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markbusby
16th Nov 2003, 03:37
Could you please tell me how to calculate climb/cruise/landing according to weight of aircraft. I have completed two successful cycles calculating weight and cost per kg/passenger but for the third cycle of my mathematics assignment, I need to advance to a more realistic approach. Is there a rule of thumb for calculating how long an aircraft (I am using a boeing 737-300) will take to get to cruise height and back down for landing according to weight? I hope to be able to transfer the calculations to a graphical format to show variation.

Cheers for your time in helping me,

Mark

E1453
16th Nov 2003, 10:16
I have the 737-300 operation manual, volume 3 - flight planning, descent

I have two tables, one for a mach.74/250kts descent and one for a M.70/280/250kts descent, both based on flight idle thrust with allowances for a straight-in approach included.

M74/250kts (LDGweight=55000KG):

press alt time(min) fuel distance (NM)

37000 23 300 111
35000 23 295 106
33000 22 290 100
31000 21 285 94

The tables don't show any time change with the variation of weight. I'm sure there is, but the manual focuses more on the distance and fuel.

as we change the weight, the distance for descent increases.

ex: 37000ft, 23 min, with 35000kg, dist = 100nm
the same with 45000kg, dist = 111nm
the same with 55000kg, dist = 116nm

I don't understand why the descent distance is greater with larger weights. It should be the same, I thought.

mutt
16th Nov 2003, 12:01
don't understand why the descent distance is greater with larger weights. It should be the same, I thought.
Nope it shouldnt as the angle of attack is different for differing weights.

Mutt.

E1453
16th Nov 2003, 21:03
I read in all books in my life that the gliding path don't changes with weight, just time rate of descent, the speed and the time.

With increased weight, the speed should be increased to keep the angle of attack at optimum. This would increase the rate of descent, the speed, reduce time and mantain the distance.

The 737-300's manual states that the distance to descent increases with weight, althought the descent speed is the same with all weights. That just don't fit in my head.

If you mantain the same speed and increase weight, the angle of attack will increase, the drag will be higher and the distance should be shorter.

The only explanation I can imagine is that the increased weight increases the distance required to reduce speed at 10,000ft and on approach.

Wizofoz
16th Nov 2003, 21:24
E1453,

That is exactley the point. IF you varied the speed to maintain a particular angle of attack (for example, that for max L/D) with changes in weight, your descent angle (and therefore distance) would remain the same.

We don't, however, routinley descend jet aeroplanes at optimum speed (and therefore optimum AOA) for the simple reasons of wishing to get there asap, and are usually restricted to 250kts below FL100. Distance therfore varies with weight AT A PARTICULAR DESCENT SPEED.

Why does it increase with increased weight? Think of it this way. You get the longest glide from flying max L/D, which will be a constant AOA. The speed to achieve this INCREASES with INCREASED weight. If we descend at a higher speed (which is almost always the case) we descend at a steeper angle.

If our aircraft is light, MAX L/D might be at 180 kts. If we descend at 280kts, we are flying 100kts above max L/D, and therefore descending much more steeply. If our aircraft is heavy, max L/D might be at 220kts. Our 280kt descent is now only 60kts over max L/D, and therefore shallower than in the case of the lighter aircraft.

Rember the oposite will be true at slower speeds. Fly the light aircraft at 180kts (Right on max L/D) and she'll glide forever. Fly the heavy one at 180kts (40 kts BELOW max L/D) and it'll drop like a rock.

Hope this helps.

E1453
16th Nov 2003, 23:44
I got it.

I think you're correct, Wizofoz. But we have to suppose the descent speeds in the manual's tables are made for higher weights.

If the speeds in the tables are for greater weights, so off course the glide distance will be larger for increased weights.

But, doesn't the FMS calculate the best descent speed for a give weight? And for ECON descent, it calculates the best speed for a given fuel versus time cost, right?

Thank's!

Wizofoz
17th Nov 2003, 00:20
Econ speeds for climb cruise and descent vary according to cost index, which (if it has been calculated correctly!) is hourly aircraft cost divided by fuel cost. Thus, a low cost index indicates high fuel costs and the FMC gives a minimum consumption profile. High cost index gives max speed.

As fuel costs vary from port to port, the most efficient procedure would be to calculate a cost index for each leg. In practice, most operators come up with an averaged number, which they review from time to time.

mutt
17th Nov 2003, 02:36
And for ECON descent, it calculates the best speed for a given fuel versus time cost, right? Garbage in garbage out..... how many airlines actually use an acurate cost index based on the specific route?

Mutt.

E1453
17th Nov 2003, 03:50
I have a concern on cost index:

the cost index calculation must consider the fuel costs and the time costs, right?

The time costs are, among many, crew and maintenance, as engines overhauls etc.

But how to calculate the cost of an overhaul that will happen many months ahead? I say this because I don't live in US, and my currency is not fixed to the dollar. The parts costs are fixed in dollars, because they are imported from US or EU, so the exact cost of an overhaul is unpredictable.

If the brazilian currency, the REAL, fluctuates, the schedule maintenance costs will change, in a manner I can't predict. So, in my case, Cost Index is bull****.

Wizofoz
17th Nov 2003, 05:11
I did work for an outfit that had a program on the crew room computer to calculate cost index for each sector. After a laborious process you came up with a number that only ever varied by two or three in any case.

I think it will always be an approximation at best, it gets thrown out the window quite often (schedule considerations, speed restrictions etc.) but I guess it nudges things in the right direction.

mutt
17th Nov 2003, 11:29
and my currency is not fixed to the dollarWe buy fuel in US\$, therefore the whole formula is based on US\$.

Mutt.

Bumblebee
18th Nov 2003, 08:52
just my tuppence worth... :)
With regard to greater weight resulting in greater distance for descent; please correct me if i'm wrong - would it be easier to explain it as a function of the total energy of the aircraft. With descent speed fixed, idle thrust, and from the same altitude in the same atmospheric conditions, the heavier the aeroplane is the more energy it has. Ergo, it will travel further. ?:8

E1453
19th Nov 2003, 07:05
When the weight is increased the total energy required to mantain the plane in the air is also increased: the angle of attack is larger and so is the drag coefficient.