Glide Speed and Bank Angle

Jaybird180

Jaybird180

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Inspired by a recent "impossible turn" thread.

I was thinking sarcastically, but now seriously wondering if a graph could be made showing how best glide speed changes (?) relative to bank angle and how the graphs intersect with the stall speed decreasing with bank angle. Is it possible to mathematically derive this from available POH data for most airframes?
 
Performance data is best determined by flight test/actual performance. When we design a plane we estimate the performance, but what you see in the AFM/POH/FCOM is based on/validated by actual testing.

The benefit is, if you go out and conduct some tests, carefully, you will increase your comfort level with said activity and it may save your life.

Could you mathematically derive this type of data from what is in the AFM/POH/FCOM? Maybe. Better to just go learn your plane and your level of comfort in using it to its fullest performance.

Specific to the impossible turn subject, I recommend people just go out, get to a safe height, and explore the possibilities, then set hard rules for when and when and not to try it.

'Gimp
 
Jaybird180 said:
...wondering if a graph could be made showing how best glide speed changes (?) relative to bank angle and how the graphs intersect with the stall speed decreasing with bank angle. Is it possible to mathematically derive this from available POH data for most airframes?
Click to expand...

I don't see how, since parasite drag varies with airspeed and induced drag with angle of attack. Those factors aren't unbundled in the POH.

Do you want to be at best glide speed anyway for the first half of the turn? Wouldn't that put you farther from the runway? Especially if you took off into the wind?

dtuuri
 
If you assume best L/D to be approximately constant (not entirely unreasonable for a modest range of speeds), then you multiply the best glide speed by the square root of the load factor.
 
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AcroGimp said:
Specific to the impossible turn subject, I recommend people just go out, get to a safe height, and explore the possibilities, then set hard rules for when and when and not to try it.
Click to expand...


This. A book, no matter how accurate, can't teach you what it looks like, nor what your comfort level is in any particular airframe.

And a flight to go do some practice at altitude isn't that hard to get done. One frakkin' flight. Just go do it.
 
I pull the power abeam the numbers and glide on in, almost every landing. So every landing is a spot landing power off one. Well not EVERY landing. But most. Do a LOT of those and pretty soon you get good at it. I find that "knowing the field" really helps, so its good to do it at airports youve never been to. I just tried the "impossible turn" from 500' (doable) and then 400' (not really safely doable). So now I have some data. But it depends on so many things, how the plane is loaded, headwinds, how steeply I climbed out etc. One thing, on both landings I came to the runway well beyond the threshold, almost to the 1/2 way point. In th 400' one, I had trouble completeing the turn, not trouble getting beyond the threshold of the runway. Also, a real engine out is likely going to be much more stressful and not go as well as a simulated one. For one thing, you probably wont start making the turn immediately because you have to make up your mind what to do. And you may well be trying to restart. That stuff detracts from it succeeding, but may be worth doing. All depends.
 
Jaybird180 said:
Is it possible to mathematically derive this from available POH data for most airframes?
Click to expand...
Short answer: Yes.

Longer answer: It's pretty straightforward. Stall AOA and AOA for L/Dmax (and the resulting lift and drag coefficients) don't change with bank angle or load factor. If you know the speeds for these conditions at one load factor (i.e. 1g) you can calculate them at other load factors. The load factor to bank angle relationship is known too, although keep in mind that you'll need more than just the level flight bank to g relationship if you're doing power-off numbers.

Would I use this as gouge for a turnback? No way.

Nauga,
and his degrees of freedom
 
nauga said:
Short answer: Yes.

Longer answer: It's pretty straightforward. Stall AOA and AOA for L/Dmax (and the resulting lift and drag coefficients) don't change with bank angle or load factor. If you know the speeds for these conditions at one load factor (i.e. 1g) you can calculate them at other load factors. The load factor to bank angle relationship is known too, although keep in mind that you'll need more than just the level flight bank to g relationship if you're doing power-off numbers.

Would I use this as gouge for a turnback? No way.

Nauga,
and his degrees of freedom
Click to expand...
Why not? Once you have the data, you have a reference point. The only change are human stress factors.
 
coloradobluesky said:
I pull the power abeam the numbers and glide on in, almost every landing. So every landing is a spot landing power off one. Well not EVERY landing. But most. Do a LOT of those and pretty soon you get good at it. I find that "knowing the field" really helps, so its good to do it at airports youve never been to. I just tried the "impossible turn" from 500' (doable) and then 400' (not really safely doable). So now I have some data. But it depends on so many things, how the plane is loaded, headwinds, how steeply I climbed out etc. One thing, on both landings I came to the runway well beyond the threshold, almost to the 1/2 way point. In th 400' one, I had trouble completeing the turn, not trouble getting beyond the threshold of the runway. Also, a real engine out is likely going to be much more stressful and not go as well as a simulated one. For one thing, you probably wont start making the turn immediately because you have to make up your mind what to do. And you may well be trying to restart. That stuff detracts from it succeeding, but may be worth doing. All depends.
Click to expand...

What are you flying? Are you dealing with other traffic or are you talking farm fields?
 
I know you were asking for a formula but it seems it would also be possible to derive the numbers (or verify them if obtained through a formula) by holding specific bank angles and using the A/S and VSI correlations.
 
nauga said:
Short answer: Yes.

Longer answer: It's pretty straightforward. Stall AOA and AOA for L/Dmax (and the resulting lift and drag coefficients) don't change with bank angle or load factor.
Click to expand...
L/Dmax occurs where the net drag is least. The induced drag curve would shift toward a higher airspeed with an increase in load factor, but the parasite drag curve wouldn't. So, IMO, L/Dmax would favor a slightly slower value than simply multiplying the one 'g' value by the square root of the load factor would predict. But that's being picayune of me.

dtuuri
 
nauga said:
Short answer: Yes.

Longer answer: It's pretty straightforward. Stall AOA and AOA for L/Dmax (and the resulting lift and drag coefficients) don't change with bank angle or load factor. If you know the speeds for these conditions at one load factor (i.e. 1g) you can calculate them at other load factors. The load factor to bank angle relationship is known too, although keep in mind that you'll need more than just the level flight bank to g relationship if you're doing power-off numbers.

Would I use this as gouge for a turnback? No way.

Nauga,
and his degrees of freedom
Click to expand...
Stall AoA doesn't change with load factor??? Trying to wrap my head around that one. Explain please.
 
dtuuri said:
So, IMO, L/Dmax would favor a slightly slower value than simply multiplying the one 'g' value by the square root of the load factor would predict. But that's being picayune of me.
Click to expand...
You are correct, it is not simply the square root of the load factor. The 'bucket plot' everyone learns with induced and parasitic drag is all based on level flight. You can be anywhere on a drag polar (or that bucket plot) at *any* speed if you remove the level flight constraint. L/Dmax occurs at the same AOA regardless of load factor (and L/Dmax doesn't *vary* with load factor). The relationship between L/Dmax and glide angle and speed *does* vary with load factor. That's why included the last sentence of the 'long answer' paragraph you clipped from your quote.

Nauga,
the polar bear
 
Jaybird180 said:
Stall AoA doesn't change with load factor??? Trying to wrap my head around that one. Explain please.
Click to expand...
The AOA for maximum lift is pretty much a function of the airfoil shape and not speed (within a reasonable range of speeds) and a "stall" happens any time you try to exceed the AOA for maximum lift. This is why the stall speed increases with load factor - the speed necessary to support the aircraft goes up as the load goes up.

Look at just about any plot for lift from a wing section - lift coefficient is plotted against the angle of attack pretty much one curve (there may be multiple curves at different Reynolds numbers). The peak of that curve is the maximum lift and beyond that is the "stall".
 
Jaybird180 said:
Stall AoA doesn't change with load factor??? Trying to wrap my head around that one. Explain please.
Click to expand...
FAA Pilot's Handbook of Aeronautical Knowledge, chapter 4, does a decent job of explaining all of this. A wing stalls at its critical angle of attack. This AOA changes with configuration (i.e. flaps extended, etc) but doesn't change with flight conditions like speed, g, altitude (within reason, exceptions for trans/supersonic, Reynolds number effects, etc). lift a wing generates *does* change with speed (by a factor of speed^2), and the g's you feel changes with lift (linearly) so you'll be at different speeds if you stall at different g's, or at different g's when you stall at different speeds - but they all occur at the same AOA - assuming coordinated flight and no other disturbances.

Nauga,
g-whiz
 
As I mentioned in the other thread, ideally for the turn itself you'd want minimum rate of descent (aka minimum sink rate) speed (for the selected bank), not best L/D.
If you chose the latter, for much of that turn you'd just get farther from the runway and lower than possible, which is definitely not your goal.
The ideal bank angle in this case is a compromise between minimum radius (ideally you'd want to turn on a dime), and minimum sink rate. The consensus among experts who have studied this appears to be 45 degrees.
Once you are aimed at the runway and reasonably aligned, you might want to switch to best glide speed (best L/D) if you are low. If you are high, you can maintain a lower speed and possibly feed in flaps, do S-turns, slips, or whatever you need to get down quickly and not overshoot.
 
paflyer said:
What are you flying? Are you dealing with other traffic or are you talking farm fields?
Click to expand...

Aviat Husky. I do power off landings at normal airports. I have to make sure I dont cut someone off who is on a wider approach base or final.

The impossible turn is best practiced when no one else is in the pattern.

This manuver is required for the Commercial.
 
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Jaybird180 said:
Why not? Once you have the data, you have a reference point. The only change are human stress factors.
Click to expand...
Because these speeds are far from the only tools you have or need to do a turnback. They might be a place to start *testing* to determine the best turnback performance, but you don't need these kind of mental gymnastics to come up with a good test matrix - specially if you've got AOA in the cockpit.

As far as the only change being stress factors, I disagree - Vstall and Vbg speeds like you're asking for in and of themselves tell you nothing about the best way to fly the maneuver and the sensitivity of performance to being off-condition *or* the sensitivity to errors in the book speeds you used as an anchor. It's an interesting mental exercise but not particularly useful in and of itself for determining performance and/or procedures.

Nauga,
bracketed
 
nauga said:
L/Dmax occurs at the same AOA regardless of load factor (and L/Dmax doesn't *vary* with load factor).
Click to expand...
What I'm trying to say is, induced drag (only) occurs at the same AoA. Parasite drag occurs at the same airspeeds. Therefore, L/Dmax won't occur at the same AoA under a 'g' load. But it won't be too far from it for most planes I suppose.

dtuuri
 
dtuuri said:
What I'm trying to say is, induced drag (only) occurs at the same AoA. Parasite drag occurs at the same airspeeds. Therefore, L/Dmax won't occur at the same AoA under a 'g' load.
Click to expand...
The characteristics you're talking about assume constant *lift* at fixed weight to get their characteristic shape. At a constant *CL* (and thus a constant AOA) parasitic and induced drag both vary the same amount in relation to airspeed - they're linearly proportional to the square of airspeed. Lift, of course, varies by the same relationship. Because lift and drag *both* vary linearly with the square of airspeed (L = q*S*CL, D = q*S*CDtotal), L/D = CL/CD. CL and CD, for the environment we're talking about with GA airplanes, are purely functions of AOA (and other secondary effects like sideslip and control deflections not relevant here). Changing bank angle, g, or speed, etc... changes the magnitudes of L and D and the AOA required to get them, but L/Dmax will be L/Dmax at the same AOA for L/Dmax. You'll get it at a different speed at different g's, and your flight path will be a result of all of these factors, but L/Dmax and the AOA for it will not change.

But none of this has any bearing on whether or not you can calculate these relationships. You can. But they're pretty useless in an everyday flying sense. Once again I seem to have dragged a thread down into minutae, so I won't keep at it much longer. It's a lot easier to say with math :D

Nauga,
whose pepper is clean :rofl:
 
nauga said:
The characteristics you're talking about assume constant *lift* at fixed weight to get their characteristic shape. At a constant *CL* (and thus a constant AOA) parasitic and induced drag both vary the same amount in relation to airspeed - they're linearly proportional to the square of airspeed. Lift, of course, varies by the same relationship. Because lift and drag *both* vary linearly with the square of airspeed (L = q*S*CL, D = q*S*CDtotal), L/D = CL/CD. CL and CD, for the environment we're talking about with GA airplanes, are purely functions of AOA (and other secondary effects like sideslip and control deflections not relevant here). Changing bank angle, g, or speed, etc... changes the magnitudes of L and D and the AOA required to get them, but L/Dmax will be L/Dmax at the same AOA for L/Dmax. You'll get it at a different speed at different g's, and your flight path will be a result of all of these factors, but L/Dmax and the AOA for it will not change.

But none of this has any bearing on whether or not you can calculate these relationships. You can. But they're pretty useless in an everyday flying sense. Once again I seem to have dragged a thread down into minutae, so I won't keep at it much longer. It's a lot easier to say with math :D
Click to expand...


Well, I don't know if everything you said is right, but I do know that part of what I said was wrong--I was thinking of a different graph. :redface: In this case, the induced drag curve moves to the right with increased 'g' load while the parasite drag curve stays in the same place. The result is that L/Dmax moves rightward the same amount as the stalling speed increases. Of course, total drag goes up too at the higher speed, but the valley between the two is still the best bang for the buck under the increased 'g' load. I apologize for making you defend your position because of my error.

dtuuri
 
In the Texan II doing a 360 degree turn at 60* bank netted a 1000 foot loss. 45* bank 1500' loss, 30* bank 2000' loss. This was at a constant 120KIAS. So at least in that aircraft, both turn radius and altitude loss was minimized at higher bank angles. Of course, strapped to a Martin Baker zer0-zero0 helps a lot when the mill quits.
 
Yes you could create a chart, but you would not have time to get it out and review it when the fan quits. Get a simulator and try it. Most people are not willing to point the nose at the ground to make the turn. There is a lot of brown that needs to be seen to make it back. This was a 172 and MSX. I did one 500 foot loss turn up high once.
 
nauga said:
...But they're pretty useless in an everyday flying sense. Once again I seem to have dragged a thread down into minutae, so I won't keep at it much longer. It's a lot easier to say with math :D
Click to expand...

What I was hoping for
 
Jaybird180 said:
What I was hoping for
Click to expand...
What, the math? I was referring to L/Dmax invariant with AOA when I said it was easier with math but of you're looking for the math for Vbg in turning flight and the relationship to stall speed any basic flight dynamics textbook will have rigid body equations of motion. That's a good start. You could also look at some of the many papers that have been written on the turnback, including those that consider unsteady maneuvering, where the 45 deg angle of bank assumption begins to fall apart.

Nauga,
at the ready
 
Yes, as I interpreted the original post he was looking for the math, not a flying lesson :rolleyes:
 
nauga said:
Because these speeds are far from the only tools you have or need to do a turnback. They might be a place to start *testing* to determine the best turnback performance, but you don't need these kind of mental gymnastics to come up with a good test matrix - specially if you've got AOA in the cockpit.

As far as the only change being stress factors, I disagree - Vstall and Vbg speeds like you're asking for in and of themselves tell you nothing about the best way to fly the maneuver and the sensitivity of performance to being off-condition *or* the sensitivity to errors in the book speeds you used as an anchor. It's an interesting mental exercise but not particularly useful in and of itself for determining performance and/or procedures.

Nauga,
bracketed
Click to expand...


I agree and here's another reason... You'll need to convert calibrated airspeed to indicated for the entire maneuver. I'd say you'd be lucky to get the same numbers every time if you can't keep that turn exactly the same every attempt. In some aircraft it's going to make a significant difference.
 
The more I read this thread, the more I'm thinking an AOA instrument is a good idea...
 
The more I read these threads where people convince themselves they can do the impossible turn the more I shake my head.
When the fan goes away look no more than 30 degrees left and right and pick the spot to put the plane.
That inviting soccer field will be just out of reach and you will die if you try it.
The one you can actually reach will be almost under the nose.
Have enough airspeed left at the end that you have control response adequate to put the fuselage between the houses/trees and not straight into one.
Vastly better to to stop by shearing the wings off in flat glide as opposed to stalling 50 feet up and stuffing it straight into the ground.
There are two reasons why I fly a twin.
 
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