Lift/drag max equals minimum drag?

[Daniel Hofer]

Hi Roy,

> Thus, if you hold L constant, as D gets smaller, L/D gets bigger, and thus
L/D (max) is
> when D is at its minimum.

so simple... yes, now I understand. Lift remains constant normally.

Thank you very much!

Daniel

[neuhart]

> Another question about lift/drag ratio.
> In some books is written that lift/drag max is equal minimum drag. I don't
> understand why this should be.
> In some other books they write that's wrong.
> Can anybody explain me this problem?

It is not necessary that the condition of maximum lift/drag (L/D) always be
the condition of minimum drag. The confusion may arise from the fact that
the lift was not initially stated as being held constant.

Consider a plot of L/D versus aircraft angle of attack, lift versus angle of
attack and drag versus angle of attack.

At the angle of minimum drag, the lift is often quite low. As angle of
attack increases, the lift increases approximately linearly, at a constant
rate. Also, as angle of attack increases, drag increases at a slower rate at
first and then at a faster rate at higher angles of attack. This is because
drag varies in a non-linear (approximately quadratic) way with angle of
attack. Since lift increases intially at a faster rate than drag, there is a
point at which L/D is maximized because lift has increased so much faster
than drag. As angle of attack continues to increase, the drag increases at a
faster rate than the lift, so the L/Ddecreases. So, the peak L/D isn't
necessarily the point of minimum drag, but a point at some higher angle
where the drag is slightly higher, the lift is higher, and the ratio of lift
to drag is maximum.

If you would like a reference with a figure, I would be glad to supply it.

[Todd Pattist]

>It is not necessary that the condition of maximum lift/drag (L/D) always be
>the condition of minimum drag. The confusion may arise from the fact that
>the lift was not initially stated as being held constant.

Lift is a function of airspeed, air density, angle of attack
and the airfoil/aircraft properties. The usual assumption,
(and the one that explains why minimum drag occurs at
maximum L/D) is that lift is constant. However, if we do
not assume that lift is constant, but we DO assume that the
aircraft, airfoil and air density have not changed, then
doesn't minimum drag occur at zero airspeed with minimum
lift?

>Consider a plot of L/D versus aircraft angle of attack, lift versus angle of
>attack and drag versus angle of attack.

OK

>At the angle of minimum drag, the lift is often quite low.

True, and so is lift, as you said, so L/D is far from its
maximum.

>As angle of
>attack increases, the lift increases approximately linearly, at a constant
>rate. Also, as angle of attack increases, drag increases at a slower rate at
>first and then at a faster rate at higher angles of attack. This is because
>drag varies in a non-linear (approximately quadratic) way with angle of
>attack. Since lift increases intially at a faster rate than drag, there is a
>point at which L/D is maximized because lift has increased so much faster
>than drag.

And this is the classic best L/D angle of attack where the
L/D ratio is maximum and drag is minimum for this assumed
constant amount of lift. If I change airspeed to cut the
lift in half, the drag will fall by half too (ignoring
Reynolds No. effects), the ratio of L/D will be unchanged
and drag will be minimum for this new assumed constant
amount of lift. Of course, there is a wide range of angles
where the drag for half the lift is less than the drag for
twice the lift, but I don't see how that is relevant.

>As angle of attack continues to increase, the drag increases at a
>faster rate than the lift, so the L/Ddecreases. So, the peak L/D isn't
>necessarily the point of minimum drag, but a point at some higher angle
>where the drag is slightly higher, the lift is higher, and the ratio of lift
>to drag is maximum.

I don't see how you get this.

>If you would like a reference with a figure, I would be glad to supply it.

I would like to see it, or a better explanation of your point.
Thank you.

Todd Pattist
(Remove DONTSPAMME from address to email reply.)

[Burkhard Domke]

>Another question about lift/drag ratio.
>In some books is written that lift/drag max is equal minimum drag. I don't
>understand why this should be.
>In some other books they write that's wrong.
>Can anybody explain me this problem?

In horizontal flight conditions, min drag (speed) and max L/D (speed)
are different.

An efficient design will operate near max L/D at cruise speed for
maximum range (or max Mach times L/D if transonic). It has to operate
at minimum drag speed (=min fuel flow) for maximum endurance -
yielding less range, as min drag speed usually is less than max L/D
speed.

You can look up the different formulae for both points in any book on
hardcore aerodynamics or design.

Regards
Burkhard

[Todd Pattist]

>In horizontal flight conditions, min drag (speed) and max L/D (speed)
>are different.

No they are not. As has been previously posted, in
"horizontal flight conditions" the lift must balance the
aircraft weight, so lift remains constant and the ratio of
L/D must be maximum at the point where drag is minimum.

>An efficient design will operate near max L/D at cruise speed for
>maximum range

Correct, assuming the efficiency you want to maximize is
fuel burned per kilometer flown.

>It has to operate
>at minimum drag speed (=min fuel flow) for maximum endurance -

>yielding less range min drag speed usually is less than max L/D
>speed.

This is incorrect. Maximum endurance and minimum fuel flow
does not occur at minimum drag. Maximum endurance occurs
where minimum power is consumed to maintain level flight.
Power consumed is the force of drag times the airspeed.
The force of drag is minimum at the speed for best L/D, but
airspeed drops faster than drag increases below that speed.
Thus min power required to maintain flight occurs at a
higher drag, but lower airspeed than best L/D.

Flying at the minimum drag speed uses the least fuel per km.
Flying at the minimum power speed uses the least fuel per
minute despite being at a higher drag. They are just
different optimums - force vs power.

>You can look up the different formulae for both points in any book on
>hardcore aerodynamics or design.

Correct.

[Spaghettibone]

>Maximum endurance and minimum fuel flow
>does not occur at minimum drag. Maximum endurance occurs
>where minimum power is consumed to maintain level flight.
>Power consumed is the force of drag times the airspeed.
>The force of drag is minimum at the speed for best L/D, but
>airspeed drops faster than drag increases below that speed.
>Thus min power required to maintain flight occurs at a
>higher drag, but lower airspeed than best L/D.
>
>Flying at the minimum drag speed uses the least fuel per km.
>Flying at the minimum power speed uses the least fuel per
>minute despite being at a higher drag. They are just
>different optimums - force vs power.
>

I had a tough time with this issue years ago. I first learned to fly propeller
driven airplanes, then helicopters. In these aircraft I learned that maximum
range corresponded to L/Dmax. What a shock I had when I transitioned to flying
jets: In a jet, L/Dmax corresponds to best endurance airspeed!

The difference is the powerplants. In a prop driven aircraft or chopper, fuel
consumption is proportional to power output. In jets, fuel consumption is
proportional to thrust output.

In a jet, minimum thrust required occurs at the airspeed corresponding to
minimum drag (L/Dmax).

Check any textbook references you find for qualifying statements about props or
jets. Most texts aimed at the general aviation pilot deal exclusively with
prop powered aircraft.

W. Zelenski

[Todd Pattist]

> I first learned to fly propeller
>driven airplanes, then helicopters. In these aircraft I learned that maximum
>range corresponded to L/Dmax. What a shock I had when I transitioned to flying
>jets: In a jet, L/Dmax corresponds to best endurance airspeed!
>
>The difference is the powerplants. In a prop driven aircraft or chopper, fuel
>consumption is proportional to power output. In jets, fuel consumption is
>proportional to thrust output.
>
>In a jet, minimum thrust required occurs at the airspeed corresponding to
>minimum drag (L/Dmax).

The simple model for a prop/piston engine is a constant
power device. The simple model for a jet is a constant
thrust device. In both cases, "minimum thrust required

occurs at the airspeed corresponding to minimum drag

(L/Dmax)" This must be true as the thrust produced is the
force that exactly counteracts the opposing force of drag.

The difference, as you point out, is that for these
simplified models, the jet produces minimum thrust at its
minimum fuel flow, while the prop/piston engine does not. I
agree that I should have pointed this out, and looking back
on my post, I see that it was too centered on the
prop/piston engine model. Mea culpa.

Neither of these simplified models for the jet or the piston
engine driven prop are exact. The constant power model fits
a constant speed prop better than a fixed pitch prop where
propeller efficency plays a bigger part. If you really want
to know where maximum range and maximum endurance occur, you
need to look at the details of the engine (and prop)
efficiencies.