Glide Distance

[Bally Heck]

Brain the size of a planet.....but I can't work this one out.

Two identical aircraft under identical flight conditions.

One is heavier than the other.

Engines stop.

Which one will glide the greatest distance?

[Chimbu chuckles]

If the two identical aeroplanes are flown at a speed/AoA corresponding to L/Dmax then there gliding performance will be the same. The heavier aircraft would need to be flown at a higher IAS to achieve L/Dmax but would glide the same distance....it would just get there quicker. :D

Chuck.

[bookworm]

The "first order" answer is that the aircraft have the same lift and drag coefficients at optimum AOA, and therefore glide at the same distance/height ratio, but at different speeds.

The "second order" answer is that the heavier aircraft glides slightly faster -- it therefore has a higher Reynolds number and a lower skin friction drag coefficient. So it goes marginally further.

[Checkboard]

...and the lighter aircraft can make better advantage from any lift experienced along the way, and (as it can stay in the air longer) can take better advantage of any tailwind, while the heavier aircraft can minimise the losses experienced from any headwind.

[Chimbu chuckles]

Checkboard....under identical flight conditions. I would have thought as both aircraft are experiencing identical conditions then the result would still be the same.

Chuck.

[ 18 July 2001: Message edited by: Chimbu chuckles ]

[ 18 July 2001: Message edited by: Chimbu chuckles ]

[18-Wheeler]

FWIW, on the 747 when you're heavy on the drop, eg, ~275 tonnes, you have to add a few miles to the top of descent compared to when you're light, say, 200 tonnes.
That's at the same M 0.85/290kias/250kias schedule.

[Prof2MDA]

The reason your 747 (or any other aircraft in this scenario) is coming down at a steeper angle at the lighter weights is a bit of a different issue than this thread. To put it simply, you are descending on a constant speed schedule that is not adjusted for weight. However, your IAS/Mach for L/Dmax _does_ vary with weight. The typical transport descent schedule speeds are well over the L/Dmax for any weight. So, at the heavier weights the corrosponding higher L/Dmax for that weight happens to be closer to your actual speed, which nets more glidepath.

Can also do this with vectors, but then I'd have to somehow draw pictures here.

[BEagle]

This is a classic - and the answer depends upon the constant used. At the optimum AoA - that is at the AoA which corresponds to (Cl/Cd)max - weight has no effect if you discount the 'glider' factors of atmospheric motion or the effects of compressibility at high IAS.

Whereas the situation is totally different if the aircraft uses a 'standard descent schedule' - then, only one weight (or rather 'mass') value corresponds to the optimum AoA - any deviation from this would reduce glide range.

If you want to design an efficient people mover, arrange for it to have an optimum (Cl/Cd)max AoA when descending on its optimum descent schedule at max ZFW and min certificated landing fuel mass.

[18-Wheeler]

True enough, but I think I'm still at least partly answering the original question, albeit indirectly.
If the 747 is heavy, then we can go further on the drop if we want. ;)
I've often been light and had to add power to stay on profile, where it wouldn't have been a problem with another ten or twenty tonnes to help.

[Prof2MDA]

18-

I'd disagree that you are answering the question at hand at all. I think you're just confusing the issue by bringing in this scenario.

As has been pointed out, the heavier airplane will go farther than a light one, if both are operated at the L/Dmax AoA. This is what you are alluding to, I presume? However, in actual fact, the difference in the glide distance due to the change in Reynolds number (and associated drag reduction) is likely going to be so small that it would be nearly impossible to measure, let alone for you to see in an operational environment. I stick to the reasons I gave previously for your observations!

[henry crun]

Many modern sailplanes (gliders) carry water ballast when lift conditions are strong so that they can fly faster between areas of lift and thus go more quickly between A and B, but the glide ratio ballasted or unballasted remains essentially the same. Surely if a powered aircraft loses its power it becomes a glider so is the situation being discussed here any different to the glider analogy

[BEagle]

To summarise:

Descending at same (Cl/Cd)max AoA at whatever speed is required to achieve it: No difference with change of mass.

Descending at a standard descent schedule (e.g. M.82/290KIAS/250KIAS): Lighter ac descends at a steeper rate as it is no longer operating close to (Cl/Cd)max value of AoA.

[ 19 July 2001: Message edited by: BEagle ]

[bookworm]

However, in actual fact, the difference in the glide distance due to the change in Reynolds number (and associated drag reduction) is likely going to be so small that it would be nearly impossible to measure, let alone for you to see in an operational environment.

One might think so, but I'm not sure that's the case. Skin friction drag coeffients vary as Re^(-1/2) for a laminar boundary layer and Re^(-1/5) for a turbulent one.

A 20% increase in weight gives a 10% increase in best glide speed, and therefore in Re. So that's a 2 to 5% reduction in skin friction drag, or a 1 to 2.5% reduction in total drag.

Compare that to simply getting the glide speed wrong. All else equal, a 10% pilot deviation from best glide speed (i.e. the speed that puts you at the minimum of the drag curve) causes only a 2% increase in total drag. I think that the continual whining of my old instructor to "nail the glide speed" suggests that 2% is important.

[ 19 July 2001: Message edited by: bookworm ]

[Prof2MDA]

Book,

I am pretty sure you're missing something here, but don't have time at this moment to sort it out. However, I will point you to Flightwise, Volume 1, page 210:

"In fact, we do not usually relate the idea of a critical Reynolds number to aerofoils at all. In practice, to a fairly good approximation, the behaviour of most aerofoils at "flight Reynolds numbers', which of course range over a fairly large numerical range, is fairly consistent with no funny jumps or sudden changes. This is extremely convenient because it means that, as far as aeroplanes (but not models) are concerned, the coefficients of lift and drag may be regarded as totally independent of Reynolds number, and only dependent on aerofoil shape and orientation. Pilot, then, never need to be concerned with Reynolds numbers, since the changes involved have insignificant effects."

Sorry for any typos, but am thinking that while the drag due to skin friction may be less with the higher RN, the total drag does NOT decrease as you increase speed! This would match the graphs I have seen!

[safety_worker]

PROF2 - has got the answer to the querry in the first post.
Anything else needs a new thread? :rolleyes:

[bookworm]

I am pretty sure you're missing something here, but don't have time at this moment to sort it out. However, I will point you to Flightwise, Volume 1, page 210:...

I wouldn't necessarily disagree with the flavour of Carpenter's conclusion. After all, if skin friction Cf varies as Re^(-1/5), that simply means that skin friction drag actually varies as v^1.8 rather than v^2. Using a constant Cf is probably good enough for government (or Airbus, or Boeing :)) work.

Anderson derives the skin friction drag coefficient for laminar flow and quotes the result for turbulent flow in Chapter 17 of 'Fundamentals of Aerodynamics', so all I can do is point you to that if you're not convinced.

Abbott and von Doenhoff also derive the turbulent case in chapter 4 of 'Theory of Wing Sections'. They reconcile the results with experiment which demonstrate a slightly (but not substantially) weaker dependence on Re.

[Jetlagged]

Uh, Check out A.C. Kermodes book "Mechanics of Flight" Chapter 6 Pg 188.

It's nothing but the truth.....