totm october 2020 Airplane Design Q&A

[K^2]

16 hours ago, mikegarrison said:

The most popular landing gear configuration for a long time is still known as "conventional" gear, even though it is no longer very conventional to use it.

The CFI I had teaching me to fly taildraggers didn't know they were also called "conventional gear". So yeah, that name's definitely going out of fashion. Though, it's still in a lot of manuals.

[benzman]

Tricycle undercarriage makes an aircraft much easier to land. After the main wheels touch and the nosewheel starts to come down the wing angle of attack lessens and the wing develops less lift.  So a nosewheel aircraft has a  much less tendency to bounce back into the air as the wing can no longer develop enough lift to allow the aircraft to fly. Once a nosewheel aircraft touches the ground it tends to stay there.

 

[mikegarrison]

Datums:

OK, this information is going to be pretty specific to one manufacturer (the one I work for). I don't know if other manufacturers do exactly the same thing or not.

Some of our design methods originated in shipbuilding. That's why we have a three-axis coordinate system that features "stations" (increasing from nose to tail), "waterlines" (increasing from bottom to top), and "buttock lines" that are 0 right down the middle and positive going out toward one side but negative going out the other side.

Stations are based off of a datum that is actually forward of the plane's nose. So the nose might be station 130, for example. This is so stations are always positive numbers. Likewise, waterlines are based off of a datum that is below the furthest extension of the landing gear, so all waterlines are also positive numbers. We do ours in inches, so station 155 is five inches aft of station 150. They don't have to be whole integers; station 155.6579 is 5.6579 inches aft of station 150.

Waterlines are parallel to the floor of the cabin, but the floor of the cabin is not necessarily parallel to the ground when the plane is sitting on its landing gear. (They also are not necessarily parallel to where the actual waterline would be if the plane is floating.)

When an airplane is lengthened, we put in "plugs". So let's say there is a 4 frame plug inserted in front of station 520. Well, a frame might be 20 inches, or 22 inches, or whatever. It depends on the actual spacing of the frames on the airplane. But let's say 20 inches. So before the plug is inserted, the frames go 460, 480, 500, 520, 540.... When the plug goes in, it is numbered 500A, 500B, 500C, 500D. That way all the rest of the airplane keeps its original station numbering. The actual stations run something like this: 518, 519, 500A, 500A+1, ... 500D+18, 500D+19, 520, 521,...

However, we also have concept of "absolute stations". This is simply the number of inches behind the station datum. So if a plug is inserted (or really two plugs, always one in front of the wing and one behind), the absolute station of the tail changes, but the station does not. That means drawings for the tail that are referenced by station don't need to be updated for the plug. But for issues like whether the tail is going to strike the ground during rotation, absolute station of the landing gear and the tail would be used.

The wings have their own coordinate system.

Turbine engines typically have a radial coordinate system based off the centerline of the shaft.

Referencing the interfaces between these different coordinate systems can get tricky, but the 3-D modeling tools we use now can do it easily. You can point to a spot on the computer model and it will print out the station, the absolute station, the waterline, the height above ground, etc.

====

I mentioned "frames". In the traditional semi-monocoque fuselage, frames are the stiffeners that run circularly around the fuselage, like a hoop. Stringers are the stiffeners that run along the skin from front to aft. So a frame is at a constant station, and a stringer is at a constant waterline (usually -- it gets complicated when the fuselage tapers in front and aft). Wings have a similar structure. They have stringers that run from root to tip, but instead of "frames" they have "ribs".

Monocoque is a design where all the loads are carried in the skin. Semi-monocoque is a design where some of the loads are carried in the skin, but others are carried in stiffeners that are attached to the skin. It turns out that with good design of the stiffeners, semi-monocoque is lighter than monocoque, so that's why it is used.

Edited October 7, 2020 by mikegarrison

[mrfox]

Would you mind doing a treatment on wingsweep?

Why does the airflow behave as if it is travelling in a direction normal to the leading edge? This never made any sense to me - as spanwise flow should instead be directed outwards and back towards the tips. Why can this component be ignored, when the actual flow of air particles and it’s associated interactions and energies are actually going in this direction? What happens to the analysis at the wing root, tips, fences and other obstruction?

This has always been a topic that I could not get comfortable around explaining. I can regurgitate it, but lack an intuitive understanding. Any input would be deeply appreciated.

[mikegarrison]

2 hours ago, mrfox said:

Would you mind doing a treatment on wingsweep?

Why does the airflow behave as if it is travelling in a direction normal to the leading edge? This never made any sense to me - as spanwise flow should instead be directed outwards and back towards the tips. Why can this component be ignored, when the actual flow of air particles and it’s associated interactions and energies are actually going in this direction? What happens to the analysis at the wing root, tips, fences and other obstruction?

This has always been a topic that I could not get comfortable around explaining. I can regurgitate it, but lack an intuitive understanding. Any input would be deeply appreciated.

OK, I'm going to have to look this up. It's one of those things I learned so long ago that I now just accept it's true, like that the sum of the angles in a triangle adds up to 180 degrees.

I'm going to try to go through this without much math, but this is definitely a math-intensive subject.

Let's start with a definition of wing sweep.

Are these wings swept?

Well, yeah, maybe. The Mustang on the right actually looks like it has a slight bit of forward wing sweep, although that little bit at the front of the root might be cancelling it out. The Spitfire looks pretty straight.

The usual definition for wing sweep is to look at the line of the 1/4 chord of the wing. That is, 1/4 of the way from the leading edge to the trailing edge. An unswept wing will have the 1/4 chord line perpendicular to the fuselage center line. If we say an airplane has 10 degrees of sweep, we usually mean that it is swept toward the back and that instead of making a 90 degree perpendicular it would be an 80 degree angle between the wing and the fuselage.

In subsonic flight, wing sweep is basically inefficient. It has the effect or reducing the aspect ratio.

But in transonic flight, even though the airplane is not exceeding the speed of sound, air can be going supersonic locally. As we discussed before, the air on the top of the wing is moving faster than the free stream air (due to circulation), so that air can be supersonic even if the airplane is not.

Supersonic air is just fine, but when it slows back down again to subsonic conditions it has to go through a shock. And how bad that shock is for losing energy depends on what angle the shock makes to the airflow. And this seems to be where the confusion is coming in.

In a straight wing, that shock in the picture is a nearly-normal shock. Normal shocks cause the most energy loss, and always result in supersonic flow becoming subsonic.

But if you sweep that wing, now the shock is swept too. So it becomes an oblique shock. And oblique shocks cause less energy loss. Roughly they are like if only the velocity component normal to the shock is going through the shock. So this is where you are getting to your question of "Why does the airflow behave as if it is travelling in a direction normal to the leading edge?" It's because going through a shock at an angle loses less energy than going through a shock head on.

The result is that for transonic airplanes, those flying between around 0.7 Mach and 0.95 Mach, the more swept the wing, the less energy is lost to the shock. Which basically means that you can get a pretty good estimate of the design Mach number for the plane by looking at the wing sweep angle.

==========

As you mention, though, wing sweep has some negative consequences. One of them is spanwise flow. Essentially a component of the airflow is moving along the wing rather than over it, so that reduces the effectiveness of the wing and increases drag. You could also think of this as answering the earlier question. While in reality the air pretty much goes over the wing in a straight line relative to the path of the airplane, with math we can break that down into a spanwise and a chordwise component. And if some of the velocity is going spanwise, that means the chordwise velocity component is a bit smaller (because that spanwise part is taking some of the total velocity). And since the chordwise velocity is a little smaller, it's like the airplane is flying a little slower, so it's like the Mach number is lower. So the shock is a little less draggy.

That's just a different way of looking at the same thing.

==========

Swept wings are also prone to yaw-roll coupling, which can lead to a nasty condition called "Dutch roll". Pretty much all swept-wing planes have a "yaw damper" that automatically tweaks the rudder to stop that Dutch roll positive feedback loop. The way it works is that if the airplane yaws left, that makes the left wing slightly more swept and the right wing slightly less swept. That causes the left wing to lose a little lift and the right wing to gain a little, so the airplane rolls. The stabilizer then swings the plane back to zero yaw, but like a pendulum it swings out the other direction. So the plane rolls in the other direction. And back and forth, rolling and yawing, making everybody quite sick unless it is damped out.

Edited October 8, 2020 by mikegarrison

[mikegarrison]

ps. As a passenger, one of my favorite things to do is watch the shock on the top of the wing out the window. When the light is at the right angle the shock casts a shadow, and you can see the shadow on the wing.

The reason it casts a shadow is because of the difference in air density in front and behind the shock. That causes the light to refract, and it ends up making a shadow.

https://en.wikipedia.org/wiki/Schlieren

[mrfox]

9 hours ago, mikegarrison said:

But if you sweep that wing, now the shock is swept too. So it becomes an oblique shock. And oblique shocks cause less energy loss. Roughly they are like if only the velocity component normal to the shock is going through the shock.

My poor brain can't seem to rotate the cross-section axis to an orientation that makes sense. All I can see is a bunch of your above diagrams, with their normal shocks, stacked laterally and offset by sweep angle. Which orientation do I need to be looking from to see the wedge geometry that creates the oblique shock?
 

Edit: Well I’m going to try answer my own question since the wing platform is the obvious wedge...?
 In this orientation, how would the normal shock from a straight wing look? How would they both look from an overhead prospective of the two geometries, and its associated shockwaves? I’m still somewhat unclear as to how this all looks

 

Edited October 8, 2020 by mrfox

[mikegarrison]

It would be a little more helpful if these arrows were labeled, but here goes:

The shock is the red line. The air comes into it with pretty much the freestream velocity (that arrow straight down, top left). When it hits the shock it hits at an angle. Oblique shocks turn the flow as well as slow it down, so coming out of the shock it has bent out toward the tip a little. It's now the right-side arrow on the bottom.

So that's the real flow -- straight down, hits the oblique shock, bends out a little.

The other arrows are vector components of that real flow. One component points to the tip. This is the spanwise component, and it's generally undesirable. We want our air to be flowing over our wing chord, not along it. The other component is the chordwise flow. It follows the chord, from leading edge to trailing edge, and this is the part of the flow we like. It keeps our airplane in the sky.

But ... that chordwise flow goes straight through the shock as a normal shock. That's bad for transonic drag.

If we had a straight wing, all the flow would be chordwise. (Almost all. Induced drag actually self-generates some spanwise flow from the vorticity.) If all the flow is chordwise, that's good -- subsonically. But when you get to transonic speeds, it forms that nasty normal shock and our wave drag gets really bad, really fast.

With this swept wing, we eat the subsonic loss due to the spanwise flow, but in return we gain that the shock is oblique. We only lose as much energy to the shock as we would if we were flying slower. How much slower? The speed of the chordwise velocity. So that means overall the airplane can fly faster before it runs into the wave drag wall.

One last thing ... those spanwise arrows on top and bottom? They are the same. The velocity parallel to the shock doesn't change by going through the shock. But the arrows that are normal to the shock? The one on top is longer than the one on the bottom, because going through the shock slows down the flow. So another way to think of all this is that by sweeping the wing we make part of our airflow be unaffected by the shock, and that's why the drag is less.

Edited October 8, 2020 by mikegarrison

[Silavite]

A little extra about the geometry of oblique shocks from NACA Report 1135:

Wherein,

• P is pressure
• ρ is density
• T is temperature
• a is the local speed of sound
• M is the local Mach number
• s is the mass-specific entropy
• V is the resultant/total velocity
• u is the component of velocity normal to the shock
• v is the component of velocity parallel to the shock

You can see from (115) that (117) reduces to v₁ = v₂. As the v-component of velocity is conserved, its energy is conserved as well. 

(I'm thinking that I should probably write a post later going over the basic equations of mass, momentum, and energy conservation for fluid flows, since I basically just dropped these equations out of thin air, if you'll pardon the pun )

Edited October 8, 2020 by Silavite
Equations are not well-explained

[mikegarrison]

Re-reading what I wrote about shocks, I thought I would mention something about reference frames.

There are two major reference frames used with airplanes. They have formal names, but I can't remember what they are. Anyway, one is that of the airplane. In this reference frame the airplane is motionless and the air is blowing past it. The other one is the frame of an air molecule, in, for instance, a wind tunnel, as it is blown past a test object (ok, now I remember that this one is called the Lagrangian).

(There is also the regular Earth-based reference frame, for which airplane ground speed, track over the ground, and height a.g.l. -- above ground level -- is important.)

Most of the time, for the airplane, the reference frame that is easiest to use for aerodynamic analysis (and most convenient in the steady state) is the one where the airplane is fixed and the air is blowing past it. So in that reference frame, air is blowing past the plane at, say, Mach .84. It accelerates over the wing to supersonic speeds, then goes through a shock. In the wake of the airplane it is going slower (that momentum loss is drag) and moving down (which is how the plane gets lift).

But in the reference frame of the air, it's just sitting there. An airplane comes shwooshing in, pushes it around the wing, pushes so many other air molecules into it so fast that it can't get out of the way (shock), and then drags it along behind the airplane as a wake.

These are equally valid reference frames, but as humans we usually don't care what is happening to the air molecule. We do care what is happening to our airplane. So the reference frame we usually use is the one centered on the airplane, where it is assumed that the air is actually blowing past the airplane rather than the airplane is moving through the air.

Edited October 9, 2020 by mikegarrison

[benzman]

On 10/8/2020 at 5:43 PM, mikegarrison said:

There is a youtube clip of those two aircraft at Duxford.  It is quite beautiful to watch, and listen to.

 

[mikegarrison]

I used to have an office right next to Paine Field, where the late Bill Allen placed his "Flying Heritage" museum. One day everybody gathered at the windows and watched a Mustang and Spitfire flying around, engaging in mock dogfights, and generally just playing with each other.

An office full of aeronautical engineers is quite vulnerable to distraction by airplane.

Edited October 10, 2020 by mikegarrison

[JoeSchmuckatelli]

Did any of those WW 2 fighters get close to the sound barrier and survive?  Or did the wing shapes produce so much drag that they couldn't get close? 

[mrfox]

Transonic buffeting effects had also been widely reported by pilots of propeller-driven Allied fighters including the Supermarine Spitfire, P-38 Lightning, P-47 Thunderbolt and P-51 Mustang, aircraft that were known to have top diving speeds of less than 0.85 Mach (although one Spitfire was measured at 0.92 Mach). Allied fighter pilots reported seeing supersonic shock waves and popped rivets during dives as the high-speed air rushing over the wing exceeded Mach 1 even though the forward airspeed of the overall aircraft was well below that speed.

https://en.m.wikipedia.org/wiki/Hans_Guido_Mutke
 

[mikegarrison]

Yeah, as discussed before, the airflow over the wing can be supersonic even if the airplane isn't. This leads to a condition known as "buffet". (Side note, if you Google "wing buffet" you will get links to restaurants selling chicken. But if you Google "Mach buffet" you should find what we're talking about.) Buffet is when the air behind the shock separates and starts shaking the airplane. It's basically the high-mach limit for a subsonic airplane.

The buffet limit is part of the famous "coffin corner". As altitude increases the stall speed gets higher and higher, until it intersects with the buffet limit. So the plane can reach a point where it can't go any faster or it will be in buffet, but it can't go any slower or it will stall. And that's just in level flight -- maneuvers reduce the margins even further. The U-2 was pretty famous for being designed to operate right up against the coffin corner, so much so that it had a special autopilot that made sure all flight maneuvers in cruise were very, very gentle.

Swept wings delay the onset of Mach buffet (as discussed above), allowing higher airplane Mach numbers before hitting the buffet limit.

[Silavite]

I promised a post about the fundamental conservation equations, so here it is. I originally wanted to do derivations, but the amount work and number of images I'd need to attach would be... well... more than my limited patience allows (though writing this whole thing ended up taking about 3 hours anyway... I have a newfound respect for textbook writers and my professors). Instead, I've decided to present the finished product and explain what each term represents.

Notes:

• Variables in bold font are vectors, while scalars use regular font.
• The equations come from Fundamentals of Aerodynamics, Sixth Edition by John D. Anderson.
• A control volume is basically a box (or any closed shape one desires, really) in space. Fluid can flow through it, surface forces (like pressure) can act on its walls, and body forces (like gravity) can act on everything inside of it.
• Internal energy (e) is all of a system's energy which is not macro scale kinetic or potential energy. For example, internal energy includes the energy present from random molecular and atomic motion. 

 

Mass Conservation (or Continuity)

This equation is represents the conservation of mass, otherwise known as continuity. Each term has the dimensions of mass over time, or MT^-1. Going from left to right, each term represents:

1. The rate at which the mass within the control volume is increasing. Density (ρ) is mass per unit volume, the triple integral across a space results in the volume of a space (V), and the time derivative (d/dt) shows how the value (mass) is changing with respect to time.
2. The flow of mass across the boundary (or surface) of the control volume. More specifically, the mass flow rate exiting the control volume. Density (ρ) times velocity (V) times the area of the surface (S) is equal to the mass flow rate across that surface. That said, this relation only holds if the velocity is exactly normal to the surface in question. For this reason, the area is "oriented" in the sense that the actual scalar area is multiplied by the unit vector which is normal to and points outwards from the surface. The dot product between the velocity (V) and the surface (S) ensures that only the velocity normal to the surface (or, alternatively but equivalently, the surface normal to the velocity) is accounted for when the two quantities are multiplied. The fact that the surface normal unit vector points outward has an important consequence on the sign of the term. This means that a velocity vector going into the control volume would be pointing in the opposite direction of the surface normal unit vector, which would result in a negative sign for the term when the control volume's mass is actually increasing.
3. Mass is conserved, so any increase in mass inside the control volume must be exactly equal to the mass which exits that volume across its boundary. Thus, the equation equals zero.

It is frequently practical (and convenient) to assume that the control volume in question is at a steady state, such that no quantities vary with respect to time. By definition, the time derivative (d/dt) of a quantity which does not vary with time will be zero. Thus, for a steady state, the equation for mass conservation is:

 

Momentum Conservation

This equation represents the conservation of momentum. It's important to note that momentum is a vector quantity, so this equation may be divided into three scalar components. In addition, from Newton's second law, force is equal to the change in momentum over time. Each term has the dimension of force times mass over time, or MLT^-2. Going from left to right, each term represents:

1. The rate at which the net momentum of the control volume is increasing. This term looks quite similar to the first term of the mass conservation equation, but since momentum is mass times velocity, it is multiplied by the velocity vector (V).
2. The flow of momentum across the boundary (or surface) of the control volume. More specifically, the momentum flow rate exiting the control volume. Again, this term looks quite similar to the second term of the mass conservation equation, but since momentum is mass times velocity, it is multiplied by the velocity vector (V).
3. The rate at which pressure adds momentum to the control volume. Pressure is force per unit area, hence why it is multiplied by the area and surface normal unit vector (S) of the surface to find the force applied.
4. The rate at which body forces (such as gravity) add momentum to the control volume. The f represents the body force per unit mass. Field forces like gravity and magnetism have the ability to act on the entire control volume body, hence the triple (volume) integral. Since f is per unit mass, it is multiplied by density (ρ) and volume (V).
5. Any viscous forces which may act on the control volume. Viscous forces are... complicated, so any possible viscous forces are represented by a simple (if rather nebulous) F_viscous.

For most aerodynamic applications, the effects of gravity are small (and it is unlikely that other body forces will be acting on the control volume. I suppose plasma could have electromagnetic interactions, but that's getting a little ahead of things), so term 4 can usually be dropped. Viscous forces are vital within the boundary layer, but can be neglected in the free stream, so term 5 can be dropped unless inside the boundary layer. Finally, as with mass conservation, it is frequently practical (and convenient) to assume that the control volume in question is at a steady state, so term 1 may be dropped. Thus, for a situation with no body forces, inviscid flow, and at steady state, the equation for momentum conservation is:

Additionally, for low-speeds wherein density is constant (usually considered to be speeds below Mach 0.3), it is possible to fully analyze flows using only mass conservation and momentum conservation. Density cannot be considered to be constant once speeds increase beyond that point, so we must turn to...

 

Energy Conservation

This equation represents the conservation of energy (equivalently, the first law of thermodynamics). This one looks rather imposing, but it's really not that bad.  Each term has the dimensions of energy over time, or ML²T^-3. Going from left to right, each term represents:

1. The rate at which energy is added to the control volume as a result of heat from a body source. This could be from radiation or a chemical reaction within the control volume. Mathematically, q_dot is heat addition per unit mass per unit time, which then becomes heat addition per unit time after being multiplied by the density (ρ) and volume (V).
2. The rate at which energy is added to the control volume due to heat from viscous effects. Viscous effects are, again, complicated, so it's convenient just to leave contributions by viscous effects in this simple state.
3. The rate at which pressure adds energy to the control volume. Pressure (p) times area (S) is force, and force times velocity (V) is power, or energy per unit time. The dot product ensures that the pressure gradient force is actually acting to accelerate the flow, rather than simply changing its direction.
4. The rate at which energy is added to the control volume due to body forces. Similar to term 4 of the momentum equation, but multiplied by velocity (V) since force times velocity is power, or energy per unit time.
5. The rate at which energy is added to the control volume due to work done by viscous effects. Viscous effects are, once again, complicated, so it's convenient just to leave contributions by viscous effects in this simple state. (This term seems a bit... strange to me, personally, since viscous effects act to turn organized motion into random motion over small scales. There's likely something here that I'm not understanding, or perhaps it's present simply for completeness.)
6. The rate at which the net energy of the control volume is increasing. Conceptually, this is similar to term 1 of the mass and momentum equations. Within the parenthesis are internal energy per unit mass (e) and the macroscopic/organized kinetic energy per unit mass (V^2 / 2). The net energy per unit mass is then multiplied by density (ρ) and volume (V) to obtain the net change in energy per unit time of the control volume.
7. The flow of energy across the boundary (or surface) of the control volume. More specifically, the energy flow rate exiting the control volume. Conceptually, this is similar to term 2 of the mass and momentum equations. Within the parenthesis are internal energy per unit mass (e) and the macroscopic/organized kinetic energy per unit mass (V^2 / 2).

For most aerodynamic applications (outside of a combustion chamber, of course), body heating is negligible, so the flow may be assumed to be adiabatic and term 1 can be dropped. As was said with momentum: viscous effects are important within the boundary layer, but can be neglected in the free stream, so terms 2 and 5 can be dropped unless inside the boundary layer. For most aerodynamic applications, the effects of body forces are typically small, so term 4 can usually be dropped. Finally, as with mass and momentum conservation, it is frequently practical (and convenient) to assume that the control volume in question is at a steady state, so term 6 may be dropped. Thus, for a situation which is adiabatic, inviscid, without body forces, and at steady state, the equation for energy conservation is:

 

(After waking up this morning, I realized that I should write a little more about the simplified versions of these equations which result from applying them to streamtubes. Stay tuned!)

Edited October 14, 2020 by Silavite
Streamtube simplifications (Coming soon to a fluid near you)

[JoeSchmuckatelli]

@mikegarrison  Can you talk to the Corsair vs Mustang debate?  I know both were fantastic and designed for different roles, with Corsair being quite a bit heavier. Iconic wing shape of Corsair being largely dictated by the space needs of a carrier - what impact do the different wing shapes have on flight characteristics?

 

Bonus question: while the Lightning was a clearly capable aircraft - why did it's design not last?  Is there anything inherently better about the Mustang design over the Lighting? 

[Entropian]

As far as I know, the Corsair was basically the biggest engine you could fit into the smallest airframe.  The gull wing (I think that's the term) was for folding the wings for efficient storage on aircraft carriers and allowing the giant propeller blades to fit.

EDIT: Ok, I double-checked my knowledge of the P-51.  It was meant to be unusually high altitude, so that may have had an effect on the wing design.  Mustangs were mainly bomber escorts during WW2 on the Western Front.  The problem with current escorts was that the Luftwaffe was shifting from the Eastern Front to the Western, so a new, more effective design was created to continue the Allied bombing campaign.

EDIT 2: Just remembered the bonus question.  The P-38 had problems with mach tuck during development and service and sub-optimal maneuverability was also present.  The P-51 was also cheaper and had a fighting chance against the rising jet era of aviation.  The P-38 was also designed as a medium bomber, but when jets like the P-80 were developed, there was no need for them, as the newfangled jets could provide more and better bombing services.

Edited October 15, 2020 by Entropian

[mikegarrison]

You guys are missing the main point about the wing shape of the Corsair. Remember my post about landing gear?

The Corsair had a huge engine, and to turn all that power into thrust it had a huge propeller. And that propeller needed ground clearance. So they needed landing gear height. But landing gear is heavy and hard to fit into the airplane, so it's good to make it as short as possible.

Thus, in order to get more ground clearance, they angled the wings down (anhedral), put in the landing gear at their lowest spot, and then angled the wings up (dihedral).

Dihedral, by the way, causes roll stability for a low-wing airplane, which is why most airplanes have some dihedral. High-wing airplanes sometimes have anhedral wings.

This is because dihedral creates aerodynamic roll stability and anhedral creates aerodynamic roll instability. And having the fuselage weight above the wing creates pendulum roll instability while having the fuselage weight below the wing creates pendulum roll stability.

So low wing planes need dihedral to counteract the fuselage's desire to be below the wing, while high wing planes often need anhedral to counteract the fuselage's tendency to not let them roll the plane when they want to roll it.

Edited October 15, 2020 by mikegarrison

[Entropian]

8 minutes ago, mikegarrison said:

You guys are missing the main point about the wing shape of the Corsair. Remember my post about landing gear?

The Corsair had a huge engine, and to turn all that power into thrust it had a huge propeller. And that propeller needed ground clearance. So they needed landing gear height. But landing gear is heavy and hard to fit into the airplane, so it's good to make it as short as possible.

Thus, in order to get more ground clearance, they angled the wings down (anhedral), put in the landing gear at their lowest spot, and then angled the wings up (dihedral).

I thought I said that here:

3 hours ago, Entropian said:

As far as I know, the Corsair was basically the biggest engine you could fit into the smallest airframe.  The gull wing (I think that's the term) was for folding the wings for efficient storage on aircraft carriers and allowing the giant propeller blades to fit.

 

[Silavite]

4 hours ago, JoeSchmuckatelli said:

@mikegarrison  Can you talk to the Corsair vs Mustang debate?  I know both were fantastic and designed for different roles, with Corsair being quite a bit heavier. Iconic wing shape of Corsair being largely dictated by the space needs of a carrier - what impact do the different wing shapes have on flight characteristics?

 

Bonus question: while the Lightning was a clearly capable aircraft - why did it's design not last?  Is there anything inherently better about the Mustang design over the Lighting? 

The second question is probably more open-and-shut. A single P-51 took fewer resources to produce than a single P-38, and the P-51 could do the job of bomber escort just as well as the P-38.

That still begets the question of why the P-38's configuration didn't last. To answer that, something of a dive into supercharging is required. (Note: if I say "gear driven supercharger" I mean a centrifugal supercharger driven by the engine driveshaft through gearing.)

The reason that the P-38's twin boom design came about in the first place (and why the P-47 is such a beast of an airplane) has to do with the fact that the USAAF bet on turbo-supercharging rather than two-stage supercharging for engine compression. A quick summary of the difference between the two: a turbocharger and supercharger both compress the charge entering the engine, but a turbocharger is driven by an exhaust gas turbine, whereas a supercharger is driven by the engine's driveshaft through gearing. The term "two-stage" simply means that the supercharger has two compressors. The first stage is used for low altitude, and the second stage is engaged at higher altitude. There are also two-speed superchargers, which have a single compressor which can rotate at two different speeds via a change in gear ratio. The two-stage design is more potent, however, since the compression ratio between compressors in series is multiplicative (two compressors in series with a compression ratio of 5 give you a compression ratio of 5², or 25). The term turbo-supercharger is used because the system used by USAAF aircraft has both a driveshaft-driven supercharger and a turbocharger. Here's a schematic of the P-47's system (the gear driven supercharger is 3, and the turbocharger is 13):

Spoiler

The gear-driven supercharger is designed to do all of the compression at sea level, while the turbocharger adds its assistance as altitude increases. This retains the advantages of multiplicative compression ratio in a two-stage system without requiring the gear-driven stage to be throttled (more on throttling losses later).

This is a NACA report from 1932 which probably influenced the USAAF's decision: The Comparative Performance of Superchargers. In this context, a turbo-supercharger has two advantages over a two-stage centrifugal supercharger: efficiency and throttling. (This report also includes a vane-type and roots-type geared supercharger, but these aren't relevant.)

The turbo-supercharger uses exhaust gasses to to drive a turbine which drives the compressor, which is (nearly) a free lunch, energy-wise. There are some losses from increased back pressure on the engine's exhaust (the exhaust gas turbine prevents gasses from flowing smoothly to the free atmospheric pressure), but these losses are smaller than what a gear-driven supercharger takes directly from the engine. Figure 4 shows the comparative power produced from each type for an engine which has 100 horsepower at sea level (not including throttling losses, which we'll get to soon):

Spoiler

The turbo has another ace in its hole: it doesn't suffer from throttling losses. In the words of the report,

Quote

Throttling air at the supercharger inlet to limit the quantity inducted makes it necessary to compress the throttled air so that it will be discharged at sea-level pressures. Considering the net engine power this method is very unsatisfactory, because the engine power at sea level and at low altitudes is greatly reduced by two factors; the loss of the power used in compressing the throttled air, and the loss in power due to the decreased weight of the charged caused be the high carburetor air temperatures resulting from compression.

This means that an engine with a gear-driven supercharger will suffer a loss in power below its critical altitude (the critical altitude occurs when the compressor can no longer keep up with the decrease in atmospheric density, so the density of the charge entering the engine begins to fall and engine power begins to drop off). The effects of throttling losses are quite significant, as figure 7 shows:

Spoiler

A two-stage geared centrifugal supercharger averts the worst of throttling losses via effectively increasing its critical altitude when the second stage is engaged, but there are still losses, especially in the area between the critical altitude of each stage. The altitude range situated near the midpoint of the critical altitudes of a two-stage or two-speed system is known as the "supercharger gap". A turbocharger (or turbo-supercharger) suffers from no such gap because the turbocharger's compression can be smoothly varied by changing the amount of exhaust which passes through the exhaust gas turbine. (Bonus content: Throttling losses can be averted with a continuously variable supercharger gear ratio. Such a system was used on the German DB 605 via a fluid coupling.)

Things are currently sounding pretty grim for the gear-driven supercharger, but the gear-driven system has one gigantic (or, should I say, tiny?) advantage: its size. The gear-driven system is much lighter and requires much less space than an exhaust-gas driven turbocharger. Here's another illustration of the P-47's system:

Spoiler

As you can see, the ducting for cooling air (the exhaust gas turbine gets extremely hot, so getting enough air to cool it is quite the engineering challenge on its own) and sundry other equipment required by the turbo-supercharger makes it very difficult to fit into a single-engine fighter. Some attempts are... well, they resulted in airplanes with appearances that only their mothers could love:

Spoiler

The Curtiss P-37

The Bell XP-39

The impetus behind the P-38's twin-boom design was so that the whole turbo-supercharger assembly could fit in a streamlined package. Even with its twin-boom design, the P-38 still ended up leaving the exhaust gas turbine exposed to the airstream for cooling purposes.

Spoiler

The fact that the P-47 managed to have an exhaust gas turbine which is adequately cooled while also being fully enclosed within the fuselage was one of the triumphs of its design. Contrastingly, the compact gear-driven supercharger on the Merlin made it a great fit for the (relatively) small and excellently streamlined design of the P-51.

To conclude: The twin-boom design was born out of necessity from the turbo-supercharger system's large size. The twin-boom design wasn't revisited because the P-51 performed well with its gear-driven system and the P-47 performed well with its turbo-supercharger system enclosed within a single fuselage.

[Silavite]

4 hours ago, mikegarrison said:

Dihedral, by the way, causes roll stability for a low-wing airplane, which is why most airplanes have some dihedral. High-wing airplanes sometimes have anhedral wings.

This is because dihedral creates aerodynamic roll stability and anhedral creates aerodynamic roll instability. And having the fuselage weight above the wing creates pendulum roll instability while having the fuselage weight below the wing creates pendulum roll stability.

So low wing planes need dihedral to counteract the fuselage's desire to be below the wing, while high wing planes often need anhedral to counteract the fuselage's tendency to not let them roll the plane when they want to roll it.

I don't think that the lateral stability of a high wing is due to a pendulum effect. Intuitively, this sounds very much like the pendulum rocket fallacy. An aircraft rotates about its center of mass, so gravity cannot exert a moment in any way. The center of pressure and lift vector will be in the vertical plane of symmetry, so lift cannot create a rolling moment.

Spoiler

A post about this very question on aviation stack exchange, and another, related post.

A high wing aircraft will have added lateral stability in a sideslip, but that is due to how the relative wind moves over the fuselage.

Spoiler

From page 80 of Flight Stability and Automatic Control by Nelson

 

From stack exchange

 

[mikegarrison]

OK, first of all, I'm not an S&C specialist (stability and control). So apologies.

https://en.wikipedia.org/wiki/Keel_effect

You are correct that the weight doesn't directly cause a rolling moment. But having the fuselage above the wing *does* tend to create roll instability, while having it below the wing *does* tend to create roll stability (sometimes too much). And this is why high wing airplanes tend to have anhedral wing angles.

The question is how this works, and the links you provided are illustrative. It is called "pendulum effect" but the name is misleading because it acts like a pendulum, but it doesn't work the same way as a pendulum.

[Silavite]

1 hour ago, mikegarrison said:

OK, first of all, I'm not an S&C specialist (stability and control). So apologies.

https://en.wikipedia.org/wiki/Keel_effect

You are correct that the weight doesn't directly cause a rolling moment. But having the fuselage above the wing *does* tend to create roll instability, while having it below the wing *does* tend to create roll stability (sometimes too much). And this is why high wing airplanes tend to have anhedral wing angles.

The question is how this works, and the links you provided are illustrative. It is called "pendulum effect" but the name is misleading because it acts like a pendulum, but it doesn't work the same way as a pendulum.

No worries, I hope I didn't come across as accusatory.

[mikegarrison]

14 minutes ago, Silavite said:

No worries, I hope I didn't come across as accusatory.

It's fine. If I say something wrong, I want to get corrected.