Va: maneuvering speed ad nauseam

[Koopas Ly]

After the reading the Va threads of my past questions, I found a
wonderful way to confuse myself. I notice that I've become quite good
at confusing myself and making things complicated. To give myself
some credit, I did search old messages but found no resolution. So
here we go...

I am sure most know the typical textbook definition of Va...goes
like..."the minimum speed at which the wing can produce lift equal to
the design load limit" or "the speed at which the pilot can use full
control deflections without over-stressing the airplane".

Essentially, it's the minimum airspeed that, coupled with a control
deflection to give you the critical angle of attack and CLmax, will
result in + 3.8 g's. Pulling any harder won't help since you'll stall
the airplane. Pulling with all your might as speeds below Va will
result in the airplane stalling without reaching the limit load factor
+ 3.8 g's. In essence, Va is the stall speed at the design load
factor of + 3.8 g's.

Now, the above seems to be what's commonly accepted.

Here's my question for this thread: Idealize the wing as a
cantilevered Euler beam representative of the wing spar ("the wing").
Assume the lift load to be a distributed elliptical spanwise,
transverse load, acting at the centroid of the section. Further
assume no other external loading such as drag loads.

The predominant stresses are bending (axial) stresses at the outer
regions of the spar caps and shear stresses in the spar web. Assume
that the failure mode is via the former.

Alright, so here, clearly, the failure of the wing is due to excessive
loading. The distributed load, expressed in X number of pounds per
inch, was too great. In fact, for the sake of simplicity, let's make
the distributed load a point load in pounds.

Now, we can say that the failure of the wing was due to excessive
FORCE which induced excessive stresses in the structure.

Consider that a certain airplane weighed at maximum takeoff weight is
designed to withstand + 3.8 g's (its design load). Actually,
airliners that I am familiar with are tested to ultimate load, or
1.5*design load (+ 5.7 g's before permanent deformation). For now,
we'll assume that at + 3.8 g, the plane's wings break off. That would
equal to a total force on both wings of 3.8 x 2550 lb or almost 10,000
lbs.

The thing that bothers me about Va is that it equates to a number of
g's ("design load") AND that Va is being rescaled for weight. By
doing so, Va becomes more of an acceleration criterion rather than a
structural criterion. It appears as though Va limits positive g
acceleration to + 3.8 g, not load itself.

In other words, Va adjusted for say, a lower weight, tells the pilot
"You will not exceed 3.8 g for your current weight, as you will stall
first". If the current weight was 2,000 lbs, the total load on the
wings would only equate to 7,600 lbs at + 3.8 g's, lower than the
design limit of 10,000 lbs of + 3.8 g's at max. takeoff weight. The
acceleration on the airplane would be a "limit load acceleration" but
would not produce a limit load condition, per se, structurally.

If Va was truly a structural consideration, it would not change
(regardless of weight), since no airspeed below Va coupled with any
non-stalled AOA, could produce limit loads of + 3.8 g as tested at max
takeoff weight of 2,550 lbs.

There may be severe flaws in my reasoning...please no flames and be
nice. It's a holiday.

Alex

[Andrew Rowley]

The wing is not the only thing in the aircraft that might break.
Rework it assuming that the first thing to break is the engine mount
at 3.8g

[Dan Thomas]

(Koopas Ly) wrote in message >...

> ....Consider that a certain airplane weighed at maximum takeoff weight is
> designed to withstand + 3.8 g's (its design load). Actually,
> airliners that I am familiar with are tested to ultimate load, or
> 1.5*design load (+ 5.7 g's before permanent deformation). For now,
> we'll assume that at + 3.8 g, the plane's wings break off. That would
> equal to a total force on both wings of 3.8 x 2550 lb or almost 10,000
> lbs.
>
> The thing that bothers me about Va is that it equates to a number of
> g's ("design load") AND that Va is being rescaled for weight. By
> doing so, Va becomes more of an acceleration criterion rather than a
> structural criterion. It appears as though Va limits positive g
> acceleration to + 3.8 g, not load itself.
>
> In other words, Va adjusted for say, a lower weight, tells the pilot
> "You will not exceed 3.8 g for your current weight, as you will stall
> first". If the current weight was 2,000 lbs, the total load on the
> wings would only equate to 7,600 lbs at + 3.8 g's, lower than the
> design limit of 10,000 lbs of + 3.8 g's at max. takeoff weight. The
> acceleration on the airplane would be a "limit load acceleration" but
> would not produce a limit load condition, per se, structurally.
>
> If Va was truly a structural consideration, it would not change
> (regardless of weight), since no airspeed below Va coupled with any
> non-stalled AOA, could produce limit loads of + 3.8 g as tested at max
> takeoff weight of 2,550 lbs.
>
> There may be severe flaws in my reasoning...please no flames and be
> nice. It's a holiday.
>
> Alex

Not a dumb question, and many have misunderstood Va. I'm no
expert either, but as I understand it, the 3.8 G limit is predicated
on gross weight, or as you point out for your particular airplane,
almost 10,000 lbs.
Flying at less than gross, the airplane will be less likely to
stall as say, full up elevator is abrubtly applied, and will tend to
climb. Climbing reduces the angle of attack, preventing the stall and
maintaining the load on the wing, and the same 10,000 lbs of force
could be achieved easily. It would be higher than 3.8 G, but as I
said, the G load factor is based on gross weight.
So for less than gross weights, Va must be reduced by the square
of the decrease in weight. As Kirschner calculates it, a 20% weight
reduction should give a 10% Va reduction, and a 40% weight reduction
should give a Va 20% lower.
Don't forget that the wing is not the only structure in the
airplane. Several aircraft have been know to fail the tail first;
airplanes like the 210 and Bonanza, which are slippery and build speed
rapidly in the typical spiral entered after the non-instrument pilot
enters cloud. Upon popping out of the overcast at 400 feet, with the
ground coming up fast, he pulls back hard and the stab fails downward,
the airplane pitches forward over onto its back, and the wings fail
downward. End of story.

Dan

[Koopas Ly]

Andrew Rowley > wrote in message >...
> The wing is not the only thing in the aircraft that might break.
> Rework it assuming that the first thing to break is the engine mount
> at 3.8g

Andrew,

I think I understand now. Let me see if I get it...

To rework the analysis, I'll assume that the weight of the airplane is
mainly supported by the wings, and that other components such as the
engine mount are essentially invariant in static 1g weight. In other
words, by overloading the airplane with other bodies, ballast, and
such, the weight of the engine mount does not change. If that is so,
I can see how such *individual* components may be "g limited" with
respect to their own inertia. Does this follow your reasoning?

Thanks,
Alex

[Andrew Rowley]

(Koopas Ly) wrote:

>I think I understand now. Let me see if I get it...
>
>To rework the analysis, I'll assume that the weight of the airplane is
>mainly supported by the wings, and that other components such as the
>engine mount are essentially invariant in static 1g weight. In other
>words, by overloading the airplane with other bodies, ballast, and
>such, the weight of the engine mount does not change. If that is so,
>I can see how such *individual* components may be "g limited" with
>respect to their own inertia. Does this follow your reasoning?

almost... the engine mount needs to support the weight of the engine
multiplied by the number of Gs. so if the engine weighs 100kg at 3.8G
the mount is supporting 380kg. At 5G it has to support 500kg. So force
on the wings at high Gs may go down as your total weight goes down,
but the force on other items (engine mount, baggage floor, basically
any part of the airframe that has to support something) does not.

[Dan Thomas]

Andrew Rowley > wrote in message >...
> (Koopas Ly) wrote:
>
> >I think I understand now. Let me see if I get it...
> >
> >To rework the analysis, I'll assume that the weight of the airplane is
> >mainly supported by the wings, and that other components such as the
> >engine mount are essentially invariant in static 1g weight. In other
> >words, by overloading the airplane with other bodies, ballast, and
> >such, the weight of the engine mount does not change. If that is so,
> >I can see how such *individual* components may be "g limited" with
> >respect to their own inertia. Does this follow your reasoning?
>
> almost... the engine mount needs to support the weight of the engine
> multiplied by the number of Gs. so if the engine weighs 100kg at 3.8G
> the mount is supporting 380kg. At 5G it has to support 500kg. So force
> on the wings at high Gs may go down as your total weight goes down,
> but the force on other items (engine mount, baggage floor, basically
> any part of the airframe that has to support something) does not.

The engine mount on most light aircraft is designed to withstand 9
G's minimum. And as I said earlier, the 3.8 figure is based on gross
weight. Reducing gross would allow them to take a higher G figure but
the same net force.
Cessna also states in the 172 POH that it's designed to 150% of
the G figures given, or 5.7 G's. I think the 3.8 figure would be the
yield point, where things begin to bend, and the 150% figure would
break them entirely. Or something like that.

Dan

[Greg Esres]

<<The engine mount on most light aircraft is designed to withstand 9
G's minimum. >>

Where do you get this figure?

[Robert Moore]

(Dan Thomas) wrote
> Cessna also states in the 172 POH that it's designed to 150% of
> the G figures given, or 5.7 G's. I think the 3.8 figure would be
> the yield point, where things begin to bend, and the 150% figure
> would break them entirely. Or something like that.

The C-172 is probably wing limited, since at 200-300 under maximum
gross weight, it falls in the Utility Category with +4.4g allowed
for the limit load and +6.6g for the ultimate load.

Bob Moore

[Andrew Rowley]

(Dan Thomas) wrote:

> The engine mount on most light aircraft is designed to withstand 9
>G's minimum. And as I said earlier, the 3.8 figure is based on gross
>weight. Reducing gross would allow them to take a higher G figure but
>the same net force.
> Cessna also states in the 172 POH that it's designed to 150% of
>the G figures given, or 5.7 G's. I think the 3.8 figure would be the
>yield point, where things begin to bend, and the 150% figure would
>break them entirely. Or something like that.

One of the earlier posts assumed for the purposes of calculation that
the wings break when exceeding 3.8g at gross weight. I was merely
continuing that assumption. All I was trying to illustrate was that
there are some parts of the airframe where the loads are not
aerodynamic and where the loads do not reduce with reduced aircraft
weight - which is why Va reduces with reduced weight.

[Koopas Ly]

Andrew Rowley > wrote in message >...
> (Koopas Ly) wrote:
>
> >I think I understand now. Let me see if I get it...
> >
> >To rework the analysis, I'll assume that the weight of the airplane is
> >mainly supported by the wings, and that other components such as the
> >engine mount are essentially invariant in static 1g weight. In other
> >words, by overloading the airplane with other bodies, ballast, and
> >such, the weight of the engine mount does not change. If that is so,
> >I can see how such *individual* components may be "g limited" with
> >respect to their own inertia. Does this follow your reasoning?
>
> almost... the engine mount needs to support the weight of the engine
> multiplied by the number of Gs. so if the engine weighs 100kg at 3.8G
> the mount is supporting 380kg. At 5G it has to support 500kg. So force
> on the wings at high Gs may go down as your total weight goes down,
> but the force on other items (engine mount, baggage floor, basically
> any part of the airframe that has to support something) does not.

Thanks for the clarification.

What is the critical "item" that will break at 3.8 g's on a light GA
airplane like a C172? Is it the engine mount? I see that's it's
often mentioned as the "weakest link".

It's my opinion that the definition of Va taught to private pilots
leads to a false understanding that the wings will break at 3.8 g's.
The nuance we've discussed is not stressed. Why? I don't know.

Best regards,
Alex

[Andrew Rowley]

(Koopas Ly) wrote:

>What is the critical "item" that will break at 3.8 g's on a light GA
>airplane like a C172? Is it the engine mount? I see that's it's
>often mentioned as the "weakest link".
>
>It's my opinion that the definition of Va taught to private pilots
>leads to a false understanding that the wings will break at 3.8 g's.
>The nuance we've discussed is not stressed. Why? I don't know.

I don't know. The engine mount is just one to pick as an example - but
as others have said it isn't the most likely. It could be almost
anything - on aircraft with tip tanks it could be the attachments for
those for example. All up I don't think it matters - these are just
possible reasons why Va doesn't get higher as weight decreases.

You may be right, but the aerodynamics taught to private pilots is
rather simplified in general. I did find out about it in my training,
but it was probably a result of asking the same question you are
asking - why does it decrease not increase.

Physics is something some people find very difficult, so requiring
that everybody understands why Va decreases with decreasing weight may
be too difficult.

[Koopas Ly]

> The engine mount on most light aircraft is designed to withstand 9
> G's minimum.


Where is that specified? Does Cessna provide max. g limits for items
on the aircraft or are max. g limits for these items explicitly
specified in FAR 23?


> And as I said earlier, the 3.8 figure is based on gross
> weight. Reducing gross would allow them to take a higher G figure but
> the same net force.


Agreed. This may sound like a stupid question, but how do you define
"gross weight"?


> Cessna also states in the 172 POH that it's designed to 150% of
> the G figures given, or 5.7 G's. I think the 3.8 figure would be the
> yield point, where things begin to bend, and the 150% figure would
> break them entirely. Or something like that.


You're correct. An airplane has to sustain ultimate loads, typically
50% beyond limit load (highest in-service load to be experienced) and
show no failure (fracture). An airplane has to sustain limit loads
without permanent deformation (yielding). At least, that's for FAR 25
aircraft.


>
> Dan

[Julian Scarfe]

"Koopas Ly" > wrote in message
m...

> I am sure most know the typical textbook definition of Va...goes
> like..."the minimum speed at which the wing can produce lift equal to
> the design load limit" or "the speed at which the pilot can use full
> control deflections without over-stressing the airplane".

[Not answering Alex's questions but...]

maybe that's better as "*one* full control deflection".

http://www.dft.gov.uk/stellent/groups/dft_avsafety/documents/page/dft_avsafety_025533.hcsp

is not unlike

http://www.ntsb.gov/events/2001/AA587/default.htm

though closer to home for those of us who fly light aircraft.

Julian Scarfe

[Robert Moore]

(Koopas Ly) wrote

> Agreed. This may sound like a stupid question, but how do you
> define "gross weight"?

Ah yes...a grossly misused term and.....one not used in the FAR.

Section 23.25: Weight limits.
(a) Maximum weight. The maximum weight is the highest weight at
which compliance with each applicable requirement of this part
(other than those complied with at the design landing weight) is
shown. The maximum weight must be established so that it is --

However a web search shows that "gross weight" is used mainly by
state motor vehicle codes as follows:

Gross Vehicle Weight or GVW
The combined weight of a commercial vehicle and its load.

And the military:

Definition of: > gross weight
(DOD, NATO) 1. Weight of a vehicle, fully equipped and serviced for
operation, including the weight of the fuel, lubricants, coolant,
vehicle tools and spares, crew, personal equipment, and load. 2.
Weight of a container or pallet including freight and binding. See
also net weight.


Using "gross weight" for aircraft can be misleading....for example:

The Boeing-707 had a maximum "taxi weight" of 336,000 lbs, and a
maximum "takeoff weight" of 333,100 lbs. And....its maximum
takeoff weight might be limited to the maximum landing weight plus
the weight of the fuel burned during the flight or to the maximum
weight that would allow compliance with the second segment climb
requirements.

What was its "gross weight"?

Pilots who use the term "gross weight" aren't very well versed in
the FARs.

Bob Moore

[Dan Thomas]

Greg Esres > wrote in message >...
> <<The engine mount on most light aircraft is designed to withstand 9
> G's minimum. >>
>
> Where do you get this figure?


Canadian Aviation Regulations 523.561 gives some numbers for
protection of occupants in an emergency landing (a crash). Seats and
belts, for example, have to withstand 9 Gs forward, 6 Gs downward, 3.0
upward for Normal and 4.5 for Aerobatic. Items of mass within the
cabin must be able to withstand 18 Gs forward.
The structure itself must be able to withstand, in the event of
"complete turnover" during a crash, 9.0 Gs forward, and some lesser
numbers in other directions. This structure would include engine
mounts.
Somewhere else in the many sections are more numbers specifying
componemt strengths. The FARs would have an equivalent section. The
minimum legal flight load strengths for any Normal Category airplane
is 3.8 Gs. Note that flight loads and "emergency landing" loads are
not the same, but the airplane must meet those requirements.
A 3.8 G engine mount would be most dangerous. In training students
in our Citabria, we have seen well over 3 Gs on the G meter in botched
landings. The wings and tail don't much care about that impact, since
they don't experience any air-load increases, but the gear, fuselage
and engine mount do. Imagine, for a minute, the effect of an engine
departing the airframe in such a spot: airspeed at or near stall
speed, an airplane that's suddenly 350 pounds lighter, and a CG back
around the trailing edge of the wing. People killed, maybe, for the
lack of one pound (or less) of 4130 tubing?


Dan