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# Help me with a brain teaser - guaranteed to drive aerody gurus insane!?!

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# Help me with a brain teaser - guaranteed to drive aerody gurus insane!?!

23rd Aug 2005, 23:55

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Help me with a brain teaser - guaranteed to drive aerody gurus insane!?!

O.K. - Here's a doozy of a question I was posed recently...

"If two aircraft are at the same altitude, IAS and bank angle, but one is light weight and the other is heavy weight, which statement is true?"

A. The heavy aircraft will have a greater turn radius but a lower turn rate.

B. The heavy aircraft will have a greater radius but the same rate.

C. Both the light and heavy aircraft will have the same rate and radius

D. The light aircraft will have the same radius and but a higher rate.

Any ideas?? My answer was C. I cannot for the life of me justify it aerodynamically, but from experience, I have flown dissimilar formations where the exact question description has occured. By virtue of being "in formation" the same rate & radius has occured. But, as we all know, reality is not always the correct reasoning when it comes to obscure "knowledge based" questions!

Help me sleep at night by justifying it aerodynamically PLEEEEASE

24th Aug 2005, 00:38

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Refer to this crappy diagram I made

m=mass
V=speed
teta=bank angle
tan(teta)=tangent of angle teta

Centrifugal force (blue arrow) = Weight (red arrow) X tan(teta)

(m V^2) / r = (m g) tan(teta)

r = (m V^2) / ( (m g) tan(teta) )

r = V^2 / ( g tan(teta) )

The radius of turn doesn't depend on the aircraft mass. All other data is the same, so the radius will be the same for the two aircraft.

If the radius is the same, the length of a complete circumference is the same. Since both aircraft have the same speed, they will fly a complete turn in the same time. Their rate of turn is the same.

Using formulae:

omega=turn rate

r = V^2 / ( g tan(teta) )
V = omega r
r = (omega r V) / ( g tan(teta) )
omega = ( g tan(teta) ) / V

Also the turn rate (omega) does not depend on mass.

I hope this helps.

Aerolearner

Last edited by aerolearner; 24th Aug 2005 at 01:12.

24th Aug 2005, 08:15

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Aerolearner - you sir, are a genius...

I salute you!

24th Aug 2005, 09:15

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you sir, are a genius...
Nah, I'm just a rocket scientist

27th Aug 2005, 11:40

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Great response!

Made me laugh. Great explination too. Thanks from me.

Dan.

27th Aug 2005, 14:06

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Only difference is the heavier aircraft will require more AOA.

27th Aug 2005, 17:55

Eidolon

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L Peacock,

Only difference is the heavier aircraft will require more AOA.
Not true...

27th Aug 2005, 17:59

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Have I got it wrong?
Higher mass, more Alpha for same g?

27th Aug 2005, 19:50

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L Peacock & swh

Take two identical B737s one at 40T other at 60T both at FL100 250kts level. The 60T aircraft will need a higher nose attitude (higher AOA) leading to greater induced drag as such requiring more thrust.

So the only difference would be attitude (AOA) & thrust.

Last edited by Squealing Pig; 28th Aug 2005 at 12:11.

27th Aug 2005, 22:19

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Squealing Pig is right. I found this other explanation of what aerolearner was communicating.

other explanation

An aircraft of greater mass needs to generate more lift to maintain a level turn. As shown in the diagram on the right in the above link, lift provides the centripedal acceleration while in a bank, which turns the aircraft's direction of flight. The heavier the aircraft, the greater the lift needed to remain level, thus more centripetal acceleration is available at a given bank angle to turn a heavier aircraft.

As aerolearner said, the mass is cancelled out of the equation, thus the turn radius remains the same.

28th Aug 2005, 00:31

Eidolon

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Squealing Pig & Flight Safety,

This used to be a common instructor rating question.

To clearly illustrate my point, compare the Concorde, 767, 777, and 747.

For a given airspeed, the AoA for a turn with a 767, 777, and 747 is fairly similar ( the Cl for the wing section of each aircraft is between 2.5 and 3), however, Concorde being lighter than the 777 & 747, and much the same weight as the 767 would have a much higher AoA (its wing section Cl is less than 1).

So to compensate for having a poor low lift generating wing (i.e. low Cl), to generate lift Concorde needs a much higher AoA.

Even the same model aircraft, a heavier aircraft can have similar or lower AoA though using high lift devices.

Referring back to the original question "If two aircraft are at the same altitude, IAS and bank angle, but one is light weight and the other is heavy weight, which statement is true?"

Therefore the statement

"Only difference is the heavier aircraft will require more AOA."

Is clearly incorrect, in the example I have given above the lightest aircraft may have the highest AoA.

28th Aug 2005, 02:51
See and avoid

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What does the SR-71 weigh relative to the Concorde? What was their relative abilty to make a tight turn?

28th Aug 2005, 04:34

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I do see what your saying swh, however it would be wise on this question to compare eggs with eggs. ie 60T 737 v 40T 737 rather than a light v heavy type.

28th Aug 2005, 05:08

Eidolon

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Squealing Pig,

The aircraft type is irrelevant, so is the weight.

I used to ask if you had a 747 and Seneca at 150 kts were doing a rate one orbit, which would have the larger turn radius ? which would have the higher angle of bank ? which would finish the orbit first ?

They both have the same turn radius, and 22.5 degrees AoB, and finish at the same time.

The aircraft type and weight are irrelevant, the size of the aircraft has no effect on the radius of turn. Two aircraft flying at the same angle of bank and velocity will make the same radius of turn even if one is 1000 times larger than the other.

This is a basic principle that is used for calculation of approach plate splays for aircraft categories and ATC turning requirements.

Falling for this trap is common for people who don’t understand the basic theory, explaining the theory as aerolearner has above reinforces the theory, that’s what teaching is about.

28th Aug 2005, 07:52

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swh

At no point did I say the radius of turn would be different I was stating that AOA would be different as weight varied.

Refer to the post you made posted 27th August 2005 17:55

--------------------------------------
L Peacock,

quote:
--------------------------------------------------------------------------------
Only difference is the heavier aircraft will require more AOA.
--------------------------------------------------------------------------------

Not true...
--------------------------------------

Thankyou

Last edited by Squealing Pig; 28th Aug 2005 at 10:21.

28th Aug 2005, 09:41

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SWH

Think you've gone off at a tangent. It was established early on that turn radius will be unaffected to mass.

My point was that AOA would be affected (increased for increase in mass to maintain same g). Of course it would require a comparison of identical airframe types.

High lift devices would also fudge the issue (again like for like comparison required). But then high lift devices usually have the effect of increasing the wing alpha anyway, so probably reinforce the point.

28th Aug 2005, 10:03

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R = TAS^^2 / (g x tan AoB)

And that's it.

The 'g' loading is equal to L/W and thus = sec AoB.

The question was asked when I was going through the CFS course. They used the example of the BBMF Lancaster, with the Spitfire (on the outside) and Hurricane (on the inside) in formation with it and asked which a/c had the greatest AoB.

The answer they wanted was that they would all have the same AoB. But that is incorrect as the radii of turns differ, even though the turn rate must be constant to stay in formation. Quite complicated to work it out - first assume a bank angle and TAS for the Lancaster to obtain the radius of turn and turn rate. Then assume the formation separation distance for the 2 fighters. Work out their radii of turn, substitute into the turn rate and obtain their TAS. Then from TAS and turn radius for each, recalculate the AoB for each......

Woody (RIP) changed the question after that as he didn't really understand algebra - much less trigonometry!

28th Aug 2005, 10:29

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SWH, I see your location is 'Some hole' I'm sure thats where your talking from.

28th Aug 2005, 11:00

Eidolon

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Squealing Pig, L Peacock, T3HUY,

My humblest apologies, being an engineer it must be my English comprehension skills which has let me down as I didn’t see in the original question posed by Macchi where they asked to compare the angle of attack and mass/weight of on identical airframes in a steady turn.

I will contact my aerodynamics professors that are still alive and advise them they were all wrong, and that for turn performance “heavier aircraft will require more AOA” and “the only diffence [difference] would be attiude [attitude] (AOA) & thrust”.

T3HUY and as you no doubt are aware a swh is short for “some watering hole”, commonly known as a pub, bar, or an establishment for the consumption of fine beverages, and is somewhere one tends to frequent when in need of rehydration. No doubt you have participated in such practices and locations before.

28th Aug 2005, 11:50

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swh,

i think you are confusing AOB and AOA.

turning or not, if aircraft x has a greater weight than aircraft y, then aircraft x MUST, given the same airspeed, generate a greater lift force to remain in level flight. Other than generating additional lift forces using other means, the AOA (Angle of Attack) must be greater. Straight flight or turning this is still the case.

If I'm wrong, I'd better revoke the 200 or so pilots I gave CPLs to!