Thrust required for approach
 

Nice question raised in another part of this forum

Quote: "On a 3 degree final descent what requires more thrust a heavy or light aircraft?"

Sorry, but can't figure out the correct answer.

Considering a power-off situation, both (light and heavy) aircraft flying at their respective speed giving optimum angle of attack get the same lift/drag ratio => same angle of descent

On cruise, if both aircraft fly with the same respective speed, I expect the heavier aircraft to need more thrust than the lighter one.

Correct?

Thus can we consider the 3° descent as an intermediate position between the cruise and the power-off situation?

But we should as well consider the fact that Vtgt (or Vref) isn't maybe exactly the same as the V for best glide...

Thanks for the help

In general if you have two identical aircraft except for the weight then yes the heavier one will need more power to maintain level flight. In general the same will apply when descending at a constant rate.

.. but that's only in general. You would have to test your particular plane. For example under some flight conditions some gliders have a lower sink rate when carrying ballast - it allows the wing section to operate on a more efficient part of the curve.

For simnplicity, assume the aircraft to be at 0 deg AoA when at Vref, for both the light and heavy cases. That allows us to have the thrust aligned with the direction of travel, which simplifies things a little bit.

Consider the forces acting both along and normal to the flight path.

Normal: We have the aircraft lift, plus a component of the weight (cos 3 degs * the weight, in fact)

Along: We have the drag, the thrust, and a component of gravity (sin 3 degs * the weight)

If we assume equilibrium, then:

Lift = W*cos3
Drag=T + W*sin3

In order to see the relationship between T and W for this case, we need to eliminate Lift and Drag. If we assume they are a fixed ratio k for all cases of W (which seems fair for a fixed AoA approach condition), then:

L/D=k
>
L = D * k
>
W*cos3 = ( T + W * sin3) * k
which, after further messing about, gives:

Thrust = Weight * ( (cos3 - ksin3) / k)

Therefore, as long as (cos3-ksin3) is positive, thrust will increase with increasing weight. If it changes sign, then thrust DECREASES with increasing weight.

So, the question is, what is the L/D for the approach case.

If (L/D) sin3 = cos 3 then we have the diciding case

i.e. L/D = 19 (approx) is the dividing case.

So, if your L/D is less than 19 (which seems a reasonable assumption) you should have increasing thrust with increasing weight for a 3 deg glideslope (for the other minor assumptions). But you will need less thrust than in level flight for both cases (of course)

Now, if you assume a rather steeper descent rate the case becomes of more general interest, since the L/D value for the swapover becomes lower (for 10 degrees, it's below 6)

Yeah, whatever......but I know if you are heavier, it takes more thrust on final approach.

..for the type you are familiar with, for your approach conditions.

If someone asks a generic question, they're entitled to a generic answer, and maybe a bit of the background, not just empiricism.

Otherwise you'd all be trying to fly by flapping your arms, since "thats how birds do it".

Not quite...

Those gliders -- just like any airplane -- have their optimum/best glide RATIO at a higher speed when at a higher weight. So, if the glider is attempting to conplete a long-distance course in the best time, it is an advantage to be able to fly the course at a higher speed without losing excess altitude. OTOH, it may be harder for that glider to climb in a small-diameter area of lift, because the higher speeds make it harder to stay within the small circle.

On approach, an airliner flys at a slower airspeed at a lighter weight, maintaining roughly the same angle of attack. The power required is therefore less at the lighter weight and slower airspeed.

Are you saying flapping my arms doesn't help my takeoff run?

hey, thanks for the answers.

I knew I needed more thrust beeing heavier (on my aircraft type), but wanted a general demonstration.

Thanks for it, Mad Scientist

I remember reading on a checklist for some airline that the PNF should flap their arms in the event of an engine failure after V1 .. hmm... :\

:)
 

In that company the PF could also flap his arms too. I do not think any PF in a company such this could save an aircraft in any case anyway :D

Hehe

Pilot Flapping? Never, most unflappable type myself... :suspect:

Power curve
 

In which part of the power curve is the Vref normally found? It is supposed to be 1,3 times the stalling speed plus a safety margin for gusts. The minimum power/sink rate speed and the maximum glide ratio speed are somewhat higher than the stall speed... so which side of them should Vref be found?

Nice analysis Mad Scientist. Interestingly for the 747...

"The maximum lift-drag ratio of the aircraft, (L/D)max, is estimated to be about 18, as compared with a value somewhat over 19 for the 707,

..but of course that's in a clean config. On approach you need to fly slower than optimium and that means all the twiddly bits hanging out in the breeze. The LD will be a lot less than 18. I couldn't immediatly find that figure on the web.