Assuming neither plane is over gross, and both are trimmed for best glide, I would guess the difference would be negligible.

cheers,
Joe

yeah... I've tossed this back and forth many times... and to me... logically, the heavier one would not be able to travel as far as the lighter one... but the answer dictates that they will travel the same distance... but why... why would they both travel the same distance? Is it that the heavier one is more flying than falling, and the lighter one is more falling than flying... and somehow that just works out to be the same rate of descent? Or maybe it's magic? haha... I have no idea on this...

Actually... the only way for this to make any sort of sense to me at all is if the lighter one is the one falling... because the heavier one needs the faster airspeed... therefore it's nose is pointed down, and there's more air flowing over the wings... so that would be the one that's more flying than falling... whereas I'm starting to think that the lighter one appears to be more falling than flying, because it doesn't require as much of a nose down attitude as the heavier one. Kind of like they're both descending at the same rate... just with different attitudes. In either case though, the wind would definitely affect the gliding distance, and no two airplanes are the same, even if they are the same model or make. We as pilots have the ability to change things too, just because we can be consistent, does not mean that our actions will result in the same consequences, if all other variables are negligible. But yeah... this is quite a question, thank god that instructor never asks why they can both glide the same distance... haha

A great question... let Professor Insomniac explain... 

There is nothing vague or mysterious about the effect of weight on glide performance, and it's very easy to test the laws involved in any airplane.

Gliders illustrate it very clearly... training for the PP-G, I have seen the difference when I am gliding, say, from the usual top of final to the usual touchdown point when solo vs. with someone in the back seat. I've often done this on the same day, with the same wind conditions.

But the same principles apply to anything with wings.

Here's the straight dope:

Increased weight requires increased speed for a given performance parameter, whether it's airspeed necessary to maintain level flight, rate of turn, rate of climb, or rate of sink. This is true whether you have an engine or not.


Power pilots should know that in a turn, or any time the load factor is increased, V-speeds go up. They go up by a factor equal to the square root of the increase in load factor. Vs, Vne, MCA, and, of course, Vbg or best glide speed (the speed at which you will cover the most ground in a power-off glide from a given altitude) all increase with increases in load factor.

So why does increased load factor require increased airspeed for increased lift? Remember how a wing produces lift, to overcome weight? It needs to be moving forward, and it needs an angle of attack. If our wing is loaded more, we can try to get more lift by increasing A of A, but that will also slow the wing down, which will start to reduce the lift. Reducing the A of A yields more airspeed, which actually works better, generally speaking. This is why best rate of climb speed with powered airplanes (Vy) is actually higher (lower A of A) than best angle of climb speed (Vx). Speed increases lift more efficiently than A of A... with most aircraft, increases in A of A are more desirable when speed must be reduced... when low airspeed takes priority over high lift.


Now we just need to understand that gross weight affects an aircraft the same way load factor does!  Changes in weight have the same effect as changes in load factor. Makes sense, right?

Now make a note of this, this is important:
The result of the effect of increased load on the wings also means that to achieve a higher airspeed, you will not need as low an A of A. Think of an accelerated stall: Vs will come at a higher airspeed, right? Because A of A is the key to airspeed, assuming no change in thrust, the pitch angle will be less than when you stall with the wings level, right? It is for this reason that higher weight allows you to glide faster without gliding more steeply. Weight makes a difference.


Power pilots may recall seeing a graph in an airplane POH that shows glide distances at Vbg (best glide speed) from various altitudes... look at it again, and you will probably see a notation that indicates that Vbg will only yield these results at max gross weight. What's implied there, indirectly, is that different weights require different airspeeds in order to achieve the same glide ratio.

Here's a big-picture view, if the discussion of A of A and load factor isn't making it clear...

We'll use a glider as an example, so we can forget about power,prop drag, etc. Let's also assume the air is perfectly still, because wind changes distance (along the ground). It's a 2-seater, with a broad CG range to match.

  The glide ratio, which is determined in the design by the ratio of lift to drag, is 20:1.  That means that from 1000 feet AGL, we can glide 20,000 feet horizontally. But this is true only if we have the correct glide angle... Picture altitude and distance as two legs of a triangle, and you will see a third side, which is the glide path. The angle between alt. and distance is 90 degrees, always. If the lenghts of those two sides are constant in their relation to one another (20 to 1 in this case), the glide angle must also be constant...no matter what. Remember: still air, no thrust. It has to be a constant glide at a constant angle.

We have a certain distance to cover (20,000 feet), and only so much altitude to do it (1,000 feet).We know that while this happens, some period of time will elapse.
If the weight of the plane changes, something in the equation has to give, but it can't be the altitude or the distance, because those parameters are fixed for our "mission". So is the glide angle. I mentioned the effect of load on lift, but forget that for a minute, and consider it more abstractly. Something has to change, but not the altitude or distance... hmmmm...

What's left to change?
The time!!!

If our weight increases, our time must decrease. We must go faster, or we will not cover the distance with the altitude available. If we go at the same speed as we did when lighter, we will sink faster (load factor affecting lift/drag), which means the angle will change, which means the distance gets shorter. So again: if weight changes, something else must change,because the wing is loaded more, affecting lift... and time is the only factor we can change. So we need to change our airspeed. And the only way to do that, assuming a power-off glide, is... decreasing A of A.
 

You're in the 2-seat  glider, solo, at 1,000 feet AGL. The touchdown point is 20,000 feet away. You know your glider will sink the least amount per horizontal distance (not time) at 62 mph at this weight, so you have trimmed for 62 indicated. Works like a charm, and you touch down at the 20,000 foot mark.

Then someone climbs into the back seat. CG will of course change slightly, but that's not important... it's the weight that matters. On your next approach, from the same altitude and distance, if you trim for 62 mph you will come up short! To maintain the same ratio of lift to drag, you need a lower angle of attack, mostly because of the increase in load factor on the wing. Lower A of A means... class? Yes, it means higher airspeed. With two aboard, the glider yields 20: 1 at more like 65 mph IAS. You fly the same path: same distance over the ground, from the same altitude, at the same angle  but you take less time doing it. It's true that to get that higher airspeed, you may need a slightly lower A of A, but not enough to spoil the glide angle, and not nearly as much as you would without the added weight (which would definitely spoil the angle)!

But now you're probably wondering about the vertical speed... yes, it increases, but so does your forward speed. Remember, we can change the "time" part of the equation, to our benefit.

Note that with gliders, you have "best L/D" speed, which is basically Vbg, then you have the lower "minimum-sink" speed (used in lifting air), which keeps you up longer, but steepens the glide, shortening your glide distance (which is irrelevant when circling in thermals or riding ridge or wave lift). The same is true of powered planes, but power pilots don't usually have much use for minimum-sink, even if the engine quits.  Like a power pilot with a busted engine who wants to have the widest possible radius to find a landing spot, our goal in this glider exercise is to find the appropriate L/D speed,so as to get a given horizontal distance for altitude lost, not to stay aloft for the longest period of time. So increasing vertical speed is not necessarily bad, if you are also moving forward more rapidly.

But of course there's a "sweet spot", pitch-wise, for every V-speed, including Vbg...  it's somewhere between mushing and diving, but that sweet spot changes with weight,
because the speeds change with weight.

If none of that is convincing, consider this:

High-performance gliders used for glider racing often have water-ballast tanks. They start off with the tanks full, and actually use the increased weight to increase their airspeed without increasing their glide angle.  They have to go faster, because of the increased weight (and load factor), otherwise their glide ratio will suffer. So at a higher weight, they can actually sink the same amount relative to the distance covered, yet still cover ground faster. The point of doing this is to  get the best time between waypoints  without sacrificing precious altitude (per mile).  To get the same airspeeds without the weight of the ballast, they'd have to pitch down much more ('cuz the wing is loaded differently), which would steepen the glide angle.

This is another way of looking at the weight/speed thing... but it illustrates it clearly, right?  We have seen that if we are loaded closer to max gross weight, we have to fly faster to cover a given distance from a given altitude, at the resulting angle.
So, for racing, if we want to decrease the time, we must increase the weight.... because merely pitching down for speed will only steepen the glide angle, which means less ground covered.  If everything I said above were not true, this wouldn't work for the racers. But it does, and quite effectively.

The ballast gets dumped upon entering the pattern- airspeed can now be reduced without compromising lift/drag, allowing tighter maneuvering (lower airspeeds mean smaller turn radii at a given bank angle) and more time to set up the approach.

It also means less energy when you touch down.... for gliders as well as airliners, the main problem, with landing heavy  (aside from dynamic loads exerted on landing gear, etc.) is not that you will land long, but that you will be moving faster when you touch down (remember, even Vso is higher at higher weights!), requiring more effort- and possibly more room-to stop rolling.

To Professor Insomniac:    

You did an excellent job of helping visualize it.. And as a compulsive number-cruncher, and graph addict; I like it when indisputable physics defy intuition.

However.. here's my problem with it all..

-Our mission is to move a load across the ground, because altitude is a constant.

-Our only source of energy is gravity, (stored in the form of altitude).. and it's vector is a constant.

-We accomplish the mission by making the most of the stored energy.


How can we increase our workload, and accomplish the same mission.. when our only source of energy is carved in stone ? Intuitively, that's as goofy as saying that a lightly loaded airplane can't reach a higher altitude over a set distance, than a heavily loaded airplane 


Let's say you can have a computer control pitch (maintaining BG) as you keep re-flying the scenario, adding a pound every flight. There is a weight where aerodynamics matter not, and the air plane simply won't fly.. and of course well before reaching that weight, you'd be over the airplane's rated, max weight.

SOOOO.. as we keep re-flying the scenario, and the computer pilot keeps reaching the same touch-down point with every added pound, we'd all agree that there's a weight where the distance to that touch-down point starts gradually decreasing. I mean surely we can't expect that at XXX pounds it reaches the touch-down point, and at XXX+1 pounds it falls out of the sky. There's a "curve" to it; even well past max weight.

I suggest that there's a "curve" in the, touch-down-point vs weight graph, even if we stay under the max load.



Psssst:  Va increases with weight

Brett_Henderson wrote on Jan 15^th, 2010 at 8:02am:


Opps; better fix that. Sometimes Prof. Insomniac thinks he's still alert, but he is not.


I'll get back to you on the other stuff (about how weight affects climb performance)... need time to figure out how to describe it.

machineman9 wrote on Jan 15^th, 2010 at 11:58am:



You're forgetting that we can change how the wing deals with gravity, by changing the A of A. The wing does not fight gravity by creating drag, like an old-fashioned round parachute, it does it by moving the air a certain way. That way is variable, thanks to the elevator.

  If the pilot of the heavier glider cannot change A of A and thus airspeed, yes, he will not cover the same distance from the same altitude. His A of a will be too high, to the point where the lift gained by more A of A will not overcome the lift lost by the lower airspeed (remember, speed and angle work together to produce lift). Pitching up more will just make things worse, just as they do if you try to maintain a climb with pitch only in any aircraft. So he has to lower the nose- just a little- to pick up a little more speed. The vertical speed will increase, but it will go farther in the time it takes to run out of altitude, because it is moving forward faster, too.


On the other hand, let's say the competition is to stay aloft the longest period of time, in still air (no lifting air of any kind). This is completely different from trying to achieve a given distance from a given altitude!! Best-glide speed is not the same as minimum sink speed!!
As long as the heavier glider can adjust its airspeed (by changing a of A), it can maintain the same vertical speed as the lighter glider, and stay up just as long.

Keep adding weight to it, and yes, eventually the wing won't lift so well regardless of A of A, but with a 2-seater, designed so that the same rate of vertical speed can be achieved with one or two people aboard, if the weight is within limits, the same endurance can be achieved... IF the airspeed is changed. The heavy glider, gliding at a higher indicated airspeed, will not necessarily be sinking faster, IF that indicated airspeed is yielding "minimum sink".  Minimum sink is achieved by assigning a specific A of A, and thus airspeed, to the wing... it is a V-speed. And V-speeds change with load factor, including load increased because of a higher payload.

Suppose that you, say, have both engines wrecked at the top of the climb by features like ash, vultures or overheating the engines... and find yourself at 40 000 feet with no prospect of relighting and 170 tons of fuel with absolutely no use except to power the postcrash fire.

When and where would you rather dump it?

L/D depends only slightly on weight.

If it did not depend on weight at all then the distance you could glide would be independent on the weight. Jets at cruise altitude are decent gliders... Azores Glider covered 140 km, so if the engines had failed for other reasons, and the tanks had been full, the same distance would have been covered, only faster.

But it does depend on weight.

For one, Mach number depends on true air speed. If the best glide speed for a fully loaded, 340 t airplane at altitude were, say, 0,84 M then after dumping the fuel, at 170 t empty weight, the best glide would turn out to be just 0,6 M.

Actually, lowering M improves L/D, at least in subsonic range (Not sure how to pick best glide speed and weight at the range 1...1,5 M. If you have 90 tons of fuel you do not want powering post-crash fire, would you start dumping right away at FL600 and M2,0, or after you have successfully gone to FL300 and M0,9, or at the end of the trip below FL100?).

Now, how about Reynolds number? At small Mach numbers, how does decreasing the weight and thus TAS affect L/D?

I'll have to ask him next week when I have his Human Factors class again... I'm sure he knows a bit more than he leads on to. The whole reason why it came up though was because he said he suspects that's what happened to that plane that went down last year in Buffalo, where they couldn't recover. He did however say that it's rare, the conditions have to be right, and it's hard to tell, because he did say the nose dips, so it could look like just a normal stall, in either case, it's kind of a scary thing, and I really have no idea what else could be done to recover other than that pulling back on the stick, which does make sense somewhat now. I have a feeling though he's not going to say much else about it, there might be a few others that I could ask about it though.

chornedsnorkack wrote on Jan 15^th, 2010 at 4:33pm:


I need to look up "Reynolds number", LOL, but my "horseback guesstimate" is that TAS, like any airspeed, will have to increase with weight to yield the desired L/D (not the L/D speed, but the actual lift-to-drag ratio). Look at it this way: weight, like load factor, has to be considered, even though they don't call it "L/D/W".  I know odd things happen in the transsonic zone, but I'll wager my two cents that the same rule about weight applies in that case.

I kind of have a sneaking suspicion that those two climbing planes would make it relatively closer to the same time. My reasoning is that, while both airplanes will have to increase their airspeed as height increases to maintain the rate of climb they want (assuming they're both climbing at the same rate), then the heavier airplane will have to be traveling at a faster velocity than the lighter one, simply because of drag I think. I think it's very possible to get the two planes at point B at the same time.

Reynolds number on the other hand has more to do with airflow, and can be used to find where the transition point between laminar and turbulent airflow over a wing.  I can't really make some of these symbols... so bare with me... Reynolds number can be expressed as Re= (VL)/v, where V is the velocity in ft/s, L is the exposed m.a.c., and v is the kinematic viscosity, which I had to pull that one off of wikipediahttp://en.wikipedia.org/wiki/Reynolds_number#Transition_Reynolds_number... it's not even listed in my own notes. The higher V is, the higher the Reynold's number. V is comprised of two variables, Mach number, and the speed of sound "a". Both variables can change, so if you're mach number is higher, and "a" has remained constant, than you're Reynolds number will be higher, meaning you will have more turbulent flow over the wings than laminar flow, which means more drag. How's that for a whole lot of late night information just being thrown into the wing... haha, anyhow, for the dumping of the fuel, there's probably a checklist to follow that would include when an appropriate time for that would be. If it were me, McGyvering my way through such a scenario, I would probably dump it sooner than later, just to give me more time to set up, and less stuff to worry about later. I mean, if you dump it after giving up hope on the engines, than you'll have time to set up the attitude you want (because it will change), and it's one less thing to worry about later on. Now that could be the wrong thing to do, I certainly don't know, I mean, traveling at such a quick speed brings so many different variables like possibly compressible flow which depends how fast you really are traveling and all sorts of drag. Kind of makes sense to me to get light as quick as possible to shed the drag, but again, I don't know, I've never traveled anywhere near as fast, or as high, as the speeds and altitudes. Also, please correct me if I made any mistakes in attempting to explain Reynolds number, not that I need this information for the slow flying in small planes that I do, but it never hurts to store some of this stuff away in the back of the brain.

beaky wrote on Jan 15^th, 2010 at 7:31pm:


You have it right rotty.  The tailplane is essentially an upside down wing.  Think about how you correct a stall for the wing, you pitch down to reduce AOA.  On the tail, by pulling back you raise the elevators, which reduces the AOA, and hopefully gets the tail flying.  This may have been one of the factors in the Buffalo crash last year.  The crew failed to recognize a tail stall, and did not take the appropriate action.  A tail stall and normal stall will seem similar, the aircraft seems to quit flying and pitches down.  Unfortunately the correct action for each stall is reverse.

beaky wrote on Jan 16^th, 2010 at 1:34pm:



I think the same would apply.

An  "A-to-B" glide (where the effective hypotenuse is the same), is different than an  "A-to-B" climb.

We all agree (grudgingly) that identical airplanes of different (reasonable) loads can execute the same glide hypotenuse... because a glide counts on the long-since stored energy of the weight already AT altitude. More weight.. more stored energy.

And of course there's no argument that a heavily loaded airplane cannot climb the same hypotenuse as an identical, lighter loaded airplane... because the heavier load does not bring its own, extra energy along for the climb.

A quick glance at a C172 takeoff chart shows a 35% higher FPM climb-rate at  Vy  for a 1700lb airplane, compared to a 2300lb airplane.

This applies to any altitude increase.. (doesn't it ?) 

Quote:


That's moot, in our discussion.. we're assuming a full power-climb, so the heavier airplane doesn't have the luxury that the heavier "glider" has (available energy that varies by load).

You might be able to get to point B at  Vx, but that throws another variable in there. At Vy, the heavier airplane will have to fly a big "S" (lengthening the hypotenuse) to reach  B  without having to bouble back (an that introduces the lost lift during the turns..   )

Yeah.. my head hurts too..

beaky wrote on Jan 16^th, 2010 at 7:31pm:
Been reading along - nodded off a couple of times and my head, teeth and butt hurt.  Still think my avatar says it all about flying  .