Best L/D and most efficient AOA

[gundernak]

Hi everyone,

Actually I am just a single PPL pilot, and I have a theoretical question. I can not find the answer and I am confused a little bit. That's why I am here to ask for help.

These are 4 statements on L/D max and AOA for max L/D:
· L/Dmax AOA produces the minimum total drag
· At L/Dmax AOA, parasite drag and induced drag are equal
· L/Dmax AOA produces the greatest ratio of lift to drag
· L/Dmax AOA is the most efficient angle of attack

These above can be found in so many aviation literature.

In the following I will be speaking about prop common light aircraft.

When you fly straigh and level at Vmd, your L/D is at max, you fly at the most efficient AOA, and this is the speed for best range and minimum drag. Vmd is a quiet low cruise speed.

If you increase your airspeed in level flight to reach a normal cruise speed, the AOA will decrease and the plane leaves the most efficien AOA.

But you can find statements about it wich confuse the hole thing (I mean confuse to me). They say at the most used cruise speed, the plane will fly at the AOA of the best L/D. And the horizontal axes will be paralell to the relative airflow, thanks to the right incidence angle.

Well, now at wich speed will fly the plane at the most efficient AOA?:
- at Vmd or
- at normal cruise

Futhermore I have made a little flight test (in a software), and monitored the specific values of different situations. The aerofoil best L/D is at 3 deg. Here are the results:

Max Cruise
power: full
IAS: 130 kts
AOA: 2 deg.
L/D: 12,5

Normal Cruise
power: 2300 RPM
IAS: 110-120 kts
AOA: 3 deg.
L/D: 14,5

Level flight at Vmd:
power: 1500 RPM
IAS: 85 kts
AOA: 7 or 8 deg.
L/D: 15,5 (max L/D)

Now you can see at level flight at speed Vmd the L/D is max. But the AOA is not the L/Dmax AOA of the aerofoil.

At normal cruise the AOA refers to the most efficient AOA of the aerofoil, but the L/D is not the best.

May I ask you to enlighten me about this contradiction, please. I really need a help here.

Thank you in advance

FA
Hungary

[Dit]

Gundernak, your post is a bit confusing but I'll try and answer. Oh and all this is based on my memory of Aerodynamic and you really should double check it to make sure I'm right.

"These are 4 statements on L/D max and AOA for max L/D:
1) L/Dmax AOA produces the minimum total drag
2) At L/Dmax AOA, parasite drag and induced drag are equal
3) L/Dmax AOA produces the greatest ratio of lift to drag
4) L/Dmax AOA is the most efficient angle of attack"

As far as I'm concerned statement 1 and 3 are the same thing: At L/Dmax in straight and level flight the Lift produced by the wing equals the weight of the a/c and therefore is a constant. Thus the only variable is Drag, so you get L/Dmax with the minimum total drag, therefore also the greatest ratio of lift to drag.

Statement 2 is proved by this graph (from wikipedia)
http://upload.wikimedia.org/wikipedia/en/1/12/Drag.jpg

Now for statement 4. In my mind an angle itself cannot be efficient, however the AoA at L/Dmax allows the aircraft to operate at it's most efficient in regards to time (in regards to distance you want Vminpower which is a different speed).

You say near the end: "Now you can see at level flight at speed Vmd the L/D is max. But the AOA is not the L/Dmax AOA of the aerofoil." However, when you look at your own results the second sentance you've written is wrong

AOA: 3 deg - L/D: 14,5
AOA: 7 or 8 deg - L/D: 15,5 (max L/D)

I don't know where you found out the L/Dmax AoA of the aerofoil but you've disproved it with your own test... unless I'm missing something.

Dit

[keith smith]

Some points worth remembering:
1.Parasite drag equals induced drag at(L/D) max comes from simple algebra--para increases as V squared, while induced is inversely proportional to V squared.
2.Minimum drag speed results in smallest glide angle in event of loss of thrust.
3.Minimum drag and corresponding speed will be a function of flap setting.
Keith

[Tinstaafl]

Dit, you have it backwards w.r.t. min drag and min power vs best range and best endurance. You wrote

...L/Dmax allows the aircraft to operate at it's most efficient in regards to time (in regards to distance you want Vminpower which is a different speed...

In a piston aircraft best *range* ie most distance per unit of fuel occurs at the tangent to the power curve, the speed for which also corresponds to minimum drag. Best *endurance* ie most time per unit of fuel corresponds to minimum power.

[Mark1234]

They say at the most used cruise speed, the plane will fly at the AOA of the best L/D. And the horizontal axes will be paralell to the relative airflow, thanks to the right incidence angle.

Well, now at wich speed will fly the plane at the most efficient AOA?:
- at Vmd or
- at normal cruise

The most efficient (lowest drag) AOA will be at vmd. If we limit ourselves to aeroplanes at typical unpressurised prop aircraft (low) altitudes, that will be a lot below cruise.

I believe your first statement is referring to the rigging angle of the wing on the fuselage - usually set such that the deck angle of the fuselage is level at cruise speed AOA.

As you climb and the air thins, IAS reduces, and things get more complicated. I believe the average airliner is cruising somewhere around Vmd way up there at 3X,000 ft, but I haven't really looked into that side.

[bookworm]

I can't see any inconsistency in your original statements as they apply to a particular object. As far as I can see, the crux of your observation is:

Now you can see at level flight at speed Vmd the L/D is max. But the AOA is not the L/Dmax AOA of the aerofoil.

i.e. that the drag curve of the overall flight vehicle is not the same as the drag curve of the aerofoil in isolation. Is that surprising?

[Tick Tock Man]

Having just read pilotmike's answer I have to correct him in turn!

Vmd is coincident with L/Dmax in level flight, both occur at the lowest point on the drag curve. Flying at Vmd means you will be flying at the AofA for best L/D ratio, which is typically 4°. Neither will flying at Vmd give the best endurance in a glide or cruise as suggested. Vmd gives the best range in a glide or cruise (piston); it is minimum power (Vmp) that gives best endurance.

Note: Vmd and L/Dmax are at a tangent to the power curve; they're at the bottom of the drag curve. Maybe this is where the point is being confused?

To summarise:
Best endurance for a piston, power on or glide, is Vmp which is slower than Vmd.
Best range for a piston, again power on or glide, is Vmd (the bottom of the drag curve) which is also coincident with L/Dmax.

[Mohit_C]

I think pilotmike is confusing prop and jet aircraft.

For a prop aircraft maximum range occurs, as Tick Tock Man said, at minimum drag speed; L/D max. When you plot the graph Drag against Airspeedthe minimum point of the graph is essentially the speed for minimum drag, however when you plot the Power Required against Airspeedgraph the tangent to the graph gives the speed for minimum drag.

For a jet aircraft maximum range occurs at 1.32 times the speed of minimum drag which in this case when you plot the Drag or Thrust Required against Airspeed occurs at the tangent to the graph.

I reckon this is correct.

[Checkboard]

Have a look at this site:

MAXRNG

It is the best explanation of piston cruise efficiency that I have found.

[Wizofoz]

Tinnstaffl has (as usual) nailed it, Tick Tock got close, Pilot Mike made some pompous statements, and was wrong!!

Tick Tock, best range would be at Best L/D (Which IS co-incident with Minimum Drag) IF power was equal at all speeds. It isn't. Hence we have a power curve. Best range occurs at Maximum Excess Power, max endurence at Maximum Excess Thrust.

[Tick Tock Man]

Ahh, okey dokes. Then for my own education... I realise that there are two distinct graphs (drag/ias, power/tas) when looking at piston and jet aircraft. I understood that both Vmd and L/Dmax always occurred in the same place: at the tangent to the power curve and at the bottom of the drag curve.

Are you saying the two are not always coincident or are you simply saying that the speed for max excess power is not necessarily the same speed as for Vmd/LDmax? (I suspect the latter!)

If so they "learned" me wrong. "...always fly Vmd in a piston for best climb rate, range in the cruise or range in a glide..." Bah.

gundernak - you clear now?

[bookworm]

Tick Tock, best range would be at Best L/D (Which IS co-incident with Minimum Drag) IF power was equal at all speeds. It isn't. Hence we have a power curve. Best range occurs at Maximum Excess Power, max endurence at Maximum Excess Thrust.

Well, even that isn't quite there. If you're talking about maximum rate or angle of climb, it's reasonable to talk about "Maximum Excess ...". But we're talking about level flight where there's no excess power or excess thrust. So it's not about the maximum power or thrust that can be obtained, but rather the efficiency at which the fuel can be turned into power or thrust.

For a piston engine, (power) specific fuel consumption varies somewhat with the power actually produced, hence the lowest fuel flow required may not be exactly at the minimum of the power required , but it will be close. For a jet engine, thrust specific fuel consumption increases significantly with speed, so best endurance (lowest fuel flow) speed may be at significantly less than Vmd, and best range may not be at as high as 1.32 Vmd.

[Capt Pit Bull]

<cough> Prop efficiency versus airspeed <cough>

Especially for fixed pitch props...

[Wizofoz]

OOOPPSSS!!!

Bookworm, you are absolutely right- I was using the formula for Vx and Vy, QUITE different from max range and endurance.

[MaverickSu35S]

Originally Posted by gundernak

Normal Cruise
power: 2300 RPM
IAS: 110-120 kts
AOA: 3 deg.
L/D: 14,5

Level flight at Vmd:
power: 1500 RPM
IAS: 85 kts
AOA: 7 or 8 deg.
L/D: 15,5 (max L/D)

Now you can see at level flight at speed Vmd the L/D is max. But the AOA is not the L/Dmax AOA of the aerofoil.

At normal cruise the AOA refers to the most efficient AOA of the aerofoil, but the L/D is not the best.

May I ask you to enlighten me about this contradiction, please. I really need a help here.

Thank you in advance

FA
Hungary

Hello "gundernak",

I am an aerodynamicist and I can confirm that a wing with an aspect ratio of around 10 which uses lightly cambered airfoils (around 2..3% camber ratio) along it's span will find the highest L/D ratio (or glide ratio respectively) around a relatively low angle of attack somewhere near 3. As the relative camber of an airfoil increase and the further towards the trailing edge the camber goes, the lower the AoA for maximum L/D. The lower the camber of the airfoil and the closer the camber's position to the leading edge, the higher the AoA for max. L/D.

As your software tells that the AoA for max. L/D is around 3 degrees, this suggests that you were testing a wing of a given aspect ratio (usually higher than 6) with a cambered airfoil (such as NACA 2412 or 2410), which has a solid confirmation from real life tests, so the "normal cruise" resulted max. L/D AoA is correct.

As airspeed increases and Reynolds number increase, the maximum L/D AoA doesn't vary much and usually varies towards decreasing rather than increasing. As far as I know, at higher speeds the drag becomes more and more AoA sensitive due to compressibility effects, so you can't have lower drag for the same lift (for example) at higher AoA at higher speeds.

If you'd look at most of the airliners as example, the wing's incidence (angle between the wing's root chord and the fuselage's X-axis) is generally found at a value which helps the wing's MAC (mean aerodynamic chord) AoA be exactly the one for maximum L/D during cruise, while maintaining the fuselage's AoA as close to zero as possible (where the fuselage produces minimum drag). The philosophy is simple: make the plane ride only on the surfaces that produce the highest L/D at it's corresponding angle and keep all other surfaces that have bad/low L/D at an AoA where they produce the lowest drag, even if their lifting contribution is null. This is why an airliner's fuselage looks perfectly horizontal (because it actually flies near 0 AoA) during cruise, while the wing is the only thing producing the needed lift at an AoA corresponding to maximum L/D. The maximum L/D is the main ingredient which helps all airliners gain maximum flight range or lowest fuel consumption and also the most economic or highest climb rate. You always want to fly near or at maximum L/D AoA, which depending on weight will correspond to an airspeed and altitude.

It may seem surprising parallel to your test, but an AoA of around 3 is generally found to be that for maxumum L/D during cruise for many airliners.

The fact that in the "Level flight at Vmd" test the software somehow sees the max. L/D AoA to increase so dramatically suggests that there might be some mathematical model limitations within equations used by the software or some sort of "trouble" in it. As far as I know, increasing the maximum L/D AoA can only be possible by varying the wing's aspect ratio (such as a variable wing geometry aircraft as the F-14) and/or it's airfoils shape or maybe by controlling the BL (boundary layer) in a manner towards slightly disrupting the airflow up to an AoA slightly lower than the target AoA for which you'd like the maximum L/D to occur.

The AoA is the major factor (usually the only factor) which affects the L/D ratio, so, there's definitely something strange happening in the calculations for the "Level flight at Vmd".


Regards,
Mav.

[eckhard]

This is why an airliner's fuselage looks perfectly horizontal (because it actually flies near 0 AoA) during cruise,

I'm neither an aerodynamicist nor a structural engineer but all the airliners that I have flown seem to cruise with the nose about 3 degrees above the horizon.

By 'horizon', I mean a reference that equates to a level attitude, not the visible horizon which at typical cruising altitudes is depressed by about 3 degrees below the true 'horizontal' due to the curvature of the earth.

If I am right, that would imply that the wings are actually mounted at close to zero angle of incidence. Can any structural engineer or test pilot shed some light?

[Piltdown Man]

Ignore the engine. It is irrelavent. What counts is the wing and the way it works. Flying just above the stall you will have a high angle of attack and high drag. As you lower the nose and increase airspeed, the angle of attack will reduce and the drag will reduce. Keep lowering the nose. You will keep increasing speed but the total drag will continue to reduce until you get to minimum drag speed. Keep increasing reducing the AofA and increasing airspeed and you will arrive at best Lift/Drag ratio. And further reduction AofA will result in more speed and drag. At speeds below minimum drag, the greatest proportion of total drag is induced drag as the wing worked "hard" (moving fewer air molecules a greater distance). At speeds above minimum drag where the wing worked less hard (where many air molecules were forced to do a small amount of work) the greatest contributor to total drag was parasitic.

In each case above the lift remained constant. One variable changed, the AofA. That in turn reduced a specific airspeed and drag value.

Eckhard: Many wings generate life at a negative angle of attack. Also, rather unfortunately we rarely know the actual (average) AofA; we are not given that rather useful value. But we can be assured that the wing's angle of incidence will be calculated to give the best body angle/AofA/handling compromise.

PM