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Suppose an unpowered parafoil (e.g. a ram air parachute or paraglider) is descending (gliding) in a standard atmosphere. Suppose a pitot tube is positioned to always point into the relative wind (e.g. hanging by a string with fletching) and is recording IAS.

  1. I know that the TAS (true air speed) is expected to be higher at higher altitudes due to the reduced drag. How is the IAS (indicated air speed) expected to change with altitude?

  2. Would the answer be different for a fixed wing glider that has all control surfaces locked in a neutral position? In other words, does the self-adjusting/ pendular pitch of the parafoil affect the IAS it stabilizes at?

Edit: Let's assume there is no control input from the pilot or any other changes taking place that are unrelated to altitude.

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2 Answers 2

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If the pitch trim is held constant, the IAS will be constant.

A rigid glider will control trim with an elevator trim tab. The paraglider will control trim through slight shifts in the CG via tensioning the wires.

So long as the trim lift coefficient (and thereby angle of attack) is left fixed, the IAS will stay constant.

For a steady glide, we can write:

$L=W \cos(\theta)$

$-D=W \sin(\theta)$

We often think in terms of glide slope (instead of descent angle).

$GS=-\frac{1}{\tan(\theta)}$

Also,

$GS=\frac{L}{D}=\frac{C_L}{C_D}$

If we take our lift equation and put it in terms of lift coefficient:

$C_L=\frac{W \cos(\theta)}{q\,S_\mathrm{ref}}$

If trim is held constant, then $C_L$ is constant.

$W$ is constant (unless you drop ballast).

Since $C_L$ is constant, we're at constant $C_D$ (ignoring Reynolds number and Mach effects). Which means we're at constant $L/D$.

Constant $L/D$ means constant descent angle $\theta$.

And $S_\mathrm{ref}$ the reference area of the wing is constant.

So, all that together means that we will glide at constant dynamic pressure - $q$.

$q=0.5 \rho V^2$

Where $V$ is TAS and $\rho$ is density. Which shows that as you descend and $\rho$ increases, $V^2$ must decrease to maintain constant dynamic pressure.

But this is the exact relationship that is used to define IAS and EAS. Constant EAS is defined as constant $q$.

IAS is EAS as measured by a particular installation -- but nothing about the installation is changing (most importantly angle of attack). So, flight at constant $q$ is flight at constant EAS is flight at constant IAS.

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  • $\begingroup$ Thanks! I'm a little unclear about the "pitch trim" you discuss. Are you saying your answer is valid only if the paraglider pilot takes conscious action to keep the trim constant? Or that a parafoil with a dead weight will automatically keep the trim constant? $\endgroup$
    – Oleg
    Mar 24, 2023 at 5:34
  • $\begingroup$ Just to clarify, I'm asking about the case where there is no input from the pilot. I'm curious if the pitch of the parafoil changes at higher altitudes due to the reduced drag on the wing having more effect than the reduced drag on the smaller pilot. $\endgroup$
    – Oleg
    Mar 24, 2023 at 5:46
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    $\begingroup$ @Oleg-- re last comment above-- the Drag force on any given part of the aircraft isn't reduced just because the TAS is higher for a given IAS. L/D is constant, L = weight * cos glide angle, glide angle is determined by L/D.so D is constant. If you want to incorporate that specific comment into question, I'll edit my answer to address. $\endgroup$ Mar 24, 2023 at 14:39
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    $\begingroup$ @Oleg -- see my "Addendum" at end of my answer. $\endgroup$ Mar 24, 2023 at 14:49
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    $\begingroup$ The pilot does not need to take conscious action to keep the trim constant. If they hold the lines in the same place, they will hold it constant. This may not be easy for a long period of time (if holding trim requires holding constant pressure) -- but if trim can be adjusted for 'hands off' flying, then it is the easy / default way to go. $\endgroup$ Mar 24, 2023 at 16:06
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Would the answer be different for a fixed wing glider that has all control surfaces locked in a neutral position? In other words, does the self-adjusting/ pendular pitch of the parafoil affect the IAS it stabilizes at?

You seem to have an intuition that a parafoil (or paraglider or hang glider) tends to trim to a constant pitch attitude, and that this is somehow different from a more conventional aircraft's tendency to trim to a constant angle-of-attack. In reality -- at least as long as we make no changes in the aircraft's configuration (physical shape), and we don't introduce Thrust into the picture, these are just two different ways of describing the same thing.

In an unpowered glider, the glide ratio with respect to the airmass is determined by the L/D ratio. We can think of the glider's pitch attitude as being the result of the angle-of-attack minus the glide angle relative to the airmass; this result may be either positive or negative. Also note that as long as we make no changes in the configuration (physical shape) of the aircraft, and as long as we don't introduce a thrust force from a motor, then each possible value of the L/D ratio, and thus each possible value of the glide angle relative to the airmass, corresponds to one particular angle-of-attack. Therefore, tending to trim to a constant pitch attitude is the same as tending to trim to a constant angle-of-attack--either way, the glider will trim to a given glide ratio, and a given Indicated airspeed. So the answer to your question is "no".

Now, if we were varying the glide ratio by deploying wing-mounted spoilers, or by adding some power, then in some hypothetical aircraft (perhaps with an autopilot in the loop?) that always trimmed to a given pitch attitude, that would generate a change in angle-of-attack, and therefore a large change in Indicated airspeed1.

Note also that if the spoilers (or the thrust force) generated no pitching moment relative to the aerodynamic center of the aircraft, they would generate a strong pitch torque relative to the CG of the aircraft, if the CG is far below the aerodynamic center of the aircraft. This would result in a change in the trim angle-of-attack.

In the hang glider case specifically2, one valid way to analyze this situation is to view the wing itself as a free body, with a tendency to trim to given specific angle-of-attack, while the pilot's body exerts a pitch torque on the wing that (at least in steady-state flight) varies with the pitch attitude of the aircraft and thus tends to bias the angle-of-attack in a way that is dependent on pitch attitude.

Another valid way to analyze this situation is to simply note that the spoiler (or the thrust force) is generating a net pitching torque about the CG of the whole system, even if it is acting with zero moment-arm relative to the aerodynamic center of the wing.

If we introduce a thrust force that acts through the CG of the whole system, rather than through the aerodynamic center of system, we'll find that the wing still tends to trim to a constant angle-of-attack (and thus a nearly constant airspeed3) as we vary the thrust force, even though the pitch attitude will vary with the climb or descent angle.

So even though the "pendulum stability" provided by the arrangement of the CG far below the aerodynamic center of the wing does play an important role in the flight dynamics of parafoils, paragliders, hang gliders (in the case where pilot is holding a fixed position in the control frame), etc, it's not really true that such aircraft have an absolute tendency to trim to a fixed pitch attitude. But for the simple case of steady-state4 wings-level gliding flight in a fixed configuration, that is a valid way to look at the dynamics. We'll come up with a "no" answer to the questions quoted above regardless of whether we view the aircraft as tending to trim to a constant angle-of-attack, or to a constant pitch attitude.

Addendum: a comment by the questioner has indicated that he believes that Drag may be reduced during flight at high altitudes, and wonders if the Drag is reduced proportionally on all parts of the aircraft, and if not, whether this would affect the aircraft's trim angle-of-attack, considering the large vertical distance between the various parts of the aircraft. In steady-state gliding flight, L = W * cosine (glide angle) = W * cosine (arctan (D/L)), and D = W * (sine (glide angle)) = W * sine (arctan (D/L)). Therefore in steady-state gliding flight, the L and D values are completely determined by the L/D ratio which is completely determined by the angle-of-attack, regardless of how high the Indicated Airspeed must be to generate those values of L and D.5 Therefore there is no reduction in drag on any part of the aircraft just because the altitude is increased.

Read more about "pendulum" pitch stability in this answer to a related ASE question: Does "pendulum effect" apply to hang gliders or any aircraft?

Footnotes:

  1. Consider an aircraft whose trim characteristics are such that it perfectly holds a given angle-of-attack regardless of changes in thrust, or changes in configuration that increase the drag coefficient (without affecting the lift coefficient). Even such an aircraft will still experience some change in Indicated airspeed when the Thrust is altered, or when the drag coefficient is altered. The reason for this is that the total Lift required for steady-speed (wings-level) flight is not constant, but rather varies according to the cosine of the descent or climb angle. For more, see this related ASE answer: Does lift equal weight in a climb?

  2. We refer to a hang glider specifically, because the wing shape of a paraglider or parafoil may have no tendency to trim to any given angle-of-attack without the pilot attached, even the wing could somehow be made to maintain its shape. Note also that we're assuming the pilot either has his "hang strap" attached somewhat below the CG of the wing itself, or we're assuming that the pilot is holding himself in a fixed position relative to the control frame. If neither of these things are true-- if the pilot's weight is attached exactly at the CG of the wing, and the pilot is just hanging freely and exerting no muscle force on the control frame, then his weight effectively acts at the CG of the wing, not below it. In a paraglider or parafoil, the multiple lines act as fixed struts that hold the pilot in a completely fixed position relative to the wing, unless he is making intentional control inputs by pulling on the lines etc, so in way these aircraft provide an even better example of the dynamics we're exploring, except for the lack of inherent pitch stability in the wing itself -- these aircraft are totally dependent on "pendulum stability*.

  3. See footnote (1).

  4. Re "steady-state": for further insight into what "pendulum stability" does and does not mean, search up some videos of hang glider and paraglider aerobatics. Though limited to positive G-loadings, the maneuvers that can be performed in such aircraft may surprise the reader!

  5. Ignoring any variation in lift and drag coefficients due to Reynolds number. Note that if the drag coefficients of the pilot and the wing are affected differently by the change in Reynolds number due to decreased air density and increased TAS, then that could produce a change in the trim angle-of-attack and L/D ratio, even if the L/D ratio corresponding to any given angle-of-attack remained unchanged. Note also that if we're bringing Reynold's number effects into the picture, we can't assume that the L/D ratio corresponding to any given angle-of-attack will remain unchanged. So-- "it's complicated". But the effect of changes in Reynold's number on the lift and drag coefficients appears to be beyond the intended scope of the question.

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  • $\begingroup$ Thank you! Two great explanations. I wish I could accept both, since I'm using both. $\endgroup$
    – Oleg
    Mar 24, 2023 at 16:23
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    $\begingroup$ @Oleg -- you are welcome, no problem, I understand you need to choose 1 -- $\endgroup$ Mar 24, 2023 at 16:24
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    $\begingroup$ @Oleg -- I haven't thoroughly thought through yet the case where, if Drag were somehow reduced, and were reduced proportionally on all parts of aircraft, and Lift were reduced proportionally as well (so no change in L/D for given angle-of-attack), that might affect trimmed angle-of-attack. Seems it might be equivalent to change in pilot weight-- i.e. the relevant balance between aerodynamic torques and torques due to pilot weight below CG might be changed. But, I think it's not relevant to actual question, because in reality (at least if we ignore Reynolds number effects) the drag (ctd) $\endgroup$ Mar 24, 2023 at 17:55
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    $\begingroup$ (ctd) the Drag forces are not changed. $\endgroup$ Mar 24, 2023 at 17:56

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