Which of these is true for a glider flying with constant angle of attack?

I'm trying to answer the following question, but I'm not sure of which one is correct.

A glider is gliding with constant angle of attack along its path. We can assume the hypothesis of small angles. Under these conditions, the following has to be fulfilled:

a) None of the other answers is correct.

b) $C_L=C_{Lopt}$

c) $\hat{D} =$ constant

d) $\alpha=\alpha_{max}$

e) V must remain constant

Note: D with hat means dimensionless drag.

I've been trying to discard some of them but I'm still doubting about if the correct answer is (a) or (e). Can you help me guess which one is the right one?

• Can you discuss your reasoning on narrowing it down to (a) or (e)? – fooot Nov 4 '15 at 20:11
• is this a homework problem? doesn’t really make sense and seems light on context. – Peter Nov 4 '15 at 20:31
• I have discarded (d) because the fact that the angle is constant doesn't mean it has to be maximum. Also, I discarded (b) because the optimal lift coefficient is attained at a specific angle of attack, not at a constant given one. I also discarded (c) because the dimensionless drag depends on dimensionless speed and load factor, which do not need to be constant. So I have left, (e) and (a). I'm not sure if the fact of having a constant angle of attack makes a constant speed, and if this one's not correct, the only left is (a). And yes, this is a question from an old exam I am trying to solve. – user3780731 Nov 4 '15 at 20:34
• This is not a very good question because it is not clear whether the path is linear, or as one answer suggested, whether a "phugoid"-like motion might possibly be involved. If the former, the answer would have to be c and e. – quiet flyer Jul 9 '19 at 14:44

Two things are important here:

• It is about a glider, so no fuel is consumed, and the mass is constant over time.
• The angle of attack is constant. This means also that the lift and drag coefficients are constant.

If the mass and the lift coefficient are constant, and we assume a constant load factor (implied by the gliding along its path description), the dynamic pressure is also constant, and the airspeed changes with the square root of air density. Gliding implies that the altitude decreases, so the indicated speed will be constant, but the true speed will decrease. Unfortunately, the condition e) is not precise enough to make this distinction. e) could be correct or not, depending on the definition of V.

I would suggest that also c) could be a correct answer: If the angle of attack and the mass are constant, so should be the drag coefficient. However, gliding down also implies that the Reynolds number changes because true speed decreases and temperature increases over the glide. Strictly speaking, this would also mean a very slowly changing drag coefficient.

Answers b) and d) are false and I agree with your reasoning.

• Just a minor point, gliding does not have to imply a decrease of altitude, if you are gliding within a rising air mass (very common with gliders in fact ;-)) – Lnafziger Nov 4 '15 at 22:02
• @Lnafziger: Only in wave lift would the air be calm enough for the angle of attack to stay constant, but, yes, this is possible. All other forms of updrafts would cause AoA variations, so I was assuming flight in calm air. – Peter Kämpf Nov 4 '15 at 22:08
• Thank you very much! Your answer made me see the approach better. I agree with you that (c) is the most correct one! @PeterKämpf – user3780731 Nov 4 '15 at 22:18
• As this is a exam's question, assuming the glider glide long enough so that the renolds number increase may be incorrect. The question assumes small glide angle so the altitude variation may be negligeable (not to mention that the calm air hypothesis is not mention). – Manu H Nov 5 '15 at 16:21
• "mass is constant over time" not with a relief tube! I disagree with the statement that there are AOA changes in lift. Lift can be quite steady, and this is an idealized question anyway. – rbp Nov 29 '15 at 23:05

Constant angle of attack implies a constant CD and constant CL.

The fact that the aircraft is a glider implies a constant mass.

'along its path' does not imply that the path angle is constant.

In a phugoid motion, the flight path angle is oscillating and so are the speed and the load factor, but the AoA is constant (by approximation).

We can assume the aircraft is in a phugoid motion with low amplitude and/or long period, so that the hypothesis of small angles is valid.

I suppose the dimensionless drag is constant during the phugoid motion even though both velocity and load factor are constantly changing. They cancel each other out. The fact the dimensionless drag coefficient CD is constant is also a hint here.