Why would a ram air parachute need less brake input to stall at a higher altitude?

Question

I have some anecdotal evidence that a ram air sport parachute requires less toggle input to stall at higher altitudes. A pilot needed one wrap of the brake lines around the hands to quickly, definitively, and repeatedly stall above 6,000 feet or so, and two wraps below that.

The stall maneuver was:

• fly in brakes for a few seconds to slow down
• quickly lock out arms to maximum extension

Although I'm not discounting the possibility of this pilot being mistaken, I'm curious if this is expected behavior and what the physics behind it are (or might be) that are specific to parafoil type gliders. See my thoughts below on why a stall might be particularly complex here.

Update: Three different very experienced (in acro and/ or XC) paragliders just told me similar observations about higher altitude stalls: "lower brake pressure", "less brake travel/ range", "more dynamic", "similar to flying heavy or on a smaller glider".

What I found so far:

• A stall is caused by too high AoA.

• AoA, pitch, and IAS are expected to remain constant across altitudes for an unpowered parafoil in a stabilized glide.

• TAS increases with altitude if IAS is constant

• A rule of thumb to get TAS is to add 2% to the CAS/IAS for every 1000 feet of altitude.

• This question about stall IAS varying with altitudes has an answer that seems to mostly apply to powered aircraft. It mentions Reynolds number for smaller aircraft. Would that really be significant here?

• Random explanation of paraglider controls, which are essentially the same as for a ram air parachute.

More info in case it helps:

A parachute like this is about 200 square feet. The total system weight is around 200 lb. The wing itself weighs 10 lb including the lines/ risers, which are around 15 feet long. It attaches to the pilot's harness at only two points, one on each shoulder. The fabric forms an arch in flight around 20 feet wide tip to tip, 5 feet tall in the middle, and 10 feet at the deepest (tapered).

The indicated or sea level airspeed is around 40mph with no brake input and 20mph in deep brakes. The glide is between 2.5 to 3.0 for all speeds (so components are significant).

The stalls were practiced at random altitudes between 12,000 and 3,000 feet.

More thoughts:

This type of stall is a dynamic maneuver, and a ram air parachute is a soft wing with a CG far below the CL.

Here's my current understanding of what goes on before the stall fully develops:

• pilot pulls down the brake lines
• the wing changes shape, increasing camber and becoming less streamlined
• the wing accelerates up and back as lift and drag increases
• the pilot (ballast/ CG) has more momentum due to being much heavier than the wing and continues moving close to the original velocity for a while
• line tension increases (increasing wing loading and therefore also stall speed?)
• the wing pitches up due to the rolling moment caused by the CG moving forward relative to the CL
• the stall starts to develop, reducing lift
• at some point, I presume the stall causes enough loss of lift that the wing starts to deform (is this due to loss of line tension?), causing more loss of lift, etc... and allows the stall to progress even as the CG returns to below the CL, the wing pitches forward, and the lines slacken

Is it possible to analyze all this complexity to see which parts would be affected by altitude (e.g. air density or TAS) and whether that effect is significant?

Or am I overthinking this and there's some simple well known explanation?

Answer 1

I was able to find a single research paper from Airborne Systems that reports something similar:

An increase in turn responsiveness, specifically turn rate for a given stroke amount, has been observed on multiple planforms and sizes at higher altitudes up to 25,000 ft. MSL.

The paper does not mention stalls/ pitch changes. However, the only difference between pitch changes and turns is two toggles down vs just one and the body swinging forward vs out to the side.

Summary of Relevant Section

The paper explains this as due to two factors (pages 4-6):

1. Mass ratio. The mass of the air inside the wing decreases as air density decreases, which moves the center of gravity down slightly and changes the moment of inertia.

2. Kinetic energy. Kinetic energy is proportional to the square of the velocity and thus increases greatly with altitude. See below for my current understanding of the effects of this.

Complexity

The mass ratio is pretty straightforward, but I had to hire an aerospace engineer and an astrophysics professor as tutors to try to get some formulas for the kinetic energy part.

We did find the formulas. It's a field called "flight dynamics", and there are even adaptions for parafoils that include the "apparent mass" of the air being "dragged along" by the canopy.

Unfortunately, the math is REALLY complicated. It would have taken my tutors more time than I wanted to pay for to simplify the equations down to just control changes with altitude.

If anyone wants to go through the trouble of modeling it, hit me up and I'll get you started.

Until that happens, I don't think this question is "truly" answered. However, it's enough to temporarily satisfy my curiosity. I figured I'd post the understanding I gained in the process, in case it helps someone.

My Current Understanding

I came up with the following explanation with the help of those tutors and a mentor who has built and designed a few dozen ultralight airplanes.

The pilot mass is 10 times that of the wing. When the wing wants to change direction due to increased angle of attack/ camber from the brake inputs, the pilot resists the change in motion for much longer, due to the 10x higher momentum. This causes the wing to rotate back and down due to the lines holding it back.

Momentum (which the paper does NOT mention) is what allows the pilot's body to keep moving forward (or out, for a turn) relative to the wing after a fast control input. It's proportional to velocity (not velocity squared). So the differences with altitude may or may not be significant, since it's proportional to all the other velocity-related changes (such as the radius of the resulting arc).

Since the wing is pitching up due to rotating back like this, lift and drag are increasing even more than what the initial control input would cause. Once the pilot body starts accelerating up and back, it "overshoots", swinging up relative to the canopy. This pitches the canopy up even more.

Kinetic energy (proportional to the square of the velocity) can be converted into potential energy (altitude). Thus, it determines how high the pilot's body swings up during the overshoot, and thus how far the canopy pitches back (or rolls, for a turn) at the maximum. This is the significant factor.

("Body swing" is an over-simplification. In reality, the body and wing swing/ glide/ rotate together, affecting each other dynamically.)

To get back to stalls: a stall is caused by too high angle of attack. A sudden pitch change increases the angle of attack. The kinetic energy determines the maximum pitch change caused by the body moving up relative to the canopy, and kinetic energy is much higher at high altitudes. Thus, the same control input at a higher altitude might stall the canopy even if it did not stall at a lower altitude.

Compared to other aircraft: Parafoils/ canopies are much more affected by this, since their center of lift is so far from the center of mass, resulting in a greater pitching/ turning moment when the body swings up. (Similar to a long prybar being more effective vs a short one.) This would explain why it's not a well known effect in general aviation/ fixed wing gliders.

Answer 2

This may have to do with "reduced" flare abilities at higher density altitudes.

Let's look at it this way: a lighter aircraft worries about excessive G's with full pitch application, whereas a heavier plane worries about stalling from too high an AoA.

the heavier plane cannot change course as fast as the lighter one

So it's rate of AoA increase will be higher. The lighter plane's change in course "keeps up" with its change in pitch (literally rotation on the pitch axis relative to line of flight) better.

We then substitute higher and lower density altitude for heavier and lighter weight (or even larger and smaller wing), and the same effect is present.

As pointed out by the OP, Reynolds number may not change enough to be a major factor, but should not be discounted completely.

The thought that an object with a higher TAS, therefor a higher momentum, will be harder to turn does bear validity, in that it too will have a lower angle of departure from its course for a given perpendicular force applied because it's v, not its m, is higher.