wing loading / g force / turn rate
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wing loading / g force / turn rate
I came across this post on another forum, and my initial "private pilot knowledge level" reaction was "hmm I'm not sure I believe this" but I honestly don't know the answer.
The discussion was regarding whether a (relatively) low wing loaded plane could out-turn a higher wing loaded plane, the reasoning being that the lower wing-loaded plane had more "angle of attack left" to achieve the same g-loading as the the higher wing-loaded plane.
Is that true?
I thought that wing-loading irrelevant, and that an XXX degree bank at ZZ speed would produce the same turn rate regardless of the aircraft weight ..... and wouldn't the angle of attack also be the same for both planes ?
Mike
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>>"By the way, it really doesn't matter if you are in an Eagle or Falcon, a 9G turn is the same radius of action in either airplane, this means there is no trade-off between aircraft weight and wing surface area, the basic lift equation resultant will be equal for both jets."
"Not quite. A 9G turn is a 9G turn, yes. However, the wing loading makes a huge difference in how a plane is able to maintain these conditions.
For example, we have two 40,000 pound planes. One has a wing loading of 80 lbs./sq. ft., the other has a wing loading of 160 lbs./sq. ft. In a 9-G turn, both planes' centrifugal force will increase ninefold. In order to maintain a 9-G turn, the lift (centripetal force) must also increase ninefold. To do this, the 160 lbs./sq. ft. wing-loaded plane must increase its angle of attack a certain amount, but the 80 lbs./sq. ft. wing-loaded plane doesn't have to increase its angle of attack as much as the first plane has to.
Because the second plane can make a 9-G turn at a lower angle of attack, it can increase it's G-forces (rate of turn), to turn inside the first plane. In other words, at the same angle of attack, the second plane is producing more lift proportional to G-forces than the first plane is.
Wing loading is one indicator of turning ability, but others (such as wing geometry, camber, aspect ratio, etc.) all have influence as well.
Also keep in mind that if lift acts perpendicular to the chord line then a higher angle of attack will creater a higher backwards vector and create a resultant which works against forward motion. "
The discussion was regarding whether a (relatively) low wing loaded plane could out-turn a higher wing loaded plane, the reasoning being that the lower wing-loaded plane had more "angle of attack left" to achieve the same g-loading as the the higher wing-loaded plane.
Is that true?
I thought that wing-loading irrelevant, and that an XXX degree bank at ZZ speed would produce the same turn rate regardless of the aircraft weight ..... and wouldn't the angle of attack also be the same for both planes ?
Mike
==================
>>"By the way, it really doesn't matter if you are in an Eagle or Falcon, a 9G turn is the same radius of action in either airplane, this means there is no trade-off between aircraft weight and wing surface area, the basic lift equation resultant will be equal for both jets."
"Not quite. A 9G turn is a 9G turn, yes. However, the wing loading makes a huge difference in how a plane is able to maintain these conditions.
For example, we have two 40,000 pound planes. One has a wing loading of 80 lbs./sq. ft., the other has a wing loading of 160 lbs./sq. ft. In a 9-G turn, both planes' centrifugal force will increase ninefold. In order to maintain a 9-G turn, the lift (centripetal force) must also increase ninefold. To do this, the 160 lbs./sq. ft. wing-loaded plane must increase its angle of attack a certain amount, but the 80 lbs./sq. ft. wing-loaded plane doesn't have to increase its angle of attack as much as the first plane has to.
Because the second plane can make a 9-G turn at a lower angle of attack, it can increase it's G-forces (rate of turn), to turn inside the first plane. In other words, at the same angle of attack, the second plane is producing more lift proportional to G-forces than the first plane is.
Wing loading is one indicator of turning ability, but others (such as wing geometry, camber, aspect ratio, etc.) all have influence as well.
Also keep in mind that if lift acts perpendicular to the chord line then a higher angle of attack will creater a higher backwards vector and create a resultant which works against forward motion. "
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Had to sit down and read the original post twice, but here is what I came up with. I am a pilot and have no aerodynamic training beyond what is required for an ATPL, so I might not be using the correct terminology.
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Wing loading and G loading are not the same thing. If both planes fly at the same speed and bank angle (and experience the same G loading as a result of this bank angle), they will have exactly the same radius of turn.
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I'd say that when comparing two airframes of similar weight but one with twice the wing loading (ie half the wing area), the aircraft with the higher wing loading is most probably designed to fly significantly faster. Therefore, with both at their design speed at any given bank angle and hence G loading, the faster aircraft will have a greater radius of turn. If both do fly at their design speeds, they could well fly at a similar angle of attack and there is no reason why the faster aircraft would 'run out of spare angel of attack' sooner than the other.
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Now, if both of them do fly at the same speed (the design speed for the slower aircraft), the aircraft with the higher wing loading will be flying closer to its stalling angle of attack, to compensate for the loss of speed.
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If in this situation they both fly a turn at a given bank angle the radius is still the same. However, the faster aircraft will be the first to reach a bank angle (and associated G loading and angle of attack) that will make the wing stall.
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So, at slow speeds the aircraft with the lower wing loading could out-turn the one with the higher wing loading. But only because the aircraft with the higher wing loading is flying at a speed it is not designed for (ie too slow) and would be the first to stall.
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Hope this make sense and that I haven't upset too many of the pros on here by using the incorrect terminology.
.
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Wing loading and G loading are not the same thing. If both planes fly at the same speed and bank angle (and experience the same G loading as a result of this bank angle), they will have exactly the same radius of turn.
.
I'd say that when comparing two airframes of similar weight but one with twice the wing loading (ie half the wing area), the aircraft with the higher wing loading is most probably designed to fly significantly faster. Therefore, with both at their design speed at any given bank angle and hence G loading, the faster aircraft will have a greater radius of turn. If both do fly at their design speeds, they could well fly at a similar angle of attack and there is no reason why the faster aircraft would 'run out of spare angel of attack' sooner than the other.
.
Now, if both of them do fly at the same speed (the design speed for the slower aircraft), the aircraft with the higher wing loading will be flying closer to its stalling angle of attack, to compensate for the loss of speed.
.
If in this situation they both fly a turn at a given bank angle the radius is still the same. However, the faster aircraft will be the first to reach a bank angle (and associated G loading and angle of attack) that will make the wing stall.
.
So, at slow speeds the aircraft with the lower wing loading could out-turn the one with the higher wing loading. But only because the aircraft with the higher wing loading is flying at a speed it is not designed for (ie too slow) and would be the first to stall.
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Hope this make sense and that I haven't upset too many of the pros on here by using the incorrect terminology.
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Sounds good IRRenewel.
I think the clue is in this statement (my bolding):
This isn't true is it? If the apparent weight of the aircraft doubles, then the lift must double to compensate. If the speed is the same and all the other parts of the lift equation are the same allowing us to only change the angle of attack, then the AoA must also double to achieve the extra lift. This is the same for the high wing loading and low wing loading aircraft.
The difference comes about because the high wing loading aircraft already has a higher angle of attack and as IRR says, it will reach its stalling angle sooner, but up until it stalls, it's turn rate and radius would be the same as for the other aircraft.
Reading it again, I think he is correct but isn't quite saying what you think. It seems to me that he's basically saying the low wing loading aircraft can pull more Gs than the other aircraft and can therefore out turn it, but it must pull more to do it.
I think the clue is in this statement (my bolding):
In a 9-G turn, both planes' centrifugal force will increase ninefold. In order to maintain a 9-G turn, the lift (centripetal force) must also increase ninefold. To do this, the 160 lbs./sq. ft. wing-loaded plane must increase its angle of attack a certain amount, but the 80 lbs./sq. ft. wing-loaded plane doesn't have to increase its angle of attack as much as the first plane has to.
The difference comes about because the high wing loading aircraft already has a higher angle of attack and as IRR says, it will reach its stalling angle sooner, but up until it stalls, it's turn rate and radius would be the same as for the other aircraft.
Reading it again, I think he is correct but isn't quite saying what you think. It seems to me that he's basically saying the low wing loading aircraft can pull more Gs than the other aircraft and can therefore out turn it, but it must pull more to do it.
Last edited by AerocatS2A; 9th Sep 2007 at 11:13. Reason: typo
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My take:
9G at the same speed, they should follow the same trajectory. F=MA, given F comes from lift, A=9G, F will need to be less in the lighter plane (less M), therefore less lift/unit area of wing, therefore less AOA. PPL level aerodynamics teaches me that Vs increases with weight (well, load factor)...
In theory the lighter plane ought to be able to increase the A (>9G), but the pilot will probably pass out. However, the lighter plane should be able to pull 9G at lower airspeed than the heavier one therefore turning tighter (can't remember the equations for circular motion, but the faster it goes, the harder it needs to pull)
Perhaps more importantly, will bleed less energy (less AOA, less induced drag) while turning. Downside is all that unnecessary wing area causing parasitic drag when going flat out in a straight line...
Or, to relate to something more practical; my little sailplane stalls considerably slower than the C150 I'm flying. They both double their stall speed in a tightly banked turn. Double the sailplane's stall speed is a lot less than double the C150's stall speed; so at equal speed / load factors underneath the stall, the sailplane is at a lesser AOA, so I can pull harder and turn inside.
I'd put money on the sailplane to out-turn the C150 at any speed. In fact, it'd probably still be turning when the wings peeled off the little cessna.. but it's designed to a higher load factor
Sure the military folks could give you chapter and verse, this would be right up their street I guess!
<Gliderpilot, PPL in training>
/Mark.
9G at the same speed, they should follow the same trajectory. F=MA, given F comes from lift, A=9G, F will need to be less in the lighter plane (less M), therefore less lift/unit area of wing, therefore less AOA. PPL level aerodynamics teaches me that Vs increases with weight (well, load factor)...
In theory the lighter plane ought to be able to increase the A (>9G), but the pilot will probably pass out. However, the lighter plane should be able to pull 9G at lower airspeed than the heavier one therefore turning tighter (can't remember the equations for circular motion, but the faster it goes, the harder it needs to pull)
Perhaps more importantly, will bleed less energy (less AOA, less induced drag) while turning. Downside is all that unnecessary wing area causing parasitic drag when going flat out in a straight line...
Or, to relate to something more practical; my little sailplane stalls considerably slower than the C150 I'm flying. They both double their stall speed in a tightly banked turn. Double the sailplane's stall speed is a lot less than double the C150's stall speed; so at equal speed / load factors underneath the stall, the sailplane is at a lesser AOA, so I can pull harder and turn inside.
I'd put money on the sailplane to out-turn the C150 at any speed. In fact, it'd probably still be turning when the wings peeled off the little cessna.. but it's designed to a higher load factor
Sure the military folks could give you chapter and verse, this would be right up their street I guess!
<Gliderpilot, PPL in training>
/Mark.
I dont have my textbooks handy but isn't excess power available the determining factor for maximum rate / minimum radius turns?
(Ignoring the glider where energy comes from elsewhere, and assuming no height loss)
(Ignoring the glider where energy comes from elsewhere, and assuming no height loss)
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Load Factor = G. Turn Rate at 9G is the same irrespective of speed but Turn Radius increases with speed. Excess thrust helps but only in a level fight, normally you just stick you nose low to maintain energy.
The AoA to achieve the required G reduces as speed increases and conversely when slowing down you run out of Aoa to achieve the required load factor and so cannot maintain the turn rate. This means the low wing loader does better when slower. So if an F-15 fought a Spit, the 15 would opt for rate, the spit for radius and the higher rate would generally enable the 15 to get the nose on earlier but maybe at min range.
The AoA to achieve the required G reduces as speed increases and conversely when slowing down you run out of Aoa to achieve the required load factor and so cannot maintain the turn rate. This means the low wing loader does better when slower. So if an F-15 fought a Spit, the 15 would opt for rate, the spit for radius and the higher rate would generally enable the 15 to get the nose on earlier but maybe at min range.
Turn Rate at 9G is the same irrespective of speed
Nonsense. Acceleration is rate of change of speed. To turn 180 degrees you need to go from plus V to minus V. A higher speed needs more G for the same turn rate.
Nonsense. Acceleration is rate of change of speed. To turn 180 degrees you need to go from plus V to minus V. A higher speed needs more G for the same turn rate.
Load Factor = G. Turn Rate at 9G is the same irrespective of speed but Turn Radius increases with speed.
Gosh, Tally ho chaps.
Well despite the theory the older "military folks" will tell you the simple answer is don't get into a horizontal turning fight with a low(er) wing loader and if you've got the power..use the vertical.
Bugging out.
Well despite the theory the older "military folks" will tell you the simple answer is don't get into a horizontal turning fight with a low(er) wing loader and if you've got the power..use the vertical.
Bugging out.
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Gosh, Tally ho chaps.
Well despite the theory the older "military folks" will tell you the simple answer is don't get into a horizontal turning fight with a low(er) wing loader and if you've got the power..use the vertical.
Bugging out.
Well despite the theory the older "military folks" will tell you the simple answer is don't get into a horizontal turning fight with a low(er) wing loader and if you've got the power..use the vertical.
Bugging out.
P.S.
I dont have my textbooks handy but isn't excess power available the determining factor for maximum rate / minimum radius turns?
(Ignoring the glider where energy comes from elsewhere, and assuming no height loss)
(Ignoring the glider where energy comes from elsewhere, and assuming no height loss)
Last edited by Mark1234; 10th Sep 2007 at 15:48.
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Corner is typically around 420 and most 3rd generation fighters had to go nose low to base and when there would end up sustaining around about 4g with rockets on. The big mouth F-16 was better, next generation platforms should be kinematically in another league.
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A good illustration of this is the "stall-wingover" movie available at http://www.tf51d.com/stall_wingover.avi - it takes about 2 min. to download on a DSL connection.
If you are used to the rate of turn in a SE Cessna or Piper, you'll find at a similar bank angle a Mustang turns much slower.
If you are used to the rate of turn in a SE Cessna or Piper, you'll find at a similar bank angle a Mustang turns much slower.
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Don’t overcomplicate things by bringing in power or thrust. Let’s stick to the original question.
Aircraft flying at the same speed using the same angle of bank will have the same radius of turn.
Example 1: The Battle of Britain Memorial Flight. A big Lancaster with a Spitfire and Hurricane in perfect formation (as always) on each wing. Lanc puts on 25 degrees of bank, Spit and Hurricane put on 25 degrees of bank. Result? They all go around the corner together in perfect formation.
Example 2: Air-to-air refuelling. Tristar tanker trailing hoses with an F3 Tornado hooked up and a pair of Harriers in close formation on the Tristar’s wing waiting for their turn. Tristar turns using 20 degrees of bank, Tornado banks likewise to stay hooked up, and so do the Harriers. All turn neatly together.
That’s the speed, angle of bank and radius bit sorted. Different wings, different weights, but at the same speed and angle of bank, they all stick together.
Aircraft pulling the same G in level flight will have the same rate of turn.
If a Tucano, Tornado, Typhoon and F15 all pull 4 G in level flight, they will turn at the same rate. In other words their noses will move through the same points of the compass at the same time. Neither will be able to get their nose onto the other if they stay at the same G in level flight. The speed, angle of bank and radius of turn and power they each need to achieve this level of G will differ according to their wing loading and other aerodynamic factors, but whilst pulling the same G neither will be able to out-turn the other in level flight.
This is why in air combat you have to learn about using the vertical, ie to get out of level flight and use earth’s gravity to increase your actual G relative to your opponent (the “combat egg”, high and low yo-yos etc) and the principles of lag pursuit and lead pursuit which accounts for different wing loading in dissimilar air-to-air combat.
Google the above and no doubt someone, somewhere, will give you the mathematical formulae in a format you can understand. I've given you the real world examples.
Aircraft flying at the same speed using the same angle of bank will have the same radius of turn.
Example 1: The Battle of Britain Memorial Flight. A big Lancaster with a Spitfire and Hurricane in perfect formation (as always) on each wing. Lanc puts on 25 degrees of bank, Spit and Hurricane put on 25 degrees of bank. Result? They all go around the corner together in perfect formation.
Example 2: Air-to-air refuelling. Tristar tanker trailing hoses with an F3 Tornado hooked up and a pair of Harriers in close formation on the Tristar’s wing waiting for their turn. Tristar turns using 20 degrees of bank, Tornado banks likewise to stay hooked up, and so do the Harriers. All turn neatly together.
That’s the speed, angle of bank and radius bit sorted. Different wings, different weights, but at the same speed and angle of bank, they all stick together.
Aircraft pulling the same G in level flight will have the same rate of turn.
If a Tucano, Tornado, Typhoon and F15 all pull 4 G in level flight, they will turn at the same rate. In other words their noses will move through the same points of the compass at the same time. Neither will be able to get their nose onto the other if they stay at the same G in level flight. The speed, angle of bank and radius of turn and power they each need to achieve this level of G will differ according to their wing loading and other aerodynamic factors, but whilst pulling the same G neither will be able to out-turn the other in level flight.
This is why in air combat you have to learn about using the vertical, ie to get out of level flight and use earth’s gravity to increase your actual G relative to your opponent (the “combat egg”, high and low yo-yos etc) and the principles of lag pursuit and lead pursuit which accounts for different wing loading in dissimilar air-to-air combat.
Google the above and no doubt someone, somewhere, will give you the mathematical formulae in a format you can understand. I've given you the real world examples.
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The turn radius is given by:
Radius = V² / (9.81 x tan bank angle)
Radius in metres
V in metres / second
bank angle in degrees
Not much use in the cockpit but someone did ask
Regards
csd
Radius = V² / (9.81 x tan bank angle)
Radius in metres
V in metres / second
bank angle in degrees
Not much use in the cockpit but someone did ask
Regards
csd
Aircraft pulling the same G in level flight will have the same rate of turn.
If a Tucano, Tornado, Typhoon and F15 all pull 4 G in level flight, they will turn at the same rate. In other words their noses will move through the same points of the compass at the same time. Neither will be able to get their nose onto the other if they stay at the same G in level flight. The speed, angle of bank and radius of turn and power they each need to achieve this level of G will differ according to their wing loading and other aerodynamic factors, but whilst pulling the same G neither will be able to out-turn the other in level flight.
If a Tucano, Tornado, Typhoon and F15 all pull 4 G in level flight, they will turn at the same rate. In other words their noses will move through the same points of the compass at the same time. Neither will be able to get their nose onto the other if they stay at the same G in level flight. The speed, angle of bank and radius of turn and power they each need to achieve this level of G will differ according to their wing loading and other aerodynamic factors, but whilst pulling the same G neither will be able to out-turn the other in level flight.
First of all, bank angle is directly related to G. A balanced 60 degree banked turn in level flight will result in 2g, it must, just have a look at the old lift vector diagrams. At 60 degrees, the lift vector must be twice as big as the weight vector to give a vertical component of lift equal to the weight vector. G is directly related to the relative size of the lift vector.
To illustrate how it is wrong, you need to go to some extremes, this is where my tiger moth traveling at 85 mph and your Foxbat travelling at Mach 3 help out.
My tiger moth, in a 60 degree banked turn will pull 2 gs and whip around through 360 degrees in under a minute. Your Foxbat, travelling at Mach 3 will take a long long time to do 360 degrees in a 2 g turn.
Another illustration. A rate one turn which is defined as being 360 degrees in two minutes, requires a higher angle of bank, and therefore higher g, the faster you are going. In a light twin, a rate one turn is generally less than 25 degrees bank, in a faster passenger jet, the rate one turn requires more angle of bank, to the point where passenger jets are limited by 25 degrees bank angle during instrument procedures and light twins are limited by rate one. The only reason for this is that the passenger jet is going faster, if it slowed down to the speed of the light twin, the rate would be the same.
So. An aircraft travelling at the SAME SPEED and pulling the SAME G and therefore at the SAME BANK ANGLE, will have the SAME RATE and SAME RADIUS. Doesn't matter if it is a Tiger Moth or a Foxbat.
Lets look at extremes again to see why an aircraft with a low wing loading can out turn an aircraft with a high wing loading. Lets say the low wing loading aircraft is the Tiger Moth and the high wing loading aircraft is an experimental aircraft very similar to the Tiger Moth except it has such stubby wings that at 85 mph it requires an angle of attack close to the stalling angle to generate enough lift to maintain height.
Both aircraft cruising along at 85 mph together and they both enter a gentle 15 degree bank to the right. Both aircraft increase angle of attack slightly to maintain altitude. This brings the experimental aircraft even closer to the stalling AoA but at the moment it's not quite stalling.
Both aircraft are now at the same speed, pulling the same G and getting the same rate and radius of turn.
But what happens when the Tiger Moth increase bank angle even further? The experimental with very high wing loading tries to match it but doesn't have any excess angle of attack to use and stalls. Meanwhile the Tiger happily putts around in a nice tight turn.
So while the Gs and speed were the same, the aircraft had the same turning performance. But the low wing loading on the Tiger Moth meant it had plenty of excess angle of attack to use to further increase bank and therefore rate, radius and G.
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Aircraft pulling the same G in level flight will have the same rate of turn.
See the Mustang video I mentioned earlier. Because of its greater VELOCITY it needs a bigger turn radius than a light SE plane, and thus has a SLOWER turn rate. Note the greater weight of the aircraft is not a factor, except for the fact more power and more lift are needed to pull the same G's (same bank angle).
The SR-71 often needed three or four STATES to complete a 180 - giving rise to the maxim "You haven't been lost until you've been lost at Mach 3!"
