Best Glide Speed And Bank

[Adrock]

Ok so I just read parts of the FAA's Glider Handbook and read: In all gliding, constant airspeed turns, it is necessary to increase the angle of attack of the wing as the bank

progresses by adding nose-up elevator pressure. This is required because the total lift must be equal to the vertical component of lift plus the horizontal lift component.
​

I also found the familiar load factor/bank diagram in the glider book that us fixed wing pilots are use to. There is 2-Gs in a 60bank turn while gliding and if a constant glide speed were held through a turn the angle of attack would have to be increased. This increase in angle of attack will cause the best glide AOA to be exceeded and more drag will be induced. Given this information, it would seem to me that if one wanted to maintain best glide angle and corresponding angle of attack during a 60bank turn requiring twice the lift, the airpseed would have to be increased to 1.414 times (double the airspeed quadruple the lift) the unbanked glide speed.​

 

[drunkenbeagle]

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I also found the familiar load factor/bank diagram in the glider book that us fixed wing pilots are use to. There is 2-Gs in a 60bank turn while gliding and if a constant glide speed were held through a turn the angle of attack would have to be increased. This increase in angle of attack will cause the best glide AOA to be exceeded and more drag will be induced. Given this information, it would seem to me that if one wanted to maintain best glide angle and corresponding angle of attack during a 60bank turn requiring twice the lift, the airpseed would have to be increased to 1.414 times (double the airspeed quadruple the lift) the unbanked glide speed.​

100% correct.

 

[fish314]

I had the same thought at first, but there is one time I can think of when such knowledge could be beneficial. If one were trying to make "the impossible turn" following an engine failure on takeoff. Gliders do it all the time as a training maneuver from 200' AGL, but it varies with aircraft and airplanes need a lot more altitude to make that turn.

The aerodynamically best angle of bank for making a gliding turn with the least loss of altitude is 45 degrees. However, there are a lot of other factors that come into play including the offset from the runway one will have after completing a 180 degree turn. The stalling speed goes up by about 20% in a 45 degree bank and 40% in a sixty degree bank. The G Force in a 45 degree bank is the square root of two, or approximately 1.414. To get the best glide speed for a 45 degree bank turn, it would take data for 1.414 times the aircraft's weight and most likely that would be something over the MGW and not published.

However, exactly as you noted, there isn't a practical application for using either minimum sink speed or best glide speed in a steep spiral maneuver.

Hey Guy, do you have a reference or a rationale for the bolded? I used to teach in T-6's, which are relatively high performance compared to most single engine aircraft, and we taught the guys to use a combination zoom climb and turn. We would teach about 70 degrees of bank, 2-3 g for the turn towards the runway. The theory was that at high g you bleed off energy quicker, but at low bank, low g, you have a larger ground track, the turn takes longer, and consequently you spend more time pointing away from the runway.

I never saw a more rigorous mathematical explanation of it, though, so I never fully trusted that explanation.

 

[Adrock]

The real issue in the "Impossible Turn" back to the runway isnt best glide but best rate-of-turn with the least sink. 45 degree angle makes sense to me given that it result in the farthest distance for a given force in ballistics. I have just experimented with combinations of bank and airspeed and found the 45 degree turn with 1.19 percent of Vs gives the best glide back to the runway.

 

[fish314]

The real issue in the "Impossible Turn" back to the runway isnt best glide but best rate-of-turn with the least sink. 45 degree angle makes sense to me given that it result in the farthest distance for a given force in ballistics. I have just experimented with combinations of bank and airspeed and found the 45 degree turn with 1.19 percent of Vs gives the best glide back to the runway.

Hmmm.... for an engine failure on the initial takeoff leg, we typically wouldn't even consider turning (assumes lower altitude/airspeed combination). We would just use the 0/0 ejection seat, and give the jet back to the tax-payers. About the crosswind leg is where you would first consider trying to make the runway (for us, anyway). Kind of an ORM decision... and until you got to that point the best option was the silk elevator.

Our immediate turn towards the runway applied pretty much from that point in the sortie on, but in the scenario I was thinking about we were at low altitude, but relatively high airspeed (200 KIAS, stall speed about 85, best glide 125). That would be the scenario on downwind leg, or on a low level. I can see how in a single piston GA, the high G turn wouldn't be particularly useful. You probably don't have the 75 knots of excess airspeed to maintain 2 g all the way around the turn without losing altitude in an airplane like that, much less 3g.

Yeah, if I were already at 125 (best glide), I wouldn't go trying to pull 2-3g. 2g stall would be like 121, so I would have tried to baby it around at about 1.5 g or so. Pretty close to 45 degrees of bank.

 

[Inverted25]

Hmmm.... for an engine failure on the initial takeoff leg, we typically wouldn't even consider turning (assumes lower altitude/airspeed combination). We would just use the 0/0 ejection seat, and give the jet back to the tax-payers. About the crosswind leg is where you would first consider trying to make the runway (for us, anyway). Kind of an ORM decision... and until you got to that point the best option was the silk elevator.

Our immediate turn towards the runway applied pretty much from that point in the sortie on, but in the scenario I was thinking about we were at low altitude, but relatively high airspeed (200 KIAS, stall speed about 85, best glide 125). That would be the scenario on downwind leg, or on a low level. I can see how in a single piston GA, the high G turn wouldn't be particularly useful. You probably don't have the 75 knots of excess airspeed to maintain 2 g all the way around the turn without losing altitude in an airplane like that, much less 3g.

Yeah, if I were already at 125 (best glide), I wouldn't go trying to pull 2-3g. 2g stall would be like 121, so I would have tried to baby it around at about 1.5 g or so. Pretty close to 45 degrees of bank.

200 feet in a glider and the rope breaks I'm turning back to the runway. In fact on the commercial add on checkride I was soo high after turning back when the examinder pulled the release at 200 I did a 540 over the end of the runway then landed. Gotta love 40:1+ performance.

 

[drunkenbeagle]

200 feet in a glider and the rope breaks I'm turning back to the runway. In fact on the commercial add on checkride I was soo high after turning back when the examinder pulled the release at 200 I did a 540 over the end of the runway then landed. Gotta love 40:1+ performance.

One overlooked thing about the 200' rope break - you are being towed at 73kts, not the typical 55kts that you would turn at. I can typically get another 60' or so CLIMBING in my turn while I slow to 55. The one I demonstrated yesterday, we were at 190' on short final. And I pulled at 200' on the nose. I needed full dive brakes and a slip to hit the touchdown point.

 

[fish314]

200 feet in a glider and the rope breaks I'm turning back to the runway. In fact on the commercial add on checkride I was soo high after turning back when the examinder pulled the release at 200 I did a 540 over the end of the runway then landed. Gotta love 40:1+ performance.

One overlooked thing about the 200' rope break - you are being towed at 73kts, not the typical 55kts that you would turn at. I can typically get another 60' or so CLIMBING in my turn while I slow to 55. The one I demonstrated yesterday, we were at 190' on short final. And I pulled at 200' on the nose. I needed full dive brakes and a slip to hit the touchdown point.

Gosh, I haven't flown gliders since the academy. That was a good time though! But yeah, don't have that kind of glide performance, and never have (even back then we were in Schweitzer 2-33's, not the high performance gliders. I think they got like 23:1... but those are some OLD synapses I'm drawing on there. I wouldn't trust my recollection.)

The 73knots vs 55 knot best glide speed might be akin to the scenario I'm talking about. Basically significant excess airspeed, to the point where you could maintain level or even climb a bit, trading the airspeed for altitude, while accomplishing the turn. In such scenarios, what bank/g is best? Is anyone out there familiar with a mathematical analysis of this type of scenario, rather than just anecdotal evidence or trial and error?

 

[drunkenbeagle]

The 73knots vs 55 knot best glide speed might be akin to the scenario I'm talking about. Basically significant excess airspeed, to the point where you could maintain level or even climb a bit, trading the airspeed for altitude, while accomplishing the turn. In such scenarios, what bank/g is best?

I believe that is called the "Hoover Approach." Money in the bank, taking it out...

 

[pwapilot]

Gosh, I haven't flown gliders since the academy. That was a good time though! But yeah, don't have that kind of glide performance, and never have (even back then we were in Schweitzer 2-33's, not the high performance gliders. I think they got like 23:1... but those are some OLD synapses I'm drawing on there. I wouldn't trust my recollection.)

The 73knots vs 55 knot best glide speed might be akin to the scenario I'm talking about. Basically significant excess airspeed, to the point where you could maintain level or even climb a bit, trading the airspeed for altitude, while accomplishing the turn. In such scenarios, what bank/g is best? Is anyone out there familiar with a mathematical analysis of this type of scenario, rather than just anecdotal evidence or trial and error?

Not sure if you have already come across these, but I think they will give you some of the analysis you're trying to find:

http://jeremy.zawodny.com/flying/turnback.pdf
http://www.nar-associates.com/technical-flying/impossible/nonoptimalcost_screen.pdf

 

[Guy]

Hey Guy, do you have a reference or a rationale for the bolded?

Not a good one, but here is one I found after a little Google exercise:

http://www.aviationservicesdirectory.com/permalink.php?id=1074

Worth quoting from the article is the steps Barry Schiff wrote:

Set up on a cardinal heading.
Climb halfway between Vx and Vy.
Pull the throttle to idle at a pre-established altitude.
Hold the same climb pitch for five seconds.
Roll into a 45-degree bank turn.
Pitch for best glide speed.
Turn 270 degrees.
Roll wings level.
Simulate a flare to stop the sink rate.
Note altitude lost.
Add 50 percent of the altitude lost for a safe cushion.


My original source of information came from a glider club that was heavily populated with engineers. They delighted in the theoretical aspects of aviation and I was often trapped in their discussions. The "45 degree bank is optimum" came from a presentation one of them did during a safety meeting. However, one other thing I noted from the data and graph that was used is that as long as the bank angle is somewhere between 30 and 60, the results are going to be pretty close.

However, in the case you cited where your group advocated a 70 degree bank, they may have been right without knowing why. Perhaps the additional maneuvering to get back on the same piece of concrete is greater than the loss incurred by making a turn that ends up aligned more closely with the concrete. Another possibility is that the performance of the T-34 may have been great enough that if a more "optimal" bank angle were used, it would result in being too high, so losing a little extra in the turn compensated for that. Of course, I'm just taking guesses on those possibilities.

 

[Guy]

I think they got like 23:1... but those are some OLD synapses I'm drawing on there. I wouldn't trust my recollection.

Your old synapses are doing just fine.

Of course, you didn't need anything high performance in that part of the world. I once had occasion to fly a helicopter there and I was able to "thermal" the helicopter with the collective on the floor. Is it any wonder gliders function so well in the environment.

 

[Guy]

If your engine quits, and you see a really good flat field down to your left front between the few cumulus you were flying over, having the knowledge and skill to fly either best rate or best sink, as the situation dictates, would be a very attractive practical application. To me.

The following three PTS tasks are all different:

· Approach and landing with an inoperative engine(simulated)

· Steep spiral

· Emergency descent

I wrote "steep spiral". Your response deals with approach and landing with an inoperative engine, which is a different task.

 

[fish314]

Not sure if you have already come across these, but I think they will give you some of the analysis you're trying to find:

http://jeremy.zawodny.com/flying/turnback.pdf
http://www.nar-associates.com/technical-flying/impossible/nonoptimalcost_screen.pdf

Thanks for those! The second link is exactly the kind of thing I was looking for. The first one was blocked from the work account, but I'll check it out from home.

Just from a quick skim of the material in the second link, it appears that 45 degrees is optimal at least in the case where you can't really "zoom climb" anymore. The analysis considers the problem by modelling after initial loss of the engine, the airplane is instantaneously in a descending banked turn. Also, the problem assumes a Vx climb up until that point... so not much extra airspeed available to zoom or to bleed off in a turn.

 

[pericynthion]

I believe the 45 degrees is not an exact number, the actual optimum varies with the particular airplane, but 45 degrees is pretty close for most GA aircraft. I don't have a reference though, I'm afraid. I wouldn't recommend trying this in an engine-failure-at-takeoff situation unless you've practiced it in that aircraft at altitude and know how much height it's going to use up. Better to have a controlled crash flying forward than an uncontrolled impact trying to turn back with high bank, high rate of descent and possible stall/spin.

 

[fish314]

I believe the 45 degrees is not an exact number, the actual optimum varies with the particular airplane, but 45 degrees is pretty close for most GA aircraft. I don't have a reference though, I'm afraid. I wouldn't recommend trying this in an engine-failure-at-takeoff situation unless you've practiced it in that aircraft at altitude and know how much height it's going to use up. Better to have a controlled crash flying forward than an uncontrolled impact trying to turn back with high bank, high rate of descent and possible stall/spin.

45 degrees comes from the formula for the altitude lost in a gliding turn. I can't do equations justice on this site, but it's:

(dh/dΨ)=CD/CL^2 *4W/ρSg *1/sin2φ

dh/dΨ is the derivative of altitude with respect to heading. Basically how much the altitude changes with respect to time versus how much the heading changes with respect to time. Essentially, this describes how much altitude you lose in the process of the turning. We are looking for which values make this derivative the smallest.

On the other side of the equals sign are basically three sets of factors. First is the Coefficient of Drag divided by the Coefficient of lift squared. Both of these are functions of angle of attack, and that number is smallest when CL is largest. In this case that occurs at stall speed, since the critical angle of attack is the maximum lift angle of attack. Now, at the critical angle of attack CD is also relatively large... but because the CL term in the denominator is squared, it's the dominant term of that part of the equation. So that's where the idea to do the turn at 5% above stall speed comes from. Stall speed would really by ideal... but it would also provide 0 room for error to prevent entering a stall.

The middle set of terms is 4 times the Weight, divided by rho (air density) times S (surface area of the wing) times g (acceleration due to gravity). Generally, there is nothing we can do to change any of these parameters in flight, so there really is nothing to manipulate here.

So we're on to the last term, 1/sin2φ. Phi (φ) is the bank angle, so this is the term that's going to give us the optimum bank angle. We are looking for the value that makes 1/sin2φ the smallest, which means we are looking for the value of phi that makes that sin2φ in the denominator the largest. Well, sine oscillates from -1 through 0 to 1. At 0, the 1/sin2φ quantity is undefined, and numbers that approach 0 would make 1/sin2φ approach either positive or negative infinity. If that doesn't make sense mathematically, it may make sense physically. If the bank angle is very close to 0, how long will it take to do a 180 degree turn? Basically forever, right? So how much altitude would you lose before you finished the 180 degree turn? All of it... no matter what altitude you started at, because you're not really turning.

So what we're looking for is for sin2φ to equal 1, which is the largest value it CAN equal. That occurs at sin(90 degrees). So that means 2φ=90 degrees, and therefore φ=45 degrees exactly.


So the 45 degrees is exact, at least for the way they modeled this problem (basically you lose the engine, and are instantaneously at the airspeed and bank angle you want for the turn). That's probably a reasonable assumption shortly after takeoff, because you probably aren't very far off of the stall speed anyway. 1.3 Vstall for 0 bank, something like that. Just banking the airplane to 45 degrees will put you below stall speed (45 bank stall speed is 1.414 * 0 bank stall speed) so you would actually have to gain a couple of knots as you rolled into the bank to make this work.

For the scenario I mentioned, where you are well above either 0 bank stall or 45 bank stall speeds, I think the analysis needs to be reconsidered. I just haven't thought it all the way through yet.


Still, I think the last part of your advice stands... This doesn't sound like a maneuver to attempt the first time during the emergency unless the straight ahead options are just awful. I would want to practice it at altitude a bunch of times first (or in a really good simulator), before I considered using it in an actual scenario.

 

[Guy]

(dh/dΨ)=CD/CL^2 *4W/ρSg *1/sin2φ

There. That should make it clear to those folks.

 

[Ziggyfuzz]

This is true, when you roll 60 degrees the only way you will pull 2G's is if you hold you altitude. In a steep spiral you are obviously not holding altitude. And Ryan, the reason why you would hold best glide in a steep spiral is because the PTS calls for it...

...that shows your experience.....do a 60 degree banked gliding turn without loading the wing and see if you can avoid the Vne dive! You certainly can see 2 or more g's in a steep spiral!

 

[Ziggyfuzz]

The best way to perform the impossible turn is to not do it. There is a reason it's called the impossible turn.

I worked a program years ago where we did it in C-172/182 aircraft all the time. At MGW you need at least 700 agl and a bank of close to 60 to make it happen. Alos helps to be well coordinated so you reduce the form drag caused by a poorly coordinated turn...

 

[Ziggyfuzz]

The following three PTS tasks are all different:

· Approach and landing with an inoperative engine(simulated)

· Steep spiral

· Emergency descent

I wrote "steep spiral". Your response deals with approach and landing with an inoperative engine, which is a different task.

The practical application of the Steep Spiral manuever in the Commercial pts is actually for a confined area or limited choice of fields engine out approach. That is why the spiral must also have a constant radius around a specified point on the ground. A saavy CFI will combine a power off 180 with the steep spiral; because there are some DE's that will do just that! At an uncontrolled airport, you can go up to around 3000 agl and idle the engine, make 3 complete turns around the 1000 footers, roll out on a specified heading (downwind) and then continue the glide in the power off 180 to touch down on the point you used as your reference in the spiral!! This can be done in a "steep" bank, or in a "loose" turn, shallow bank. You can actually lose less altitude in the manuever if you go for the more shallow bank. The PTS only specifies that the bank shall not exceed 60...why...cause then you'd need a parachute! If a pilot were to maintain a constant radius as the pts states, from top to bottom, then you must consider how this radius appears. If the radius is to appear the same all the way down (ie using some land marks) then the angle of bank actually must increase as altitude decreases. Illustrated from the side, may look like a tornado. Consequently, you must increase glide speed, mainly to avoid a stall, forget the mathematics and science of it, just don't stall the aircraft. EG typica. PA 28 variant glides at 80 ish. The stall speed for that airplane in a 60 degree bank is 81!