising fast but you've added a few more people. This means you'll require a larger AoA to maintain level flight. If now at a high speed cruise with 4 fatties onboard the AoA is 9 degrees, it'll only require 2g to stall the wing......(2x9=18).....

And so on....

[Tinstaafl]

The force in F=ma is the increased L that is causing the a/c to accelerate, caused by the changed AoA. That acceleration imposes loads on structural items such as wing roots, engine mounts etc. The loads experienced by those structural items aren't what is causing the acceleration/'g' force. They're a reaction to it.

[Rivet gun]

Fly-sd, thanks for posting the link

http://www.flightlab.net/pdf/8_Maneuvering.pdf.

I had not seen that one before, but it gives a good explanation of your original question.

Worth pointing out though that this discussion concerns only the manouver envelope, and makes no mention of the gust envelope. In particular their use of the term "Vc" is misleading since it is quite different to the usage of the term Vc in FAR/CS 23.

In CS23 "Vc" means design cruising speed, and is the speed at which the aircraft will tolerate a 50 fps "design gust" up to 20000 ft.

[fly_sd]

The force in F=ma is the increased L that is causing the a/c to accelerate, caused by the changed AoA. That acceleration imposes loads on structural items such as wing roots, engine mounts etc. The loads experienced by those structural items aren't what is causing the acceleration/'g' force. They're a reaction to it.

Agreed but that was not my original question. The fact is that a lighter aircraft can pull more 'g's on the wings than a heaver one due to the reasoning I mentioned. The reason for slowing down the aircraft when lighter is to prevent excess loading to the parts that bear a fixed weight - not the wings.

[fly_sd]

Fly-sd, thanks for posting the link
http://www.flightlab.net/pdf/8_Maneuvering.pdf.
I had not seen that one before, but it gives a good explanation of your original question.
Worth pointing out though that this discussion concerns only the manouver envelope, and makes no mention of the gust envelope. In particular their use of the term "Vc" is misleading since it is quite different to the usage of the term Vc in FAR/CS 23.
In CS23 "Vc" means design cruising speed, and is the speed at which the aircraft will tolerate a 50 fps "design gust" up to 20000 ft.

Yes good point - in most cases people seem to refer Va with reference to gusts but as you point out they are different.

[DFC]

Put an average PPL in an average light aircraft in moderate turbulence and watch then slap the controls from side to side (large abrupt aileron movements) trying to keep the wings level.

Makes good sense to recomend that such pilots limit speed to Va in such cases so that the aircraft is not overstressed by over control.

Remember also that the Vn envelope is single axis non-reversed. At a speed below Va, acceleration in more than one axis (pitch and roll for example) or a sudden reversal in loading can overstress. See the AAIB report into the Piper Arrow break-up.

Regards,

DFC