Aspect ratio
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Aspect ratio
Can anybody here explain why wings with high aspect ratio have reduced rate of roll as compared to with low aspect ratio.
What are the limiting factors for increasing the aspect ratio of an aerofoil?
Thanks
What are the limiting factors for increasing the aspect ratio of an aerofoil?
Thanks
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Aspect ratio is high means the wing span is comparatively much wider than the wing chord - wider thin wings.
lets get an example. Lockheed U-2 has high aspect ratio comparing to Lockheed F-104 Startfighter which has low aspect ratio wing (this aircraft barely have a wing!!).
an aircraft is fixed with a hi aspect ratio wing to gain more lift and to have a statistically and dynamically much more stable flight. the "rolling" which occurs on the longitudinal axis of the aircraft is somewhat "slow" comparing to a highly maneuverable F-104.
high aspect ratio wing has a short chord lenght. hence the pressure difference of making different angles of attack are slower. hence rolling takes place little slower. Most cargo aircraft (and passenger) have high aspect ratio wings for this case. Generally, a high aspect ratio wing aircraft takes more take off run than a low aspect ratio wing for the same reason. many high aspect ratio aircraft are fixed with complicated leading edge and trailing edge high-lift generating devices for this matter. And some high aspect ratio aircraft have gone into the extent of STOL characteristics by having these high lift devices. On the other hand a Cessna 152 with a low aspect ratio wing, easily takes off at a small pressure on the column. I also think (not sure about this one yet) a high aspect ratio wing is fixed at a higher angle of incidence than a low wing (will clarify this matter in future).
on the other hand a low aspect ratio wing has a lengthy chord. allowing more air to pass over and below the wing, creating a high pressure difference between the surfaces. so little more u turn the control column your aircraft will response more quickly and promptly. Cessna 152-172s have low aspect ratio wings. little more you turn lot more it rolls. closely monitor most of high aspect ratio wings have vortex generators near control surfaces, ideally before ailerons to energize the airflow.
Also, there is another thing. tips of high aspect ratio wings are at a risk of stall. when you make a tight turn the tendency to stall the tips are much more. so high aspect ratio wings generally do not have high angles of bank. comparatively, a low aspect ratio aircraft is with a wider flight envelop than of a high aspect ratio aircraft.
summer it up! pressure difference created by low aspect ratio wings are much more high than a high aspect ratio wing. this pressure difference is the key factor for aircraft "rolling" maneuver.
lets get an example. Lockheed U-2 has high aspect ratio comparing to Lockheed F-104 Startfighter which has low aspect ratio wing (this aircraft barely have a wing!!).
an aircraft is fixed with a hi aspect ratio wing to gain more lift and to have a statistically and dynamically much more stable flight. the "rolling" which occurs on the longitudinal axis of the aircraft is somewhat "slow" comparing to a highly maneuverable F-104.
high aspect ratio wing has a short chord lenght. hence the pressure difference of making different angles of attack are slower. hence rolling takes place little slower. Most cargo aircraft (and passenger) have high aspect ratio wings for this case. Generally, a high aspect ratio wing aircraft takes more take off run than a low aspect ratio wing for the same reason. many high aspect ratio aircraft are fixed with complicated leading edge and trailing edge high-lift generating devices for this matter. And some high aspect ratio aircraft have gone into the extent of STOL characteristics by having these high lift devices. On the other hand a Cessna 152 with a low aspect ratio wing, easily takes off at a small pressure on the column. I also think (not sure about this one yet) a high aspect ratio wing is fixed at a higher angle of incidence than a low wing (will clarify this matter in future).
on the other hand a low aspect ratio wing has a lengthy chord. allowing more air to pass over and below the wing, creating a high pressure difference between the surfaces. so little more u turn the control column your aircraft will response more quickly and promptly. Cessna 152-172s have low aspect ratio wings. little more you turn lot more it rolls. closely monitor most of high aspect ratio wings have vortex generators near control surfaces, ideally before ailerons to energize the airflow.
Also, there is another thing. tips of high aspect ratio wings are at a risk of stall. when you make a tight turn the tendency to stall the tips are much more. so high aspect ratio wings generally do not have high angles of bank. comparatively, a low aspect ratio aircraft is with a wider flight envelop than of a high aspect ratio aircraft.
summer it up! pressure difference created by low aspect ratio wings are much more high than a high aspect ratio wing. this pressure difference is the key factor for aircraft "rolling" maneuver.
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Please don't confuse rate of roll with controllability. The F-104 was built as an interceptor, up, kill, and down. Don't take this lady to a knifefight.
The U-2 was designed to fly very high, and loiter. It had no defenses, except one cyanide pill.
Both these a/c were designed by Kelly Johnson, and built by Lockheed. They are also the "same" planform, minus engine and wings.
For roll rate and sweet performance, the T-38 Talon is your ride. Ask an AF guy, they all learned on this little hot rod.
How is 760 degrees rate of roll/second?
bear
The U-2 was designed to fly very high, and loiter. It had no defenses, except one cyanide pill.
Both these a/c were designed by Kelly Johnson, and built by Lockheed. They are also the "same" planform, minus engine and wings.
For roll rate and sweet performance, the T-38 Talon is your ride. Ask an AF guy, they all learned on this little hot rod.
How is 760 degrees rate of roll/second?
bear
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For geometrically similar airplanes at a given speed, roll rate will vary inversely with span (b). I believe this is because although the pressure differential (thus rolling force) created by the aileron will be the same in relative terms. The physical distance that the wing tip has to travel is greater for the longer wing thus overall roll rate is reduced. Therefore for two wings of the same area, aspect ratio will be a measure of the difference in span and thus roll rate. Not entirely sure though!
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Another consideration is the moment of inertia about the roll axis (ie spanwise mass distribution). If the wing is low aspect ratio and tapered, there's little roll inertia to overcome. OTOH if tip tanks are installed, roll inertia increases.
Further - if a biplane, four ailerons help!
Further - if a biplane, four ailerons help!
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I am a great believer in answering the questions posed.
This question is probably too generic to admit of much of a contentful answer. The straight answer is: because they are designed that way.
But why are they designed that way? Structural reasons. Building something that is long and thin and light versus building something that is short and light.
Say you had a 27m-long half-wing (that is, span of 54m+fuselage-width).** That is not a lot compared with some aircraft flying. And say you wanted to achieve the 760°/second roll rate mentioned by bearfoil. Let's just take 720°/s, because that is twice around full circle. Let's rotate the airplane about the longitudinal fuselage axis so the tips are describing a circle, radius 7.5m + 1/2 fuselage width. The tips would be going through two circumference lengths, about 353m, in 1 second. The speed of sound at 15°C is about 340 m/s. So you would be wanting to accelerate your wing tips from 0 to over the speed of sound and back to zero again in 1 second.
Guess what? People don't try to do that. They want to roll fast, they generally stick to stubby.
If you are talking just about designing aircraft with no context, then mostly structural. But if you are talking transport aircraft, they have to fit into gates at airports, and that limits the wing span, which again limits the achievable aspect ratio.
** Edit Note: I originally had a (much!) lower figure here, which bearfoil points out (below) is a mistake.
PBL
Originally Posted by p tango
Can anybody here explain why wings with high aspect ratio have reduced rate of roll as compared to with low aspect ratio.
But why are they designed that way? Structural reasons. Building something that is long and thin and light versus building something that is short and light.
Say you had a 27m-long half-wing (that is, span of 54m+fuselage-width).** That is not a lot compared with some aircraft flying. And say you wanted to achieve the 760°/second roll rate mentioned by bearfoil. Let's just take 720°/s, because that is twice around full circle. Let's rotate the airplane about the longitudinal fuselage axis so the tips are describing a circle, radius 7.5m + 1/2 fuselage width. The tips would be going through two circumference lengths, about 353m, in 1 second. The speed of sound at 15°C is about 340 m/s. So you would be wanting to accelerate your wing tips from 0 to over the speed of sound and back to zero again in 1 second.
Guess what? People don't try to do that. They want to roll fast, they generally stick to stubby.
Originally Posted by p tango
What are the limiting factors for increasing the aspect ratio of an aerofoil?
** Edit Note: I originally had a (much!) lower figure here, which bearfoil points out (below) is a mistake.
PBL
Last edited by PBL; 4th Oct 2010 at 13:20. Reason: bearfoil pointed out a mistake
I am a great believer in answering the questions posed.
coz really long wings roll slower.
coz really,really long wings might snap off
coz really,really long wings might snap off
For geometrically similar airplanes at a given speed, roll rate will vary inversely with span (b). I believe this is because although the pressure differential (thus rolling force) created by the aileron will be the same in relative terms. The physical distance that the wing tip has to travel is greater for the longer wing thus overall roll rate is reduced. Therefore for two wings of the same area, aspect ratio will be a measure of the difference in span and thus roll rate. Not entirely sure though!
roll helix angle = Pb/2V, p= rate of roll
so, p = Roll helix angle*2V/b..roll rate is directly proportional to V and inversely proportional to 'b'...
aspect ratio is more important wrt to discussing
Cd...as spanwise circulation at a finite AR is not negligible,.also much depends on the Jones Edge factor, which is a parameter not a variable.
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PBL
Please do check your math. Two circumferences are 2(3.14)D= ~ 90 meters, call it 300 feet/second. This is airspeed additive, so the resultant tip velocity is handsome, but not 0/M/0/second. The Talon is a trainer, and barely transonic, so Mach number needs to be >as.
edit: the wingspan of the Talon is 25 feet total. the circumference then is 85 feet for a doubling to 170fps. Still remarkable, but not unbelievable.
bear
Please do check your math. Two circumferences are 2(3.14)D= ~ 90 meters, call it 300 feet/second. This is airspeed additive, so the resultant tip velocity is handsome, but not 0/M/0/second. The Talon is a trainer, and barely transonic, so Mach number needs to be >as.
edit: the wingspan of the Talon is 25 feet total. the circumference then is 85 feet for a doubling to 170fps. Still remarkable, but not unbelievable.
bear
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Roll Acceleration = Roll Moment / Roll Inertia
Roll Moment: produced by ailerons, limited by wing flex (especially high aspect) and local maximum lift coefficient. More span adds more Rolling moment as the lever arm increases.
Roll Inertia: the mass multiplied by its distance to the roll axis. It will increase much faster than the roll acceleration of the aileron.
Now, roll acceleration creates roll rate. Roll rate is damped by roll damping (master of the obvious). And again, roll damping is function of span. The induced vertical velocity at the wing creates a different local angle of attack that opposes the roll direction. Upward wing will see "air flowing downward", thus lowering local angle of attack and creating a damping. That's why roll rate is so excellently damped on basically all aircraft, except maybe a flat-spinning Starfighter.
Roll Moment: produced by ailerons, limited by wing flex (especially high aspect) and local maximum lift coefficient. More span adds more Rolling moment as the lever arm increases.
Roll Inertia: the mass multiplied by its distance to the roll axis. It will increase much faster than the roll acceleration of the aileron.
Now, roll acceleration creates roll rate. Roll rate is damped by roll damping (master of the obvious). And again, roll damping is function of span. The induced vertical velocity at the wing creates a different local angle of attack that opposes the roll direction. Upward wing will see "air flowing downward", thus lowering local angle of attack and creating a damping. That's why roll rate is so excellently damped on basically all aircraft, except maybe a flat-spinning Starfighter.
CabinMaster---you've just described all of the factors used to describe the RHA
I thought this was very good and I always check my links for horse hooey
http://www.flightlab.net/Flightlab.n...ngDynamics.pdf
I thought this was very good and I always check my links for horse hooey
http://www.flightlab.net/Flightlab.n...ngDynamics.pdf
Last edited by Pugilistic Animus; 3rd Oct 2010 at 00:14.
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Originally Posted by bearfoil
Please do check your math.
Circumference is 2 x Pi x R, and I want twice around (2 x 2 x Pi x R) to be greater than 340. I get R (now :-) ) to be about 27 m, a little more than the 7.5m I originally wrote. I have no idea how that happened.
Even so, 27 m is less than the semi-wing span of A330/40 or Boeing 747 / 777 aircraft, which is also attained by some recent high-aspect-ratio smaller airplanes such as those used for HALE-type research projects, none of which you would want to try to snap-roll.
PBL
