Top of Descent Versus Gross Weight
 

I fly the 737 NG series.
Recently my captain showed me something which completely foxed me and forced me to come here and share my qaundry with you folks.
My captains theory was that taking the same set of conditions for two aircraft, a heavier one will start its descent earlier!!:confused:
We checked this on the FMC and a difference of 10 tonnes to the ZFW on the Perf init caused to ToD to shift approximately 30 miles out!!!
Could somebody please explain how this works!:O
Regards,
A

Of course it descends earlier! For a given IAS a light-weighing aircraft will fall out of the sky. Reverse for heavier wieghts.

Compare now to a case of a given AoA for descent. The clue is in the green dot speed which varys with GW ( or in nonglass-speak "best lift/drag speed clean" ).

Muse over those 2 lines above while dusting off your Student Pilot theory book and the penny'll drop (without a FMC box!) ;)

Hi airborne

You are puzzled because typically the test questions are about airplanes gliding at best gliding speed (best gliding AoA, actually). In that case, weight makes no difference in gliding distance, only in gliding time (heavier, faster).

However, as said in the previous post, when two airplanes are gliding at a given airspeed, say 300 kt, the heavier glides more miles. Why? Because the heavier one is gliding at a more efficient angle of attack.

Gliding distance is proportional to the Lift-Drag ratio. The mor L/D, the more distance. Lift-Drag ratio is equal to Lift Coefficient-Drag Coefficient ratio. These depend solely on the angle of attack (well, mach number also has an influence...). Remember how weight, AoA and speed are related and you will see that heavier at constant speed means less AoA, and therefore (in the stable speed region, of course) more L/D.

I hope it helps.

The same reason gliders load up with water to go cross country.

Is it always so?
 

I thought I knew the answer to this but you two guys really got me confused.

Considering that two identical airplanes can glide the same distance regardless of different weight, but at different speeds, I understand there must be (lower) speeds at which a lighter airplane will glide further if both glide at the same speed.

What am I missing? Thanks in advance! :ok:

All true,

HOWEVER a consequence of just that is that if you fly the lighter aircraft at its best L/D speed, and fly the heavier aircraft at that same speed, the HEAVIER aircraft will now descend more steeply.

Surely, the simplest way of explaining it is to say that the heavier aircraft has more Kinetic Energy (1/2mv²), which will carry it further before it reaches the ground ... ?

Similarly, a heavier aircraft will take longer for a given speed reduction than a lighter one ...


JD
:)

Jumbo,

No, nothing to do with it. As I said, fly the light aircraft at best L/D, and the heavier one at that speed, and the heavier aircraft will descend more steeply. Fly them BOTH at best L/D and glide distance will be identical.

It's a little complicated by the fact that they are NOT gliding, and the residual thrust will have a greater effect on the lighter aircraft than the heavier one, but the principle is as outlined

The heavier one may have more energy to dissipate, but it will also produce more drag, so it kinda evens out.

35hrPa28,

Our answers crossed, but yes, you are right. HOWEVER the usual descent speed for jets are well in excess of their best L/D speeds, so in any usual situation, the heavier aircraft will glide further.

This got me a little confused at first because I was thinking that a heavier aircraft at the same IAS would require a greater value of Cl ie greater angle of attack, more drag. But I guess if normal descent speeds are above best L/D speed, then this would make sense as the drag curve shifts to the right with increasing weight. Does this mean that if the normal speed for descent was the best L/D speed, that a heavier aircraft would glide less distance for the same IAS?

Wiz,

I must admit that I though Jumbo's idea was closer except the heavier aircraft possesses more POTENTIAL energy (ht above ground x mass) which is then converted during the descent as Jumbo says into Kinetic energy via 1/2mV2, and therefore has more energy to glide further. I can see that the polar diagram for LD changes with mass but I would have thought that the energy the aircraft possesses at the start of descent will be the bigger influence.

I am standing to be corrected!

TOD

QJB,

Not quite sure what you mean.

If Best L/D were the usual descent speed, a heavier aircraft would descend at a higher speed than a lighter one.

I guess the best way to put it is this- Best L/D speed increases as a function of weight. Fly faster OR slower than best L/D, and you will not glide as far.

I would think that a descent with an FMC cost index of zero would have the aircraft descending at very near best L/D, perhaps modified slightly for residual thrust. Would anyone like to clarify that?

Normal descent speeds are 290-310 KIAS. I don't know of any current transport airplane (get rid of Concorde and SR-71) whose L/Dmax is at 300 KIAS at landing weight. Therefore, a lighter airplane descending at 300 KIAS will not go as far as the heavier airplane, because the heavier one is closer to L/Dmax.

it has to do with the momentum folks..if they start their desent at the same point the heavier aircraft has the chance to overspeed to keep up the profile.. that not being allowed makes it start descent ealier.:ok:

isn,t it simply L/D?
 

Assume still air, ISA, M0.78 and FL360. Aircraft a) = 60000kgf; b) = 50000kgf. The L/D for a) is 16.98 and for b) is 15.84 so that all things being equal aircraft a) has the advantage of cleaving through the air more efficiently at ToD and therefore must commence its descent earlier. QED?

At the same speed, a lighter aircraft must descend more steeply so that the reduced weight vector provides enough effective thrust to counter the effectively-constant drag:

http://i521.photobucket.com/albums/w...descending.jpg

Recall reading that an emergency descent in a light weight 747 is something to behold, very steep nose down attitude. Similar principles at play.

How many posts!

It is all about L/D ratio. Of course we can look at it from the point of view of Energy or Momentum if we take into account all the factors.
However, the L/D is the best explanation.

1-The gliding ratio is equal to the L/D ratio (By geometry)
2-The L/D ratio is equal to de CL/CD ratio (Dividing L formula by D formula)
3-Both CL and CD depend on the AoA alone (and Mach Number, ok...)
3-For a constant IAS and straight flight path, the heavier the airplane, the greater the angle of attack (From Lift formula)
4-flying in the stable speed region (AoAs above best finesse) the heavier has a more efficient AoA. (see any CL/CD versus AoA graph)
5-Therefore, the heavier airplane has a better L/D. It glides more miles for altitude.

If the descent speed was very very low so that the heavier was flying in the reverse command region, wich would be nonsense, it would glide less than the lighter one, because it would have a less efficient AoA.

You got to look at the wing airfoil to understand this.

Modern commercial transports use laminar flow airfoils which
utilize a drag polar 'bucket'. Where you are in the bucket
depends directly on your AoA. As the planes burn fuel during
cruise, step climbs into thinner air are performed to maintain
that optimal lowest-drag AoA.

Since these airplanes are designed for efficient cruise at higher weights
and high altitudes, when they get light and low, the AoA is too
shallow to keep the wing inside the low Cd area and drag actually increases.

The lighter the plane, the shallower the AoA at a given altitude.
-> the higher the drag from the wing.

So, at the same speed, the light plane will have more drag than
the heavy one and needs to do a steeper descend to maintain airspeed.

XPM

XP,

It is exactley the same for DC3, C172, Tiger moths and gliders- nothing to do with modern aerofoils.

mansah- nothing to do with momentum either.

I didnt say that, but since you brought it up, modern airliners use
supercritical airfoils which usually have a "flatter" bottom drag bucket.
They also have a higher L/D ratio for the same Cl than conventional "old" airfoils
so I wouldn't say "exactley the same".. .

XPM