How does adding flaps Change LD MAX?

[fish314]

Never mind. Power...thrust...grr. :-\

However, another question. Flaps let you go slower and at slower speeds thrust is increased in a propeller aircraft. Is it possible that the reduced speed offsets the increased drag?

Sure, this the general idea on which most STOL kits are based on. Some kits even go as far as to droop the ailerons a few degrees.

Theoretically, yes (only in a prop aircraft), since climb angle is Arcsin[(Thrust-Drag)/Weight], as long as the thrust increases by more than the drag increases, climb angle could increase. Practically speaking, I don't know if that actually occurs, or how often it occurs. My general sense is that there are probably few if any airplanes designed this way, because it would mean the engine that can develop a lot of power at very slow speeds, but the power bleeds off very quickly as speed increases. You could design an engine like this if you wanted the plane to climb really, really well but the tradeoff would mean that it cruises really inefficiently. This would probably be a really poor design for an airplane/engine combination for most uses... unless the ONLY thing you cared about was climb angle and short takeoff.

I would caution using STOL as the example to prove this (thrust increase larger than drag increase). I have no doubt that some airplanes use some highly deflecting flaps, and droop the ailerons... but I think the primary effect that you are seeing in their takeoff performance is due to lowered stall speed (due to the changed CL discussed above). The speed change probably didn't effect the engine as much as the flaps effected the drag.

Flaps reduce takeoff distance regardless of whether thrust increases or not, because they reduce the stall speed (and hence the takeoff and landing speeds). In other words, the airplane is able to fly slower and get airborne quicker(assuming thrust available remains above drag), even if nothing happened with regards to the engine. I think the better thing to look at would be climb angles.

Remember the takeoff phase is a whole different problem than the climb phase. Getting an airplane airborne quickly is not necessarily indicative of the angle that it climbs at once it is airborne.

 

[shdw]

Theoretically, yes (only in a prop aircraft), since climb angle is Arcsin[(Thrust-Drag)/Weight],

I'm still having problems here. Sorry bare with me. I'm referencing pages 265-281 in John D Andersons book Aircraft Performance and Design. Particularly focused on page 272-273 and here we go:

Now I'm having trouble differentiating between jet/prop since the author blends the two together. So my first issue arises from a possibly incorrect interpretation of a jet climb equation applied to a propeller aircraft (eq 5.94):

Sin theta max (climb angle) = T/W - 1/(L/D) max

The paragraph prior to this equation states, (paraphrasing) "Since thrust in a jet aircraft is constant with airspeed, maximum climb angle will occur at L/D max."

This would lead me to believe that, since thrust increases in a propeller aircraft with reduction in velocity, maximum climb angle for a propeller aircraft would be slightly below L/D max. Driving further, then, it lends to the belief (in my confused head) that decreasing L/D max speed (such as with flaps) should yield a greater climb angle.

An aside: This entire analysis would seem to be highly subject to the type of high lift device we were using. In such a way that it would be unlikely that climb angle could increase if we were talking about, say, plain flaps. Though if we discussed extended flaps it would seem to be possible that these devices could increase climb angle. Thoughts?

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I do note that on the 10 or so pages prior to this section Anderson speaks to the purpose of flaps. He only makes mention of their use to increase Clmax in such a way that stall speed be reasonably low. There is no mention of, or connection between, that I've found, high lift devices being used to adjust climb angle. Only the curious mention of L/D max directly effecting it.

I say this to show you that I'm not trying to be argumentative, despite my reputation for stirring things up on this forum. I am quite simply just plain confused. It doesn't help much that I'm not always sure what variables are being held constant and which are just ignored. Are we talking theory in a 2d tunnel or 3d world? Etc.

Your original post had me completely lost right from the first paragraph because I didn't realize, until talking to T about it, that for flaps to cause L/D to decrease we must assume a constant velocity, thereby keeping lift coefficient constant. Otherwise, with a subsequent reduction in velocity, L/D could be increased. Anyways this is neither here nor there, let's continue with the questions!


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On page 274 it states (in reference to propeller aircraft, though this same statement is made on the previous page in reference to jet aircraft), "It is possible for V theta max to be less than V stall."

Now I'm making a bold assumption after reading these two cautionary notes by this author (and a book I have by Raymer) that theoretical maximum climb angle speed is typically below the speed we fly for Vx. In other words, adding flaps, by allowing us to get closer to the theoretical maximum, should thereby increase our climb angle despite the drag penalty.

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I can't find a formula in this text that seems to indicate the formula you gave for climb angle. Is it a derivation of a more complex formula that I'm just not seeing? I do note that equation 5.90 is similar, but still only a lead into the equation I posted above. Eq 5.90 is:

sin theta = T/W - D/W


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A bit earlier in the text, page 267, Anderson talks about setting cos theta to 1 in the drag expression. The preceding discussion deals with an ever increasing portion of lift being supported by weight as climb angle increases. The result is an ever decreasing value of drag due to lift. He states that even at 50 degree angles the error in calculated climb angle is 2.5 or smaller and rate error is 3% or less. If I'm reading this right, he is saying that, by setting cos theta to 1 in the drag expression, we are ignoring the reduction in drag due to reduction in wing lift?