Aerodynamicists Question

[VH-XXX]

Here is a question that I hope someone can answer.

Let's say you had a current MTOW of 1,000 kg's with a stall speed of 50 knots. Easy round figures to start with.

You somehow lower the stall speed of the aircraft, eg. wing extension, wing-tips, vortex generators, flap modification etc. As a result you have lowered the stall speed by 5 knots, to 45 knots.

I then need to work out what the weight needs to be to stall the aircraft back at 50 knots.

Eg., 1,200 kg's.

This is probably not possible and I realise flight testing would be a good start but it would be good to start with some numbers to work back from.

[ForkTailedDrKiller]

Ohhhhh! My head hurts!

Dr

[matt_mccarty]

L=1/2. ρ.V^2 .S.Cl
In this instance, ρ and S (density and reference area) remain constant, by making the aerodynamic addition you are increasing the Cl at which stall occurs.
If the new stall speed is 45kts (23.2 m/s) at 1000kg mass (weight of 9800 N), then the new Cl (the Cl at which stall occurs) can be found (along with the constants ρ and S)
1/2.ρ.S.Cl=L/V^2
= 9800/(23.2^2)
= 18.3

Then the lift at a speed of 50kts (25.7m/s) can be found as well.
L=(1/2. ρ .S.Cl).V^2
= (18.3) . 25.7^2
= 12087 N
This is equal to a mass of 1233kg.

[john_tullamarine]

.. or, if you want to do it without any brain strain -

Recalling that

(a) at the stall, CL = CLmax and is presumed to be constant

(b) L = W, if we make the dubious presumption of level flight

Then, where "1" indicates before, and "2" after ..

CLmax = L1/(1/2.rho.V1^2.S) = L2/(1/2.rho.V2^2.S)

so, cancelling out the common factors

W1/V1^2 = W2/V2^2

from which you get either

V2 = V1.sqrt(W2/W1), or

W2 = W1.(V2/V1)^2

So, with the example figures given, and presuming that the speeds are CAS, not IAS

W2 = 1000.(50/45)^2 = 1234.6 (call it 1235)


This only has some validity for a constant configuration comparison.

Also, and this is very important, PEC gets interesting around the stall so IAS won't hack it (we've all seen a Cessna with naught on the clock at the stall - means nothing due to PEC) so you have to do the sums in CAS to get anything in the way of sense out of the sums.

I think that this was where Matt was coming from ?

[The Green Goblin]

Simple,

You will stall when the aerofoil exceeds the critical angle

Weight and Airspeed have zilch to do with it!

[john_tullamarine]

It would appear that The Green Goblin attended a different uni and/or PoF lectures at the flying school to most of us ?

[FGD135]

Well done matt and John!

I got the same answer - actually 1234.567 kg - a coincidentally interesting number!

[The Green Goblin]

It would appear that The Green Goblin attended a different uni and/or PoF lectures at the flying school to most of us ?

A consequence of going to slow is exceeding the critical angle which results in a stall.

A consequence of being to 'heavy' is exceeding the critical abgle by attempting to generate additional lift which results in a stall.

So therein lies your answer!

As a result you have lowered the stall speed by 5 knots, to 45 knots.

No, you have just reduced the minimum steady in flight speed to 45 knots from 50, Vs being the minimum steady in flight speed

[ReverseFlight]

Quick calculation in the field:
50/45 = 1.111 recurring, square it to get 1.2345678
Then multiply by 1000 kgs = 1234.5678 kg

[rmcdonal]

It would appear that The Green Goblin attended a different uni and/or PoF lectures at the flying school to most of us ?

No The Green Goblin is correct. Vs is just the minimum speed that an aircraft flying at the critical angle can maintain S+L flight.
A stall occurs not when you go below the stall speed, but when you exceed the critical angle.

[VH-XXX]

Thanks guys, there's a couple of good ideas there. I'll get cracking on flight testing to try and back up the findings before writing my "amendment"

[Jabawocky]

I know what you are doing!

[VH-XXX]

I know nuffink !!!

[john_tullamarine]

A stall occurs not when you go below the stall speed, but when you exceed the critical angle.

There is some validity in that but the posters miss the thrust of the thread. A bit like saying "the sky is blue" which doesn't give any information as to the what, when, how or why.

Either way, and all jokes aside, I really do suggest that you both revisit the books and then go ask for your money back from whomever did your initial principles of flight instruction - coz either you wuz ripped orf or weren't paying all that much attention

... we are talking flow angles in terms of the parameters which affect the indirect measurement of those angles.


Mr McDonal doesn't indicate which airline it is for which he flies. You have the option of asking your ops engineering section to run over the engineering again for your interest. I am quite sure that they will opt for a variation on your story.

[training wheels]

Originally Posted by The Green Goblin

Simple,

You will stall when the aerofoil exceeds the critical angle

Weight and Airspeed have zilch to do with it!

Try explaining that to the guys who wrote the CASA Flight Instructor's Manual.

From the said manual, page 33;

RELATIONSHIP BETWEEN CRITICAL ANGLE AND STALLING SPEED
Explain that for a given weight at ‘1’ g every angle of attack including the critical angle, has its associated indicated airspeed. As the angle of attack of the wings invariably cannot be observed, reference is therefore made to an aeroplane’s stalling speed.

FACTORS AFFECTING THE STALLING SPEED
The basic stalling speed of an aeroplane, such as referred
to in an Operations Manual or Owner’s Handbook means
the indicated airspeed at which the aeroplane will stall
from straight and level flight, with power off.
Explain that the stalling speed will vary, depending on:
(a) Weight
(b) Power
(c) Flap and/or Slat position
(d) Manoeuvre
(e) Ice on or damage to wings

[Oktas8]

I love it. Green Goblin & rmcdonal (who?) correcting Mr Tullamarine on a point of P of F. Can't work out whether it's funny or tragic. But it's certainly priceless, either way.

[The Green Goblin]

As the angle of attack of the wings invariably cannot be observed, reference is therefore made to an aeroplane’s stalling speed."

Answered your own argument there mate!

Come on guy's! I can't believe something so trivial as this is causing such confusion!

This is why 'stalling speed' is so en grained in peoples collective thoughts. As an instructors we teach the lesson on stalling by demonstrating it with a decreasing airspeed. Don't forget when we demonstrate stalling we get you to look out the window at the increasing angle of attack relative to the horizon.

You can stall at high speed, you can stall at low speed, you stall anytime you exceed the critical angle of attack.

Vs is simply the minimum steady flight speed. Reduce the airspeed anymore and you will need to increase the angle of attack to generate more lift. Increase the angle of attack anymore and you will stall.

Either way, and all jokes aside, I really do suggest that you both revisit the books and then go ask for your money back from whomever did your initial principles of flight instruction - coz either you wuz ripped orf or weren't paying all that much attention

... we are talking flow angles in terms of the parameters which affect the indirect measurement of those angles.

You're clutching at straws mate

FACTORS AFFECTING THE STALLING SPEED
The basic stalling speed of an aeroplane, such as referred
to in an Operations Manual or Owner’s Handbook means
the indicated airspeed at which the aeroplane will stall
from straight and level flight, with power off.
Explain that the stalling speed will vary, depending on:
(a) Weight
(b) Power
(c) Flap and/or Slat position
(d) Manoeuvre
(e) Ice on or damage to wings

Obviously we generate lift three ways. Through angle of attack, airspeed or camber. So to support that increased weight we need to adjust one of these three things to support it. An increased weight will result in an increased Vs simply because we require a larger angle of attack to generate the additional lift for a given airspeed. Notice when you're aircraft is heavy it will not get the same TAS? Nor climb as fast? It would't be because you're taking a larger bite of the air would it?

I'm still struggling to comprehend how smart people get something so simple, so wrong!

[GADRIVR]

Goblin.....you are a **** stirrer...though correct....love it.
A stall can happen at any old time. Just pull the stick, exceed critical angle, hey presto....stalled aerofoil.

[Deaf]

Of course another consideration is that

L=1/2. ρ.V^2 .S.Cl

is an oversimplification/half truth/something/certainly not worth too many significant figures.

Cl varies with Reynolds number ie with rho, V and chord (a big compnent of S) and that variation is different for different airfoils.

Now if the reduction in stall speed is achieved with wing extension then we have a change in aspect ratio; whole new sets of things to play with.

[RHLMcG]

As an instructors

You're an INSTRUCTOR ?? ... Christ Almighty !! The standards have plummeted to abysmal depths !!