flipfloppity

Hello all,

I'm trying to figure out whether or not (L/D)max corresponds to the minimum point on the total drag curve (i.e. drag vs. velocity). If you look at Page 2 in this thread, particularly posts #16 and #19, there is some disagreement about the topic, but it doesn't seem to have been fully resolved. Originally I thought that (L/D)max was independent of the minimum drag, since the drag curve does not account for lift, which is obviously an input to finding (L/D)max. Now I'm not so sure. Can anyone shed some light on this? Thanks!!

TonyC

Post #16 is correct. Post #19 says Post #16 is incorrect, but then cites a source that contradicts himself and supports Post #16.

POST #16:

POST #19:

Of the 3 hyperlinks, only one, the 2nd one, "13.2 Power Required", still works. That's a link to a Massachusetts Institute of Technology source ... I would give it a high score for credibility.

Once you get there, look for the "Next" buttons to take you to successive pages. Click on "Next" twice and you'll land on "13.4 Aircraft Endurance."

There you'll find a diagram that shows the relationship between Min Drag and L/D max, Figure 13.5:
(The Y-axis is labeled P sub R (Power Required), and we know for level, unaccelerated flight, Power Required = Total Drag.)



As you can see, L/D Max occurs at the tangent of a line from the origin of the diagram to the total drag curve ... as was stated in Post #16.






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HuggyU2

I'm not an Aero major, but from everything I was taught, L/Dmax is the same as Min Drag... that's how it is defined. And that would mean post #16 is incorrect.
I know that contradicts what is written on some soaring sites, but that's all I know.

TonyC

That's not how it's defined. At the velocity where the ratio of Lift to Drag is at its maximum, the Total Drag is more than the Minimum Total Drag. As you increase Velocity from the Minimum Drag speed, you increase Total Drag, but you increase lift by a larger ratio, thus the ratio of Lift to Drag improves. As you continue to accelerate, you come to a point where the increase in drag is greater in proportion to the increase in lift. Between those two regions, where the ratio improves and where the ratio decreases, is the point where the ratio is at its maximum, Max L/D.

There's a forumula for the line that begins at the origin (0 velocity, 0 drag) and intersects the Total Drag curve -- it's not just an arbitrary line. At the point where the line intersects the curve on a tangent is where the maximum Lift to Drag RATIO.

If the two were the same, our Maximum Endurance and Maximum Range speeds would be the same.






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HuggyU2

Interesting. If it is as you describe, maybe the way we were taught was purely a simplification of the actual theory.

I did take a look at "Aerodynamics for Naval Aviators". On page 94 (while referencing a chart on page 93), it states "The point of minimum total drag occurs at a speed of 163 knots. Since this speed incurs the least total drag for lift-equal-weight flight, the airplane is operating at (L/D)max", which would contradict you statement.

JabroniJohn

Perhaps there are aircraft-specific exceptions?

UAL T38 Phlyer

Huggy:

I struggled with this one for a while, as an engineer! But this example was told to me and helped:

Min drag might be your holding-speed...least fuel-flow per hour, because you are trying to get the most TIME out of your fuel....and you AREN’T trying go anywhere; ie, you don’t want any miles made. Typically in the 230 kt range for jets like the T-38.

Best L/D is more like best (no-wind) CRUISE speed. Fuel-flow may be higher, but you get the best “miles per gallon.” More like 320 kts in a T-38 (yeah, I know, 0.50 Mach plus altitude....which always ends up 320+/-7) 😝

All for the reasons on the drag-polar that Tony posted....just an easier way to visualize it.

rickair7777

You might be able to design a plane such that min drag and L/D max are very close.

But as UAL and Tony pointed out, they are not typically the same, they are located at different points on the graph. PRmin = min drag, since thrust = drag in steady state level flight.

galaxy flyer

Somehow in the recesses of my brain, the correct answer is different for propeller versus jets. I need to look at “Aerodynamics for Naval Aviators”.

tnkrdrvr

In the KC-135 best range and max endurance were significantly different and varied by gross weight. Best range was always faster than endurance speed. However, the lighter you were, the closer they were. I would imagine for lighter aircraft they could be so close as to be indistinguishable. Pretty sure endurance was at L/D max, but my memory may be wrong and I don’t have a performance manual handy.