Expert: Paul Soderman - 7/4/2009

Question
QUESTION: Hi Paul

Can you estimate how much lift is expected to increase in a small aircraft
flying at level flight and constant speed with constant wind resistance, if wing
loading would decrease with 10 - 15 % during flight, all other factors
remaining unchanged. I am looking only for a rough estimation. Also how
much longer is the airplane expected to glide with such an increase in lift?
Thanx a lot :)

ANSWER: You haven't told me how you are changing wing loading.  I can think of three ways to do it.

1.  Reduce weight 10% by dropping a bomb or something.  The lift would be almost unchanged so the aircraft would climb.  The pilot would then reduce angle of attack or airspeed to regain level flight and the new lift would be 10% lower than the previous lift.

2.  Reduce wing area somehow.  The aircraft would sink, so the pilot would increase angle of attack or airspeed until level flight was obtained with the same lift as before.

3.  Retract the flaps to reduce wing camber.  The aircraft would sink again and so on.

Perhaps you are really asking about glide rate and not keeping level flight.  For that situation we need to know the lift-to-drag ratio (L/D), which depends on which of the above scenarios you choose.  The glide distance S is then:

S = h L/D  where h is the altitude at start of glide.  When you change wing loading you also affect lift and drag depending on how it is done.  Your question is somewhat ill-posed because you can't change wing loading and keep all the factors you list unchanged.
Paul

---------- FOLLOW-UP ----------

QUESTION: Paul! Sorry about mixing up terminology, Iam not an engineer :) So let me try to make this more clear. I have scenario 1. The aircraft's glide ratio is 9:1 prior to droping the weight. However I cannot estimate how the glide ratio will change after reducing the weight of the aircraft 10-15% during flight. Can u help? THANX !

ANSWER: Jim
This is an interesting problem. Because I know nothing of your airplane I had to make a number of assumptions.  I assumed that the glide speed and angle are constant so we deal with the forces shown here:

http://www.grc.nasa.gov/WWW/K-12/airplane/ldrat.html

The L/D ratio is then equal to the glide ratio d/h which is 9 for your initial condition.  I also assumed that the aircraft glides at max L/D for max glide range.  This corresponds to minimum drag and the induced drag and form drag are equal (see http://www.adl.gatech.edu/classes/dci/aerodesn/dci03aero.html). So the total drag is twice the induced drag. When the weight changes we just need to see how L/D changes.  For simplicity I assumed small glide angles so lift is approximately equal to weight.

When I do the calculations for a 10% weight reduction I find that the lift reduces 10% and that is accomplished by either a speed reduction or angle of attack reduction.  Take the speed reduction.  As the lift goes down, the drag goes down by the same amount because the dynamic pressure reduces.  Thus, L/D does not change.  A similar thing happens with angle of attack reduction.  Thus, to first order a small weight reduction does not change glide angle.  A large weight reduction is different, but 10%-15% is not large.  The way to increase glide range is to reduce drag by cleaning up the aircraft or increasing aspect ratio.  That is what gliders do.
Paul

---------- FOLLOW-UP ----------

QUESTION: Paul thanx for the detailed answer ! A lot of useful stuff !
Since you mentioned an interesting point that increasing aspect ratio can
reduce drag, is there a simple way of estimating if lets say we increase aspect
ratio by a certain amount "x" then it is expected that glide range will increase
by a certain amount "y" ?
Thanx a lot ! ! !

Answer
Yes.  The glide ratio is equal to L/D and equal to Cl/Cd, the ratio of lift coefficient to drag coefficient.  At max L/D the drag coefficient is inversely proportional to aspect ratio.  For a fixed lift coefficient, the glide ratio then is directly proportional to aspect ratio.  If you could magically double aspect ratio only, the glide ratio doubles.  However, when the drag reduces because of higher aspect ratio, the aircraft speed will increase and move away from max L/D.  To regain max L/D the aircraft must be trimmed to reduce speed and lift.  This will cause the glide ratio to increase even more. We would have to know the lift and drag characteristics of the aircraft to find the exact amount.  But there is the complication that increasing aspect ratio probably requires increasing aircraft wing area and weight, which also changes lift and drag and L/D.
Paul